Let f(1)=2, f(2)=4, and let f(n+1)=f(n)! for every integer n≥2. Edmund Landau's conjecture states that the set P(n^2+1) of primes of the form n^2+1 is infinite. Landau's conjecture implies the following unproven statement Φ: card(P(n^2+1))<ω ⇒ P(n^2+1)⊆[2,f(7)]. Let B denote the system of equations: {x_j!=x_k: i,k∈{1,...,9}}∪{x_i⋅x_j=x_k: i,j,k∈{1,...,9}}. The system of equations {x_1!=x_1, x_1 \cdot x_1=x_2, x_2!=x_3, x_3!=x_4, x_4!=x_5, x_5!=x_6, x_6!=x_7, x_7!=x_8, x_8!=x_9} has exactly two solutions in positive integers x_1,...,x_9, namely (1,...,1) and (f(1),...,f(9)). No known system S⊆B with (...) a finite number of solutions in positive integers x_1,...,x_9 has a solution (x_1,...,x_9)∈(N\{0})^9 satisfying max(x_1,...,x_9)>f(9). For every known system S⊆B, if the finiteness/infiniteness of the set {(x_1,...,x_9)∈(N\{0})^9: (x_1,...,x_9) solves S} is unknown, then the statement ∃ x_1,...,x_9∈N\{0} ((x_1,...,x_9) solves S)∧(max(x_1,...,x_9)>f(9)) remains unproven. Let Λ denote the statement: if the system of equations {x_2!=x_3, x_3!=x_4, x_5!=x_6, x_8!=x_9, x_1 \cdot x_1=x_2, x_3 \cdot x_5=x_6, x_4 \cdot x_8=x_9, x_5 \cdot x_7=x_8} has at most finitely many solutions in positive integers x_1,...,x_9, then each such solution (x_1,...,x_9) satisfies x_1,...,x_9≤f(9). The statement Λ is equivalent to the statement Φ. It heuristically justifies the statement Φ . This justification does not yield the finiteness/infiniteness of P(n^2+1). We present a new heuristic argument for the infiniteness of P(n^2+1), which is not based on the statement Φ. Algorithms always terminate. We explain the distinction between existing algorithms (i.e. algorithms whose existence is provable in ZFC) and known algorithms (i.e. algorithms whose definition is constructive and currently known). Assuming that the infiniteness of a set X⊆N is false or unproven, we define which elements of X are classified as known. No known set X⊆N satisfies Conditions (1)-(4) and is widely known in number theory or naturally defined, where this term has only informal meaning. *** (1) A known algorithm with no input returns an integer n satisfying card(X)<ω ⇒ X⊆(-∞,n]. (2) A known algorithm for every k∈N decides whether or not k∈X. (3) No known algorithm with no input returns the logical value of the statement card(X)=ω. (4) There are many elements of X and it is conjectured, though so far unproven, that X is infinite. (5) X is naturally defined. The infiniteness of X is false or unproven. X has the simplest definition among known sets Y⊆N with the same set of known elements. *** Conditions (2)-(5) hold for X=P(n^2+1). The statement Φ implies Condition (1) for X=P(n^2+1). The set X={n∈N: the interval [-1,n] contains more than 29.5+\frac{11!}{3n+1}⋅sin(n) primes of the form k!+1} satisfies Conditions (1)-(5) except the requirement that X is naturally defined. 501893∈X. Condition (1) holds with n=501893. card(X∩[0,501893])=159827. X∩[501894,∞)= {n∈N: the interval [-1,n] contains at least 30 primes of the form k!+1}. We present a table that shows satisfiable conjunctions of the form #(Condition 1) ∧ (Condition 2) ∧ #(Condition 3) ∧ (Condition 4) ∧ #(Condition 5), where # denotes the negation ¬ or the absence of any symbol. No set X⊆N will satisfy Conditions (1)-(4) forever, if for every algorithm with no input, at some future day, a computer will be able to execute this algorithm in 1 second or less. The physical limits of computation disprove this assumption. (shrink)

It is well known that the following features hold of AR + T under the strong Kleene scheme, regardless of the way the language is Gödel numbered: 1. There exist sentences that are neither paradoxical nor grounded. 2. There are 2ℵ0 fixed points. 3. In the minimal fixed point the weakly definable sets (i.e., sets definable as {n∣ A(n) is true in the minimal fixed point where A(x) is a formula of AR + T) are precisely the Π1 1 (...) sets. 4. In the minimal fixed point the totally defined sets (sets weakly defined by formulae all of whose instances are true or false) are precisely the ▵1 1 sets. 5. The closure ordinal for Kripke's construction of the minimal fixed point is ωCK 1. In contrast, we show that under the weak Kleene scheme, depending on the way the Gödel numbering is chosen: 1. There may or may not exist nonparadoxical, ungrounded sentences. 2. The number of fixed points may be any positive finite number, ℵ0, or 2ℵ0 . 3. In the minimal fixed point, the sets that are weakly definable may range from a subclass of the sets 1-1 reducible to the truth set of AR to the Π1 1 sets, including intermediate cases. 4. Similarly, the totally definable sets in the minimal fixed point range from precisely the arithmetical sets up to precisely the ▵1 1 sets. 5. The closure ordinal for the construction of the minimal fixed point may be ω, ωCK 1, or any successor limit ordinal in between. In addition we suggest how one may supplement AR + T with a function symbol interpreted by a certain primitive recursive function so that, irrespective of the choice of the Godel numbering, the resulting language based on the weak Kleene scheme has the five features noted above for the strong Kleene language. (shrink)

Regarding the relation of Plato’s early and middle period dialogues, scholars have been divided to two opposing groups: unitarists and developmentalists. While developmentalists try to prove that there are some noticeable and even fundamental differences between Plato’s early and middle period dialogues, the unitarists assert that there is no essential difference in there. The main goal of this article is to suggest that some of Plato’s ontological as well as epistemological principles change, both radically and fundamentally, between the early and (...) middle period dialogues. Though this is a kind of strengthening the developmentalistic approach corresponding the relation of the early and middle period dialogues, based on the fact that what is to be proved here is a essential development in Plato’ ontology and his epistemology, by expanding the grounds of development to the ontological and epistemological principles, it hints to a more profound development. The fact that the bipolar and split knowledge and being of the early period dialogues give way to the tripartite and bound knowledge and benig of the middle period dialogues indicates the development of the notions of being and knowledge in Plato’s philosophy before the dialogues of the middle period. -/- Keywords Plato; early dialogues; middle dialogues; being; knowledge; development -/- Introduction The differences between two groups of the early and middle period dialogues have always been a matter of dispute. Whereas the developmentalists like Vlastos, Silverman (2002), Teloh (1981), Dancy (2004) and Rickless (2007) think that from the early to the middle dialogues Plato’s philosophy changes, at least in some essential points, the unitarists like Kahn, Cherniss and Shorey believe that there happens no development and the differences must be taken as natural, ignorable and even pedagogic. In his well-known article, Socrates contra Socrates in PLATO, Vlastos lists ten theses of difference between two groups of dialogues. The first group which includes Plato’s early dialogues he divides to 'elenctic' (Apology, Charmides, Crito, Euthyphro, Gorgias, Hippias Minor, Ion, Laches, Protagoras and Republic I) and 'transitional' (Euthydemus, Hippias Major, Lysis, Menexenus and Meno) dialogues. These transitional come after all the elenctic dialogues and before all the dialogues of the second group which compose Plato’s middle period dialogues, including (with Vlastos' chronological order) Cratylus, Phaedo, Symposium, Republic II-X, Phaedrus, Parmenides and Theaetetus (1991, 46-49). Vlastos asserts strictly that his list of differences are 'so diverse in content and method that they contrast as sharply with one another as with any third philosophy you care to mention, beginning with Aristotole’s' (ibid, 46). Vlastos’ list of differences between two Socrateses is considered a view breaking sharply between the early and the middle dialogues. Besides all ten differences between the two Socrateses in Vlastos’ list that can be supportive for our doctrine here, we intend to focus on some ontological as well as epistemological distinctions that have not completely been discussed hitherto. Contrary to the developmentalist theory of Vlastos, unitarian theory of Charles Kahn wishes to eliminate any substantial difference between the early and the middle dialogues. He distinguishes seven 'pre-middle' or 'threshold' dialogues including Laches, Charmides, Euthyphro, Protagoras, Meno, Lysis and Euthydemus from the other Socratic dialogues which he calls 'earliest group' (1996, 41). The threshold dialogues, Kahn thinks, 'embarke upon a sustained project' that is to reach to its climax in the middle period dialogues, namely Phaedo, Symposium and Republic. Believing in that there is no 'fundamental shift'between the early and middle dialogues (ibid, 40), Kahn thinks the Socratic dialogues are just the 'first stage' with a 'deliberate silence' towards the theories of later periods (ibid, 339). One of the reasons of the surprising fact that Plato gives no hint of the metaphysics and epistemology of the Forms in the early dialogues, he thinks, is the pedagogical advantages of aporia. He thinks that Plato 'obscurely', and mostly because of education, hinted to some doctrines and conceptions in his early dialogues and with the aim of clarifying them only in the later ones (ibid, 66). The seven threshold dialogues, Kahn asserts, 'had been designed from the first' to prepare the pupils and readers for the views expounded in the middle period dialogues (ibid, 59-60). To show that the differences of the two Socrateses of the early and middle period dialogue are in their onto-epistemological grounds and thence cannot be explained by a unitaristic view, we try to draw the ontological and epistemological principles of the early dialogues in the first part below in order to show, in the second part, that those principles have been developed in the middle period dialogues. -/- A. The Onto-Epistemologic Principles of the Early Dialogues Socratic dialogues are paradoxical about knowledge because while being knowledge-oriented always searching for knowledge, they deny it and even never discuss it directly. Three elements of Socrates’ way of searching Knowledge throughout the early dialogues, i.e. Socratic 'what is X?' question, his disavowal of knowledge and his elenctic method combined together produce something like a circle which works, more or less, in the same way in these dialogues. Though this circle is an embaressing inquiry always resulting in ignorance instead of knowledge, its motivation is surprisingly Socrates’ passionate enthusiasm for knowledge, an intensive love of wisdom. The starting point of this circle is Socrates’ confession of having no knowledge which might be explicitly asserted or presupposed, maybe because it was one of the famous characteristics of Socrates; a confession always paradoxically accompanied with his intense longing for knowledge (e.g., Gorgias 505e4-5). Every time Socrates encounters with someone who thinks he knows something (οἴεταί τι εἰδέναι) (Apology 21d5) and tries to examine him. This examination seems to be the simplest one asking just what it is that he knows. Socrates’ elenchus, therefore, is always connected with 'what is X?' (τίς ποτέ ἐστιν) question, a question that most of the early dialogues of Plato are concerned with; 'what is courage?' in the Laches, 'what is piety?' in Euthydemus, 'what is temperance?' in Charmides and 'what is beauty?' in Hippias Major. This question we call here 'Socratic question' and probably is the very question the historical Socrates used to employ, is tightly interrelated with both his disavowal and his elenchus. He disclaims knowledge because he cannot find the answer to the question himself and he rejects others’ since they cannot offer the correct answer too. Every interlocutor can claim he knows X, if and only if he can answer the Socratic question. Otherwise, he is more of an ignorant than of a knower of τί ποτέ ἐστι X. Knowing the answer to this question is, thus, knowledge’s criterion for Socrates. Having found out that he cannot answer what it is which he would claim to know, the interlocutor comes to the point Socrates was there at the beginning. The least advantage of this circle is that he becomes as wise as Socrates does about the subject, becoming aware that he does not know it. At the end of the circle they are both still at the beginning, not knowing what X is. So let us first take a glance at these three elements. Socratic disavowal of knowledge is strictly asserted in some passages. At Apology 21b4-5, Socrates says: -/- I do not know of myself being wise at all (οὔτε μέγα οὔτε σμικρὸν σύνοιδα ἐμαυτῷ σοφὸς ὤν) -/- Moreover, at 21d4-6: -/- None of us knows anything worthwhile (καλὸν κἀγαθὸν εἰδέναι) …. I do not know (οἶδα) neither do I think I know. -/- In Charmides Socrates speaks about a fear about his probable mistake of thinking that he knows (εἰδέναι) something when he does not (166d1-2). The somehow generalization of this disavowal can be seen in Gorgias. After calling his disavowal 'an account that is always the same' (509a4-5), Socrates continues (a5-7): -/- I say that I do not know (οἶδα) how these things are, but no one I have ever met, like now, who can say anything else without being absurd. -/- At the end of Hippias Major (304d7-8), Socrates affirms his disavowal of knowledge of 'what is X?' this time about the fine: -/- I do not know (οἶδα) what that is itself (αὐτὸ τοῦτο ὅτι ποτέ ἐστιν). Some other passages, however, made a number of scholars dubious about Socrates’ disavowal. Vlastos mentions Apology 29b6-7 as an evidence : 'that to do wrong and to disobey one’s master, both god and men, I know (οἶδα) to be evil and shameful'. He thinks that if we give this single text 'its full weight' it can suffice to show that Socrates does claim knowledge of a moral truth (1985, 7). Vlastos’ claim is not admittable since it would be too strange, I think, for a man like Socrates to violate his disavowal claim just after emphasizing it. We can see his claim just before the already mentioned passage: -/- And surely it is the most blameworthy ignorance to believe that one knows what one does not know. It is perhaps on this point and in this respect, gentlemen, that I differ from the majority of men and if I were to claim that I am wiser than anyone in anything it world be in this, that, as I have no adequate knowledge (οὐκ εἰδὼς ἱκανῶς) of things in the underworld, so I do not think I have (οὐκ εἰδέναι) (Apology 29b1-6) Vlastos tries to solve what he calls the 'paradox' of Socrates’ disavowal of knowledge distinguishing the 'certain' knowledge from 'elenctic' knowledge (1985, 11) and thinking that when Socrates avows knowledge, we must perceive it as an elenctic knowledge, a knowledge its content 'must be propositions he thinks elenctically justifiable' (ibid, 18). Irwin’s solution is the distinction of knowledge and belief. He approves that Socrates does not 'explicitly' make such a distinction, but still thinks that Socrates’ 'test for knowledge would make it reasonable for him to recognize true belief without knowledge, and his own claims are easily understood if they are claims to true belief alone' (1977, 40). While I agree with Vlastos up to a point, I strongly disagree with Irwin about the early dialogues. As I will try to show below, we are not permitted to consider any kind of distinction within knowledge in Socratic dialogues because only one category of knowledge is alluded to there and the distinction of knowledge and belief thoroughly belongs to the second Sorcates. Although no kind of distinction can be admittable here, I think Vlastos’ distinction can be accepted only if we regard it as a distinction between knowledge, which is unique and without any, even incomparable, rival, and a semi-idiomatic and ordinary one that is a necessary requirement for any argument, and thus, unavoidable even for someone who does not claim any kind of knowledge. An apparent evidence of this is Gorgias 505e6-506a4: -/- I go through the discussion as I think it is (ὡς ἄν μοι δοκῇ ἔχειν), if any of you do not agree with admissions I am making to myself, you must object and refute me. For I do not say what I say as I know (οὐδὲ γάρ τοι ἔγωγε εἰδὼς λέγω ἃ λέγω) but as searching jointly with you (ζητῶ κοινῇ μεθ᾽ ὑμῶν). -/- The minimal degree of knowledge everyone must have to take part in an argument, conduct it and use the phrase "I know" when it is necessary is what Socrates cannot deny. We can call it elenctic knowledge only if we agree that it is not the kind of knowledge that Socrates has always been searching, the one that can be accepted as the answer of Socratic 'what is X?' question. His disavowal of knowledge is applied only to the knowledge which can truly be the answer of Socratic question and pass the elenctic exam; a knowledge that, I believe, is never claimed by first Socrates. Socrates conducts his method of examining his interlocutors’ knowledge, our second element here, by almost the same method repeated in Socratic dialogues. That whether we are allowed to regard all the examinations of Socrates in the early dialogues as based on the same or not has been a matter of dispute. Vlastos himself (1994, 31) distinguished Euthydemas, Lysis, Menexenns and Hippias Major from the other Socratic dialogues because he thinks Socrates has lost his faith to elenchus in there. Irwin (1977, 38) distinguishes Apology and Crito where Socrates’ own convictions is present. Contrary to some scholars like Benson (2002, 107) who take elenchus in all the Socratic dialogues as a unique method, Michelle Carpenter and Ronald M. Polansky (2002, 89-100) argue pro the variety of methods of elenchus. Thomas C. Brickhouse and Nicholas D. Smith (2002, 145-160) even reject such a thing as Socratic elenchus which can gather all of the Socrates’ various arguments under such a heading. There can be no solution for the problem of elenchus, they think, is due to 'the simple reason that there is no such thing as 'the Socratic elenchos"'(p.147). Though we consider elenchus a somehow determined process and a part of Socratic circle in the early dialogues, all we assume is that whatever differences it might have in different dialogues, it has the same onto-epistemological principles and, thus, we are not going to take it necessarily as a unique method. This method sets out to prove that the interlocutors are as ignorant as Socrates himself is. That whether elenchus is constructive, capable of establishing doctrines as Vlastos (1994) or Brickhouse and Smith (1994, 20-21) believe or not is another issue to which this paper is not to claim anything. What is crucial for our discussion here is that elenchus does not reach to the very knowledge Socrates is looking for. This is strictly against Irwin who thinks that not only elenchus leads to positive results, 'it should even yield knowledge to match Socrates’ conditions'(1977, 68, cf. 48). He does not explain where and how they really yield to that kind of knowledge. He explains his elenctic method in his apology in the court (Apology 21-22), that how he used to examine wise men, politicians, poets and all those who had the highest reputation for their knowledge and every time found that they have no knowledge. If we accept, as I strongly do, that Socrates’ disavowal of his knowledge is not irony, it might seem more reasonable to agree that the process that has that disavowal as its first step cannot be irony as well. The key of the circle which can explain why Socrates disclaims knowledge and how he can reject others’ claim of having any kind of knowledge lies in the third element, Socratic question. In Hippias Major (287c1-2), Socrates asks: 'Is it not by Justice that just people are Just? (ἆρ᾽ οὐ δικαιοσύνῃ δίκαιοί εἰσιν οἱ δίκαιοι). He insists at 294b1 that they were searching for that by which (ᾧ) all beautiful things are beautiful (cf. b4-5, 8). At Euthyphro 6d10-11 it is said that the Socratic question is waiting for 'the form itself (αὐτὸ τὸ εἶδος) by which (ᾧ) all the pious actions are pious; and at 6d11-e1: -/- Through one form (που μιᾷ ἰδέᾳ) impious actions are impious and pious actions pious. -/- Since the X itself is that by which X is X, knowing 'X itself' is the only way of knowing X. It is probably because of this that Socrates makes the distinction between the ousia as a right answer to the question and effect as a wrong one: -/- I am afraid, Euthyphro, that when you were asked what piety is (τὸ ὅσιον ὅτι ποτ᾽ ἐστίν) you did not wish to make clear its nature itself (οὐσίαν … αὐτοῦ) to me, but you said some effect (πάθος) about it. (Euthp. 11a6-9) -/- 1. Knowledge of what X is Now it is time to look for the onto-epistemological principles of Socratic circle and its three elements. It cannot reasonably be expected from the first Socrates to present us explicitly and clearly formulated principles of his onto-epistemology when such explications cannot be found even in the second Socrates who has some obviously positive theoris. Since there must be some principles underlying this first systematic inqury of knowledge, we must seek to them and be satisfied with elicitation of the first Socratas’ principle. What will be drawn out as his principles cannot and must not, thus, be taken as very fix and dogmatic principles. Some very slightest principles and grounds suffice for our purposes here. The first principle that is the prima facie significance of the Socratic question and his implementation of all those elenctic arguments I call the principle of 'Knowledge of What X is' (KWX): -/- KWX To know X, it is required to know what X is. -/- Aristotle (Metaphysics 1078b23-25, 27-29, 987b4-8) takes Plato’s τί ἐστι question as seeking the definition of a thing that is the same as historical Socrates’ search but applying to a different field. That Plato’s 'what is X?' question was a search for definition became the prevailed understanding of this question up to now. I am going neither to discuss the answer of Socratic question nor to challenge taking it as definition. What I am to insist is that knowledge is attached firmly to the answer of the question: Knowledge of X is not anything but the knowledge of what X is. It entails, certainly, the priority of this knowledge to any other kind of knowledge about X but it also has something more fundamental about the relation of knowledge and Socratic question. Socrates’ exclusive focus on the answer of his question can authorize the consideration of such an essential role for KWX in his epistemolgoy. The total rejection of his interlocutors’ knowledge when they are unable to answer the question can be regarded as a strong evidence for it. Socrates’ elenctic method and his rejection of others’ knowledge in the early dialogues, which all end aporetically with no one accepted as knower and nothing as knowledge, prevent us from finding any positive evidence for this. We have to be content, therefore, of negative evidences which, I think, can be found wherever Socrates rejects his interlocutors’ knowledge when they are not able to give an acceptable answer to his 'what is X?' question. 2. Bipolar Epistemology Socrates’ rejection of his interlocutors’ knowledge has another epistemological principle as its basis. Let me call this principle Bipolar Epistemology' (BE): BE There is no third way besides knowledge and Ignorance. -/- BE says that about every object of knowledge there are only two subjective statuses: knowledge and Ignorance. Socrates’ disavowal, however, says nothing but that he is ignorant of knowledge of X because he does not know what X is. This means that BE is presupposed here. Socrates’ elenchus and his rejection of interlocutors’ having any kind of knowledge are the necessary results of the fact that he does not let any third way besides knowledge and ignorance. The first Socrates never let anyone partly know X or have a true opinion about it, as he would not let anyone know anything about X when he did not know what X is. -/- 3. Bipolar Ontology The principle of BE in first Socrates’ epistemology is parallel to another principle in his ontology. Plato’s bipolar distinction between being and not being is as strict and perfect as his distinction between knowledge and ignorance. This principle I shall call the principle of 'Bipolar Ontology' (BO): BO Being is and not being is not. BO is apparently the same with the well-known Parmenidean Principle of being and not being (cf. Diels-Kranz (DK) Fr. 2.2-5). Euthydemus’ statement against the possibility of false knowledge can be good evidence for this principle: -/- The things which are not surely do not exist (τὰ δὲ μὴ ὄντα … ἄλλο τι ἢ οὐκ ἔστιν). (Euthydemus 284b3-4) -/- He continues (b4-5): -/- There is nowhere for not being to be there (οὖν οὐδαμοῦ τά γε μὴ ὄντα ὄντα ἐστίν). -/- That BE does not let true opinion as a third option besides knowledge and ignorance seems to be related to BO’s rejecting a third option besides being and not being, which is itself the basis of the impossibility of false belief. Socrates’ elaborate discussion of the problem of false belief in Theatetus that leads to a more decisive discussion and finally to some solutions in Sophist can make our consideration of BO for the first group of dialogues authentive. -/- 4. &5. Split Knowledge and Split Being The fourth principle I shall call the principle of 'Split Knowledge' (SK): -/- SK Knowledge of X is separated from any other knowledge (of anything else) as if the whole knowledge is split to various parts. -/- This Principle is hinted and criticized as Socrates’ way of treating with knowledge in Hippias Major: -/- But Socrates, you do not contemplate the entireties of things, nor do people you have used to talk with (τὰ μὲν ὅλα τῶν πραγμάτων οὐ σκοπεῖς, οὐδ᾽ ἐκεῖνοι οἷς σὺ εἴωθας διαλέγεσθαι). (301b2-4) -/- Contrary to Rankin who regards the passage as 'antilogical, almost eristic in tone rather than presenting a serious philosophy of being' (1983, 54), I think it can be taken as serious. Hippias criticizes Sorcates that he does not contemplate (σκοπεῖς) the entireties of things (ὅλα τῶν πραγμάτων), a critique which Socrates is not its only subject but all those whom Socrates accustomed to talk with (ἐκεῖνοι οἷς σὺ εἴωθας διαλέγεσθαι). This last phrase, I think, extends this critic beyond this dialogue to other Socratic dialogues. Hippias’ use of the perfect tense of the verb ἔθω (to be accustomed) is a good evidence of this extension. We can get, thus, these ἐκεῖνοι as Socrates’ interlocutors in his other dialogues that hints that this criticism has the epistemological groundings of the previous dialogues as its subject. What ἐκεῖνοι οἷς σὺ εἴωθας διαλέγεσθαι points to is that Hippias does not have in mind Socrates’ way of treating things only in this dialogue, but he is also criticizing Socrates’ way throughout his dialogues. At 301b4-5, Socrates and his interlocutors’ way of beholding things is described as such: -/- You people knock (κρούετε) at the fine and each of the beings (ἕκαστον τῶν ὄντων) by taking each being cut up in pieces (κατατέμνοντες) in words (ἐν τοῖς λόγοις). This leads us to our next principle that is parallel to, and the ontological side of, SK, the principle of 'Split Being'(SB): -/- SB Everything (being) is separated from any other thing as if the whole being is split to many beings. -/- Socrates and his interlocutors and thus, as we saw, the Socratic dialogues are accused to regard everything as it is separated from all other things. This separation is en tois logois that, I think, can reasonably be taken as saying that Socratic dialogues (it refers of course to the dialogues before Hippias Major) cut up all things which have the same name/definition from all other things and try to understand them separately, without considering other things that are not in their logos. They, for example in Hippias Major, are cutting up to kalon and try to understand what it and all others inside this logos are by separating it from all other things. This is directed straightly against Socratic question and the way Socratic dialogues follow to find its answer, every time separating one logos. As Meyer (1995, 85) points out, every question 'presupposes that the X in question in a logos is something' and 'every answer to every question aims at unity' (84). The critique of Hippias Major is, therefore, at the same time a critique of SK and SB. It is also a critique of KWX because it is only based on KWX that Socratic dialogues could search for the answer of 'what is X' question supposing that knowing what X is is enough for the knowledge of X. SK and KWX are absolutely interdependent. What Socrates and all his previous interlocutors have neglected in Socratic dialogues, Hippias says, was 'continuous bodies of being' (διανεκῆ σώματα τῆς οὐσίας) (301b6). Either this theory actually belongs to the historical Hippias as it is being said or not, it is strictly criticizing SB. We have the same phrase with changing sūma to logos some lines later at 301e3-4: διανεκεῖ λόγῳ τῆς οὐσίας. Although this theory that can be observed as both an ontological and an epistemological theory is rejected by Socrates (301cff.), it is still against first Socrates’ onto-epistemological principles and might let us look at what is rejected as Socratic prineple. -/- 6. Knowledge is of Being The sixth principle that I think is presupposed by the first Socrates, is the 'Knowledge of Being' Principle (KB): -/- KB Knowledge is of Being. -/- This principle is obviously the source of the problem of false knowledge, a very important problem throughout Plato’s philosophy. We face this problem maybe for the first time in Euthydemus. In less than 20 Stephanus’ pages, 276-295, we are encountered with different interwoven problems about knowledge , all grounded in the problem of false opinion. Having challenged the obvious possibility of telling lies at 283e, at 284 Euthydemus discusses it saying that the man who speaks is speaking about 'one of those things that are (ἓν μὴν κἀκεῖνό γ᾽ ἐστὶν τῶν ὄντων)' (284a3) and thus speaks what is (λέγων τὸ ὄν) (a5). He must necessarily be saying truth when he is speaking what is because he who speaks what is (τὸ ὄν) and the things that are (τὰ ὄντα) speaks truth (τἀληθῆ λέγει) (a5-6). This is based on Parmenidean principle of the impossibility of being of not being which Euthydemus restates (284b3-4) and we mentioned discussing BO principle above. The things that are not are nowhere (οὐδαμοῦ) and there is no possibility for anyone to do (πράξειεν) anything with them because they must be made as being before anything else can be done, which is impossible (b5-7). The words, then, are of things that exist (εἰσὶν ἑκάστῳ τῶν ὄντων λόγοι) (285e9) and as they are (ὡς ἔστιν) (e10). The result is that no one can speak of things as they are not. It is this impossibility of false speach that is extended to thinking (δοξάζειν) at 286d1 and leads to the impossibility of false opinion (ψευδής … δόξα) (286d4). The general conclusion is asserted at 287a extending this impossibility to actions and making any kind of mistake. Not only knowledge is of being but speech, thought and action are of being simply because of the fact that nothing can be of not being. -/- B. First Socrates’ Principles in the Middle Period Dialogues Out of what were presupposed or criticized mostly in five dialogues, Euthyphro, Euthydemus, Hippias Major, Laches and Charmides, we tried to draw the first Socrates’ principles. Our inquiry here is directed to find out the fate of these principles in the three dialogues of the middle period, Meno, Phaedo and Republic. To do this, first we ought to check the situation of Socratic circle in these dialogues. The Socratic circle that was predominant in the early dialogues, does not look like a circle here anymore though they certainly have some features in common. Meno, Phaedo and Republic II-X are not committed to the principles of the circle and the whole circle in disrupted in them. The difference of the two Socrateses towards acquiring knowledge is obvious. The Socrates of Meno, Phaedo and Republic is evidently more self-confident that he can get to some truths during his arguments as he does. They are in their first appearance, as almost all other dialogues, committed to Socrates’ disavowal. All of them try to keep the shape of the Socratikoi Logoi genre, which is committed to the historical Socrates’ way of discussion; a dramatic personage who is to challenge his interlocutors, ask them and refuse the answers. Nevertheless, the fact is that what we have in common between two groups of dialogues is mostly a dramatic structure. Whereas the first group’s arguments are based on Socrates’ disavowal and lead to no positive results, the second group is decisively going to achieve some positive results. The aim of the first Socrates was to show others that they are ignorant of what they thought they knew. The new Socrates of Meno, on the opposite, makes so much efforts to show that the slave boy has within himself true opinions (ἀληθεῖς δόξαι) about the things that he does not know (οἶδε) (85c6-7). Despite his lack of knowledge, he has true opinions nevertheless. The way from these true opinions to knowledge, as Socrates states, is not so long. These true opinions are now like a dream but 'can become knowledge of the same things not less accurate than anyone’s' (οὐδενὸς ἧττον ἀκριβῶς ἐπιστήσεται περὶ τούτων) (c11-d1), if they be repeated by asking the same questions. The most outstanding text regarding Socrates’ disavowal is Meno 98b where he explicitly claims knowledge: -/- And indeed I also speak as (ὡς) one who does not know (εἰδὼς) but is guessing (εἰκάζων). However, [about the fact] that true opinion and knowledge are different, I do not altogether expect (δοκῶ) myself to be guessing (εἰκάζειν), but if I say about anything that I know (εἰδέναι) -which about few things I say- this is one of the things that I know (οἶδα). (98b1-5) This passage is very significant about Plato’s disavowal of knowledge. There can hardly be found, I think, anywhere else in Plato’s corpus where Socrates speaks about his knowledge of something as such. He says first that he speaks as someone who does not know. This ὡς οὐκ εἰδὼς λέγω comparing with what he used to say in the first group, οὐκ οἶδα, has this added ὡς. Socrates does not claim strongly anymore that he does not know anything but speaks only as someone who does not know. He needs this ὡς not only because he is going to accept that he does know some, though few, things immediately after this sentence, but also because he needs his previous disavowal to be loosened from Meno on. He does not merely say here that he knows something. It is then different from the examples mentioned before which could be taken as idiomatic or at least not emphatic. Socrates’ remarkable emphasis on distinguishing εἰδέναι from εἰκάζειν departs it from all other passages where he says only he knows something. Moreover, he claims definitely that he has knowledge about few (ὀλίγα) things. From the early to the middle dialogues, Socrates’ attitude to knowledge has totally renewed its face. He brings forth a new concept, true opinion, and he does not speak of knowledge as he used to before; the rough, perfect and unachievable knowledge of the first group has turned to something more smooth, realistic and achievable. Comparing with the early dialogues that did not set out from the first to reach positive results, the middle ones are extraordinarily and surprisingly positive and hence destroy the basis of the Socratic circle. The questions and answers are purposely directed to some specific new theories; most of them are not directly related to the topics or the main questions of the dialogues. They are suggested when Socrates draws the attention of the interlocutor away from the main question because of the necessity of another discussion. Even if the main question remains unanswered, we have still many positive theories, prominently of metaphysical type. These theories are so abundant and dominant in these dialogues, especially Phaedo and Republic, that one might think that they may appear to be arbitrarily sandwiched in there. This helps dialogues to keep their original Socratic structure while they are suggesting new theories. Hence, the Socratic question of 'what is X?', though is still used to launch the discussion, is loosened and is forgotten for most part of the dialogues. Meno that has first a differently formulated question, 'can virtue be taught?', leads finally to the Socratic question of 'What is virtue?'. Phaedo is dedicated to the demonstration of the immortality of soul and the life after death without having a central Socratic question. The case of Republic is more complicated. The first book, on the one hand, has all the criteria of a Socratic circle: its 'what is justice?' question, Socrates’ strong disavowal (e.g. 337d-e), his rejection of all answers and coming back to the first point without finding out any answer. This Book, considered alone, is a perfect Socratic dialogue, as many scholars regard it as early and separated from other books. The books II-X are, on the other hand, far from implementing a Socratic circle. They have still the 'what is justice?' question as their incentive leading question, but they are, in most of the positive doctrines and methods that encompass the main parts, ignoring the question. Even these books that, I believe, are the farthest discussions from the Socratic circle are so cautious not to break the Socratic structure of the dialogue as long as it is possible. What is changed is not the structure of the dialogue but the ontological and epistemological grounds based on which new theories are suggested. -/- 1. Knowledge of the Good We can clearly see in the second group of dialogues that the KWX principle loses the place it had before in our first group. It is not, of course, rejected, but still we cannot say that it has the same situation. KWX that was based on Socratic question, as we discussed before, was the leading principle of the first Socrates’ epistemology and of the highest position. Other epistemological principles, SK directly and BE indirectly, were relying on Socratic question and therefore on KWX. Such a position does not belong to KWX from Meno on. What makes it different in the second Socrates is another principle that is needed it not only as its complementary principle but also as what is more fundamental. Plato, then, does not reject KWX in this period, but, it seems, he transcends to another more basic principle; a principle we shall call the principle of 'Knowledge of the Good' (KG): -/- KG Knowledge of X requires knowledge of the Good. -/- Whereas all the dialogues of our first group are free from any discuscon about KG, it bears a very important role in the second group so as becomes the superior principle of knowledge in Republic. Trying to solve the problem of teachability of virtue, Socrates says that it can be teachable only if it is a kind of knowledge because nothing can be taught to human beings but knowledge (ἐπιστήμην) (Meno 87c2). The dilemma will be, then, whether virtue is knowledge or not (c11-12) and since virtue is good, we can change the question to: whether is there anything good separate from knowledge (εἰ μέν τί ἐστιν ἀγαθὸν καὶ ἄλλο χωριζόμενον ἐπιστήμης) (d4-5). Therefore, the conclusion will be that if there is nothing good which knowledge does not encompass, virtue can be nothing but knowledge (d6-8). What let us discuss KG as an epistemological principle for the second Secrates is the relation he tries to establish between knowledge and the Good which, though is alongside with the mentioned thesis and the idea of virtue as knowledge, goes much deeper inside epistemology asking to regard the Good as the basis of knowledge. The effort of Phaedo cannot succeed in establishing the Good as the criterion of explanation and knowledge since, I think, it needs a far more complicated ontology of Republic where Socrates can finally announce KG. What is said in Republic is totally compatible with Phaedo 99d–e and the metaphor of watching an eclipse of the sun. In spite of the fact that we do not have adequate knowledge of the Idea of the Good, it is necessary for every kind of knowledge: 'If we do not know it, even if we know all other things, it is of no benefit to us without it' (505a6-7). The problem of our not having sufficient knowledge of the Idea of Good is tried to be solved by the same method of Phaedo 99d-e, that is to say, by looking at what is like instead of looking at thing itself (506d8-e4). It is this solution that leads to the comparison of the Good with sun in the allegory of Sun (508b12-13). What the Good is in the intelligible realm corresponds to what the sun is in the visible realm; as sun is not sight, but is its cause and is seen by it (b9-10), the Good is so regarding knowledge. It has, then, the same role for knowledge that the sun has for sight. Socrates draws our attention to the function of sun in our seeing. The eyes can see everything only in the light of the day being unable to see the same things in the gloom of night (508c4-6). Without the sun, our eyes are dimmed and blind as if they do not have clear vision any longer (c6-7). That the Good must have the same role about knowledge based on the analogy means that it must be considered as a required condition of any kind of knowledge: -/- The soul, then, thinks (νόει) in the same way: whenever it focuses on what is shined upon by truth and being, understands (ἐνόησέν), knows (ἔγνω) and apparently possesses understanding (νοῦν ἔχειν). (508d4-6) -/- Socrates does not use agathon in this paragraph and substitutes it with both aletheia and to on. He links them with the Idea of the Good when he is to assert the conclusion of the analogy: -/- That which gives truth to the objects of knowledge and the power of knowing to the knower, you must say, is the Idea of the Good: being the cause of knowledge and truth (αἰτίαν δ᾽ ἐπιστήμης οὖσαν καὶ ἀληθείας) so far as it is known (ὡς γιγνωσκομένης μὲν διανοοῦ). (508e1-4) Knowledge and truth are called goodlike (ἀγαθοειδῆ) since they are not the same as the Good but more honoured (508e6-509a5). KG, which had been implicitly contemplated and searched in Phaedo, is now explicitly being asserted in Republic. As what was quoted clearly proves, this principle is the very one which we can observe as the most fundamental principle of the second Socrates in Republic, corresponding to the role KWX had in the first Socrates. The Form of the Good in Republic, of which Santas speaks as 'the centerpiece of the canonical Platonism of the middle dialogues, the centerpiece of Plato’s metaphysics, epistemology, ethics and …' (1983, 256) much more can be said. Plato’s Cave allegory in Book VIII dedicates a similar role to the Idea of the Good. The Idea of the Good is there as the last thing to be seen in the knowable realm, something so important that its seeing equals to understanding the fact that it is the cause of all that is correct and beautiful (517b). Producing both light and its source in visible realm, it controls and provides truth and understanding in the intelligible realm (517c). -/- 2. Tripartite Epistemology BE is thoroughy rejected in the second Socrates and substituted by its opposite, the principle of 'Tripartite Epistemolgy' (TE): -/- TE Opinion is an epistemological status between knowledge and ignorance. BE of the first Socrates was denying any third way besides knowledge and ignorance which was the foundation of Socratic circle without which Socrates could not reject his interlocutors’ possessing any kind of knowledge. We cannot say, however, that the first Socrates had a third epistemological status in mind but rejected it. Such a status was unacceptable for him so that one can say that he would reject any kind of such status if suggested. There were only two possibilities about knowledge: either one knows something or he does not know it. TE, thus, was not the first Socrates’ discovery and, I think it is not the second Socrates’discovery. All we can see in our second group of dialouges is that he uses this principle as an already demonstrated one. Having examined the slave boy in Meno for the prupose of showing the working of recollection, it truns out that he has some opinions in him while he still does not know. Without trying to prove it, Socrates takes this as the distinction between knowledge and opinion: -/- So, he who does not know (οὐκ εἰδότι) about what he does not know (περὶ ὧν ἂν μὴ εἰδῇ) has within himself true opinions (ἀληθεῖς δόξαι) about the same things he did not know (περὶ τούτων ὧν οὐκ οἶδε) (85c6-7). -/- The same distinction is set between ὀρθὴν δόξαν and ἐπιστήμην at 97b5-6 ff. (also cf. 97b1-2: ὀρθῶς μὲν δοξάζων … ἐπιστάμενος). He connects then their difference to the myth of Daedalus, the statue that would run away and escape. So are true opinions, not willing to remain long in mind and thus not worthy until one ties them down by αἰτίας λογισμῷ (98a3-4). Socrates says that this tying down is anamnesis. We face, in Phaedo, the same relation is settled between knowledge as the process of being tied down and getting the capability to give an account, on the one hand, and anamnesis, on the other hand. When a man knows, he must be able to give an account of what he knows (Phaedo 76b5-6) and since not all people are able to give such an account, those who recollect, recollect what once they learned (76c4). Although the distinction between knowledge and opinion is not explicitly used in Phaedo, referring to the parallel link between knowledge plus account and anamnesis in Phaedo and Meno, one can say that those who cannot recollect are not able to give account and, thus, are in a state of opinion. What is said at Phaedo 84a, though not yet a definite distinction between knowledge and opinion, makes a distinction between their objects so as we can agree that it is presupposed. The soul of the philosopher, Socrates says, follows reason, stays with it forever and contemplates the divine, which is not the object of opinoin (ἀδόξαστον) (84a8, cf. Meno 98b2-5). The distinction of knowledge and belief in Republic has a significant difference with what we discussed in Meno and Phaedo since the distinction of Meno was based on anamnesis and thus more an epistemological distinction. Even in Phaedo that we do not have any elaborate discussion about the distinction, the only hint to the matter at 76 is bound to the theory of anamnesis. In addition to the relation of the distinction with this theory, there is another evidence that does not permit us to consider the distinction as an ontological distinction. Let’s see Meno 85c6-7: -/- So, he who does not know about what he does not know has within himself true opinions about the same things he did not know (τῷ οὐκ εἰδότι ἄρα περὶ ὧν ἂν μὴ εἰδῇ ἔνεισιν ἀληθεῖς δόξαι περὶ τούτων ὧν οὐκ οἶδε). (85c6-7) -/- This last sentence persists that the objects of knowledge and true opinion are the same. What Socrates is to say here is that whereas he does not know X he has true opinion about the same X. I think Socrates’ sentence that the slave boy οὐκ εἰδότι ἄρα περὶ ὧν ἂν μὴ εἰδῇ and his restatement of it by saying περὶ τούτων ὧν οὐκ οἶδε is because he wants to emphasize that the slave boy who does not know, has true opinion about the same thing. Socrates could say this just with using τούτων and there would be no necessity to bring περὶ ὧν ἂν μὴ εἰδῇ for οὐκ εἰδότι if he did not want to emphasize. -/- 3. Tripartite Ontology The distinction between knowledge and true opinion in Republic, on other side, has nothing to do with recollection, but is based on an ontological principle, 'Tripartite Ontology' (TO): -/- TO There are things that both are and are not. -/- This principle I confine, among our three dialogues of the second group, to Republic not extended to Meno and Phaedo, is obviously the opposite of BO. Speaking about the lovers of sights and sounds in the fifth book, Socrates distinguishes them from philosophers because their thought is unable to understand the nature of beautiful itself besides beautiful things (476a6-8) and hence they can only have opinions. The philosopher who, on the contrary, believes in beautiful itself and can distinguish it from beautiful things (476c9-d3), has knowledge because he knows, contrasting others who have opinion because they only opine (d5-6). Since those whose knowledge were degraded as opinion will complain about Socrates’ such calling their thought, he provides them the following argument (476e7-477b1): -/- - Does the person who knows, knows (γιγνώσκει) something (τὶ) or nothing (οὐδέν)? - He knows something (τί). - Something that is (ὂν) or is not (οὐκ ὄν)? - Something that is (ὂν) for how could something that is not be known (πῶς γὰρ ἂν μὴ ὄν γέ τι γνωσθείη)? - Then we have an adequate grasp of this: No matter how many ways we examine it, what completely is (παντελῶς ὂν) is completely knowable (παντελῶς γνωστόν) and what is in no way (μὴ ὂν δὲ μηδαμῇ) is in every way unknowable (πάντῃ ἄγνωστον). - A most adequate one. - Good. Now, if anything is such as to be and also not to be (ὡς εἶναί τε καὶ μὴ εἶναι), won’t it be intermediate (μεταξὺ) between what purely is (εἰλικρινῶς ὄντος) and what in no way is (μηδαμῇ ὄντος)? - Yes, it’s intermediate. - Then as knowledge (γνῶσις) is set over what is (τῷ ὄντι), while ignorance (ἀγνωσία) is of necessity set over what is not (μὴ ὄντι) mustn’t we find an intermediate between ignorance (ἀγνοίας) and knowledge (ἐπιστήμης) to be set over the intermediate, if there is such a thing? -/- From the third status of being we must reach to the third status of knowledge. The simple reading of this text can be an existential reading, taking the "is" of the mentioned sentences as existence. The problem is that when it is said that there is something that both is and is not reading "is" existentially, it sounds too bizarre to be acceptable. It cannot easily be understandable to have something as both existent and non-existent at the same time. This problem arose so many debates and led many scholars to reject the existential reading of "is" and suggest some other readings like predicative or veridical readings. I think though Plato’s complicated ontology of Republic cannot be correctly understood by a simple existential reading, this "is" cannot be free from existential sense of being and, thus, cannot be reduced to just a predicative or veridical sense of being. -/- 4. Bound Knowledges In addition to KG, the Good is also the basis of another principle in the second Socrates, namely the principle of 'Bound Knowledge' (BK): -/- BK Knowledge of everything is bound to the knowledge of the Good. -/- We distinguished BK from KG because we want to insist, in BK, on what had not been insisted upon in KG, that is, the binding role that the Good plays in the second Socrates, contrasting the absence of such a role in the first Socrates. Socrates remembers, in Phaedo, his wonderful keen on natural philosophers' wisdom when he was young. The origin of this enthusiasm was Socrates’ hope to know the cause of everything as they used to claim. When he was searching the matters of his interest on their basis, Socrates says, he became convinced he can get no acceptable answer from them and found himself blind even to the things he thought he knew before. One day he hears Anaxagoras’ theory that 'it is Mind that arranges and is the cause of everything (ὡς ἄρα νοῦς ἐστιν ὁ διακοσμῶν τε καὶ πάντων αἴτιος)' (Phd. 97c1-2 cf. DK, Fr.15.8-9, 11-12, 12-14) and thinks that he can finally find what he has always expected, i.e. something which can explain all things. What I intend to show here is that what makes Socrates hopeful is that Anaxagoras’ theory tries 1) to explain all things by one thing and 2) this explanation is understood by Socrates as if it is based on the concept of the Good. That Socrates was searching for one explanation for all things can be proved even from what he has been expecting from natural philosophers. The case is, nonetheless, more clearly asserted when he speaks about Anaxagoras’ theory. In addition to διακοσμῶν τε καὶ πάντων αἴτιος of 97c2 mentioned above, we have τὸ τὸν νοῦν εἶναι πάντων αἴτιον (c3-4) and τόν γε νοῦν κοσμοῦντα πάντα κοσμεῖν (c4-5) all emphasizing on the cause of all things (πάντα) which can clearly prove that one of the reasons which caused Socrates to embrace it delightfully was its claim to provide the cause of all things by one thing. Another reason was that Anaxagoras’ Mind, at least in Socrates’ view, was attempting to explain everything by the concept of the Good. This connection between Mind and Good belongs more to the essential relation they have in Socrates’ thinking than Anaxagoras’ theory because there are almost nothing about such a relation in Anaxagoras. The reason for Socrates’ reading can be that Mind is substantially compatible with Socrates’ idea of the relation between good and knowledge. Both the thesis 'no one does wrong willingly' and the theory of virtue as knowledge we pointed to above are evidences of this essential relation. Nobody who knows that something is bad can choose or do it as bad. The reason, when it is reason, that means when it is as it should be, when it is wise or when it knows, works only based on good-choosing. In this context, when Socrates hears that Mind is considered as the cause of everything, it sounds to him like this: good should be regarded as the basis of the explanation of all things. We see him, thus, passing from the former to the latter without any proof. This is done in the second sentence after introducing Mind: -/- I thought that if this were so, the arranging Mind would arrange all things and put each thing in the way that was Best (ὅπῃ ἂν βέλτιστα ἔχῃ). If one then wished to find the cause of each thing by which it either perishes or exists, one needs to find what is the best way (βέλτιστον αὐτῷ ἐστιν) for it to be, or to be acted upon, or to act. On these premises then it befitted a man to investigate only, about this and other things, what is the most excellent (ἄριστον) and best (βέλτιστον). The same man must inevitably also know what is worse (χεῖρον), for that is part of the same knowledge. (97c4-d5) This passage is a good evidence of Socrates’ leap from Anaxagoras’ Mind to his own concept of the Good that can explain why Socrates found Anaxagoras theory after his own heart (97d7). Mind is welcomed because of its capability for explanation on the basis of good to 'explain why it is so of necessity, saying which is better (ἄμεινον), and that it was better (ἄμεινον) to be so' (97e1-3). What Socrates thought he had found in Anaxagoras can indicate what he had been expecting from natural scientists before. Socrates could not be satisfied with their explanations because they were unable to explain how it is the best for everything to be as it is. It can probably be said, then, that it was the lack of the unifying Good in their explanation that had disappointed him. We must insist that we are discussing what Socrates thought that Anaxagoras’ theory of Mind should have been, not about Anaxagoras’ actual way of using Mind. Phaedo 97c-98b, is not about what Socrates found in Anaxagoras but what he thought he could find in it. On the contrary, it should also be noted that it was not this that was dashed at 98b, but Anaxagoras’ actual way of using Mind. It was Anaxagoras’ fault not to find out how to use such an excellent thesis (98b8-c2, cf. 98e-99b). Socrates gives an example to show how not believing in 'good' as the basis of explanation makes people be wanderers between different unreal explanations of a thing. His words δέον συνδεῖν (binding that binds together) as a description for the Good we chose as the name of BK principle: They do not believe that the truly good and binding binds and holds them together (ὡς ἀληθῶς τὸ ἀγαθὸν καὶ δέον συνδεῖν καὶ συνέχειν οὐδὲν οἴονται). (99c5-6) -/- Having in mind Plato’s well-known analogy of the sun and the Good at Republic 508-509, we can dare to say that his warning of the danger of seeing the truth directly like one watching an eclipse of the sun in Phaedo (99d-e) is more about the difficulty of so-called good-based explanation than its insufficiency, a difficulty which is precisely confirmed in Republic (504e-505a, 506d-e). Moreover, BK is asserted in a more explicit way in the Republic, where the Good is considered not only as a condition for the knowledge of X, as was noted above discussing KG, but also as what binds all the objects of knowledge and also the soul in its knowing them. At Republic VI, 508e1-3, when Socrates says that the Form of the Good 'gives truth to the things known and the power to know to the knower (τοῦτο τοίνυν τὸ τὴν ἀλήθειαν παρέχον τοῖς γιγνωσκομένοις καὶ τῷ γιγνώσκοντι τὴν δύναμιν ἀποδιδὸν)', he wants to set the Good at the highest point of his epistemological structure by which all the elements of this structure are bound. This binding aspect of the Good is by no means a simple binding of all knowledges or all the objects of knowledge, but the most complicated kind of binding as it is expected from the author of the Republic. The kind of unity the Good gives to the different knowledges of different things is comparable with the unity which each Form gives to its participants in Republic: as all the participants of a Form are united by referring to the ideas, all different kinds of knowledge are united by referring to the Good. If we observe Aristotle's assertion that for Plato and the believers of Forms, the causative relation of the One with the Forms is the same as that of the Forms with particulars (e.g. Metaphysics 988a10-11, 988b4), that is to say the One is the essence (e.g., ibid, 988a10-11: τοῦ τί ἐστὶν, 988b4-6: τὸ τί ἢν εἶναί) of the Forms besides his statement that for them One is the Good (e.g., ibid, 988b11-13) the relation between the Good and unity may become more understandable. Since the quiddity of the Good (τί ποτ᾽ ἐστὶ τἀγαθὸν) is more than discussion (506d8-e2), we cannot await Socrates to tell us how this binding role is played. All we can expect is to hear from him an analogy by which this unifying role is envisaged, the sun. The kind of unity that the Good gives to the knowledge and its objects in the intelligible realm is comparable to the unity that the sun gives to the sight and its objects in the visible realm (508b-c). The allegory of Line (Republic VI, 509d-511), like that of the Sun, tries to bind all various kinds of knowledges. The hierarchical model of the Line which encompasses all kinds of knowledge from imagination to understanding can clearly be considered as Plato’s effort to bind all kinds of knowledges by a certain unhypothetical principle. The method of hypothesis starts, in the first subsection of the intelligible realm, with a hypothesis that is not directed firstly to a principle but a conclusion (510b4-6). It proceeds, in the other subsection, to a 'principle which is not a hypothesis' (b7) and is called the 'unhypothetical principle of all things' (ἀνυποθέτου ἐπὶ τὴν τοῦ παντὸς ἀρχὴν) (511b6-7). This παντὸς must refer not only to the objects of the intelligible realm but to the sensible objects as well. Plato does posit, therefore, an epistemological principle for all things, a principle that all things are, epistemologically, bound and, thus, unified by. -/- 5. Bound Beings The ontological aspect of BK we shall call the principle of 'Bound Beings' (BB): -/- BB Being of all things are bound by the Good. -/- We saw in our principle of Split Being (SB) how the first Socrates was criticized because of his approach to split being and separate each thing from other things. The principle of Bound Beings intends to make the things more related, a duty which is done again by the Good. In the allegory of Sun, there are two paragraphs that evidently and deliberately extend the binding role of the Good to the ontological scene: -/- You will say that the sun not only makes the visible things have the ability of being seen but also coming to be, growth and nourishment. (509b2-4) -/- This clearly intends to remind the ontological role the sun plays in bringing to being all the sensible things in order to display how its counterpart has the same role in the intelligible realm (b6-10): -/- Not only the objects of knowledge (γιγνωσκομένοις) owe their being known (γιγνώσκεσθαι) to the Good, but also their existence (τὸ εἶναί) and their being (οὐσίαν) are due to it, though the Good is not being but superior to it in rank and power. That the Good is here represented as responsible for being of things in addition to their being known means, in my opinion, that Plato wants to posit BB in addition to BK. The allegory of Cave at the very beginning of the seventh Book (514aff.) can be taken as another evidence. The role of the Good, one might say, is confined to the intelligible realm because it is asserted that the role the Good plays in this realm is corresponding to that of the sun in the visible realm. The fact that Plato wants to observe the Good also as the ontological cause of the sensible things is obvious from his saying, in the allegory of Cave, that the Form of the Good 'produces light and its source (τὸν τούτου κύριον) [i.e. the sun] in the visible realm' (517c3). We can conclude, then, that the ontological function of the Good is not confined to the intelligible realm in which it is the lord and provides truth and understanding (c3-4) because it is also responsible to produce τὸν κύριον of light. 6. Proportionality of Being and Knowledge Insofaras BE and BO principles of the first Socrates gave way to TE and TO principles of the second Socrates, we cannot expect him to preserve KB in the same way as it was in the first Socrates. The new tripartite ontology and epistemology necessitates some modifications in KB which results in the principle of 'Proportionality of Being and Knowledge' (PBK): -/- PBK To every class of being there is a proportionate category of knowledge. -/- This principle, of course, does not entail the refutation of KB and thus is not kind of rejecting PBK but only a more complicated version of it. Based on PBK, we can still agree that knowledge is of being (KB) but the issue is that since none of the concepts of knowledge and being in the second Socrates are as simple as they were for the first Socrates, we need a more complicated principle for their relation here. Although from Meno 97a where the distinction of knowledge and true opinion is drawn out in the second group of the dialogues, we can expect a new relation, it is articulated in its most complete way in Republic and specifically in the allegory of Line. All the beings are divided there hierarchically to four classes, to each of them belongs a class of knowledge: imagination to images, belief to the sensible things (more correctly: the things of which they[in previous class] were images (ᾧ τοῦτο ἔοικεν)), thought to mathematical objects (?) and understanding to the Forms and the first principle. The degree of clarity that each of the classes of knowledge shares in (σαφηνείας ἡγησάμενος μετέχειν) is proportionate to the degree that its object shares in truth (ἀληθείας μετέχει). (511e2-4) -/- Conclusion From the six onto-epistemilogical principles of the first Socrates, four principles turn to their opposite in the middle period dialogues. While bipolar epistemology and ontology of the early dialogues give place to tripartite epistemology in the middle period dialogues and tripartite ontology in Republic, the split knowledge and being of the first Socrates are inclined to be substituted by bound knowledges and bound beings in the second Socrates and specifically in Republic. Not all our system of principles in this article is necessarily determinative. Either they are rightly formulated or not, our result would not be vulnerable if we accept that 1) making the distinction of knowledge and belief, 2) accepting the being of not being and 3) trying to bind both being and knowledge by the concept of the Good happens only in middle period dialogues, having been absent in the early ones. These are the favourite results all those somehow arbitrary and even oversimplified principles were to illustrate; that there is kind of a development in the epistemological as well as the ontological grounds of Plato’s philosophy. -/- Notes . (shrink)

This paper aims to suggest a new approach to Plato’s theory of being in Republic V and Sophist based on the notion of difference and the being of a copy. To understand Plato’s ontology in these two dialogues we are going to suggest a theory we call Pollachos Esti; a name we took from Aristotle’s pollachos legetai both to remind the similarities of the two structures and to reach a consistent view of Plato’s ontology. Based on this theory, when Plato (...) says that something both is and is not, he is applying difference on being which is interpreted here as saying, borrowing Aristotle’s terminology, 'is is (esti) in different senses'. I hope this paper can show how Pollachos Esti can bring forth not only a new approach to Plato’s ontology in Sophist and Republic but also a different approach to being in general. -/- Keywords Plato; being; difference; image; pollachos esti; pollachos legetai 1. Being, Not-Being and Difference The three dialogues where the notion of "difference" attaches to the notion of being, namely Parmenides II, Sophist and Timaeus,and specifically the first two we try to discuss here. In these dialogues, Plato is going to achieve a new and revolutionary understanding of being which is not anymore based on the notion of "same" as it was before in Greek ontology. It was his discovery, I think, that the notion of being in the Greek ontology is attached to the notion of the "same" and it is because of this attachment that there have always been many problems understanding being especially after Parmenides. That being has always been relying on the "same" can be found out from the way most of the Presocratics understood it. It was based on such a relationship between being and "same" that a later Ionian, Heraclitus of Ephesus, rejected Being by rejecting its sameness: unable to be the same, being cannot be being anymore but becoming. Heraclitus’ criticism of his predecessors’ understanding of being was due to his discovery that what they call being is not the same but different in every moment. The relation of being and sameness reaches to its highest point in Parmenides. What Plato does in using the "difference" is nothing but the establishment of a creative relation between being and "difference". In this new relation, although he is in agreement with Heraclitus that being is not the same but different, he does not do it by use of becoming. He disagrees, on the other hand, with Parmenides that such a relation between being and difference leads to not being. At Parmenides 142b5-6 it is said that if One is, it is not possible for it to be without partaking (μετέχειν) of being (οὐσίας), which leads to the distinction of being and one: -/- So there would be also the being of the one (ἡ οὐσία του̑ ἑνὸς) which is not the same (ταὐτὸν) as the one. Otherwise, it wouldn’t be its being, nor the one would partake of it. (142b7-c1) -/- The fact that what is (ἔστι) signifies (σημαῖνον) is other (ἀλλο) than what One signifies (c4-5), is being taken as a reason for their distinction. The conclusion is that when we say 'one is', we speak of two different things, one partaking of the other (c5-7). Having repeated these arguments of the otherness of being and one at 143a-b, Parmenides says that the cause of this otherness can be neither Being nor One but "difference": -/- So if being is something different (ἕτερον) and one something different (ἕτερον), it is not by being one that the one is different from being nor by its being being that being is other than one, but they are different from each other (ἕτερα ἀλλήλων) by difference (τῷ ἑτερῳ) and otherness (ἄλλῳ). (143b3-6) -/- The fifth hypothesis, 'one is not' (160b5ff.) is also linked with the notion of difference. When we say about two things, largeness and smallness, that they are not, it is clear that we are talking about not being of different (ἕτερον) things (160c2-4). When it is said that something is not, besides the fact that there must be knowledge of that thing, we can say that it entails also its difference: 'difference in kind pertains to it in addition to knowledge' (160d8). Parmenides explains the reason as such: -/- For someone doesn’t speak of the difference in kind of the others when he says that the one is different from the others, but of that thing’s own difference in kind. (160e1-2) -/- Although the theory of being as "difference" is not fulfilled yet, an exact look at what occurs in Sophist can make us sure that this was the launching step for "difference" to get its deserved role in Plato’s ontology. The notion of the "difference" is not yet well-functioned in Parmenides because we can see that being is still attached to the same: -/- For that which is the same is being (ὄν γὰρ ἐστι τὸ ταὐτόν) (162d2-3). -/- The notion of difference in Sophist is the key element based on which a new understanding of being is presented and the problem of not being is somehow resolved. The friends of Forms, the Stranger says, are those who distinguish between being and becoming (248a7-8) and believe that we deal with the latter with our body and through perception while with the former, the real being (ὄντως οὐσίαν) with our soul and through reasoning (a10-11). Being is then bound with the "same" by adding: -/- You say that being always stays the same and in the same state (ἣν ἀεὶ κατὰ ταὐτὰ ὡσαύτως ἔχειν) but becoming varies from one time to another (δὲ ἄλλοτε ἄλλως). (248a12-13) -/- That the theory of the relation of being and capacity (247d8f., 248c4-5) matches more with becoming than with being (248c7-9) must be rejected because being is also the subject of knowledge which is kind of doing something (248d-e). It does, however, confirm that 'both that which changes and also change have to be admitted as existing things (ὄντα) (249b2-3). I believe that this is what Socrates would incline to do at Theaetetus 180e-181a, that is, putting a fight between two parties of Parmenidean being and Heraclitean becoming and then escaping. The solution is that becoming is itself a kind of being and we ought to accept what changes as being. This is what must be done by a philosopher, namely, to refuse both the claim that 'everything is at rest' and that 'being changes in every way' and beg, like a child, for both and say being (τὸὄν) is both the unchanging and that which changes (249c10-d4). This kind of begging for both is obviously under the attack of contradiction (249e-250b). For both and each of rest and change similarly are (250a11-12) but it cannot be said either that both of them change or both of them rest, being must be considered as a third thing both of the rest and change associate with (250b7-10). The conclusion is that 'being is not both change and rest but different (ἕτερον) from them instead' (c3-4). The notion of difference helps Plato to take being departed from both rest and change because it was their sophisticated relation with being that made the opposition of being and becoming. Plato is now trying to separate being from rest and, thus, from "same" by "difference". Such a crucial change is great enough to need a 'fearless' decision (256d5-6). The possibility of being of not being is resulted (d11-12) comes as the answer to the question 'so it’s clear that change is not being and also is being (ἡ κίνησις ὄντως οὐκ ὄν ἐστι καὶ ὄν) since it partakes in being?' (d8-9). It is then by the notion of difference that becoming is considered as that which both is and is not. This coincidence of being and not being about change is apparently similar to Socrates’ paradoxical statement at Republic 477a about what both is and is not. -/- Introduction The Republic 476-477 has always been a matter of controversy mainly about two interwoven points. The first problem is the meaning of being here; that whether what he has in mind is a veridical, existential or propositional sense of being. The second problem is his distinction between the objects of knowledge and opinion which seems to lead, some believe, to the Two Worlds (TW) theory. The crucial point in Republic is that what is considered between knowledge (ἐπιστήμης) and ignorance (α͗γνοιας), namely opinion, must have a different object that leads Socrates to draw the distinction of knowledge and opinion between their objects. The problem of understanding being in the fifth book of the Republic is that when it is said that the Form of F is F but a particular participating in F, both is and is not F, it sounds too bizarre and unacceptable. It cannot be imaginable how a thing can be existent and non-existent at the same time. At the first sight, the only solution seems to be the degrees of existence which is called by Annas (1981, 197) a 'childish fallacy' and a 'silly argument'. Kirwan (1974, 118) thinks that Republic V does not attribute 'any doctrine about existence' to Plato and Kahn (1966, 250) claims that the most fundamental value of einai when used alone (without predicate) is not "to exist" but "to be so", "to be the case" or "to be true". The problems of understanding being in Republic and Sophist besides the difficulties of the existential reading led scholars to the other senses of being, mostly related to the well-known Aristotelian distinctions between different senses of being. In the predicative reading, Annas, for example, refers this difference to the qualified and unqualified application. Whereas the Form of F is unqualifiedly F, a particular instance of F can be F only qualifiedly (1981, 221). Vlastos’ well-known substitution of 'degrees of reality' for 'degrees of being/existence' must be categorized as a predicative reading. Kahn thinks that the basic sense of being for Plato is 'something like propositional structure, involving both predication and truth claims, together with existence for the subject of predication' (2013, 96). Believing that the complete-incomplete distinction terminology is misleading about Plato, he thinks that semantic functions are only second-order uses of the verb and it is the predicative or incomplete function which is fundamental. Suggesting a veridical reading, Fine (2003, 70 ff) thinks that while both existential and predicative readings separate the objects of knowledge and belief, it is only her reading which does not force such separation of the objects and thus does not imply TW. Stokes (1998, 266) thinks that though Fine is right saying that Plato does not endorse TW in book V, she is wrong in rejecting existential in favor of the veridical reading. The reception of existential reading can be seen more obviously in Calvert who thinks, in agreement with Runciman, that 'it would be safer to say that Plato’s gradational ontology is probably not entirely free from degrees of existence' (1970, 46). At Sophist 254d-e Plato singles out five most important kinds (or Forms!?) in which the same (ταὐτὸν) and difference (θάτερον) are regarded besides being, rest and change. They are, therefore, neither the same nor the difference but share in both (b3). Being (τὸ ὄν) cannot be the same also because if they 'do not signify distinct things' both change and rest will have the same label when we say they are (255b11-c1). We have then four distinct kinds, being, change, rest and same, none of them is the other. The case of difference is more complicated. When the stranger wants to assess the relation of being and difference, he can say simply neither that they are distinct nor that they are not. He has to make an important distinction inside being to get able to draw the relation of being and difference: -/- But I think you'll admit that some of the things that are (τῶν ὄντων) are said (λέγεσθαι) by themselves (αὐτὰ καθ’ αὑτά) but some [are said] always referring to (πρὸς) other things (ἄλλα) (255b12-13) -/- The difference is always said referring to other things (τὸδέγ’ ἕτερον ἀεὶ πρὸς ἕτερον) (255d1). It pervades all kinds because each of them should be different from the others and is so due to the difference and not its own nature (253e3f.) After asserting that change is different from being and therefore both is and is not (256d), the difference is described as what makes all the other kinds not be, by making each different from being. Given that all of them are by being, this association of being and difference is the cause of their being and not-being at the same time, the issue that its version at RepublicV made all those controversies we discussed above: -/- So in the case of change and all the kinds, not being necessarily is (Ἔστιν ἄρα ἐξ ἀναγκης τὸ μὴ ὄν). Τhat’s because as applied to all of them, the nature of the difference (ἡ θατέρον φύσις) makes each of them not be by making it different from being. And we’re going to be right if we say that all of them are not in the same way. And conversely [we’re also going to be right if we say] that they are because they partake in being. (Sophist 256d11-e3) -/- Plato’s new construction of five distinct kinds and the role he gives to thedifference among them is aimed to resolve the old problem of understanding being which has always been annoying from the time of Heraclitus and Parmenides. Both the ontological status of becoming and that of not being were, in Plato’s mind, based on the absolute domination of the notion of the Same over being. Now, not only becoming is understandable as being but also not being which is not the contrary of being anymore but only different (ἕτερον) (257b3-4). Though I agree partly with Frede that the account of not being which is needed for false statements is more complicated than just saying, as Cropsey (1995, 101) says, that Plato is substituting 'X is not Y' with 'X is different from Y', I totally disagree with him that when we say X is not beautiful, Plato could not have thought that it is not a matter of its being different from beautiful because 'it would be different from beauty even if it were beautiful by participation in beauty' (1992, 411). Conversely, as we will discuss, it is exactly the relation of the beautiful thing, X, and the beautiful itself, in which X shares that is to be solved by the notion of not being as difference. Though it is beautiful because of sharing in beauty, X is not beautiful because it is different from beautiful itself. What the difference is to do is to show how something can both be and not be the same thing. The difference is what makes one thing both be and not be a certain other thing. This equips the difference with the ability to explain a certain thing’s not-being when it is. Thanks to the notion of difference, it is now possible to explain not only not being but also the simultaneous being and not being of a thing: 'What we call "not-beautiful" is the thing that ἕτερόν ἐστιν from nothing other than του̑ καλου̑ φύσεως' (257d10-11). The result is that not beautiful happens to be (συμβέβηκεν εἶναι) one single thing among kinds of beings (τι τῶν ὄντων τινὸς ἑνὸς γένους) and at the same time set over against one of the beings (πρός τι τῶν ὄντων αὖ πάλιν ἀντιτεθὲν) (257e2-4) and thus be something that happens to be not beautiful (εἶναί τις συμβαίνει τὸ μὴ καλόν); a being set over against being (ὄντος δὴ πρὸς ὄν ἀντίθεσις) (e6-7). Neither the beautiful is more a being (μα̑λλον ... ἐστι τῶν ὄντων) nor not beautiful less (e9-10) and thus both the contraries similarly are (ὁμοίως εἶναι) (258a1). This conclusion, it is emphasized again (a7-9), owes to θατέρου φύσις now turned out as being. Therefore, each of the many things that are of the nature of the difference and set over each other in being (τῆς τοῦ ὄντος πρὸς ἄλληλα ἀντικειμένων ἀντίθεσις) is being as being itself is being (αὐτοῦ τοῦὄν τοςοὐσία ἐστιν) and not less. They are different from, and not the contrary of, each other (a11-b3). This is exactly τὸμὴὄν, the subject of the inquiry (b6-7). Hence, not being has its own nature (b10) and is one εἶδοςamong the many things that are (b9-c3). Such far departing from Parmenides’ ontological principle is done on the basis of the nature of the difference. It was the discovery of such a notion that made the stranger brave enough to say that not being is each part of the nature of the difference that is set over against being (258d7-e3, cf. 260b7-8). That the relation of being and difference is difference is the key element of the new ontology. The difference is, only because of its sharing in being, but it is not that which it shares in but different from it (259a6-8). Not being is exactly based on this difference: ἕτερον δὲ τοῦ ὄντος ὄν ἔστι σαφέστατα ἐξ ἀνάγκης εἶναι μὴ ὄν (a8-b1). 2. Difference and the Being of a Copy We discussed above that the sense of being of particulars in Republic V made so many debates that whether being is there used in an existential sense or not. Particulars in Republic are regarded as images in the allegories of Line and Cave. The being of an image/copy makes, thus, the same problem. Plato’s analogy of original -copy for the relation of Forms and their particulars in Republic has obviously a different attitude to being. The main question is that what is the ontological status of a copy in respect of its original? Are there two kinds of being, 'real being' versus 'being' as Ketchum says (1980, 140) or only one kind? What is the difference of being in an original and its copy? Is it a matter of degrees of being or reality as some commentators have suggested? Is it a matter of being relational? By reducing the ontological issue to an epistemological one, Vlastos’ suggestion of degrees of reality in an article with the same name does neither, I think, pay attention to the problem nor resolve it. He agrees that Plato never speaks of "degrees" or "grades" of reality (1998, 219). What allows him to entitle it as such are some of Plato’s words in Republic as well as Plato’s words in some other dialogues (1998, 219). When Plato states that the Forms only can completely, purely or perfectly be real he means, Vlastos says, they are cognitively reliable (1998, 229); an obvious reduction of the issue to an epistemological one. He thinks that when in Republic we are being said that a particular’s being F is less pure than its Form, it is because it is not exclusively F, but it is and is not F and this being adulterated by contrary characters is the reason of our confused and uncertain understanding of it (1998, 222). Ketchum rightly criticizes Vlastos’ doctrine in its disparting from ontology thinking that 'to understand Plato’s talk of being as talk of reality is to obscure the close relation that exists between "being" and the verb "to be"' (1980, 213). He thinks, therefore, that οὐσία must be understοοd as being rather than reality, τὸὄν as "that which is" and not "that which is real" and … (ibid). His conclusion is that degrees of reality cannot interpret Plato correctly and we must accept degrees of being. Allen believes that a 'purely epistemic' reading of the passage in Republic is patently at odds with Plato’s text (1961, 325). He thinks that not only degrees of reality but also degrees of reality must be maintained (1998, 67). What Cooper suggests gets close to this paper’s solution: -/- Plato does not I think wish to suggest that existence is a matter of degree in the way in which being pleasant or painful is a matter of degree. Rather there are different grades of ontological status. (1986, 241) -/- A more ontological solution for the problem of understanding the being of a copy and its relation with the being of its original is suggested by the theory of copy as a relational entity. Based on this interpretation, 'the very being of a reflection is relational, wholly dependent upon what is other than itself: the original…' (Allen, 1998, 62). As relational entities, particulars have no independent ontological status; they are purely relational entities which derive their whole character and existence from Forms (ibid, 67). Although these relational entities are and have a kind of existence, we must also say that 'they do not have existence in the way that Forms, things which are fully real, do' (ibid). Allen (1961, 331) extends his theory to Phaedo where it is said that particulars are deficient (74d5-7, 75a2-3, 75b4-8), 'wish' to be like (74d10) or desire to be of its nature (75a2); an extension that, like F.C. white (1977, 200), I cannot admit. He correctly states that Plato did not start out with a doctrine of particulars as images and semblances but come to such a view after Phaedo, or perhaps after Republic V (1977, 202). Though we may not agree with him about Republic V, if we have to consider its last pages also, we must agree with him that not only the ontology of Phaedo but also that of Republic II-V (except the last pages of the latter book) are somehow different from (but at the same time appealing to) the ontology of original-copy which should exclusively assign to Sophist, Timaeus and RepublicVI-VII besides the last pages of book V. The answer to the problem of Plato’s sense of being in RepublicV can be reached only if we read Republic V based on and as following Sophist. We can find out his meaning of that which both is and is not only by the ontological status he assigns to a copy in Sophist. The kind of being of a copy in Sophist reveals as Plato’s key for the lock of the problem of not being. Let’s see how the ontological status of a copy is the critical point of Plato’s ontology. In the earlier pages of Sophist, we are still in the same situation about not being. To think that that which is not is is called a rash assumption (237a3-4) and Parmenides’ principle of the impossibility of being of not being is still at work (a8-9). At 237c1-4, the problem of "not being" is noticed in a new way which shows some kinds of a more realistic position to the problem of not being. Nevertheless, not being is still unthinkable, unsayable, unutterable and unformulable in speech (238c10). Soon after mentioning that it is difficult even to refuse not being (238d), the solution to the problem appears: the being of a copy (εἴδωλον) (239d). A copy is, says Theaetetus, something that is made referring to a true thing (πρὸς τἀληθινὸν) but still is 'another such thing (ἕτεροντοιου̑τον)' (240a8). Nevertheless, this 'another such thing' cannot be another such real or true thing. In answer to the question of the Stranger that if this 'another such thing' is the true thing (240a9), Theaetetus answers: οὐδαμῶς ἀληθινόν γε, ἀλλ’ ἐοικὸςμὲν (240b2). A copy’s being 'another such thing' does not mean another true thing but only a resemblance of it. Not only is not a copy another true thing besides the original, but it is the opposite of the true thing (b5) because only its original is the thing genuinely and being a copy is being the thing only untruly. The word ἐοικὸς is opposed to ὄντως ὄν in the next line (240b7): 'So you are saying that that which is like (ἐοικὸς) is not really that which is (οὐκ ὄντως [οὐκ] ὄν)'. But still a copy 'is in a way (ἔστι γε μήν πως)' (b9). While it is not really what it is its resemblance, it has its own being and reality because it really is a likeness (εἰκων ὄντως) (b11). The Stranger asks: -/- So it is not really what is (οὐκ ὄν ἄρα [οὐκ] ὄντως ἐστὶν) but it really is what we call a likeness (ὄντως ἣν λέγομεν εἰκόνα)? (b12-13) -/- This is Plato’s innovative ontological solution to the problem of not being. Theaetetus’ answer confirms this: 'Maybe that which is not is woven together with that which is' (c1-2). Therefore, a copy neither is what really is nor is not-being but only is what in a way is. Thanks to the ontological status of a copy, the third status intermediate between being and not being is brought forth. The essence of an image, in Kohnke’s words, does not consist 'solely in the negation of what is genuine and has real being' because otherwise 'it would be an ὄντως οὐκ ὄν,essentially and really a not being' (1957, 37). The characteristics of a copy can be summed up as folows: i) A copy is a copy by referring to a true thing (πρὸς τἀληθινὸν). ii) A copy is different from that of which it is a copy (ἕτερον). iii) A copy is not itself a true thing (ἀληθινόν) as that of which it is a copy but only that which is like it (ἐοικὸς). iv) It is not really that which really is (ὄντως ὄν) but only really a likeness (εἰκων ὄντως). The conclusion is that: v) A copy in a way (πως) is that means it both is and in not, the product of interweaving being with not being. This leads to the refutation of father Parmenides’ principle, accepting that 'that which is not somehow is (τό τε μὴ ὄν ὡς ἔστι)' and 'that which is, somehow is not (τό ὄν ὡς οὐκ ἔστι) (241d5-7). Besides copies and likenesses (εἰκόνων), we have also imitations (μιμημάτων) and appearances (φαντασμάτων) as the subjects of this new kind of being and thus false belief (241e3). In Timaeus, the world of becoming which cannot correctly be called and thus we have to call it "what is such" (τὸ τοιου̑τον) (49e5) or "what is altogether such" (τὸ διἀ παντὸς τοιου̑τον) (e6-7), consists solely of imitations (μιμημάτα) (50c5) which are identifiable only by the things that they are their imitations. The word τοιου̑τον which had been used to determine the situation of a copy in respect of its original, now becomes the definition of the world of becoming in which everything is an image of another thing, a Being, that stays always the same and is different and separated from its image. Cherniss, in my view rightly, draws attention to the very important point about the ontological status of an image that can at the same time be considered a criticism of the relational theory. What we are being said in Timaeus, he thinks,cannot be explained by saying that an image is not self-related and making its being relational. What is crucial about an image is that it 'stands for something, refers to something, means something and this meaning the image has not independently as its own but only in reference to something else apart from it' (1998, 296). This function finds its best explanation in the theory we are to suggest in the following. 3. πολλαχῶς ἔστι The best way to understand the ontological status of an image in Plato is to see first how his most clever pupil, Aristotle, resolved the same problem that Plato brought his theory of image for its sake. Aristotle’s theory of pollachos legetai is a brilliant and, at the same time, deviated version of Plato’s theory that is able, however, to help us read Plato in a better way. We discuss Aristotle’s theory to reach to a full understanding of Plato’s theory because it is, firstly, constructed in Aristotle in a more clear way and, secondly, it can also be taken as an evidence that our reading of Plato is legitimate. The phrase τὸ ὄν πολλαχῶς λέγεται, a so much repeated phrase in Aristotle’s works, is his resolution for some of the ontological problems of his predecessors all treating being as if it has only one sense. Aristotle is right in his criticism of the philosophical tradition specially Heraclitus, Parmenides and Plato since all did presuppose only one sense for being and his theory is, thus, a creative and revolutionary solution for many problems that all the past philosophers were stuck in. But it is at the same time somehow a borrowed theory. As we will discuss, both the structure of the doctrine and the problems it tries to resolve are the same as Plato’s doctrine (and even is comparable in its phraseology) though it is in Aristotle, as can be expected, a more clear and better structured doctrine. 1) Associated with the theory of pros hen and the theory of substance, the theory of several senses of being provides a structure which, I insist, is the best guide to understand Plato’s theory of Being in Sophist, Timeaus and Republic. a) Although the theory of pollachos legetai is not necessarily based on the theory of pros hen, they become tightly interdependent about being: -/- Being is said in many ways/senses (τὸ δὲ ὄν λέγεται μὲν πολλαχῶς) but by reference to one (πρὸς ἕν) [way/sense] and one kind of nature (μίαν τινὰ φύσιν). (Metaphysics 1003a33-34) -/- The doctrine of pros hen which is Aristotle’s initiative third alternative besides the homonymous and synonymous application of words, is primarily a linguistic theory that tries to provide a new theory to explain the different implementations of the same word. The pros hen implementation of being is to provide an alternative for the theory of the synonymous (in Plato: homonymous) implementation of being which says being is said in one sense (kath hen) (1060b 32-33). That both the pros hen and the kath hen implementation of a word has one thing (hen) as what is common, makes them in opposition to the homonymous implementation which does not consider anything in common. Whereas both pros hen and kath hen assume a common nature, with which all the implementations of the word have some kind of relation, their difference is that while kath hen takes all the implementations of the word as the same with the common nature, pros hen makes them different. Substance is called πρῶτον ὄν because it is said to be primarily: -/- For as is (τὸ ἔστιν) is predicated of all things, not however in the same way (οὐχ ὁμοίως) but of one sort of thing primarily and of others in a secondary way. So too τὸτί ἐστιν belongs simply (ἁπλῶς) to substance but in a limited sense (πῶς) to the others [other categories] (1030a21-23). -/- The word ἁπλῶς standing against κατὰ συμβεβηκός tries to make substance different from the accidents. When we are being said that τὸ ὄν πολλαχῶς λέγεται, it means that only the substance that is simply (ἁπλῶς) the ἕν, the common nature, τὸὄν. When we use the word 'being' about a substance, the being is said differently from when we use 'being' about an accident. The distinction between the substance and the other categories is a distinction between what simply is said to be and what only with reference to (pros) the substance is said to be. The doctrine of pros hen, changing kath hen to pros hen in respect of to on, makes a distinction that wants to show that while there is a kind of implementing the word being that is simply being, there is another kind which is called being only by reference to that which is simply being. In the doctrine of pros hen it is not so that all the things that are said to be are only by reference to a common one thing, but that while one thing is called being because it is that thing itself, the other things are called so without being that thing itself but only by referring to it. At the very beginning of book Γ, it is said that: -/- Being is said in many senses but all refer to one arche. Some things are said to be because they are substances, others because they are affections of substances, others because they are a process towards substances or destructions or privations or qualities of substances … (1003b5-9, cf. 1028a18-20) -/- Substance is what really is said to be and all other things that are said to be are said only in favor of it. This difference of substance from all other senses of being is what is, I believe, primarily aimed in Aristotle’s interrelated theories of pollachos legetai,pros hen and the theory of substance. b) The difference of the implementation of being in the case of substance and the accidents goes so deep that while substance is considered as the real being, the accidents are almost not being. An accident is a mere name (Metaphysics 1026b13-14) and is obviously akin to not being (b21). Aristotle adds that Plato was 'in a sense not wrong' saying that sophists deal with not being (τὸ μὴ ὄν) because the arguments of sophists are, above all, about the accidental (1026b13-16). At the beginning of book , he says about quality and quantity (which look to be more of a being than other accidents) that they are not existent (οὐδ̕ ὄντα ὡς εἰπεῖν) in an unqualified sense (ἁπλῶς) (1069a21-22). The two above-mentioned points, Aristotle’s (a) interwoven theories of pollachos legetai, pros hen and the theory of substance and (b) taking accidents almost as not being, comparedwith substance, brings forth a structure that I shall call Pollachos Legetai (with capital first letters). What is of the highest importance in this structure for me is the difference of substance from accidents and the kind of relation which is settled between them. There is a substance that without any qualification is said to be and the accidents that are said to be only by reference (pros) to it. Adding Aristotle’s point about accidents that they are nearly not being to this relation and difference, we can obviously see how much this structure is close to Plato’s original-copy ontology. We spoke of the relation of being and difference in Plato’s model and the way Plato construes the being of a copy. A copy is a copy only by referring to (pros) a model; it is different from (ἕτερον) that of which it is a copy; it is not itself a true thing as its model and not really that which is (ὄντως ὄν) but only is in a way (πῶς). If we behold the difference of substance and accident in the context of the theory of pollachos legetai and pros hen, we can observe its fundamental similarity with Plato’s original-copy theory in its structure. Allen draws attention to the fact that the relation between Forms and particulars in Plato’s original-copy model is 'something intermediate between univocity and full equivocity' (1998, 70, n. 24) and the same as what Aristotle calls it pros hen (ibid). What made us compare the two structures was not, of course, the complete similarity of two structures (we have to agree with many possible differences of the two theories) but exactly the specific relation between an original and its copy on the one hand, and a substance and its accident on the other hand. As substance and accident do not share a common character and the substance -accident model hints that they stand in a certain relation, there is no common character between the original and copy in Plato’s model as well. Furthermore, their similarity is not confined to their structure only; they are also aimed to solve the same problem. The central point of the theory is that all the predecessors took being in one sense and this was their weakness point. Besides the mentioned above passages about the relation of pollachos legetai and presocratics’, as well as Plato’s, ontology, the relation of the theory with the problem of not being is clear in several passages. In Metaphysics, it is said: 'Being is then said in many senses… It is for this reason that we say even of not being that it is not being' (1003b5-10). Discussing the accidental sense of being, Aristotle points that it is in the accidental way that we say, for example, that not-white is because that of which it is an accident is (1017a18-19, cf. 1069a22-24). We mentioned that he thought Plato was right saying that sophistic deals with not being because sophistic deals with accidental, which is somehow not being (1026b14-16). Plato turned sophistic not-being to what both is and is not and Aristotle to what accidentally is said to be. What helps Aristotle to resolve the problem of not being is his distinction between ἁπλῶς and κατὰ σθμβεβηκός. Aristotle’s "qua" (ᾕ) which is directly linked with his distinction between καθ’ αὑτο λέγεται and κατὰ συμβεβηκός λέγεται, is used to resolve the old problem of coming to be out of not being (Physics 191b4-10). He strictly asserts that his predecessors could not solve the problem because they failed to observe the distinction of "qua itself" from "qua another thing" (b10-13). He then continues: -/- We ourselves are in agreement with them in holding that nothing can be said simply (ἁπλως) to come from not being (μὴὄντος). But nevertheless we maintain that a thing may come to be from not being in an accidental way (κατὰ συμβεβηκός). For from privation which ὅ ἐστι καθ’ αὑτο μὴ ὄν, nothing can become. (Phy. 191b13-16, cf. b19-25) . (shrink)

continent. 1.1 : 3-13. / 0/ – Introduction I want to propose, as a trajectory into the philosophically weird, an absurd theoretical claim and pursue it, or perhaps more accurately, construct it as I point to it, collecting the ground work behind me like the Perpetual Train from China Mieville's Iron Council which puts down track as it moves reclaiming it along the way. The strange trajectory is the following: Kant's critical philosophy and much of continental philosophy which has followed, (...) has been a defense against horror and madness. Kant's prohibition on speculative metaphysics such as dogmatic metaphysics and transcendental realism, on thinking beyond the imposition of transcendental and moral constraints, has been challenged by numerous figures proceeding him. One of the more interesting critiques of Kant comes from the mad black Deleuzianism of Nick Land stating, “Kant’s critical philosophy is the most elaborate fit of panic in the history of the Earth.” And while Alain Badiou would certainly be opposed to the libidinal investments of Land's Deleuzo-Guattarian thought, he is likewise critical of Kant's normative thought-bureaucracies: Kant is the one author for whom I cannot feel any kinship. Everything in him exasperates me, above all his legalism—always asking Quid Juris? Or ‘Haven’t you crossed the limit?’—combined, as in today’s United States, with a religiosity that is all the more dismal in that it is both omnipresent and vague. The critical machinery he set up has enduringly poisoned philosophy, while giving great succour to the academy, which loves nothing more than to rap the knuckles of the overambitious [….] That is how I understand the truth of Monique David-Menard’s reflections on the properly psychotic origins of Kantianism. I am persuaded that the whole of the critical enterprise is set up to to shield against the tempting symptom represented by the seer Swedenborg, or against ‘diseases of the head’, as Kant puts it. An entire nexus of the limits of reason and philosophy are set up here, namely that the critical philosophy not only defends thought from madness, philosophy from madness, and philosophy from itself, but that philosophy following the advent of the critical enterprise philosophy becomes auto-vampiric; feeding on itself to support the academy. Following Francois Laruelle's non-philosophical indictment of philosophy, we could go one step further and say that philosophy operates on the material of what is philosophizable and not the material of the external world. [1] Beyond this, the Kantian scheme of nestling human thinking between our limited empirical powers and transcendental guarantees of categorical coherence, forms of thinking which stretch beyond either appear illegitimate, thereby liquefying both pre-critical metaphysics and the ravings of the mad in the same critical acid. In rejecting the Kantian apparatus we are left with two entities – an unsure relation of thought to reality where thought is susceptible to internal and external breakdown and a reality with an uncertain sense of stability. These two strands will be pursued, against the sane-seal of post-Kantian philosophy by engaging the work of weird fiction authors H.P. Lovecraft and Thomas Ligotti. The absolute inhumanism of the formers universe will be used to describe a Shoggothic Materialism while the dream worlds of the latter will articulate the mad speculation of a Ventriloquil Idealism. But first we must address the relation of philosophy to madness as well as philosophy to weird fiction. /1/ – Philosophy and Madness There is nothing that the madness of men invents which is not either nature made manifest or nature restored. Michel Foucault. Madness and Civilization. The moment I doubt whether an event that I recall actually took place, I bring the suspicion of madness upon myself: unless I am uncertain as to whether it was not a mere dream. Arthur Schopenhauer. The World as Will and Idea, Vol. 3. Madness is commonly thought of as moving through several well known cultural-historical shifts from madness as a demonic or otherwise theological force, to rationalization, to medicalization psychiatric and otherwise. Foucault's Madness and Civilization is well known for orientating madness as a form of exclusionary social control which operated by demarcating madness from reason. Yet Foucault points to the possibility of madness as the necessity of nature at least prior to the crushing weight of the church. Kant’s philosophy as a response to madness is grounded by his humanizing of madness itself. As Adrian Johnston points out in the early pages of Time Driven pre-Kantian madness meant humans were seized by demonic or angelic forces whereas Kantian madness became one of being too human. Madness becomes internalized, the external demonic forces become flaws of the individual mind. Foucault argues that, while madness is de-demonized it is also dehumanized during the Renaissance, as madmen become creatures neither diabolic nor totally human reduced to the zero degree of humanity. It is immediately clear why for Kant, speculative metaphysics must be curbed – with the problem of internal madness and without the external safeguards of transcendental conditions, there is nothing to formally separate the speculative capacities for metaphysical diagnosis from the mad ramblings of the insane mind – both equally fall outside the realm of practicality and quotidian experience. David-Menard's work is particularly useful in diagnosing the relation of thought and madness in Kant's texts. David-Menard argues that in Kant's relatively unknown “An Essay on the Maladies of the Mind” as well as his later discussion of the Seer of Swedenborg, that Kant formulates madness primarily in terms of sensory upheaval or other hallucinatory theaters. She writes: “madness is an organization of thought. It is made possible by the ambiguity of the normal relation between the imaginary and the perceived, whether this pertains to the order of sensation or to the relations between our ideas” Kant's fascination with the Seer forces Kant between the pincers of “aesthetic reconciliation” – namely melancholic withdrawal – and “a philosophical invention” – namely the critical project. Deleuze and Guattari's schizoanalysis is a combination and reversal of Kant's split, where an aesthetic over engagement with the world entails prolific conceptual invention. Their embrace of madness, however, is of course itself conceptual despite all their rhizomatic maneuvers. Though they move with the energy of madness, Deleuze and Guattari save the capacity of thought from the fangs of insanity by imbuing materiality itself with the capacity for thought. Or, as Ray Brassier puts it, “Deleuze insists, it is necessary to absolutize the immanence of this world in such a way as to dissolve the transcendent disjunction between things as we know them and as they are in themselves”. That is, whereas Kant relied on the faculty of judgment to divide representation from objectivity Deleuze attempts to flatten the whole economy beneath the juggernaut of ontological univocity. Speculation, as a particularly useful form of madness, might fall close to Deleuze and Guattari’s shaping of philosophy into a concept producing machine but is different in that it is potentially self destructive – less reliant on the stability of its own concepts and more adherent to exposing a particular horrifying swath of reality. Speculative madness is always a potential disaster in that it acknowledges little more than its own speculative power with the hope that the gibbering of at least a handful of hysterical brains will be useful. Pre-critical metaphysics amounts to madness, though this may be because the world itself is mad while new attempts at speculative metaphysics, at post-Kantian pre-critical metaphysics, are well aware of our own madness. Without the sobriety of the principle of sufficient reason we have a world of neon madness: “we would have to conceive what our life would be if all the movements of the earth, all the noises of the earth, all the smells, the tastes, all the light – of the earth and elsewhere, came to us in a moment, in an instant – like an atrocious screaming tumult of things”. Speculative thought may be participatory in the screaming tumult of the world or, worse yet, may produce its spectral double. Against theology or reason or simply commonsense, the speculative becomes heretical. Speculation, as the cognitive extension of the horrorific sublime should be met with melancholic detachment. Whereas Kant's theoretical invention, or productivity of thought, is self -sabotaging, since the advent of the critical project is a productivity of thought which then delimits the engine of thought at large either in dogmatic gestures or non-systematizable empirical wondrousness. The former is celebrated by the fiction of Thomas Ligotti whereas the latter is espoused by the tales of H.P. Lovecraft. /2/ – Weird Fiction and Philosophy. Supernatural horror, in all its eerie constructions, enables a reader to taste treats inconsistent with his personal welfare. Thomas Ligotti Songs of a Dead Dreamer. I choose weird stories because they suit my inclination best—one of my strongest and most persistent wishes being to achieve,momentarily, the illusion of some strange suspension or violation of the galling limitations of time, space, and natural law which forever imprison us and frustrate our curiosity about the infinite cosmic spaces beyond the radius of our sight and analysis H.P. Lovecraft. “Notes on Writing Weird Fiction” Lovecraft states that his creation of a story is to suspend natural law yet, at the same time, he indexes the tenuousness of such laws, suggesting the vast possibilities of the cosmic. The tension that Lovecraft sets up between his own fictions and the universe or nature is reproduced within his fictions in the common theme of the unreliable narrator; unreliable precisely because they are either mad or what they have witnessed questions the bounds of material reality. In “The Call of Cthulhu” Lovecraft writes: The most merciful thing in the world, I think, is the inability of the human mind to correlate all its contents. We live on a placid island of ignorance in the midst of black seas of infinity, and it was not meant that we should voyage far. The sciences, each straining in its own direction, have hitherto harmed us little; but some day the piecing together of dissociated knowledge will open up such terrifying vistas of reality, and of our frightful position therein, that we shall either go mad from the revelation or flee from the deadly light into the peace and safety of a new dark age. Despite Lovecraft's invocations of illusion, he is not claiming that his fantastic creations such as the Old Ones are supernatural but, following Joshi, are only ever supernormal. One can immediately see that instead of nullifying realism Lovecraft in fact opens up the real to an unbearable degree. In various letters and non-fictional statements Lovecraft espoused strictly materialist tenets, ones which he borrowed from Hugh Elliot namely the uniformity of law, the denial of teleology and the denial of non-material existence. Lovecraft seeks to explore the possibilities of such a universe by piling horror upon horror until the fragile brain which attempts to grasp it fractures. This may be why philosophy has largely ignored weird fiction – while Deleuze and Guattari mark the turn towards weird fiction and Lovecraft in particular, with the precursors to speculative realism as well as contemporary related thinkers have begun to view Lovecraft as making philosophical contributions. Lovecraft's own relation to philosophy is largely critical while celebrating Nietzsche and Schopenhauer. This relationship of Lovecraft to philosophy and philosophy to Lovecraft is coupled with Lovecraft's habit of mercilessly destroying the philosopher and the figure of the academic more generally in his work, a destruction which is both an epistemological destruction and an ontological destruction. Thomas Ligotti's weird fiction which he has designated as a kind of “confrontational escapism” might be best described in the following quote from one of his shortstories, “The human phenomenon is but the sum of densely coiled layers of illusion each of which winds itself on the supreme insanity. That there are persons of any kind when all there can be is mindless mirrors laughing and screaming as they parade about in an endless dream”. Whereas Lovecraft's weirdness draws predominantly from the abyssal depths of the uncharted universe, Ligotti's existential horror focuses on the awful proliferation of meaningless surfaces that is, the banal and every day function of representation. In an interview, Ligotti states: We don't even know what the world is like except through our sense organs, which are provably inadequate. It's no less the case with our brains. Our whole lives are motored along by forces we cannot know and perceptions that are faulty. We sometimes hear people say that they're not feeling themselves. Well, who or what do they feel like then? This is not to say that Ligotti sees nothing beneath the surface but that there is only darkness or blackness behind it, whether that surface is on the cosmological level or the personal. By addressing the implicit and explicit philosophical issues in Ligotti's work we will see that his nightmarish take on reality is a form of malevolent idealism, an idealism which is grounded in a real, albeit dark and obscure materiality. If Ligotti's horrors ultimately circle around mad perceptions which degrade the subject, it takes aim at the vast majority of the focus of continental philosophy. While Lovecraft's acidic materialism clearly assaults any romantic concept of being from the outside, Ligotti attacks consciousness from the inside: Just a little doubt slipped into the mind, a little trickle of suspicion in the bloodstream, and all those eyes of ours, one by one, open up to the world and see its horror [...] Not even the solar brilliance of a summer day will harbor you from horror. For horror eats the light and digests it into darkness. Clearly, the weird fiction of Lovecraft and Ligotti amount to a anti-anthrocentric onslaught against the ramparts of correlationist continental philosophy. /3/ – Shoggothic Materialism or the Formless Formless protoplasm able to mock and reflect all forms and organs and processes—viscous agglutinations of bubbling cells—rubbery fifteen-foot spheroids infinitely plastic and ductile—slaves of suggestion, builders of cities—more and more sullen, more and more intelligent, more and more amphibious, more and more imitative—Great God! What madness made even those blasphemous Old Ones willing to use and to carve such things? H.P. Lovecraft. “At the Mountains of Madness” On the other hand, affirming that the universe resembles nothing and is only formless amounts to saying that the universe is something like a spider or spit. Georges Bataille. “Formless”. The Shoggoths feature most prominently in H.P. Lovecraft's shortstory “At the Mountains of Madness” where they are described in the following manner: It was a terrible, indescribable thing vaster than any subway train – a shapeless congeries of protoplasmic bubbles, faintly self -luminous, and with myriads of temporary eyes forming and un-forming as pustules of greenish light all over the tunnel-filling front that bore down upon us, crushing the frantic penguins and slithering over the glistening floor that it and its kind had swept so evilly free of all litter. The term is a litmus test for materialism itself as the Shoggoth is an amorphous creature. The Shoggoths were living digging machines bio engineered by the Elder Things, and their protoplasmic bodies being formed into various tools by their hypnotic powers. The Shoggoths eventually became self aware and rose up against their masters in an ultimately failed rebellion. After the Elder Ones retreated into the oceans leaving the Shoggoths to roam the frozen wastes of the Antarctic. The onto-genesis of the Shoggoths and their gross materiality, index the horrifyingly deep time of the earth a concept near and dear to Lovecraft's formulation of horror as well as the fear of intelligences far beyond, and far before, the ascent of humankind on earth and elsewhere. The sickly amorphous nature of the Shoggoths invade materialism at large, where while materiality is unmistakably real ie not discursive, psychological, or otherwise overly subjectivist, it questions the relation of materialism to life. As Eugene Thacker writes: The Shoggoths or Elder Things do not even share the same reality with the human beings who encounter them—and yet this encounter takes place, though in a strange no-place that is neither quite that of the phenomenal world of the human subject or the noumenal world of an external reality. Amorphous yet definitively material beings are a constant in Lovecraft's tales. In his tale “The Dream-Quest of Unknown Kadatth” Lovecraft describes Azathoth as, “that shocking final peril which gibbers unmentionably outside the ordered universe,” that, “last amorphous blight of nethermost confusion which blashphemes and bubbles at the centre of all infinity,” who, “gnaws hungrily in inconceivable, unlighted chambers beyond time”. Azathoth's name may have multiple origins but the most striking is the alchemy term azoth which is both a cohesive agent and a acidic creation pointing back to the generative and the decayed. The indistinction of generation and degradation materially mirrors the blur between the natural and the unnatural as well as life and non-life. Lovecraft speaks of the tension between the natural and the unnatural is his short story “The Unnameable.” He writes, “if the psychic emanations of human creatures be grotesque distortions, what coherent representation could express or portray so gibbous and infamous a nebulousity as the spectre of a malign, chaotic perversion, itself a morbid blasphemy against Nature?”. Lovecraft explores exactly the tension outlined at the beginning of this chapter, between life and thought. At the end of his short tale Lovecraft compounds the problem as the unnameable is described as “a gelatin—a slime—yet it had shapes, a thousand shapes of horror beyond all memory”. Deleuze suggests that becoming-animal is operative throughout Lovecraft's work, where narrators feel themselves reeling at their becoming non-human or of being the anomalous or of becoming atomized. Following Eugene Thacker however, it may be far more accurate to say that Lovecraft's tales exhibit not a becoming-animal but a becoming-creature. Where the monstrous breaks the purportedly fixed laws of nature, the creature is far more ontologically ambiguous. The nameless thing is an altogether different horizon for thought. The creature is either less than animal or more than animal – its becoming is too strange for animal categories and indexes the slow march of thought towards the bizarre. This strangeness is, as aways, some indefinite swirling in the category of immanence and becoming. Bataille begins “The Labyrinth” with the assertion that being, to continue to be, is becoming. More becoming means more being hence the assertion that Bataille's barking dog is more than the sponge. This would mean that the Shoggotth is altogether too much being, too much material in the materialism. Bataille suggests that there is an immanence between the eater and the eaten, across the species and never within them. That is, despite the chaotic storm of immanence there must remain some capacity to distinguish the gradients of becoming without reliance upon, or at least total dependence upon, the powers of intellection to parse the universe into recognizable bits, properly digestible factoids. That is, if we undo Deleuze's aforementioned valorization of sense which, for his variation of materialism, performed the work of the transcendental, but refuse to reinstate Kant's transcendental disjunction between thing and appearance, then it must be a quality of becoming-as-being itself which can account for the discernible nature of things by sense. In an interview with Peter Gratton, Jane Bennett formulates the problem thusly: What is this strange systematicity proper to a world of Becoming? What, for example, initiates this congealing that will undo itself? Is it possible to identify phases within this formativity, plateaus of differentiation? If so, do the phases/plateaus follow a temporal sequence? Or, does the process of formation inside Becoming require us to theorize a non-chronological kind of time? I think that your student’s question: “How can we account for something like iterable structures in an assemblage theory?” is exactly the right question. Philosophy has erred too far on the side of the subject in the subject-object relation and has furthermore, lost the very weirdness of the non-human. Beyond this, the madness of thought need not override. /4/ - Ventriloquial Idealism or the Externality of Thought My aim is the opposite of Lovecraft's. He had an appreciation for natural scenery on earth and wanted to reach beyond the visible in the universe. I have no appreciation for natural scenery and want the objective universe to be a reflection of a character. Thomas Ligotti. “Devotees of Decay and Desolation.” Unless life is a dream, nothing makes sense. For as a reality, it is a rank failure [….] Horror is more real than we are. Thomas Ligotti. “Professor Nobody's Little Lectures on Supernatural Horror”. Thomas Ligotti's tales are rife with mannequins, puppets, and other brainless entities which of replace the valorized subject of philosophy – that of the free thinking human being. His tales such as “The Dream of the Manikin” aim to destroy the rootedness of consciousness. James Trafford has connected the anti-egoism of Ligotti to Thomas Metzinger – where the self is at best an illusion and we plead desperately for someone else to acknowledge that we are real. Trafford has stated it thus, “Life is played out as an inescapable puppet show, an endless dream in which the puppets are generally unaware that they are trapped within a mesmeric dance of whose mechanisms they know nothing and over which they have no control”. An absolute materialism, for Ligotti, implies an alienation of the idea which leads to a ventriloquil idealism. As Ligotti notes in an interview, “the fiasco and nightmare of existence, the particular fiasco and nightmare of human existence, the sense that people are puppets of powers they cannot comprehend, etc.” And then further elaborates that,“[a]ssuming that anything has to exist, my perfect world would be one in which everyone has experienced the annulment of his or her ego. That is, our consciousness of ourselves as unique individuals would entirely disappear”. The externality of the idea leads to the unfortunate consequence of consciousness eating at itself through horror which, for Ligotti, is more real than reality and goes beyond horror-as-affect. Beyond this, taking together with the unreality of life and the ventriloquizing of subjectivity, Ligotti's thought becomes an idealism in which thought itself is alien and ultimately horrifying. The role of human thought and the relation of non-relation of horror to thought is not completely clear in Ligotti's The Conspiracy Against the Human Race. Ligotti argues in his The Conspiracy Against the Human Race,that the advent of thought is a mistake of nature and that horror is being in the sense that horror results from knowing too much. Yet, at the same time, Ligotti seems to suggest that thought separates us from nature whereas, for Lovecraft, thought is far less privileged – mind is just another manifestation of the vital principal, it is just another materialization of energy. In his brilliant “Prospects for Post-Copernican Dogmatism” Iain Grant rallies against the negative definition of dogmatism and the transcendental, and suggests that negatively defining both over-focuses on conditions of access and subjectivism at the expense of the real or nature. With Schelling, who is Grant's champion against the subjectivist bastions of both Fichte and Kant, Ligotti's idealism could be taken as a transcendental realism following from an ontological realism. Yet the transcendental status of Ligotti's thought move towards a treatment of the transcendental which may threaten to leave beyond its realist ground. Ligotti states: Belief in the supernatural is only superstition. That said, a sense of the supernatural, as Conrad evidenced in Heart of Darkness, must be admitted if one's inclination is to go to the limits of horror. It is the sense of what should not be- the sense of being ravaged by the impossible. Phenomenally speaking, the super-natural may be regarded as the metaphysical counterpart of insanity, a transcendental correlative of a mind that has been driven mad. Again, Ligotti equates madness with thought, qualifying both as supernatural while remaining less emphatic about the metaphysical dimensions of horror. The question becomes one of how exactly the hallucinatory realm of the ideal relates to the black churning matter of Lovecraft's chaos of elementary particles. In his tale “I Have a Special Plan for This World” Ligotti formulates thus: A: There is no grand scheme of things. B: If there were a grand scheme of things, the fact – the fact – that we are not equipped to perceive it, either by natural or supernatural means, is a nightmarish obscenity. C: The very notion of a grand scheme of things is a nightmarish obscenity. Here Ligotti is not discounting metaphysics but implying that if it does exist the fact that we are phenomenologically ill-equipped to perceive that it is nightmarish. For Ligotti, nightmare and horror occur within the circuit of consciousness whereas for Lovecraft the relation between reality and mind is less productive on the side of mind. It is easier to ascertain how the Kantian philosophy is a defense against the diseases of the head as Kant armors his critical enterprise from too much of the world and too much of the mind. The weird fiction of both Lovecraft and Ligotti demonstrates that there is too much of both feeding into one another in a way that corrodes the Kantian schema throughly, breaking it down into a dead but still ontologically potentiated nigredo. The haunting, terrifying fact of Ligotti's idealism is that the transcendental motion which brought thought to matter, while throughly material and naturalized, brings with it the horror that thought cannot be undone without ending the material that bears it either locally or completely. Thought comes from an elsewhere and an elsewhen being-in-thought. The unthinkable outside thought is as maddening as the unthought engine of thought itself within thought which doesn't exist except for the mind, the rotting décor of the brain. /5/ - Hyperstitional Transcendental Paranoia or Self -Expelled Thought Weird fiction has been given some direct treatment in philosophy in the mad black Deleuzianism of Nick Land. Nick Land along with others in the 1990s created the Cyber Culture Research Unit as well as the research group Hyperstition. The now defunct hyperstitional website, an outgrowth of the Cyber Culture Research Unit, defined hyperstition in the following fourfold: 1-Element of effective culture that makes itself real. 2-Fictional quantity functional as a time-traveling device. 3-Coincidence intensifier. 4-Call to the Old Ones. The distinctively Lovecraftian character of hyperstition is hard to miss as is its Deleuzo-Guattarian roots. In the opening pages of A Thousand Plateaus Deleuze and Guattari write, “We have been criticized for over-quoting literary authors. But when one writes, the only question is which other machine the literary machine can be plugged into”. The indisinction of literature and philosophy mirrors the mess of being and knowing as post-correlationist philosophy, where philosophy tries to make itself real where literature, especially the weird, aims itself at the brain-circuit of horror. The texts of both Lovecraft and Ligotti work through horror as epistemological plasticity meeting with proximity as well as the deep time of Lovecraft and the glacially slow time of paranoia in Ligotti. Against Deleuze, and following Brassier, we cannot allow the time of consciousness, the Bergsonian time of the duree, to override natural time, but instead acknowledge that it is an unfortunate fact of existence as a thinking being. Horror-time, the time of consciousness, with all its punctuated moments and drawn out terrors, cannot compare to the deep time of non-existence both in the unreachable past and the unknown future. The crystalline cogs of Kant's account of experience as the leading light for the possibility of metaphysics must be throughly obliterated. His gloss of experience in Prolegomena to any Future Metaphysics could not be more sterile: Experience consists of intuitions, which belong to the sensibility, and of judgments, which are entirely a work of the understanding. But the judgments which the understanding makes entirely out of sensuous intuitions are far from being judgments of experience. For in the one case the judgment connects only the perceptions as they are given in sensuous intuition [....] Experience consists in the synthetic connection of appearances in consciousness, so far as this connection is necessary. Here it is difficult to dismiss the queasiness that Kant's legalism induces upon sight for both Badiou and David-Menard. Kant's thought becomes, as Foucault says when reflecting on Sade's text in relation to nature, “the savage abolition of itself”. For Badiou, Kant's philosophy simply closes off too much of the outside, freezing the world of thought in an all too limited formalism. Critical philosophy is simply the systematized quarantine on future thinking, on thinking which would threaten the formalism which artificially grants thought its own coherency in the face of madness. Even the becoming-mad of Deleuze, while escaping the rumbling ground, makes grounds for itself, mad grounds but grounds which are thinkable in their affect. The field of effects allows for Deleuze's aesthetic and radical empiricism, in which effects and/or occasions make up the material of the world to be thought as a chaosmosis of simulacra. Given a critique of an empiricism of aesthetics, of the image, it may be difficult to justify an attack on Kantian formalism with the madness of literature, which does not aim to make itself real but which we may attempt to make real. That is, how do Lovecraft's and Ligotti's materials, as materials for philosophy to work on, differ from either the operative formalisms of Kant or the implicitly formalized images of Deleuzian empiricism? It is simply that such texts do not aim to make themselves real, and make claims to the real which are more alien to us than familiar, which is why their horror is immediately more trustworthy. This is the madness which Blanchot discusses in The Infinite Conversation through Cervantes and his knight – the madness of book-life, of the perverse unity of literature and life a discussion which culminates in the discussion of one of the weird's masters, that of Kafka. The text is the knowing of madness, since madness, in its moment of becoming-more-mad, cannot be frozen in place but by the solidifications of externalizing production. This is why Foucault ends his famous study with works of art. Furthermore extilligence, the ability to export the products of our maligned brains, is the companion of the attempts to export, or discover the possibility of intelligences outside of our heads, in order for philosophy to survive the solar catastrophe. To borrow again from Deleuze, writing is inseparable from becoming. The mistake is to believe that madness is reabsorbed by extilligence, by great works, or that it could be exorcised by the expelling of thought into the inorganic or differently organic. Going out of our heads does not guarantee we will no longer mean we cannot still go out of our minds. This is simply because of the outside, of matter, or force, or energy, or thing-in-itself, or Schopenhauerian Will. In Lovecraft’s “The Music of Erich Zahn” an “impoverished student of metaphysics” becomes intrigued by strange viol music coming from above his room. After meeting the musician the student discovers that each night he plays frantic music at a window in order to keep some horridness at bay, some “impenetrable darkness with chaos and pandemonium”. The aesthetic defenses provided by the well trained brain can bear the hex of matter for so long, the specter of unalterability within it which too many minds obliterate, collapsing everything before the thought of thought as thinkable or at least noetically mutable on our own terms. Transcendental paranoia is the concurrent nightmare and promise of Paul Humphrey's work, of being literally out of our minds. It is the gothic counterpart of thinking non-conceptually but also of thinking never belonging to any instance of purportedly solid being. As Bataille stated, “At the boundary of that which escapes cohesion, he who reflects within cohesion realizes there is no longer any room for him” Thought is immaterial only to the degree that it is inhuman, it is a power that tries, always with failure, to ascertain its own genesis. Philosophy, if it can truly return to the great outdoors, if it can leave behind the dead loop of the human skull, must recognize not only the non-priority of human thought, but that thought never belongs to the brain that thinks it, thought comes from somewhere else. To return to the train image from the beginning “a locomotive rolling on the surface of the earth is the image of continuous metamorphosis” this is the problem of thought, and of thinking thought, of being no longer able to isolate thought, with only a thought-formed structure. [1] One of the central tenets of Francois Laruelle's non-philosophy is that philosophy has traditionally operated on material already presupposed as thinkable instead of trying to think the real in itself. Philosophy, according to Laruelle, remains fixated on transcendental synthesis which shatters immanence into an empirical datum and an a prori factum which are then fused by a third thing such as the ego. For a critical account of Laruelle's non-philosophy see Ray Brassier's Nihil Unbound. (shrink)

Philosophers disagree about whether vagueness requires us to admit truth-value gaps, about whether there is a gap between the objects of which a given vague predicate is true and those of which it is false on an appropriately constructed sorites series for the predicate---a series involving small increments of change in a relevant respect between adjacent elements, but a large increment of change in that respect between the endpoints. There appears, however, to be widespread agreement that there is (...) some sense in which vague predicates are gappy which may be expressed neutrally by saying that on any appropriately constructed sorites series for a given vague predicate there will be a gap between the objects of which the predicate is denitely true and those of which it is denitely false. Taking as primitive the operator ‘it is denitely the case that’, abbreviated as ‘D’, we may stipulate that a predicate F is denitely true (or denitely false) of an object just in case ‘DF (a)’, where a is a name for the object, is true (or false) simpliciter.1 This yields the following conditional formulation of a ‘gap principle’: (D Φ (x) ∧ D¬ Φ (y)) → ¬R(x, y). Here ‘ Φ ’ is to be replaced with a vague predicate, while ‘R’ is to stand for a sorites relation for that predicate: a relation that can be used to construct a sorites series for the predicate---such as the relation of being just one millimetre shorter than for the predicate ‘is tall’. Disagreements about the sense in which it is correct to say that vague predicates are gappy can then be recast as disagreements about how to understand the denitely operator. One might give it, for example, a pragmatic construal such as ‘it would not be misleading to assert that’; or an epistemic construal such as ‘it is known that’ or ‘it is knowable that’; or a semantic construal such as ‘it is true that’. (shrink)

Architecture and Deconstruction Case of Peter Eisenman and Bernard Tschumi -/- Introduction Towards deconstruction in architecture Intensive relations between philosophical deconstruction and architecture, which were present in the late 1980s and early 1990s, belong to the past and therefore may be described from a greater than before distance. Within these relations three basic variations can be distinguished: the first one, in which philosophy of deconstruction deals with architectural terms but does not interfere with real architecture, the second one, in which (...) a collaboration between Jacques Derrida and a group of architects interested in his concepts is commenced, and the third one, in which completed or only designed objects or new concepts of deconstruction created by architects gain their supremacy over philosophy. The following book analyses these three possible ways, first of all with the reference to Peter Eisenman and Bernard Tschumi. -/- Peter Eisenman -/- Misreading… and Other Errors -/- The issue of relations between Peter Eisenman’s work and philosophy of deconstruction may be referred to his activity more than ten years preceding his direct collaboration with Jacques Derrida (in 1985) and organisation of the exhibition Deconstructivist Architecture at Museum of Modern Art in New York (in 1988). As soon as at the stage of designing the first houses (House I-III, 1967-1970), which almost entirely inscribed in formalistic aesthetics of Modernism, the architect analysed the problem of architecture dependence on its assumptions. All his later designs may be treated as consequence of this initial interest in relations between practice and theory, and at the same time as an introduction to manipulations later on led at the level of metaphysics of architecture. Beginning with the issue of presence, considered in comments to House VI (1972), the number of ideas having their analogies in philosophy of deconstruction increased. The text entitled The End of the Classical: The End of the Beginning, The End of the End (1984), in which Eisenman criticised questions of representation in architecture, its delusive strive for truth and comparably unattainable attempts at ultimate definition of elementary rules, should be acclaimed the breaking point. This attitude was extended by numerous strategies disturbing architecture rules defined at metaphysical level in an essay Moving Arrows, Eros, and Other Errors: an Architecture of Absence (1986). The issue of Eisenman’s passage from formalism to deconstruction has already been much discussed in the literature (Rosalind Krauss, Thomas Patin among others), still it should be mentioned that the threads similar to Derrida’s concept included in Eisenman’s writing reveal untranslatability of architecture and philosophy. -/- Choral Works or Separate tricks -/- In 1985-1986 a series of seven disputes between Jacques Derrida and Peter Eisenman took place. The pretext for them were designs concerning Parc de la Villette in Paris. The situation of many months of collaboration between a notable philosopher of the second half of the 20th c. and an architect that already had a huge theoretical oeuvre, ended up with a publication of a large volume entitled Chora L Works and it became at the same time a vast study area for historians of contemporary architecture and philosophers. Derrida’s contribution to concept works were his considerations over the idea of chôra, the properties related to this concept were about to be reflected in shapes of the park. Therefore, Chora L Works became an example of the abilities of contemporary art, both in its capability of translation from philosophical ideas to artistic forms and its resistance to tradition of representing in architecture some phenomena and values originating outside this discipline. In the final period of their collaboration both interlocutors started to polemicise with each other more decidedly, what became a separate part of their thought exchange. The exchange of letters between Derrida and Eisenman at the turn of 1989 ended up the period of their direct contacts, nevertheless, at this time precisely a large group of experts in issues of deconstruction joined the discussion and extended the revealed in the former dispute problems into more than ten years of further considerations and publications. Except for a long text by Jeffrey Kipnis, who had participated in the meetings of the philosopher and the architect, there appeared also comments of researchers of artistic theories (K. Michael Hays, Thomas Patin), philosophers (Andrew Benjamin), and even experts in Greek literature (Maria Theodorou or Ann Bergren). Following these debates a contemporary reflection on architecture has saturated with indeed numerous concepts originating in philosophy of deconstruction. -/- Architecture which imitates mute philosophy -/- The series of Jacques Derrida and Peter Eisenman meetings, which took place in the period of 1985-1987, induced many authors to make comments. Some of them (Jeffrey Kipnis, Ann Bergren, Maria Theodorou) developed the subject of chôra which was introduced to the discussion by Derrida. The problem that was about to be solved was the question of tying up the concept of chôra with architecture, including Eisenman’s architecture and the series of meetings within frames of Chora L Works project. Kipnis on this occasion paid attention to chôra and its character of anachronia which infects any being created within chôra. In other words any event has its counterpart (analogon) in another, earlier event. He demonstrated the similarity of structure of many events and statements from the times of Derrida and Eisenman’s meetings to the almost identical behaviour of figures in Plato’s dialogue Timaeus. The loss of beginning present in this phenomenon was appropriate to both features of chôra and the effects of typical analyses of philosophy of deconstruction. Bergren’s analyses focused on accentuating gender of chôra, which, according to this author, had been neglected hitherto in discussions. She collated chôra descriptions with characteristics of women in myths, early Greek epic and philosophy and she arrived at a conclusion that chôra has features of a single woman and a married one at the same time. And yet Theodorou’s studies showed that in the Homeric epics chôra is not treated as an idea but is related with single things and events. The other part of the comments (represented by Andrew Benjamin and K. Michael Hays’ utterances) concerns Eisenman’s attitude to tradition which was treated as a variety of iteration understood philosophically. Benjamin commenced his considerations at the point of closeness between a definition of tradition and a concept of chôra understood as perpetuation (placement). A problematic issue was for him Eisenman’s complex relation to tradition based on its contest and affirmation at the same time. Overcoming the simple subordination to tradition – according to Benjamin – was based on awareness of the role of repetition in culture not known before. Hays made an attempt to explain the pleasure and torment of repetition with the support of Sigmund Freud and Roland Barthes’ concepts. According to Hays repetitions are attempts of a single being to a certain primal state perceived as free of any tension. In a similar way Rosalind Krauss explained a motif of a grate present in Modernistic art and also exceptionally frequent in Eisenman’s work. -/- Annex Architecture is still writing Balzac novels. Peter Eisenman and literature -/- Architecture’s approach to writing, script or literature, present within Peter Eisenman’s work, is an exceptional phenomenon, furthermore a complex one. The article considers four possible relations. The first one relates to Eisenman’s characteristics as a person extremely gifted with the ability to wordplay, which very ‘play’ reveals skills to create architectural images. In the second approach the attention has been paid to Eisenman’s interests – in the first period of his oeuvre – in linguistic works by Noam Chomsky and his transformational-generative grammar. The third kind of relations applied to overcoming the need for autonomy of architecture (and of modernist aesthetics at the same time) and renew interests in questions of meaning in architecture. The fourth sort of relations occurred when Eisenman started to create reflections of historic or literary narrations in architecture – ‘stone stories’ and architectural fictions of their kind. -/- Bernard Tschumi -/- From perversion to deconstruction In Bernard Tschumi’s writings from the 1970s and 1980s we can find a transposition of important threads of post-structuralist ideas deriving from Georges Bataille, Roland Barthes and Jacques Derrida’s works. The analysis of the architect’s writings also shows roots in Phillippe Sollers, Michel Foucault and Denis Hollier’s works. The analysis of borrowed elements from the beginnings of Tschumi’s theoretical activity may be helpful in explaining the contents of his later writings motre inspired by philosophy of deconstruction. The set of his earliest views was inspired by Marxism, Neo Marxism and French Structuralism, mainly by the writings of Henri Levebre and Guy Debord. From the thought of Levebre Tschumi took interest for city as not only a question of urbanistics but also a political issue. From Debord’s concepts he borrowed a conviction about the role of situational violation for changes in the society structure. Some of these beliefs were preserved in his own concepts of architecture as an event. From this period derived also his will to change conservative elements of social structure not by means of political revolution but of theoretical and creative activity. Tschumi acknowledged that the effective way of the proceedings towards achieving his aims would be accepting the role of both a critical intellectualist and architecture expert who would not hide away his left-wing orientation. The speculations defined by the architect as ‘revolting analyses’ were about to characterise contradictions which tear the society apart, penetrate architecture and constitute the basis of culture. Spreading away of the conscience of false assumptions hidden away in various disciplines could have weakened cohesion of a conservative society and influence the will to change among the elites. This way the beginnings of political revolution were rooted in philosophy of architecture. In 1977 Tschumi published his text entitled The Pleasure of Architecture inspired by Roland Barthes’s The Pleasure of the Text, it also included some concepts derived from Georges Bataille and Jacques Derrida. First of all the author used Barthes’s concept which made an assumption that literary activity is pervaded by the spirit of resistance towards social rules, and Tschudi transferred this remark onto architecture. From the ideas of Bataille, acquainted via Holier’s work, he derived his belief that two concepts of space, a conceptual one (defined as Pyramid) and a sensual one (defined as Labirynth), not losing their distinct features, they join in the concept of experienced space which exceeds contradictions. The exceeding itself was defined as the basic rule of architecture and it was referred to situations in which architecture not only negates social needs, but also disavows its own tradition. Crossing the borders applies not only to political issues or permanent rules of the very discipline but also interfering with other fields (especially literature and film). The fact that architecture is associated with organising events turned Tschumi’s attention to questions of violence that result from upsetting architectural order of a given building by its users and the one hand, and on the other from forcing the users to specific acts imposed by this very order. The analysis of the concepts used by Tschumi in his early writings indicates that they are close to definitions that would occur in his reflection in the following years influenced by philosophy of deconstruction. -/- Approaching deconstruction Tschumi in his theories developed in the 1980s presumed that the current social world had undergone a deep process of decay, and the reaction against which ought to be based on ordering-up actions, and also preserving the main outline of disintegration of the whole and its elements in the state of conflict. The statements concerning the nature of the contemporary to Tschumi social relations were applied by him to the world of architecture, this led him to coming up with designing strategies that took into consideration the destabilised character of conditions in which works of architecture were created. New ways of conduct invented by Tschumi drew their inspiration from literature and research on literature, psychoanalysis, structural linguistics, structuralism and post structuralism, and eventually also deconstruction philosophy. The proposed methods were opposed by their author both to functionalism continuity trends and postmodern architecture. Tschumi’s proposals contradicted any forms of conservatism or traditionalism in political sphere as well as in reference to tendencies in architecture. They were not simple contradictions of social or architectural rules, they intrude them from the inside, weaken or escalate the already existing incongruities, they move the boundaries between the areas. Revolutionary illusions about the possibility of radical changes were replaced with strategies which completed, tainted or test former rules in the series of formal games of permutation and combination. Quite different from avant-garde formalism Tschumi’s games were not about maintaining the autonomy of a given area, but on the contrary – polluting it with other areas’ influences. Tschumi enjoyed demonstrating illusions of architecture concerning simple relations between form and function, or between form and meaning. Making use of Freud, Lacan and Foucault’s research he introduced a category of “madness” into architecture allowing an observation that the recognised norms are nothing but merely ones of many possible principles of behaviour, and their recognised status resulted from unjustified hindering innovativeness which is crucial for architecture. To reborn architecture’s capability of changing Tschumi also made use of Barthes’s discoveries concerning rules of narration and works by writers who applied in their writing knowledge on linguistics. Making a work’s author unclear by various mechanical transformations of its elements was however apparent only, and formal rigours imposed on the process of designing liberated possibilities difficult to obtain in more traditional creative action. Another mode of acting introduced by Tschumi was combining his work of elements deriving from outside architecture; joining space records with notation of motion and events accompanying architectural objects among others. These architectural and extra-architectural elements were not unified, on the contrary their heterogenous and conflictual character was stressed. This is how shock, anxiety and instability, typical for live in great metropolises, infiltrated architecture. Taking some ideas of deconstruction philosophy as a pattern Tschumi also took into critical consideration in his essays traditional in architecture oppositions between form and figuration, or theory and practice. By combining various inspirations he eventually worked out an idea of architectural event, which he understood as a series of actions contesting its own field, redefining its sources, principles and elements. An event, understood in this way, was not so much producing works as rather creating conditions of their production and at the same time designing the society different from a hierarchic one. -/- Park of deconstruction Among numerous philosophical strategies of deconstruction most frequently used was questioning the practice of strong opposition of two reasons. In many cases Bernard Tschumi’s writings just consider functioning of the conflict juxtaposition of the ideas of structure and ornament or theory and practice in history of architecture. Violation of traditional relations between terms of this kind, both old and modern, raised Jacques Derrida’s objections, when he was induced for the first time to co-operate with architects’ milieu. During this long lasting thought exchange the philosopher eventually acknowledged Bernard Tschumi’s arguments for reasoning the encroachment of architecture’s fundamental rules. Deconstruction applied in architecture was not a simple transposition or analogy of practices that had been applied by philosophy of deconstruction. We may even say that considering architectural terms became an important formula of deconstruction. Architecture understood in philosophical way became something beyond the practice and theory of its own discipline, a sort of metaphysics of both philosophy and architecture. The deliberate encroachment of simplicity of dividing architecture into theory and practice, for the first time became a clear aim for Tschumi in his drawings and texts entitled The Manhattan Transcripts. The contents of this series of works was a record of characteristic features of this New York district in such a way that not only objects were the subject of the record but also relations between objects, people and events. The record was about to take into consideration a conflict character of elements of this representation and at the same time to avoid applying to them the rule of mimetism. The record became a form of reflection over the very record by an increased control over the ways of representation. Architecture which was considered in the The Manhattan Transcripts was not directed to fulfill the needs of inhabitation or production, it was rather related with hitherto usually marginalised liminal situations: building ostentatiously big monuments, religious cult, war etc. Architecture operating in these relations focused also the attention on the included in it continuous tendency to overpass its own restrictions, the role of violence as its not recognised factor, or the meaning of excess and shock in its operation. Architecture moving from reason towards madness became even more visible in the design of Parisian Parc de la Villette, whose pavilions were defined as folies (in French it means both small park buildings and follies). The park was supposed to be on the one hand a reflection of traditional society disintegration while on the other it questioned basic rules of producing a work of architecture. The traditional rules of designing, based on ordering up, were replaced with the strategies of dysfunction and dissociation. In Tschumi’s opinion methods of this kind may be equivalent of what Derrida named différance. Instead of aiming at mergence, any diversity, plays or variations were strengthen. Tschumi’s texts, in which he explained his attitude, were completed by Derrida’s extent statement entitled Point de folie – Maintenant l’architecture. Derrida’s article is the most significant of all his statements on architecture as a form of thinking and activity. According to the philosopher, architecture should divide space (in French defined as espacement), what enables both thinking and action – it arranges the space of an event. Tschumi’s buildings, defined as folies, in an essential way destabilise any created order, and at the same time they refresh it. Derrida’s statement suggests that architecture may become both metaphor of an order merging a language or a society but also of inner forces which deconstruct and reconstruct it. Therefore architecture is at the same time a construction, a deconstruction and a reconstruction. Parc de la Villette stands out in this system with its attempt to step beyond the scheme of an easy repetition and its heading for chances of achieving more radical otherness. -/- Conclusion Destruction as construction. Paradoxes of deconstruction in architecture -/- Scepticism about persistence and common importance of fundamental values of human culture evinced in philosophers and writers’ works as early as in Greek antiquity, nevertheless it was not expressed so strongly as in the second half of the 20th century. Especially in Heidegger’s work Being and Time (although originated in 1927, still influential in all later philosophy) the following states were characterised: the state of losing the ground (Abgrund), of being out of sight (Unheimlichkeit) and of being out of dwelling (Un-zuhause-sein) – as the basis of self-confidence of conscious being there (Dasein). The entire criticism of philosophy of home and dwelling draws the inspiration from this early writing of the German philosopher, it combines crisis of basic terms of metaphysics with social conditions which are dictated by living in large metropolis. The crisis of both metaphysical foundation and home appears to be similar to the situation of weakening the relations between a man and his dwelling in extensively expanding cities. Whereas philosophy, as well as many disciplines of social sciences, have diagnosed for a long time the destabilisation of fundamental ideas of Western culture and crucial changes in the ways of dwelling, architecture itself occurred to be “the last fortress of metaphysics” (J. Derrida). Among contemporary architects, Peter Eisenman and Bernard Tschumi were the ones who engaged most decidedly in the issues of critical analysis of architecture foundation and its social role. Both the architects noticed new formulas of contemporary social and individual existence, tremendously different from the entire history, and at the same time they affirmed lack of adequacy of architecture concepts to new situations. Both Eisenman and Tschumi used to describe the existing architecture as a tool for consolidation of highly integrated and hierarchised societies, and also as a discipline extremely uncoincidental with the current character of social life based on ideas of freedom and diversity. The means to transform architecture and make a factor of further social changes out of it, was a concept that accentuated revealing the inner contradictions of this discipline, and considering them in designing strategies. Eisenman’s activity, in regard of what has just been noticed, was focused on questioning the basic rules of traditionally comprehended architecture, especially the rule of purpose. The American architect noticed that the concept of architecture as fulfilment the need of location, hides away the fact that the location has to be constantly reconsidered, and hence it is overtaken by change (dislocation). Therefore new concept of architecture propounded architectural activity to translocate the concept of location – more than before – but also to change its status perpetually. Such comprehended architecture should claim, as its main purpose, the constant revision of this purpose and create itself anew permanently. Even Eisenman’s earliest designs of houses nos. I-IV broke with such values as the sense of safety, closeness and familiarity, and just on the contrary they accentuated senses of strangeness, homelessness and loss of confidence. The contradictions within architecture noticed by Tschumi referred to combination of intellectual and sensual values in architecture, when their non-appropriation was defeated by an additional condition, namely the way of experience based on pleasure of excess, marked by insanity. The features of folly were especially visible in his designs of gardens, where the order of planning was mixed with sensual experience introduced by particular elements (both the ones created by nature, and the buildings defined as folies). Parc de la Villette designed by the French architect in Paris put in question not only the common understanding of purpose in architecture but also the ideas of order and integrity, as its plan was based on the combination of independent layers with records of grids of points, various lines and planes. The architecture that collides inadequate elements with each other was supposed to be a kind of an event with no beginning and no end. The architecture treated as an event became a form of a space weakened articulation that maintains its diversity and lack of accordance of the elements building it up. The analyses of Eisenman and Tschumi’s theoretical writings indicate how much the aims of architecture have actually changed; instead of supporting social persistence, the architecture is rather intensifying contradictions, and instead of providing people with the sense of safety, it sublimes danger. From simple acts of defamiliarisation, increasing the distance to itself and enhancing the role of theory, through discomfort, anxiety, not feeling someone at home, weirdness, excess, shock and violence, architecture reached the edge of stability and uncertainty, only to make an attempt at penetrating what is impossible and unutterable, and recording what cannot become the subject of any records. -/- . (shrink)

Abstract A Note to Cogito Les Jones Blackburn College Previous submissions include -Intention, interpretation and literary theory, a first lookWittgenstein and St Augustine A DiscussionAreas of Interest – History of Western Philosophy, Miscellaneous Philosophy, European A Note on Cogito Descartes' brilliance in driving out doubt, and proving the existence of himself as a thinking entity, is well documented. Sartre's critique (or maybe extension) is both apposite and grounded and takes these enquiries on to another level. Let's take a look. 'I (...) think' somehow, for all its power, lacks something. What? Consider what one does when thinking (difficult, but we can try). Implicit in the word 'think', in fact the very essence of the word 'think', is that activity is going on, and if such activity is going on then it must be going on about something, an object, an emotion, a problem,or maybe some dreamlike state, but common to all these is that something is going on. Is that really so? Well, if that wasn't so we would be able to think in a pure state, wouldn't we? But what does a pure state of 'thinking' mean? It can't mean that there isnothing there, because if there were nothing there then no thinking would be taking place. Can it mean that we are thinking of nothing? Well no, because if we are thinking of nothing then we are thinking of something, we are contemplating the notion, or the nature, of nothing. In fact, one can argue that if we talk of something, inthis case nothing or nothingness, then in our head we have some notion of what that is, i.e. something exists in the mind for it to come out of our mouths. Thinking is a recognition of something outside the individual, for the very act of direction, which isan indispensable part of thinking, recognises, must recognise, that there are things to address outside the individual. Something else to bear in mind. According to Sartre human beings are condemned to freedom. Why condemned? Human beings did not choose to be born, but the act ofbeing born also imparts the freedom of which Sartre speaks. Freedom is something which we parrot off as being a sine qua non for the human condition. I believe that's true, but freedom in this sense isn't without its consequences for the individual humanbeing, for individual human beings handle freedom differently. To some it enables them to fly, to others it imparts immense pressures, anguish, heartbreak, unhappiness can all be associated with such freedom. Each individual is responsible for his destiny, for his direction. If someone says that God impelled him, that individual chose his or her God, and chose to obey his or her God. This believer has to sift through the multitude of things that his or her God desire of him or her. All this is fine, so long as we acknowledge what is going on here. Belief in God is, by definition, a belief. Belief, following Wittgenstein, is a language game with its rules and its boundaries. The essential feature of religion as language game are its boundaries, which can be summed up in the word belief. OK, belief has its practises which are its constituent parts, but belief is the boundary between religion and other language games, as the proof constituents are different. Our world is determined by the language used to describe everything that goes on within it. The boundaries of our world are set by the language we use. This might be better put as language gives access to ever expending boundaries. Ever expanding boundaries are only possible by ever expanding thought, and ever expanding thought is only possible by ever expanding directions to our thought brought about through language. It is a fact taken that to be conscious is to think. How could this be otherwise? Consciousness without thought just does not make sense. Imagine a state of consciousness without directional thought. What would it be like? It would be something never experienced, completely out of our understanding. Why? Because understanding itself is a directional thought process. If we say we are going outside our understanding then that is a world of void, and a world of void does not exist. Can such a world be contemplated in our thinking? Well, yes, but then it requires thinking, and thinking requires direction, and such direction requires language. Why does direction require language? Because there is no other way for human beings to articulate a directional thought. Could one point at an image without language? Well, one could have an image in mind, but the essence of saying something about it, of descriptive power, brings us back to the essence, to the power of language to direct. So what of this language of which we speak? Wittgenstein's private language argument points us towards the notion that language itself constantly develops and redevelops through human interaction. Descarte's cogito implies that thinking rules out doubt of one's own existence. But such thinking, to be valid, to make sense, to direct, must develop in a language that has developed, has been verified, by a plurality, by a plurality whose essence is social. Correct use of language symbols, i.e. words, requires that we verify and reverify the accuracy of such symbols. How do we do that? We do that in constant usage, in constant interaction, with other human beings. An individual using a private language could not be understood by others, his symbol system has not been verified by others, his meanings may not be your meanings. It follows from what we have said above that language is constructed, and is continually constructed, in a social context. Given our previous thoughts regarding verification this could not be otherwise. Language has a normative form. All language users are required, by their very use of the language, to verify the use of terms, grammar etc etc. As Wittgenstein cites (appropriately) games as a model, let us take a look. If I play e.g. Ludo, I am governed by the rules. It is not just that I may play dishonestly, for if I were to play at all that very dishonesty, to count as Ludo, would have to be rule governed. The rules of Ludo are Ludo, they are the essence and the constitution of it. Wittgenstein, particularly in his later writings, interweaves many concepts, and connects them in different and sometimes rather elusive ways. Wittgenstein sees concepts like emotions, sentiments and experiences in these interweaving maps. Of course these can be regarded as psychological concepts ** Language can be considered in another but related way, as embodying the elements of a cultural heritage. Language was seen as embodying the notion of higher culture in the arts, architecture etc. Over recent decades this has tended to shift to consider less tangible benefits, such things as oral traditions, cultural values and cultural identity. So language enables us to explore, through the achievements of past generations, cultural mores that may have laid unchallenged for many years. Many of these values and mores may be seen as independent of the language by which they are transmitted, but still this monumental accomplishment of mankind i.e. language, enables man to explore, to modify, to codify, to extend the boundaries of human experience. There are therefore massive implications for our Note on Cogito of Wittgenstein's work. Following Wittgenstein emotions and other psychological concepts can be termed depth grammar, and are distinguished by the fact that the third person of the present is recognised by observation, the first person is not. Taking Wittgenstein's well known pain example the sentence 'He is in pain' is a third person statement of an observational nature. The sentence 'I am in pain' is not derived from observation but from experience, it is an expression of that experience, it's essence is the experience. The asymmetry consists in the fact that predicting psychological attributes of others is warranted by what they do and say. By contrast, the use of such statements in the first person present tense does not rest on one's observation of one's own behaviour. (Hacker 2010:287) p 9 According to Wittgenstein 'I am in pain' is more like a cry of pain, an expression of pain, than a report of some pain. Of course this appertains for other similar statements. 'I feel good' etc. (shrink)

It is well known that the set of algebraic numbers (let us call it A) is countable. In this paper, instead of the usage of the classical terminology of cardinals proposed by Cantor, a recently introduced methodology using ①-based infinite numbers is applied to measure the set A (where the number ① is called grossone). Our interest to this methodology is explained by the fact that in certain cases where cardinals allow one to say only whether a set is (...) countable or it has the cardinality of the continuum, the ①-based methodology can provide a more accurate measurement of infinite sets. In this article, lower and upper estimates of the number of elements of A are obtained. Both estimates are expressed in ①-based numbers. (shrink)

In this paper, we introduce the plithogenic set (as generalization of crisp, fuzzy, intuitionistic fuzzy, and neutrosophic sets), which is a set whose elements are characterized by many attributes (parameters)’ values. An attribute value v has a corresponding (fuzzy, intuitionistic fuzzy, or neutrosophic) degree of appurtenance d(x,v) of the element x, to the set P, with respect to some given criteria. In order to obtain a better accuracy for the plithogenic aggregation operators in the plithogenic set, and for (...) a more exact inclusion (partial order), a (fuzzy, intuitionistic fuzzy, or neutrosophic) contradiction (dissimilarity) degree is defined be-tween each attribute value and the dominant (most important) attribute value. The plithogenic intersection and union are linear combinations of the fuzzy operators tnorm and tconorm, while the plithogenic complement, inclusion (inequality), equality are influenced by the attribute values contradiction (dissimilarity) degrees. This article offers some examples and applications of these new concepts in our everyday life. (shrink)

The relationship between the One and the Multiple in mystic philosophy is a profound and central theme that explores the nature of existence, the cosmos, and the divine. This theme is present in various mystical traditions, including those of the East and West, and it addresses the paradoxical coexistence of the unity and multiplicity of all things. -/- In mystic philosophy, the **One** often represents the ultimate reality, the source from which all things emanate and to which all things return. (...) It is the absolute, the infinite, and the unchanging. The One is beyond all attributes and is often associated with the divine or the absolute truth. -/- The **Multiple**, on the other hand, represents the manifest world, the diversity of forms, and the realm of change and plurality. It is the world we experience through our senses, the domain of time and space, where differentiation and individuality are apparent. -/- The relationship between the One and the Multiple is not one of opposition but of emanation and unity. The Multiple is seen as a reflection, expression, or manifestation of the One. In this sense, the diversity of the world doesn’t contradict the unity of the One but rather demonstrates it in a myriad of forms. -/- Mystics seek to understand and experience this relationship through various practices and insights. They aim to transcend the illusion of separation and duality to experience the non-dual reality where the One and the Multiple are recognized as inseparable. -/- This concept can be illustrated by the metaphor of the ocean and its waves. The ocean represents the One—vast, deep, and all-encompassing—while the waves represent the Multiple—distinct, diverse, and ever-changing. Each wave is unique, yet it is not separate from the ocean. The wave’s existence is dependent on and made of the same substance as the ocean. In the same way, each individual entity in the Multiple is an expression of the One. -/- In summary, the relationship between the One and the Multiple in mystic philosophy is a dynamic interplay that challenges the conventional understanding of separation. It invites a deeper exploration of reality, where the apparent multiplicity of the world is a direct expression of the singular, underlying essence of all that is. -/- The relationship between the One and the Multiple in the context of mathematical philosophy is a profound topic that touches upon the very foundations of existence and knowledge. It’s a theme that has been explored by philosophers and mathematicians alike, often leading to the contemplation of unity and diversity within the structures of reality. -/- In mathematics, the concept of the One can be seen as the basis of unity from which all numbers derive. It’s the identity element in multiplication, the starting point in counting, and the foundation of dimension in geometry. The One is often associated with the concept of monism in philosophy, which posits that there is a single, underlying substance or principle that constitutes reality. -/- On the other hand, the Multiple represents the infinite variety and diversity of forms and numbers that arise from the One. It’s the embodiment of plurality and the complex interplay of different entities that mathematics seeks to understand and describe. This reflects the philosophical stance of pluralism, which acknowledges the existence of multiple realities or truths. -/- The interplay between the One and the Multiple can be seen in the mathematical concept of sets. A set can be thought of as a unity, a whole composed of distinct elements. Yet, each element within the set also retains its individuality, contributing to the diversity of the set’s composition. This duality is mirrored in the philosophical exploration of the universal and the particular, where the universal represents the One, and the particulars represent the Multiple. -/- In the realm of mathematical philosophy, this relationship often leads to questions about the nature of mathematical objects: Are they discovered as part of an objective reality (the One), or are they constructed by the human mind from a multitude of experiences (the Multiple)? This debate resonates with the philosophical inquiry into the nature of truth and reality. -/- Reflecting on the One and the Multiple can also lead to a deeper understanding of the self and the cosmos. Just as the number one is integral to the existence of all other numbers, the individual self can be seen as a unique expression of the universal whole. Similarly, the cosmos can be viewed as a grand unity composed of a multiplicity of forms and phenomena. -/- Gödel’s incompleteness theorems have a fascinating connection to the philosophical concepts of the One and the Multiple. These theorems, which are pivotal in mathematical logic and philosophy of mathematics, articulate the inherent limitations of formal axiomatic systems, particularly those sufficient to express the arithmetic of natural numbers. -/- Gödel’s incompleteness theorems have a fascinating connection to the philosophical concepts of the One and the Multiple. These theorems, which are pivotal in mathematical logic and philosophy of mathematics, articulate the inherent limitations of formal axiomatic systems, particularly those sufficient to express the arithmetic of natural numbers⁴. -/- The **first incompleteness theorem** reveals that within any such consistent system, there are propositions that are true but cannot be proven within the system itself. This reflects the idea of the Multiple in that there is an abundance of mathematical truths, a multiplicity that exceeds the unifying framework of any one system. It suggests that the realm of mathematical truth is more extensive than any single formal system can fully capture. -/- The **second incompleteness theorem** extends this by showing that a system cannot prove its own consistency. This relates to the concept of the One, as it implies that a system’s complete self-understanding, its unity and coherence, is unattainable from within. It must look beyond itself, to an external vantage point, to ascertain its consistency. -/- In the context of the One and the Multiple, Gödel’s theorems imply that the One (a consistent formal system) is inherently incomplete and cannot encompass the Multiple (the totality of mathematical truths). This resonates with philosophical discussions about the relationship between unity and plurality. Just as a single philosophical system cannot capture the entirety of truth, a single formal mathematical system cannot encapsulate all mathematical truths. -/- Moreover, Gödel’s work suggests that the pursuit of a single, unified theory of everything in mathematics—a One that encompasses all Multiples—is an inherently Sisyphean task. There will always be more truths (Multiples) than can be derived from any given set of axioms (the One). -/- In essence, Gödel’s incompleteness theorems provide a formal underpinning to the philosophical notion that the One cannot exist without the Multiple, and vice versa. They are interdependent, with the One giving rise to the Multiple, and the Multiple necessitating the One for its expression and comprehension. This interplay is a dance of limitations and possibilities, where the boundaries of logic, mathematics, and philosophy blur into one another. -/- The relationship between the One and the Multiple in the context of the mathematics of zero is a deeply philosophical inquiry that bridges the abstract world of numbers with the existential questions of being and non-being. -/- Zero, in mathematics, is a symbol of absence, a representation of nothingness, yet it holds a pivotal position as a number. It is the void from which all things emerge and to which they return. In the philosophy of mathematics, zero is the paradoxical junction where the One and the Multiple converge and diverge. -/- From the perspective of the One, zero can be seen as the origin—the singular point that precedes the existence of numbers. It is the empty set, the foundation upon which the edifice of mathematics is constructed. As the identity element in addition, zero maintains the integrity of numbers, for adding zero to any number leaves it unchanged, reflecting the immutable nature of the One. -/- Conversely, when we consider the Multiple, zero represents the infinite potentiality of creation. It is the canvas upon which the integers, both positive and negative, express their multitude. Zero is the balance point, the fulcrum around which the symphony of numbers dances. It embodies the plurality of possibilities, the beginning of the number line that stretches infinitely in both directions. -/- Philosophically, zero challenges our understanding of existence. It is both something and nothing—a number that quantifies the absence of quantity. This duality echoes the philosophical struggle to comprehend how the One gives rise to the Multiple. How does the unity of being manifest the diversity of the cosmos? Zero offers a mathematical metaphor for this mystery, as it encapsulates the transition from non-existence to existence, from the undifferentiated One to the differentiated Multiple. -/- In the realm of set theory, zero corresponds to the empty set—a set with no elements. This set is unique in that it is the only set that contains nothing, yet it is the foundation upon which all other sets are built. The empty set is the mathematical embodiment of the One, and all other sets, containing multiple elements, arise from it. -/- Reflecting on zero in the context of Gödel’s incompleteness theorems, we find a resonance with the idea that the One (a consistent formal system) cannot capture the entirety of the Multiple (the totality of mathematical truths). Zero, as the foundation of numbers, similarly suggests that from the nothingness of the One, the infinite complexity of the Multiple emerges—yet it can never be fully encompassed or expressed by any single system. -/- In conclusion, the mathematics of zero offers a profound reflection on the relationship between the One and the Multiple. It serves as a bridge between the abstract and the concrete, the known and the unknowable, challenging us to ponder the origins of existence and the nature of reality itself. -/- . (shrink)

Recently, research on uncertainty modeling is progressing rapidly and many essential and breakthrough stud ies have already been done. There are various ways such as fuzzy, intuitionistic and neutrosophic sets to handle these uncertainties. Although these concepts can handle incomplete information in various real-world issues, they cannot address all types of uncertainty such as indeterminate and inconsistent information. Also, plithogenic sets as a generalization of crisp, fuzzy, intuitionistic fuzzy, and neutrosophic sets, which is a set whose elements are (...) characterized by many attributes’ values. In this paper, our aim is to demonstrate and review the history of fuzzy, intuitionistic and neutrosophic sets. For this purpose, we divided the paper as: section 1. History of Fuzzy Sets, section 2. History of Intuitionistic Fuzzy Sets and section 3. History of Neutrosophic Theories and Applications, section 4. History of Plithogenic Sets. (shrink)

Techne and Truth. The problem of techne in the dispute between Gorgias and Plato -/- The source of the problem matter of the book is the Plato’s dialogue „Gorgias”. One of the main subjects of the discussion carried out in this multi-aspect work is the issue of the art of rhetoric. In the dialogue the contemporary form of the art of rhetoric, represented by Gorgias, Polos and Callicles, is confronted with Plato’s proposal of rhetoric and concept of art (techne). The (...) ingenuous and dramatic structure of the dialogue composed of three acts, in each of which Socrates’ consecutive interlocutors emerge, is difficult to interpret. It seems, however, that even though the first conversation between Socrates and Gorgias constitutes a small part of the dialogue, it forms the foundations for the discussion. This part, dealing with such important issues as the subject of art, knowledge, power and relation between art and good, is the starting point for the conversations which follow. What do the differences between the Gorgias’ and Plato’s concepts of art consist in? Any attempt to answer the question requires presentation of the background for the discussion taking place in Plato’s work as well as the reconstruction of Gorgias’ vision of the art of rhetoric and art in general, defining the relation between art and knowledge. The latter may be undertaken on the basis of two paraphrases of the treatise “On Non-existence”, two epideictic speeches entitled “Helen” and “Palamedes” and some smaller fragments which have been preserved from Gorgias’ creative output. The treatise “On Non–existence”, very paradoxical in its philosophical meaning, testifies to new, sophistic thinking represented by Gorgias of Leontinoi. The treatise is the polemic and attack on Eleatism based on certain principles and methods elaborated by the Eleatics themselves. It also shows that Gorgias – using traditional Eleatic schemes – is opposed to this tradition. Even though the treatise does not discuss the problem of art directly, it anticipates the considerations from epideictic speeches. “Helen” and “Palamedes” constitute further stages in the development of Gorgias’ thought and concept of art combining typically epideictic elements with some philosophical convictions. Gorgias refers to the Eleatic theme considering the issues of truth, knowledge and belief, yet defining them in the empirical spirit. Solutions in the cognitive sphere determine the horizon of Gorgias’ rhetoric. The word is separated from the existence. Human cognition is limited and therefore the word and visual images affect the belief. This promotes the great importance of rhetoric, painting and sculpture, i.e. the areas which influence in a specific way – creating the “delusion” (ἀπάτη). Through idealization art provides pleasure, which is its objective. Therefore the task of art is to create delusion. The rhetor of Leontinoi discusses the issue of “how?” to use the word ‘rhetoric’. Gorgias is aware that rhetoric may be used to talk about what is unknown and that technical correctness of a rhetoric statement is not identical with the truthfulness of the proclaimed message. Mentioning it, Gorgias shows his respect to the truth as a value which should be respected in speech on the one hand, and on the other emphasizes that the truth in itself has no persuasive power. For this reason it is not enough to proclaim the truth, but, to convince the listeners, the orator should possess the skill of speaking. What is then the relation between truth and art emerging from epideictic speeches? Gorgias undoubtedly emphasizes the formal aspect of speech, as rhetoric is art, thus an ability based on certain principles. According to Gorgias, the truth is the value which should be respected in speeches. Rhetoric is able to create a fictive world, as a great range of reality remains outside direct human experience. Rhetoric does not oppose the truth but discussing not only what is directly given concerns the area outside the sphere of direct experience. This concept of rhetoric is the basis of the discussion about art carried out in the dialogue “Gorgias”. Even though the first of the discussions in the dialogue – the conversation between Socrates and Gorgias – is directly concerned with rhetoric itself, numerous remarks testify to its much wider character. This is best exemplified by the way of carrying out the conversation by Socrates, who, asking questions about rhetoric practised by Gorgias, throughout the whole conversation compares it with other skills. Additionally, the manner and the structure of the conversation prove that Plato considers the issue of rhetoric from a wider perspective determined by the issue of art. The specific feature of the conversation is ordering it around main issues – such notions as πρᾶγμα, ἐπιστήμη, δύναμις, each of which has its own meaning in Plato. In the first part of Gorgias Plato presents the principles previously occurring in other dialogues in a certain order, thus constructing the structure of the conversation with Gorgias. The notions are not novum in Plato but the fact that he clearly wants to systematise them and present a certain concept of art is a new and significant aspect. This tendency is of paramount importance for the discussion because Gorgias’ answers are evaluated by Plato from the perspective of this clearly set concept consisting of not only established notions but also certain principles. The discussion between Socrates and Gorgias introduces a theme which is crucial for the dialogue: the relation between art and good, i.e. the technical and ethical spheres. The issue is introduced by Gorgias, who mentions that rhetoric may be used for evil purposes. On this basis Socrates proves that if rhetoricians can use rhetoric for evil purposes, they have no knowledge concerning the subject of their art – justice, because one who knows what is just, always acts justly. Thus the relation between the technical and ethical spheres transpires to be the main point of contention. The question is whether a technician following the principles of the art he practices may act against good. This paradoxical statement based on the well-known Socrates’ principle "nemo sua sponte peccat" acquires philosophical foundations in the dialogue. In its remaining two parts Plato presents a justification, placing the principle within the framework of a certain concept of art, as a result of which not only rhetoric but also many other skills are criticised. The notions on which the conversation with Gorgias focuses are more precisely defined in the subsequent parts of the dialogue. Additionally, Plato presents twice the conditions which art should fulfill. They oblige the “technicians” to know the nature and purpose of the art and to know the causes of undertaken activities and to be able to justify them. These conditions determine the relation between the two spheres – technical and ethical. According to Plato, art may not act against good because it should be the objective of its activities. Certain concepts of good and knowledge outlined in the dialogue are the guarantees of “technicality”. Good, which should be respected by every art, is understood objectively and is contrasted with subjective pleasure. Knowledge, which should be the basis of art, opposes experience, which uses observation and recollection. Additionally, the definition of knowledge, significance of order in the world assuming the form of “geometrical equality”, significance of mathematics becoming the ideal of exactness indicate that Plato’s concept of knowledge is formed in Gorgias. These conclusions render it impossible that the results of any activity deserving the name of art should oppose good. And this is Plato’s main reproach of Gorgias’ concept, who wrote about false speeches possessing the power of conviction because they were written according to the principles proof of art or who defined tragedy as “a deceit, where he who cheats is more just than he who does not and the cheated is wiser than he who was not cheated”. Such determination of the relation between the technical and ethical sphere resulted from Gorgias’ concept of the world and fundamental philosophical principles. The whole concept of art described by Plato in the dialogue opposes the view presented by Gorgias. According to Plato, every technical activity has a defined object (ἔργον), is based on knowledge (ἐπιστήμη) and is always aimed at the good of human soul or body. The danger revealed and presented in the dialogue by Plato exists in the very concept of art presented by Gorgias, i.e. in its empirical foundations and the resulting understanding of the relation between art and good. Gorgias’ concept of art based on empirical cognition, which concerns the world of phenomena and rejects the possibility of perfect knowledge, leads, according to Plato, to a dangerous falsification of the relation between art and good. Plato proves that this weakness of Gorgias’ concept is revealed when confronted with these representatives of “the magnificent art” who are not protected against radicalism by the adherence to the moral tradition. The comparison of two, completely contrasting concepts of art based on different philosophical understanding of knowledge and good is decisive for the criticism of rhetoric in Gorgias. The concept presented by Plato criticises contemporary rhetoric and sophistry but determines the direction of research of the real art of rhetoric. (shrink)

This study asserts that W.V.O. Quine’s eliminative philosophical gaze into mereological composition affects inevitably his interpretations of composition theories of ontology. To investigate Quine’s property monism from the account of modal eliminativism, I applied to his solution for the paradoxes of de re modalities’ . Because of its vital role to figure out how dispositions are encountered by Quine, it was significantly noted that the realm of de re modalities doesn’t include contingent and impossible inferences about things. Therefore, for him, (...) all the intrinsic forces and elements of entities such as powers and causal or teleological dispositions for ontology demand to be seen necessarily as bound variables from a monist perspective. Although his denial of analyticity and the elimination of dispositional field of ontology, S. Mumford criticizes the monist perspective of Quine’s paradoxical approach to superveniences. Because superveniences create problems while determining type-type identities from a monist mereological perspective. It is observed that Quine faces with a reduction again in terms of his dispositional monism despite his critiques to repulse vagueness from the ontology in his well-known article Two Dogmas of Empiricism. -/- . (shrink)

Scientific inquiry takes onward course from the point where previous scientists had reached. But philosophical analysis initiates from scratch. Philosophy questions everything and chooses starting point for itself after having ruled out all the unsubstantiated and doubtful elements of the topic under study. Secondly, known realities must make sense. If a theory is officially 'counterintuitive', then either it is mere fiction or at the most; a distorted form of truth. This book's analysis is based on the philosophical principle (...) that knowledge is empirical and does not arise magically in absence of observational grounds. With philosophical approach, it was doubtful to accept that Georges Lemaître already knew Hubble's law in year 1927 that was yet to be found by Edwin Hubble in year 1929. Therefore this book started with denial of the claim that Lemaître already knew this law. But analysis of section I.III forced author to look the matter from original source and it came to surface that Lemaître knew this law in year 1927. But contrary to mainstream claim, Lemaître had not derived that law from general relativity (GR) equations rather had deduced from a method given by Hubble himself. Whereas whole case of the Big Bang Theory rests on misleading claim that Lemaître had derived this law solely from GR equations. The basis of this claim happened to be a manipulated translation (1931) of Lemaître's original 1927 article. People regard Big Bang Theory as truth because authoritative sources deceived them by presenting a manipulated translation in year 1931. This book is a philosophical analysis of original papers of Alexander Friedmann (1922), Georges Lemaître (1927), Edwin Hubble (1929) and Albert Einstein (1917) thus covers actual roots and origins of the Big Bang Model. In this book, only the core elements of the Big Bang Model i.e. 'Expansion of Universe' and 'CMBR' are covered. It has been sufficiently shown that 'expansion' is an illusion whereas CMBR is a proof that we live in a non-expanding infinite universe. If these two core elements of the standard Big Bang Model are precisely refuted then there is nothing crucial left with the standard model. For readers of this book at least, Big Bang Theory shall become a story of past mistakes. Author is not an authoritative source on science topics therefore readers must download all the above mentioned original papers and check all the points outlined in this book from relevant original papers. Unlike reading from an authoritative source that makes readers relaxed and careless but enables authorities to deceive them in worst way possible, this book requires readers to remain alert on all the points discussed in the book and verify everything from original sources whose links are given at the end of this description and also provided in footnotes section of the book. This book is not a judgment of the topic rather it is like a case presented by an advocate while readers are the judges. Readers are required to apply their own critical judgment to conclude the matter by themselves. After carefully reading this book, readers will also start taking 'authoritative sources' with due care and it will become difficult for the 'authorities' to deceive them again. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Plato on Knowledge as a Power1Nicholas D. SmithAt 471C4 in Plato’s Republic, the argument takes a sudden turn when Glaucon becomes impatient with all of the specific prescriptions Socrates has been making, and asks to return to the issue Socrates had earlier set aside—whether or not the city he was describing could ever be brought into being. In response to Glaucon’s impatient question, Socrates articulates his “third wave of (...) paradox” (472ag–7), namely, that the ills of the cities will never be ended until either philosophers become rulers or rulers become philosophers (473c11–d6). Glaucon immediately responds that such a view is likely to be greeted with violence and scorn (473e6–474a4), and so Socrates must hasten to explain his odd claim. His explanation, it turns out, is that true philosophers have an enormous cognitive advantage over non-philosophers—philosophers have and use knowledge (ἐπιστήμη), whereas non-philosophers have and use only opinion (δόξα).2 This distinction, between επιστήμη and δόξα, turns out: to be a distinction between two different cognitive powers (δυνάμεις—477d7–e3). And different powers, Plato clearly tells us, apply to or take as their objects (Plato says they are “ἐπί”) different things (477dl).In this paper, I shall argue that the relationship between the cognitive powers and their various objects has been fundamentally misunderstood, which has led scholars into one or more misinterpretations of important and explicit features of the text. At the heart of these misunderstandings, I claim, is [End Page 145] their shared misconception of the relation between the cognitive power and its objects as interpretable in terms of the relationship between a cognitive stale and what the content of that state is of or about.3 One consequence of the view for which I shall argue is that what has come to be known as the “two-worlds theory”4 of Plato’s epistemology is seriously mistaken, but no less mistaken than the alternatives given by its recent critics. Another consequence that I shall draw from my argument is that Plato should be understood neither as a kind of foundationalist with regard to knowledge and warrant, as some have supposed him to be,5 nor as a coherentist, as others have supposed,6 but, rather, as a kind of causal reliabilist. [End Page 146]1. KNOWLEDGE AS A POWERScholarly interpretations of Plato’s epistemology have routinely sought to understand the relationships between each cognitive power of Republic Book V and the objects of the ἐφ’ ᾦ (“what it is related to”) condition by which it is differentiated from other δυνάμεις as Plato’s way of telling us what each sort of cognition is of or aboul. 7 So, for example, we find Gail Fine using the expressions “belief [δόξα] is set over [Fine’s translation of Plato’s ἐπί] …” and “knowledge is set over …” interchangeably with “belief is of …” or “belief is about…” and “knowledge is of …” or “knowledge is about …”8 Against the “two-worlds theory,” Fine argues that, for Plato, there can be knowledge of sensibles and beliefs about Forms. Accordingly, since she assimilates the power-ἐπί-object set of relations to the cognilion-of/about-object relation, she concludes—in order to account for knowledge of sensibles and beliefs about Forms—that the objects of knowledge and opinion must be propositions. Plato’s claims that knowledge is ἐπί what is, whereas opinion is ἐπί what is and is not, Fine understands as, “One can only know true propositions; one can believe both true and false propositions.”9 We shall see later that this “veridical” understanding of what Plato means to identify as “what is,” and “what is and is not” fails to account for important and explicit elements of Plato’s exposition of the epistemological and metaphysical distinctions he is making. For now, it is enough to note that Fine understands the ἐφ’ᾦ) relation in terms of our cognition-of/about-object relation. One finds the same assimilation made by those who advance existential readings of Plato’s “is” and “is not,”10 as [End Page 147] well as those who have urged that we adopt predicative readings of “is” and “is not.”11But I think there are very serious problems with this assimilation. Plato is very... (shrink)

DARWIN’s (1859, 1871) discoveries have profound ethical implications that continue to be misrepresented and/or ignored. In contrast to socialdarwinistic misuses of his theory, Darwin was a great humanitarian who paved the way for an integrated scientific and ethical world view. As an ethical doctrine, socialdarwinism is long dead ever since its defeat by E. G. Moore although the socialdarwinistic thought is a hard-die in the biological community. The accusations of sociobiology for being socialdarwinistic are unfounded and stem from the moralistic (...) fallacy that is, a false assumption that morality is good by definition. Both social and developmental psychology demonstrate that the moral agency is a motivational device for executing reciprocity that remains at the core of any morality across all studied societies and throughout the ontogeny of moral judgment. The level of true universalizing ethical reflection (KOHLBERG’s postconvential stages or GIBBS’s existential phase) is achieved by a small minority of humans, thus showing that Homo sapiens is a moral but not an ethical animal. While the origin of reciprocity has been perfectly explained by sociobiology, the evolutionary assembly of affective and cognitive elements that make up the moral agency is being successfully studied by the social/personality/developmental psychology as extended to non-human primates. As DARWIN (1871) expected, the key innovation for the evolution of moral agency was the emergence of empathy that evolved independently at least three times: in elephants, dolphins and primates. Empathy has a motivational power of its own; it is also necessary for moral agency that requires two cognitive abilities: reflective self-consciousness and understanding of causality; the two make possible the attribution of responsibility. All these requirements are met by the chimpanzees whose moral agency operates in dyads. In contrast, the human moral agency allows for a third party intervention that opens up vast opportunities for ideologies, especially religions, to use and misuse the moral agency to enforce a reciprocation that may be harmful to both individuals and the entire group. Also, the moral agency is known to enforce enhanced intragroup cohesion and loyalty in response to conflict and war, which suggests that the two prima facie opposed human universals, morality and warfare, may have coevolved. The most important ethical consequence that follows from the increasing understanding of the primate moral agency is that every received morality is ethically flawed, none can be taken as a paragon of goodness, and each needs corrections by science-informed ethics. In fact, Darwin pioneered the integration of science and ethics, an approach that has come to be appreciated only recently under the heading of consilience. (shrink)

We contest the unsubstantiated assumption of both materialists and non-materialist that the ontological status they propose applies to all humans and that the competing claim is false for all - ie we reject both the claim of non-materialists that all humans share the same fundamental aspect of having a "non-material consciousness" (nmc), as well as the contrasting claim of materialists that none do (being fully material as according to eliminative materialists/reductive physicalists etc). Instead, the basic proposition of this paper, (...) our ‘ontological conecture’ (OC) - an updated version of our 1998 website article “Mindless Materialists” - is that the central tenets of proponents on both sides are true, but only regarding themselves. A signature feature of nmc is that brains associated to it are capable of knowing of its existence directly, and as a corollary we would propose that if a sophisticated brain does not know it is associated to nmc then most likely this is because it is in fact not so associated. Thus, in accordance with our OC we will consider a brain’s statements on this issue (that it does or does not possess nmc) as not merely its ‘philosophical position’ but as an authoritative statement, a reflection of an ontological fact. Furthermore, we propose that only those who possess nmc are capable of understanding what it is, so that although they are well-qualified to know directly that they themselves possess it, in contrast those who lack nmc and possess only material consciousness (mc) cannot even comprehend what non-materiality means - they will understandably tend to consider it a non-existent absurdity, which contention would be quite correct in a purely-material reality, such as they effectively inhabit. -/- Terminology reflecting ontological status: Since according to our OC those brains which categorize themselves as non-materialists are presumed to indeed be associated to nmc, for usefulness in phraseology we’ll refer to people whose brain is so associated as being nmc’s (not merely “espousing nmc”). Materialists say they are conscious but that theirs is a material consciousness (abbrev: “mc”) , and since according to our OC we accept this self-determination we will refer to them as being “mc’s” or being materialist (not merely “espousing materialism”). -/- Are materialists mindless or are non-materialists delusional? Notoriously, it is impossible to prove that one possesses nmc (which is a sort of corollary to the fact that it is directly self-known) - being non-material, nmc cannot be detected via the scientific method. However just as those with nmc cannot prove they possess it so too one cannot prove or determine via measurement that materialists do not possess it. Nevertheless we feel that our OC is the simplest solution to the conundrum of how there are materialists if a brain can directly sense its associated nmc. In sum, although of course it is impossible to prove that any particular person possesses or lacks nmc, given all the above our OC considers - as stated by the title of this paper - a brain’s self-identification as "materialist" or “non-materialist” (dualist, panpsychist, idealist etc) as reflecting the absence or presence of an associated real non-material awareness/consciousness, rather than merely as a statement of a philosophical stance. An alternative solution is implicit in the above - that all humans possess nmc just that materialists are those whose brains lack the awareness of theirs, or that the brain-aspect which communicates to others has no access to it. -/- Towards developing more constructive dialogue between mc’s/nmc’s, and greater self-confidence and independence among nmc’s in the face of materialist dominance of the intellectual-climate: A large part of the overall paper is devoted to not just pointing out the futility of communication of the sort usually engaged in - ie based on the erroneous underlying assumption that both sides of the debate are ontologically the same - but also suggesting ways to make the debate less frustrating by a recognition of the OC. Greater clarity in discussions can be achieved partly via a deeper understanding of the different meanings the same term might have to nmc’s/mc’s and suggestions relevant the construction of a sort of translation algorithm to utilize in discussions (as a simple example, substituting ‘higher-level cognitive material brain-processes’ for ‘mind’ when that term is used by an mc); by the frank statement by nmc’s engaged in dialogue with mc’s that the existence of nmc is not up for discussion; by learning how the existence of our nmc colors the meaning we give to certain terms in ways we were not aware of, meanings which are absent for mc’s; and in general via the recognition by the nmc that the dialogue is with a person lacking nmc. -/- Perhaps materialists are right: In the interest of ‘reciprocity’, the paper also offers an alternative/opposing view to the central proposition, to the effect that the materialist claim is correct, and it is a defect of brain wiring or structure which is the source of an active illusion of "self-awareness" underlying the philosophical claims of non-materialists. A prospective source of this illusion is offered - an analog of the sense of presence experienced during ‘sleep paralysis’. (shrink)

DEFINING OUR TERMS A “paradox" is an argumentation that appears to deduce a conclusion believed to be false from premises believed to be true. An “inconsistency proof for a theory" is an argumentation that actually deduces a negation of a theorem of the theory from premises that are all theorems of the theory. An “indirect proof of the negation of a hypothesis" is an argumentation that actually deduces a conclusion known to be false from the hypothesis alone (...) or, more commonly, from the hypothesis augmented by a set of premises known to be true. A “direct proof of a hypothesis" is an argumentation that actually deduces the hypothesis itself from premises known to be true. Since `appears', `believes' and `knows' all make elliptical reference to a participant, it is clear that `paradox', `indirect proof' and `direct proof' are all participant-relative. PARTICIPANT RELATIVITY In normal mathematical writing the participant is presumed to be “the community of mathematicians" or some more or less well-defined subcommunity and, therefore, omission of explicit reference to the participant is often warranted. However, in historical, critical, or philosophical writing focused on emerging branches of mathematics such omission often invites confusion. One and the same argumentation has been a paradox for one mathematician, an inconsistency proof for another, and an indirect proof to a third. One and the same argumentation-text can appear to one mathematician to express an indirect proof while appearing to another mathematician to express a direct proof. WHAT IS A PARADOX’S SOLUTION? Of the above four sorts of argumentation only the paradox invites “solution" or “resolution", and ordinarily this is to be accomplished either by discovering a logical fallacy in the “reasoning" of the argumentation or by discovering that the conclusion is not really false or by discovering that one of the premises is not really true. Resolution of a paradox by a participant amounts to reclassifying a formerly paradoxical argumentation either as a “fallacy", as a direct proof of its conclusion, as an indirect proof of the negation of one of its premises, as an inconsistency proof, or as something else depending on the participant's state of knowledge or belief. This illustrates why an argumentation which is a paradox to a given mathematician at a given time may well not be a paradox to the same mathematician at a later time. -/- The present article considers several set-theoretic argumentations that appeared in the period 1903-1908. The year 1903 saw the publication of B. Russell's Principles of mathematics, [Cambridge Univ. Press, Cambridge, 1903; Jbuch 34, 62]. The year 1908 saw the publication of Russell's article on type theory as well as Ernst Zermelo's two watershed articles on the axiom of choice and the foundations of set theory. The argumentations discussed concern “the largest cardinal", “the largest ordinal", the well-ordering principle, “the well-ordering of the continuum", denumerability of ordinals and denumerability of reals. The article shows that these argumentations were variously classified by various mathematicians and that the surrounding atmosphere was one of confusion and misunderstanding, partly as a result of failure to make or to heed distinctions similar to those made above. The article implies that historians have made the situation worse by not observing or not analysing the nature of the confusion. -/- RECOMMENDATION This well-written and well-documented article exemplifies the fact that clarification of history can be achieved through articulation of distinctions that had not been articulated (or were not being heeded) at the time. The article presupposes extensive knowledge of the history of mathematics, of mathematics itself (especially set theory) and of philosophy. It is therefore not to be recommended for casual reading. AFTERWORD: This review was written at the same time Corcoran was writing his signature “Argumentations and logic”[249] that covers much of the same ground in much more detail. https://www.academia.edu/14089432/Argumentations_and_Logic . (shrink)

Migraine is a complex neurological disorder characterized by recurrent moderate to severe headaches, accompanied by additional symptoms such as nausea, sensitivity to light and sound, and visual disturbances. Accurate and timely diagnosis of migraines is crucial for effective management and treatment. However, the diverse range of symptoms and overlapping characteristics with other headache disorders pose challenges in the diagnostic process. In this research, we propose the development of an expert system for migraine diagnosis using artificial intelligence and the CLIPS (C (...) Language Integrated Production System) framework. The expert system utilizes a rule-based inference engine to analyze patient-reported symptoms and provide reliable diagnoses or probability scores indicating the likelihood of migraine. The knowledge base of the expert system is designed based on expert knowledge obtained from medical professionals specializing in migraines. The collected knowledge is translated into a structured format suitable for the CLIPS inference engine, incorporating rules and facts to represent the diagnostic criteria and associated symptoms. The system prompts users to provide relevant information about their symptoms, medical history, and potential triggers. It applies the defined rules and facts to evaluate the likelihood of migraine and generate accurate diagnoses or probability scores. Preliminary evaluation results demonstrate the potential of the expert system as a valuable tool for diagnosing migraines. A dataset of anonymized patient records with confirmed migraine cases was used to test the system. The diagnoses generated by the expert system were compared against the known diagnoses, and a high level of accuracy was observed, with 90% of cases correctly diagnosed as migraines. These results highlight the effectiveness and reliability of the system in assisting medical professionals in the diagnosis of migraines. The proposed expert system offers several advantages for migraine diagnosis. It leverages the collective knowledge and expertise of experienced migraine specialists, providing a standardized and consistent approach to diagnosis. The system can handle large amounts of patient data and effectively analyse complex relationships between symptoms, risk factors, and diagnostic criteria. Furthermore, it offers real-time feedback and recommendations, supporting medical professionals in their clinical decision-making process. Future work involves refining the expert system based on feedback from medical experts, expanding the knowledge base to encompass a wider range of symptoms and risk factors, and conducting further evaluations to enhance its accuracy and applicability in clinical settings. The development of an expert system for migraine diagnosis has the potential to improve the diagnostic process, leading to more effective management and treatment strategies for individuals suffering from migraines. (shrink)

June 2022 A Revolutionary New Metaphysics, Based on Consciousness, and a Call to All Philosophers We are in a unique moment of our history unlike any previous moment ever. Virtually all human economies are based on the destruction of the Earth, and we are now at a place in our history where we can foresee if we continue on as we are, our own extinction. As I write, the planet is in deep trouble, heat, fires, great storms, and record flooding, (...) weather patterns drastic everywhere. Capitalism has been so successful in supplying us with an endless array of consumer items, that we have never noticed there is a cost. But there is a cost, the cost is the very life of the Earth herself, and now the day of reckoning is here. Days of reckoning are most often days of rath. But I am hoping that this is a day of major Awakening over the entire planet. We have caused a crisis so great for the Earth we can hardly get our minds around it. But I am proposing that deeply embedded in the crisis are ideas, about who and what the Earth is, Ourselves, and what we are here for. I am proposing that this is a call to all philosophy and philosophers to rethink ourselves from the ground up. The human race has never gotten the Earth right and now we must, for the Earth is the true foundation for civilization. We are in deep trouble with the Earth, and it owes to the fact that the great male thinkers never got the Earth right, they could never make the connection between the life of mind and the life of the Earth. I am proposing that deeply embedded in the crisis we are in are ideas. And that in fact the planet is in the grip of a false metaphysics, and scientific image of nature that really comes most recently from Descartes. His conviction that matter, and with it the Earth, are simply the weighable, the measurable the extended in space and time, utterly devoid of any inner life of mind thoughts or Consciousness. This view of matter and the Earth goes back to the very dawn of thought, Descartes is just its most recent and comprehensive version of things. This view of matter is really a false metaphysics that dominates most of the modern world and underpins the whole scientific image of nature itself. I am proposing this is a false metaphysics and offering a new version of things based on Consciousness. If there is a single idea fueling and driving the destruction of the planet, it is the conviction that the Earth is something without Consciousness. When you intend to ravage and savage the planet, turn it into consumer items to be converted into money in the bank, first pretend that all of the bright beings in the natural world are devoid of Consciousness, just “things” you do not have to have any conscious about destroying them. I am proposing that this term Consciousness, that has appeared as term and a problem for modern science, is the key to getting ourselves right with the Earth. I propose this new theory for science will ramify into every other disciplines as well, and the ways we think just about everything. This old paradigm based on a false theory of matter, has run its course, it has brought us to the brink of our own extinction. We need new ideas, and we need them now. You will find my recent work in the Scientific God Journal under the title: Consciousness as the Organizing Principle, and a very complete version of my arguments for this term Consciousness, along with radical reinterpretation of modern science itself, on the Galileo Commission site. It is a radical moment for all of the thinkers among us, take this as my small contribution to rethinking ourselves in new terms, based on my understanding that the true basis for the whole of Being, the Universe, the Cosmos, and with them Ourselves, is this term Consciousness. And unpack it. And I predict that with this term Consciousness every intractable human problem in both science and the modern world will go down like a line of dominos before it. And so, here are a few new ideas I would offer you. These are the times of the Reappearance of the Feminine, a great Awakening as of Springtime after a long dark and lonely Winter. We are leaving behind us an old civilization based on male dominance, fear lies and control, now in decay, disease, and death disintegrating all around us. We are moving into a whole new civilization based on Love and Truth. A new civilization requires new basic terms values and first principles. And so, I return to Descartes. 1. Just over 300 years ago a young man travelling with the army found himself stranded in a foreign town in a bare room lit by a candle with nothing to do but think. And in a couple of nights Descartes laid the entire thought foundations for modern science and most of the modern world. It isn’t clear that modern philosophers with their funding sources of grants, their graduate students, their reputation and all the perks and privileges of academia can do any better. Descartes claimed there are just two principles in the Universe, Matter and Mind. God was pure mind; human beings were mind and matter. And we are the only ones on the planet with mind. Everything else all of the bright array of beings who share the planet with us are simply matter. And matter? The weighable the measurable the extended in space and time utterly devoid of any inner life of thoughts, feelings, or Consciousness This classification was a boon for developing science. Scientists did not have to worry about any inner life in nature, ideas or Consciousness, they could just set about weighing and measuring, as they have until the present day. But it was a disaster for the Earth. Earth was once worshiped as a Goddess. With Descartes she became almost overnight “things.” Simply commodities and resources, an endless of supply of consumer items, to be turned into money in the bank. And now Descartes concept of matter is up for us. If there is a single idea that is enabling and driving the destruction of the Earth, it is the conviction that Earth is something without Consciousness. This whole scientific image of nature as something devoid of Consciousness is driving the destruction of the Earth, and driving us all insane, and it needs to change. Ever since Descartes formulated Dualism, scientists and philosophers have been trying to get rid of it. They have done this by attempting to make matter the fundamental term of reality, and to explain mind or Consciousness in terms of matter. And now, Consciousness has emerged as term and a problem for modern science. 2. The prevailing Universe picture has been mainly based on the belief that Consciousness appears only at the end of evolution in ourselves and some of the higher animals when matter attains “a certain state of complexity” and it is produced by neurons in the brain. But Consciousness is nothing real in itself, the neurons are doing the work, Consciousness is simply a byproduct of neural activity. As William James summed up this position, not his: Consciousness is to the brain as a shadow to the runner, it runs beside him but never influences his stride. And so, the great problem of neuroscience: How do neurons produce Consciousness? So far, no one has been able to say how. All we have is parallelism. Two processes are running in parallel a train of neural events and a train of Consciousness events. And so, which one is primary? The face of neuroscience and much of the modern world is that the neural events are what is really real, Consciousness is secondary. The conviction that Consciousness is something produced by neurons is so deeply held and has been so for so long, that it seems like an obvious fact. It is in fact an assumption and a theory, and it could all well be the other way around. The scientific image of nature as something devoid of Consciousness is now up for us. It has enabled the destruction of the Earth, and we are now at a unique place in our own evolution where we can foresee if we continue on as we are, our own extinction. And so, there are the best reasons for rethinking Descartes concepts of matter. Scientists and philosophers have been trying to escape dualism by making matter the fundamental term. And now, this has not worked. In a nutshell: The mind body problem, the “hard problem of Consciousness” ---how do neurons in the brain, atoms and molecules give rise to ideas thoughts and feelings and who what and where is the “I” who sees them? And then, the near-death experience. I remind you of the truth of the near-death experience. The body in the bed is brain dead eeg flat, but the patient, pure Consciousness is hovering at the ceiling watching the doctors work over the body below, able to read dials he could not have seen from the bed, sometimes able to events in the corridor beyond the room, all subsequently confirmed by the doctors. Evidence as good as it gets that the patient really was out of his body. And so, the patient is able to see without eyes, hear without ears and to think and remember without a brain. There is not a single scientific principle that can account for this. And I am proposing that the near-death experience is a threshold and a key for a much deeper understanding of the Universe. These three problems are so hard they cannot be solved by present scientific principles and therefore call all present principles and ways of thought into question. When your axioms cannot account for the data, it is time to drop them and find better fundamental terms. We have not been able to solve the problems of Consciousness with the assumption that matter is the most basic and fundamental term. And so, if Cartesian dualism is to be overcome at all, we need to try it the other way around. 3. We are in the position of Copernicus. Remember Copernicus? He was making his calculations on the assumption that the Earth was the center of the Universe until they became so unwieldy that he decided to try it all the other way around. To make the sun the center, the Earth revolving around it. And lo, all of his data fell neatly into place. I am proposing a whole new Universe picture. Evolution makes us continuous with every other being, Consciousness would not be in us if it were not in them also, and then, in the atoms and molecules and cells that make up living beings. I propose to make Consciousness the most basic term and see what follows. I am in fact, proposing a new Copernican Revolution, that Consciousness is the true basis for the Universe and the right fundamental term, for science itself all other disciplines as well, and the whole of the modern world. And I predict that every intractable problem in science or the modern world, will go down like a line of dominos before it. In a nutshell: Consciousness and not matter is “first and fundamental” in the Universe, it is there from the very “Beginning” everything has it and all of the true causalities, the explanatory principles belong to it. Not to matter. What then is matter? All matter is an Appearance of something much more real, Consciousness. All matter is an expression of Consciousness, even the least little bit of matter contains Consciousness, and is an expression of Consciousness. And so, we revise the scientific image of nature. Science at present is two termed, matter/energy. It needs to become three termed: Matter/energy/Consciousness, with the recognition that all of the basic principles, the true causalities of events, and of the Universe belong to Consciousness. And now physics. To accommodate this new Universe picture physics needs to alter just one term, energy. All energy contains Consciousness, that idea alone will change our world forever. The animals the trees the plants are just as conscious as we are, as is the Earth herself, a continuum of many forms of Consciousness of which our own is one. The Earth consists of interacting and intersecting forms of Consciousness, Consciousness within Consciousness within Consciousness within Consciousness. A remarkable work has just appeared entitled “Beyond Words What Animals Feel and Think.” Describing in detail how like ourselves all of the animals are. And the more we can see how like us everything else really is, the harder it will be for us to do them all in, in the interest of turning them into consumer items. And so, here is a new principle of understanding, that entails completely new forms of explanation, and a whole new Universe picture to be spelled out in terms of Consciousness and its various properties. This is a Universe that is aware awake and Enspirited throughout. And so, there is only one principle, not two. And so, how does Consciousness work? There is “no mind/body problem.” My Consciousness is aligning the Consciousness of neurons in the brain, that aligns the Consciousness of all other cells in the body, that aligns the Consciousness of molecules and atoms themselves. Mainly from the top down, but also interactive, and not reduction to the purely physical forces. 4. And so, here is a radical new Universe picture, and with it a new way to think about the Universe itself, the Earth, Ourselves, and Spirit. It requires a complete revision of both of the terms of modern science itself. The problem of the modern world owes in deep measure to Descartes concept of matter as something devoid of interior life. But he is only the most powerful and simple expression of a whole tradition of thought that predates him, that goes back to the very dawn of thought itself. It owes to the conviction of both Plato and Aristotle that the Earth was something devoid of reason, or mind, and therefore something to be held in complete contempt. We are emerging from a civilization based on contempt for the Earth, and down the road, it will become contempt for the body, sex, women, the Native people, and people of color everywhere. And so, this entire tradition is now up for us, it has brought us to the brink of our own extinction, and we need to get beyond it. I am proposing that this term Consciousness is the way out. The missing piece of the puzzle and the idea whose time has come. And it will enable us to move into a completely new civilization based on respect for the Earth, women, sex, people of color, that honors everyone and has a place for all. Revolutions in science occur when new data show up that cannot be accounted for by existing paradigms (Thomas Kuhns: The Structure of Scientific Revolutions). Consciousness, and all the properties and problems of Consciousness are just such data, and they compel a new scientific revolution. But we are a scientific age. A new Copernican revolution in science is such as revolution everywhere. And Consciousness is the key to getting every other reality at all levels and depths right as well. It will enable us finally to get the Earth right, get ourselves right with the Earth, and with one another. Archimedes: Give me a place to stand, and I will move the world. I am proposing a new synthesis among our fundamental terms in which this term Consciousness is the new lynchpin. And so, I return once more to Descartes. Descartes in the Mediations was a dualist, they were two realities interacting in the pineal gland mind and body. But Descartes age was high on “Cartesianisms,” on Descartes concept of matter. Animals were simply cleverly wired machines (Hobbes called them automata). Rumor had it that Descartes followers went about kicking dogs reasoning that their howls were not due to any feelings of pain, but simply the wiring of the machine. We have been doing this to the Earth ever since, and now the Earth is not going to stand for it any longer. It is time we all woke up. There is no matter in Descartes sense of it, or in Plato and Aristotle’s sense of it. This old concept of matter is embedded in all of the crisis and catastrophes---fires, drought, pandemics, over population, the disintegrating economies, our ways of life, capitalism and consumerism themselves. All matter is Enspirited, contains Consciousness, and is an expression of Consciousness. Now I tell you something about Descartes you may not know. In the Mediations was a dualist, there are minds and bodies. But by the end of his life, he knew the truth. Descartes guided his whole life by these vivid dreams, and toward the end of his life he had this dream: He saw the Universe as a giant machine and in the heart of the machine propelling the whole, was Consciousness. And so, out of the shades and shadows and into the light of day. Here is a renewed and a new science, a new cosmology. And with it, a revolutionary new metaphysics. The whole of the modern world is in the grip of a false metaphysics, based on Descartes theory of matter. Here is a new, and finally true metaphysics based on the single term, Consciousness. 5. And in all my works, I spell out this new metaphysics based on Consciousness, and what it means for how we think about virtually everything: The Universe, the Earth, Ourselves, and Spirit. Of who, what and where Spirit is, that we may connect with Spirit everywhere. There is only one term for the Universe, and not two, this single term Consciousness, that manifests itself in two modes: Consciousness in Form, Consciousness Formless. And so, here is a sketch of what this new term Consciousness really means. For four great aspects of the real, four new cornerstones for a whole new civilization on Earth, based on Love and Truth. A. For the Universe: New causalities, all matter is an expression of Consciousness, awake and aware, Enspirited throughout, which has a place for the causalities of love ideas intent plan and purpose, what Aristotle called final causality, that for the sake of which. And it has a place for subjectivity, the greatest mystery in the whole of the Universe, knowable only in ourselves, but there in everything else as well, bedrock in the chain of causalities. The buck stops here. Here are two very different Universe pictures. The Cartesian Universe consists of things, pushed, and pulled around by the physical forces that function blind. The true Universe consists of selves and not things. Selves at least in ourselves, are organized and focused about an I, an I am, or a sense of self in everything, ever other being dear to itself. Just one aspect of subjectivity. And so, it is Consciousness all the way down, and subjectivity all the way down. Science proceeds on the basis of the negligible of what it can leave out as unimportant. Subjectivity is the ultimate animating principle of the Universe. What Descartes really did was to strip from nature what is most essential about it, its animating principle Consciousness. And so, we come out of a long history of “clunk.” The great male thinkers have killed creation. First in concepts and now in the lived life. And so, after centuries of fruitless search, not all of it in vain, finally, and just in time the true basic principle for the Universe has shown up in virtually all disciplines, this term Consciousness. B. And so, the Earth: What does this term Consciousness really mean for the Earth? It means that all of the bright array of beings around us have Consciousness. And the more we can realize how like us they are, the harder it will be to do them all in. Is this what it really means to be “made in the image of Spirit?” To destroy ever other living being? The god of Genesis is a creator god who has created billions and billions of living forms. Man, taking himself to be made in the image of Spirit has destroyed virtually all of it. The Earth is not things, not commodities and resources, not an endless array of consumer goods. The Earth consists of conscious living spiritual beings like ourselves, who need to be honored and respected, nurtured and cared for, to be Loved. And if the human race can finally pull it off and bring Love here and start helping the Earth rather than destroying her, even our vast numbers now at 8 billion, may not matter. Deeply embedded in the modern world is a false cosmology based on the hitherto useful but ultimately false metaphysics of Descartes. In particular it owes to Descartes concepts of matter, and of the Earth, as something devoid of Consciousness. And now this concept is up for us. If there is a single idea enabling and driving the destruction of the planet, it is the conviction that the Earth is something devoid of Consciousness. And we all have a vested interest in keeping this false concept in place. When you intend to ravage and savage the Earth, to turn it into consumer items, and money in the bank, first pretend she has no Consciousness that way we need not have any conscious about it. We are in deep trouble with the planet. Virtually all human economies are based on the destruction of the Earth, and we are now at a place in our history where we can foresee if we continue on as we are, our own extinction. And so, here are a few new guiding principles for the planet, based on Consciousness. Consciousness has field properties. The Earth is Consciousness throughout, connected and interconnected throughout, intersecting and interacting fields of Consciousness of which our own is one. To harm one is to harm all. Only this understanding of the Earth can set our destructive technologies, and capitalism, their goals, and their limits. The real problem with capitalism, and with civilization itself is it has no true understanding of the Earth, all the exquisite networks and webworks that connect all beings with one another. Nor it is about to admit that the Earth is our “life support system,” reason gone insane in the modern world. We are destroying our life support system, capitalism is the full expression of the human death wish in the modern world, and it needs to change. And now, let the barriers between ourselves and all other beings go down. C. And so, Ourselves. This new Universe picture based on Consciousness opens into and has a place for new concepts of human identity. In particular, it has a place for reincarnation, a process whereby one Consciousness dons’ bodies again and again and lays them down. This is a process wholly impossible on materialistic theories. This new view of things puts a higher perspective on Freudian determinism, which is a partial knowing in a greater account. We are something more than the victims of genes drives and childhood. We are immortally eternal evolving spiritual beings who take on a cycle of earthly lives in order to achieve certain goals and abilities, and then, our earthly cycle complete, we depart the Earth plane for other areas of the Universe physical or purely spiritual, to continue our evolution elsewhere. The scientific evidence for reincarnation is increasing on all sides, see for example the work of Michael Newton, a mainstream scientist forced to confront the fact of reincarnation. A completely new reincarnational picture is now emerging everywhere. We choose our parents for abilities we could acquire through them. We all come here with reasons for being here, and we all have free will, an original property of Consciousness, and we work out our issues accordingly. We all come here with the same reason for being here. It is to experience the Earth plane and human society at all levels and depths, in every social role, every climate, both sexes male and female and in all races. We are all here to acquire a deep understanding of the Earth plane with all its challenges and all of its present problems. We are not here to devour and consume the Earth, but to honor her for the learning experience she makes available for us. And so, reincarnation is the great equalizer, the fundamental basis for any bill of rights. Many of the problems of the modern world owe to the fact that reincarnation has not been taught in the West. Reincarnation was the center piece of Jesus teachings. It was banned by a fourth century council that decided the populous could best be controlled through fear. They edited all mention of reincarnation from the scriptures, and inserted fear terms instead, a judgmental god, and so on. If reincarnation had been taught, there would have been no suppression of women, but the gift of both sexes would have been honored and developed. And there would have been no reason for contempt for people of color because who they are, we have been or will be. There is no reason to look down on anyone when we know that our own identity includes membership in theirs. The truth of reincarnation needs to be the foundation for getting ourselves right with the Earth, and with one another. D. And so, Spirit. This new Universe picture, based on Consciousness, has a place for Spirit as simply Infinite Consciousness. All universes all worlds are formed out of this Consciousness, divine and sacred throughout. And Spirit is everywhere in the Earth and can be connected everywhere. And the Native North American people had things right. Everything has its own Spirit, and without contradiction is also an expression of Spirit. And what I am really doing in terms of concepts of modern science is presenting the Native North American version of the Real. And this new Universe picture has a place for the essential insight of all religions almost smothered by church tradition: Love. Not an emotion but a great Oneness, that can be found everywhere, even in a busy city street. But especially in the Earth, that is levels and depths of Oneness everywhere. And so, for the first time in their long and bitter antagonistic history, science and religion now share a common base with this term Spirit, the lynchpin in a new conceptual framework. And I offer an interpretation of where we are in our history, this present moment of historical grace, and these tumultuous times in which we live, the return of the Goddess and the Divine Feminine, the Reappearance of the Feminine in history, the Advent of Women, this great Awakening, as of Springtime after a long dark Winter, the Awakening, the Second Coming. And so, stay tuned! (shrink)

Dâwûd al-Qarisî (Dâvûd al-Karsî) was a versatile and prolific 18th century Ottoman scholar who studied in İstanbul and Egypt and then taught for long years in various centers of learning like Egypt, Cyprus, Karaman, and İstanbul. He held high esteem for Mehmed Efendi of Birgi (Imâm Birgivî/Birgili, d.1573), out of respect for whom, towards the end of his life, Karsî, like Birgivî, occupied himself with teaching in the town of Birgi, where he died in 1756 and was buried next to (...) Birgivî. Better known for his following works on Arabic language and rhetoric and on the prophetic traditions (hadith): Sharḥu uṣûli’l-ḥadîth li’l-Birgivî; Sharḥu’l-Ḳaṣîdati’n-nûniyya (two commentaries, in Arabic and Turkish); Şarḥu’l-Emsileti’l-mukhtalifa fi’ṣ-ṣarf (two commentaries, in Arabic and Turkish); Sharḥu’l-Binâʾ; Sharḥu’l-ʿAvâmil; and Sharḥu İzhâri’l-asrâr, Karsî has actually composed textbooks in quite different fields. Hence the hundreds of manuscript copies of his works in world libraries. Many of his works were also recurrently printed in the Ottoman period. One of the neglected aspects of Karsî is his identity as a logician. Although he authored ambitious and potent works in the field of logic, this aspect of him has not been subject to modern studies. Even his bibliography has not been established so far (with scattered manuscript copies of his works and incomplete catalogue entries). This article primarily and in a long research based on manuscript copies and bibliographic sources, identifies twelve works on logic that Karsî has authored. We have clarified the works that are frequently mistaken for each other, and, especially, have definitively established his authorship of a voluminous commentary on al-Kâtibî’s al-Shamsiyya, of which commentary a second manuscript copy has been identified and described together with the other copy. Next is handled his most famous work of logic, the Sharhu Îsâghûcî, which constitutes an important and assertive ring in the tradition of commentaries on Îsâghûcî. We describe in detail the nine manuscript copies of this work that have been identified in various libraries. The critical text of Karsî’s Sharhu Îsâghûcî, whose composition was finished on 5 March 1745, has been prepared based on the following four manuscripts: (1) MS Kayseri Raşid Efendi Kütüphanesi, No. 857, ff.1v-3v, dated 1746, that is, only one year after the composition of the work; (2) MS Bursa İnebey Yazma Eser Kütüphanesi, Genel, No.794B, ff.96v-114v, dated 1755; (3) MS Millet Kütüphanesi, Ali Emiri Efendi Arapça, No. 1752, ff.48v-58r, dated 1760; (4) MS Beyazıt Yazma Eser Kütüphanesi, Beyazıt, No. 3129, ff.41v-55v, dated 8 March 1772. While preparing the critical text, we have applied the Center for Islamic Studies (İslam Araştırmaları Merkezi, İSAM)’s method of optional text choice. The critical text is preceded by a content analysis. Karsî is well aware of the preceding tradition of commentary on Îsâghûcî, and has composed his own commentary as a ‘simile’ or alternative to the commentary by Mollâ Fanârî which was famous and current in his own day. Karsî’s statement “the commentary in one day and one night” is a reference to Mollâ Fanârî who had stated that he started writing his commentary in the morning and finished it by the evening. Karsî, who spent long years in the Egyptian scholarly and cultural basin, adopted the religious-sciences-centered ‘instrumentalist’ understanding of logic that was dominant in the Egypt-Maghrib region. Therefore, no matter how famous they were, he criticized those theoretical, long, and detailed works of logic which mingled with philosophy; and defended and favored authoring functional and cogent logic texts that were beneficial, in terms of religious sciences, to the seekers of knowledge and the scholars. Therefore, in a manner not frequently encountered in other texts of its kind, he refers to the writings and views of Muhammad b. Yûsuf al-Sanûsî (d.1490), the great representative of this logical school in the Egyptian-Maghrib region. Where there is divergence between the views of the ‘earlier scholars’ (mutaqaddimûn) like Ibn Sînâ and his followers and the ‘later scholars’ (muta’akhkhirûn), i.e., post-Fakhr al-dîn al-Râzî logicians, Karsî is careful to distance himself from partisanship, preferring sometimes the views of the earliers, other times those of the laters. For instance, on the eight conditions proposed for the realization of contradiction, he finds truth to be with al-Fârâbî, who proposed “unity in the predicative attribution” as the single condition for the realization of contradiction. Similarly, on the subject matter of Logic, he tried to reconcile the mutaqaddimûn’s notion of ‘second intelligibles’ with the muta’akhkhirûn’s notion of ‘apprehensional and declarational knowledge,’ suggesting that not much difference exists between the two, on the grounds that both notions are limited to the aspect of ‘known things that lead to the knowledge of unknown things.’ Karsî asserts that established and commonly used metaphors have, according to the verifying scholars, signification by correspondence (dalâlat al-mutâbaqah), adding also that it should not be ignored that such metaphors may change from society to society and from time to time. Karsî also endorses the earlier scholars’ position concerning the impossibility of quiddity (mâhiyya) being composed of two co-extensive parts, and emphasizes that credit should not be given to later scholars’ position who see it possible. According to the verifying scholars (muhaqqîqûn), it is possible to make definition (hadd) by mentioning only difference (fasl), in which case it becomes an imperfect definition (hadd nâqis). He is of the opinion that the definition of the proposition (qadiyya) in al-Taftâzânî’s Tahdhîb is clearer and more complete: “a proposition is an expression that bears the possibility of being true or false”. He states that in the division of proposition according to quantity what is taken into consideration is the subject (mawdû‘) in categorical propositions, and the temporal aspect of the antecedent (muqaddam) in hypothetical propositions. As for the unquantified, indefinite proposition (qadiyya muhmalah), Karsî assumes that if it is not about the problems of the sciences, then it is virtually/potentially a particular proposition (qadiyya juz’iyyah); but if it is about the problems of the sciences, then it is virtually/potentially a universal proposition (qadiyya kulliyyah). This being the general rule about the ambiguous (muhmal) propositions, he nevertheless contends that, because its subject (mawdû‘) is negated, it is preferable to consider a negative ambiguous (sâliba muhmalah) proposition like “human (insân) is not standing” to be a virtually/potentially universal negative (sâliba kulliyyâh) proposition. He states that a disjunctive hypothetical proposition (shartiyya al-munfasila) that is composed of more than two parts/units is only seemingly so, and that in reality it cannot be composed of more than two units. Syllogism (qiyâs), according to Karsî, is the ultimate purpose (al-maqsad al-aqsâ) and the most valuable subject-matter of the science of Logic. For him, the entire range of topics that are handled before this one are only prolegomena to it. This approach of Karsî clearly reveals how much the ‘demonstration (burhân)-centered’ approach of the founding figures of the Muslim tradition of logic like al-Fârâbî and Ibn Sînâ has changed. al-Abharî, in his Îsâghûjî makes no mention of ‘conversion by contradiction’ (‘aks al-naqîd). Therefore, Karsî, too, in his commentary, does not touch upon the issue. However, in his Îsâghûjî al-jadîd Karsî does handle the conversion by contradiction and its rules. Following the method of Îsâghûjî, in his commentary Karsî shortly touches on the four figures (shakl) of conjuctive syllogism (qiyâs iqtirânî) and their conditions, after which he passes to the first figure (shakl), which is considered ‘the balance of the sciences’ (mi‘yâr al-‘ulûm), explaining the four moods (darb) of it. In his Îsâghûjî al-jadîd, however, Karsî handles all the four figures (shakl) with all their related moods (darb), where he speaks of fife moods (darb) of the fourth figure (shakl). The topic of ‘modal propositions’ (al-muwajjahât) and of ‘modal syllogism’ (al-mukhtalitât), both of which do not take place in the Îsâghûjî, are not mentioned by Karsî as well, either in his commentary on Îsâghûjî or in his Îsâghûjî al-jadîd. Karsî proposes that the certainties (yaqîniyyât), of which demonstration (burhân) is made, have seven, not six, divisions. After mentioning (1) axioms/first principles (awwaliyyât), (2) observata/sensuals (mushâhadât), (3) experta/empiricals (mujarrabât), (4) acumenalia (hadthiyyât), (5) testata (mutawâtirât), and (6) instictives (fitriyyât), that is, all the ‘propositions accompanied by their demonstrations,’ Karsî states that these six divisions, which do not need research and reflection (nazar), are called badîhiyyât (self-evidents), and constitute the foundations (usûl) of certainties (yaqîniyyât). As the seventh division he mentions (7) the nazariyyât (theoreticals), which are known via the badîhiyyât, end up in them, and therefore convey certainty (yaqîn). For Karsî, the nazariyyât/theoreticals, which constitute the seventh division of yaqîniyyât/certainties, are too numerous, and constitute the branches (far‘) of yaqîniyyât. Every time the concept of ‘Mughâlata’ (sophistry) comes forth in the traditional sections on the five arts usually appended to logic works, Karsî often gives examples from what he sees as extreme sûfî sayings, lamenting that these expressions are so widespread and held in esteem. He sometimes criticizes these expressions. However, it is observed that he does not reject tasawwuf in toto, but excludes from his criticism the mystical views and approaches of the truth-abiding (ahl al-haqq), shârî‘â-observant (mutasharri‘) leading sufis who have reached to the highest level of karâmah. (shrink)

The way, in which quantum information can unify quantum mechanics (and therefore the standard model) and general relativity, is investigated. Quantum information is defined as the generalization of the concept of information as to the choice among infinite sets of alternatives. Relevantly, the axiom of choice is necessary in general. The unit of quantum information, a qubit is interpreted as a relevant elementary choice among an infinite set of alternatives generalizing that of a bit. The invariance to the axiom of (...) choice shared by quantum mechanics is introduced: It constitutes quantum information as the relation of any state unorderable in principle (e.g. any coherent quantum state before measurement) and the same state already well-ordered (e.g. the well-ordered statistical ensemble of the measurement of the quantum system at issue). This allows of equating the classical and quantum time correspondingly as the well-ordering of any physical quantity or quantities and their coherent superposition. That equating is interpretable as the isomorphism of Minkowski space and Hilbert space. Quantum information is the structure interpretable in both ways and thus underlying their unification. Its deformation is representable correspondingly as gravitation in the deformed pseudo-Riemannian space of general relativity and the entanglement of two or more quantum systems. The standard model studies a single quantum system and thus privileges a single reference frame turning out to be inertial for the generalized symmetry [U(1)]X[SU(2)]X[SU(3)] “gauging” the standard model. As the standard model refers to a single quantum system, it is necessarily linear and thus the corresponding privileged reference frame is necessary inertial. The Higgs mechanism U(1) → [U(1)]X[SU(2)] confirmed enough already experimentally describes exactly the choice of the initial position of a privileged reference frame as the corresponding breaking of the symmetry. The standard model defines ‘mass at rest’ linearly and absolutely, but general relativity non-linearly and relatively. The “Big Bang” hypothesis is additional interpreting that position as that of the “Big Bang”. It serves also in order to reconcile the linear standard model in the singularity of the “Big Bang” with the observed nonlinearity of the further expansion of the universe described very well by general relativity. Quantum information links the standard model and general relativity in another way by mediation of entanglement. The linearity and absoluteness of the former and the nonlinearity and relativeness of the latter can be considered as the relation of a whole and the same whole divided into parts entangled in general. (shrink)

Consider an infinite set of discrete, finite-sized solid balls (i.e., elements) extending in all directions forever. Here, infinite set is not meant so much in the abstract, mathematical sense but in more of a physical sense where the balls have physical size and physical location-type relationships with their neighbors. In this sense, the set is used as an analogy for our possibly infinite physical universe. Two observers are viewing this set. One observer is internal to the set and is (...) of the same finite size scale as the ball elements. Another observer is external to the set and is infinite in size relative to the balls and observer within the set. This observer is of the same size scale as the set as a whole. What do these sets look like to the two observers? The finite-sized (relative to the balls inside the set) observer within the set would view the set as a space composed of discrete, finite-sized objects. The external infinite-sized (relative to the inside the set) observer would view the very same set as a continuous space and would see no distinct elements within the set. How does this relate to us? First, the differing views of set N as being composed of a discrete versus continuous space may be related to the differing views of spacetime as discrete and continuous. Second, the perspective of the observer would have an impact on the assignment of a cardinality to an infinite set. (shrink)

Aristotle defines motion as such: ‘The fulfillment of what exists potentially, in so far as it exist potentially, is motion.’ (Phy., Γ, 1, 201a10-11) He defines it again in the same chapter: ‘It is the fulfillment of what is potential when it is already fully real and operates not as itself but as movable, that is motion. What I mean by ‘as’ is this: Bronze is potentially a statue. But it is not the fulfillment of bronze as bronze which is (...) motion.’ (Phy., Γ, 1) 2) Motion: not a real thing Aristotle believes that ‘there is no such thing as motion over and above the things’ that is supposed to mean that motion cannot be something else than his categories: ‘It is always with respect to substance or to quality or to quantity or to place that what changes changes. But it is impossible to find anything common to these which is neither ‘this’ not quantum nor quale nor any of the other predicates. Hence neither will motion and change have reference to something over and above the things mentioned, for there is nothing over and above them.’ (Phy., Γ, 1, 200b32-201a3) In fact, it is what is moved that is a reality for Aristotle and not the motion itself: ‘Motion is known because of that which is moved, locomotion because of that which is carried. What is carried is a real thing, the movement is not.’ (Phy., Δ, 11) 3) Three items in each motion Aristotle distinguishes three items in each motion (Phy., E, 4): a) ‘That which’ moves; (Note: It is this item that makes a motion a unitary motion. (Phy., Δ, 11)) e.g. a man or gold b) ‘That in which’ the movement occurs; e.g. a place or an affection c) ‘That during which’ the movement takes place; e.g. time Based on the second item, Aristotle distinguishes three kinds of motion: quantitative, qualitative and local which are in respect of the three categories of quantity, quality and place. (Phy., E, 1) However, Aristotle speaks of four things in respect of which change takes place adding substance to the three mentioned categories. (Phy., Γ, 1, 200b32-35) It seems it is based on the differentiation of that in which motion takes place in these four types that Aristotle distinguishes four kinds of motion. (Phy., Γ, 1, 201a11-15): a) Alteration: the motion of what is alterable qua alterable b) Increase and decrease: the motion of what can be increased and what can be decreased c) Coming to be and passing away: the motion of what come to be and pass away d) Locomotion: the motion of what can be carried away Alteration happens in qualities, increase and decrease in quantities, coming to be and passing away in substances and locomotion in place. 4) Problem of motion as an element Discussing why Pythagoreans put motion in their column of indefinites, Aristotle somehow hints to the problem of understanding motion due to its non-elemental character: ‘The reason why they put motion into these genera is that it is thought to be something indefinite and the principles in the second column are indefinite because they are privative: none of them is either ‘this’ or ‘such’ or comes under any of the other modes of predication. The reason in turn why motion is thought to be indefinite is that it cannot be classed simply as a potentiality or as an actuality- a thing that is merely capable of having a certain size is not undergoing change, nor yet a thing that is actually of a certain size, and motion is thought to be a sort of actuality, but incomplete. The reason for this view being that the potential whose actuality it is is incomplete. This is why it is hard to grasp what motion is. It is necessary to class it with privation or with potentiality or with sheer actuality, yet none of these seems possible. There remains then the suggested mode of definition, namely that it is a sort of actuality, or actuality of the kind described, hard to grasp, but not incapable of existing.’ (Phy., Γ, 2, 201b24-) It becomes a real difficulty when it is asked whether the motion is in the mover or in the movable: ‘The solution of the difficulty that is raised about the motion-whether it is in the movable- is plain. It is the fulfillment of this potentiality, and by the action of that which has the power of causing motion; and the actuality of that which has the power of causing motion is not other than the actuality of the movable, for it must be the fulfillment of both. A thing is capable of causing motion because it can do this, it is a mover because it actually does it. But it is on the movable that it is capable of acting. Hence there is a single actuality of both alike, just as one to two and two to one are the same interval, and the steep ascent and the steep descent are one- for these are one and the same, although they can be described in different ways. So it is with the mover and the moved.’ (Phy., Γ, 3) This is not, however, the solution: ‘This view has a dialectical difficulty. Perhaps it is necessary that the actuality of the agent and that of the patient should not be the same. The one is ‘agency’ and the other ‘patiency’; and the outcome and the completion of the one is an ‘action’, that of the other a ‘passion.’ Since then they are both motions, we may ask: in what are they, if they are different? Either (a) both are in what is acted on and moved, or (b) the agency is in the agent and the patiency in the patient. … Now in alternative (b), the motion will be in the mover, for the same statement will hold of ‘mover’ and ‘moved.’ Hence either every mover will be moved, or, through having motion, it will not be moved. If on the other hand (a) both are in what is moved and acted on- both the agency and the patiency (e.g. both teaching and learning, though they are two, in the learner), then, first, the actuality of each will not be present in each, and, a second absurdity, a thing will have two motions at the same time. How will there be two alterations of quality in one subject towards one definite quality? The thing is impossible: the actualization will be one.’ (Phy., Γ, 3) This leads Aristotle to another problem, the problem of one identical actualization for two different things: ‘But (someone will say) it is contrary to reason to suppose that there should be one identical actualization of two things which are different in kind. Yet there will be, if teaching and learning are the same, and agency and patiency. To teach will be the same as to learn, and to act the same as to be acted on- the teacher will necessarily be learning everything that he teaches, and the agent will be acted on. One may reply: (1) It is not absurd that the actualization of one thing should be in another. Teaching is the activity of a person who can teach, yet the operation is performed on some patient- it is not cut adrift from a subject, but is of A on B. (2) There is nothing to prevent two things having one and the same actualization, provided the actualizations are not described in the same way, but are related as what can act on what is acting. (3) Nor is it necessary that the teacher should learn, even if to act and to be acted on are one and the same, provided they are not the same in definition (as ‘raiment’ and ‘dress’), but are the same merely in the sense in which the road from Athens to Thebes are the same, as has been explained above.’ (Phy., Γ, 3) And he continues: ‘For it is not things which are in a way the same that have all their attributes the same, but only such as have the same definition. But indeed it by no means follows from the fact that teaching is the same as learning, that to learn is the same as to teach, any more than it follows from the fact there is one distance between two things which are at a distance from each other, that the two vectors AB and BA, are one and the same. To generalize, teaching is not the same as learning, or agency and patiency, in the full sense, though they belong to the same subject, the motion; for the ‘actualization’ of X in Y’ and the ‘actualization of Y through the actualization of X’ differ in definition.’ (Phy., Γ, 3) . (shrink)

This is one of the best popular cosmology books ever written and Guth is now (2016) a top physics Professor at MIT. He tells the extremely complex story of inflation and related areas of particle physics in such an absorbing style that it reads like a detective novel-in fact, it is a detective novel-how he and others found out how the universe started! The interweaving of his personal story and that of many colleagues along with their photos and many wonderfully (...) clear diagrams allows just the right amount of relaxation from the intensity of the physics. In places the style reminds one of Watson´s famous book ``The Double Helix``. He tells how his work on magnetic monopoles and spontaneous symmetry breaking led to the discovery of the inflationary theory of the very early universe (ca. 10 to minus 35 seconds!). -/- Along the way you will learn many gems that should stay with you a long time such as: the observed universe(e.g., everything the Hubble telescope etc. can see out to ca. 15 billion light years when the universe began) is likely just a vanishingly tiny part of the entire inhomogeneous universe which is about 10 to the 23rd times larger; the big bang probably took place simultaneously and homogeneously in our observed universe; there probably have been and will continue to be an infinite number of big bangs in an infinite number of universes for an infinite time; when a bang happens, everything(space, time, all the elements) from the previous universe are destroyed; the stretching of space can happen at speeds much greater than the speed of light; our entire observed universe lies in a single bubble out of an endless number so there may be trillions of trillions just in our own entire(pocket) universe(and there may be an endless number of such); none of these infinite number of universes interact-i.e., we can never find out anything about the others; each universe started with its own big bang and will eventually collapse to create a new big bang; all this implies that the whole universe is fractal in nature and thus infinitely regresses to ever more universes(which can lead one to thinking of it as a giant hologram); disagreements between the endless(hundreds at least) variations of inflation are sometimes due to lack of awareness that different definitions of time are being used; some theories suggest that there was a first big bang but we can never find out what happened before it; nevertheless it appears increasingly plausible that there was no beginning but rather an eternal cycle of the destruction and creation, each being the beginning of spacetime for that universe; to start a universe you need about 25g of matter in a 10 to minus 26cm diameter sphere with a false vacuum and a singularity(white hole). -/- He deliberately spends little time on the endless variants of inflation such as chaotic, expanded and supernatural inflation or on dark matter´, supersymmetry and string theory, though they were well known at the time as you can find by reading other books such as Michio Kaku´s `Hyperspace` (see my review) and countless others. Of course much has happened since this book appeared but it still serves as an excellent background volume so cheap now it’s free for the cost of mailing. -/- Those wishing a comprehensive up to date framework for human behavior from the modern two systems view may consult my book ‘The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle’ 2nd ed (2019). Those interested in more of my writings may see ‘Talking Monkeys--Philosophy, Psychology, Science, Religion and Politics on a Doomed Planet--Articles and Reviews 2006-2019 3rd ed (2019), The Logical Structure of Human Behavior (2019), and Suicidal Utopian Delusions in the 21st Century 4th ed (2019). (shrink)

A resolution to the Russell Paradox is presented that is similar to Russell's “theory of types” method but is instead based on the definition of why a thing exists as described in previous work by this author. In that work, it was proposed that a thing exists if it is a grouping tying "stuff" together into a new unit whole. In tying stuff together, this grouping defines what is contained within the new existent entity. A corollary is that a thing, (...) such as a set, does not exist until after the stuff is tied together, or said another way, until what is contained within is completely defined. A second corollary is that after a grouping defining what is contained within is present and the thing exists, if one then alters what is tied together (e.g., alters what is contained within), the first existent entity is destroyed and a different existent entity is created. A third corollary is that a thing exists only where and when its grouping exists. Based on this, the Russell Paradox's set R of all sets that aren't members of themselves does not even exist until after the list of the elements it contains (e.g. the list of all sets that aren't members of themselves) is defined. Once this list of elements is completely defined, R then springs into existence. Therefore, because it doesn't exist until after its list of elements is defined, R obviously can't be in this list of elements and, thus, cannot be a member of itself; so, the paradox is resolved. This same type of reasoning is then applied to Godel's first Incompleteness Theorem. Briefly, while writing a Godel Sentence, one makes reference to a future, not yet completed and not yet existent sentence, G, that claims its unprovability. However, only once the sentence is finished does it become a new unit whole and existent entity called sentence G. If one then goes back in and replaces the reference to the future sentence with the future sentence itself, a totally different sentence, G1, is created. This new sentence G1 does not assert its unprovability. An objection might be that all the possibly infinite number of possible G-type sentences or their corresponding Godel numbers already exist somehow, so one doesn't have to worry about references to future sentences and springing into existence. But, if so, where do they exist? If they exist in a Platonic realm, where is this realm? If they exist pre-formed in the mind, this would seem to require a possibly infinite-sized brain to hold all these sentences. This is not the case. What does exist in the mind is the system for creating G-type sentences and their corresponding numbers. This mental system for making a G-type sentence is not the same as the G-type sentence itself just as an assembly line is not the same as a finished car. In conclusion, a new resolution of the Russell Paradox and some issues with proofs of Godel's First Incompleteness Theorem are described. (shrink)

It is well known that modern epistemology is a discipline that was left as a legacy by the great French philosopher René Descartes, and it is generally believed that it is a typically philosophical discipline whose problems can be dealt with only by philosophical (speculative) means of inquiry. Recently, however, the idea of naturalization of epistemological inquiry has emerged, and one of its most prominent advocates was Quine. However, the question is to what extent, if at all, the (...) proposal offered by Quine is tenable, as evidenced, apart from numerous criticisms, by significantly different interpretations regarding assumptions on which it should be based. Namely, three types of interpretations of Quine’s call for the reform of epistemological inquiry prevail in contemporary literature: behaviorist, which was largely advocated by Quine, but also coherentist and physicalist, which some of his interpreters argued for. However, while the first two of these options are in my opinion unacceptable because they are unable to provide the necessary autonomy for the epistemological context of inquiry, I will try to show that physicalism is also burdened with difficulties, albeit different ones, which make it an untenable position when it comes to epistemological inquiry. Nevertheless, even before I started writing, I thought that there were valuable insights in Quine’s proposal, and that we could learn important lessons from the failure of previous interpretations, both regarding the position that should be taken in its interpretation, and, closely related to this, the possibility of reforming epistemological inquiry in general. In other words, informed by the weaknesses of Quine’s proposal and its interpretations, I will argue that epistemological inquiry can ultimately be approached from one of two mutually incompatible theoretical positions: the traditional or Cartesian one, and the Kantian one. Given that, as noted above, Quine’s proposal was primarily a reaction to Cartesianism, I discuss the possibility of establishing the fundamental level of inquiry such as epistemological to which Quine had to aspire, but in a way that would enable the synthesis of his approach with Kant’s view, which is in my opinion the only genuine alternative to the traditional program. Although it implies taking a position that would be a kind of compromise and could not be attributed to Quine (which is why it is uncertain whether he would have supported this interpretation), I believe that, apart from preserving certain naturalistic elements, it is an interpretation that would ultimately satisfy most of the demands that Quine himself has set for epistemological inquiry. (shrink)

The INBIOSA project brings together a group of experts across many disciplines who believe that science requires a revolutionary transformative step in order to address many of the vexing challenges presented by the world. It is INBIOSA’s purpose to enable the focused collaboration of an interdisciplinary community of original thinkers. This paper sets out the case for support for this effort. The focus of the transformative research program proposal is biology-centric. We admit that biology to date has been more fact-oriented (...) and less theoretical than physics. However, the key leverageable idea is that careful extension of the science of living systems can be more effectively applied to some of our most vexing modern problems than the prevailing scheme, derived from abstractions in physics. While these have some universal application and demonstrate computational advantages, they are not theoretically mandated for the living. A new set of mathematical abstractions derived from biology can now be similarly extended. This is made possible by leveraging new formal tools to understand abstraction and enable computability. [The latter has a much expanded meaning in our context from the one known and used in computer science and biology today, that is "by rote algorithmic means", since it is not known if a living system is computable in this sense (Mossio et al., 2009).] Two major challenges constitute the effort. The first challenge is to design an original general system of abstractions within the biological domain. The initial issue is descriptive leading to the explanatory. There has not yet been a serious formal examination of the abstractions of the biological domain. What is used today is an amalgam; much is inherited from physics (via the bridging abstractions of chemistry) and there are many new abstractions from advances in mathematics (incentivized by the need for more capable computational analyses). Interspersed are abstractions, concepts and underlying assumptions “native” to biology and distinct from the mechanical language of physics and computation as we know them. A pressing agenda should be to single out the most concrete and at the same time the most fundamental process-units in biology and to recruit them into the descriptive domain. Therefore, the first challenge is to build a coherent formal system of abstractions and operations that is truly native to living systems. Nothing will be thrown away, but many common methods will be philosophically recast, just as in physics relativity subsumed and reinterpreted Newtonian mechanics. -/- This step is required because we need a comprehensible, formal system to apply in many domains. Emphasis should be placed on the distinction between multi-perspective analysis and synthesis and on what could be the basic terms or tools needed. The second challenge is relatively simple: the actual application of this set of biology-centric ways and means to cross-disciplinary problems. In its early stages, this will seem to be a “new science”. This White Paper sets out the case of continuing support of Information and Communication Technology (ICT) for transformative research in biology and information processing centered on paradigm changes in the epistemological, ontological, mathematical and computational bases of the science of living systems. Today, curiously, living systems cannot be said to be anything more than dissipative structures organized internally by genetic information. There is not anything substantially different from abiotic systems other than the empirical nature of their robustness. We believe that there are other new and unique properties and patterns comprehensible at this bio-logical level. The report lays out a fundamental set of approaches to articulate these properties and patterns, and is composed as follows. -/- Sections 1 through 4 (preamble, introduction, motivation and major biomathematical problems) are incipient. Section 5 describes the issues affecting Integral Biomathics and Section 6 -- the aspects of the Grand Challenge we face with this project. Section 7 contemplates the effort to formalize a General Theory of Living Systems (GTLS) from what we have today. The goal is to have a formal system, equivalent to that which exists in the physics community. Here we define how to perceive the role of time in biology. Section 8 describes the initial efforts to apply this general theory of living systems in many domains, with special emphasis on crossdisciplinary problems and multiple domains spanning both “hard” and “soft” sciences. The expected result is a coherent collection of integrated mathematical techniques. Section 9 discusses the first two test cases, project proposals, of our approach. They are designed to demonstrate the ability of our approach to address “wicked problems” which span across physics, chemistry, biology, societies and societal dynamics. The solutions require integrated measurable results at multiple levels known as “grand challenges” to existing methods. Finally, Section 10 adheres to an appeal for action, advocating the necessity for further long-term support of the INBIOSA program. -/- The report is concluded with preliminary non-exclusive list of challenging research themes to address, as well as required administrative actions. The efforts described in the ten sections of this White Paper will proceed concurrently. Collectively, they describe a program that can be managed and measured as it progresses. (shrink)

"The Mind is not a Vessel to be Filled but a Fire to be Kindled", and "Education is Not the Filling of Pail But the Lighting of a Fire", and ... Something About a Horse ... You can lead a horse to water, but you can’t make it smile? Because of the long face and all? (No, that can’t be it). Anyway, borrowing a bit from Plutarch and Yeats (maybe, there is no agreement on whether he said that about pails (...) and fires), and some idiom from 12th Century Old English about horses walking on water, I assume, we can glean the following gem: learning requires active participation by learners. It is almost embarrassing to have to write that, but here we are with education today, mostly unloading facts into unlit receptacles. This doesn’t work, and not just because the metaphor is mixed. Genuine learning requires focus, which requires motivation, which is cultivated by interest, which needs curiosity, which is not something teachable through the typical educational curricula. I can, as Aristotle tells us, teach students the basics of some ethical theory, but I cannot make them virtuous. Ah-ha! I can lead a horse to water, but I can’t make it abide by the categorical imperative (No, that’s not quite right. Although it’s true--most horses are utilitarians). One way that seems to work in piquing student interest in learning philosophy is to use humor as you make the case that a philosophical attitude is very similar to a humorous attitude. Both rely heavily on questioning our collective presuppositions, both cultivate rational skepticism, and both are never content with accepting traditions and values that are mindlessly received. I’ve got it now: You can lead a horse to water, but you can’t make it an iconoclast! (still not it). Friedrich Nietzsche published a book in 1889 titled Twilight of the Idols: Or How to Philosophize with a Hammer. This was during his most frenetic and fecund period, just before the syphilis set in rendering him somewhat less than his lauded Ubermensch. The “Idols” for Nietzsche were “false gods” or the ubiquitous errors that philosophy should expose. He is likely borrowing (without citation!) from sir Francis Bacon, whose “idols” are fetishes which can divert us from the pursuit of truth. Learning is hard, but it doesn’t have to be gloomy, hence, I advocate for a different sort of hammer to act as a “tuning-fork” sounding out the hollow and dangerous idols handed down to us that have passed for sagacity. (shrink)

(...) However, whether we chose a weak or strong approximation, the set would not make any sense at all, if (once more) this choice would not be justified in either temporal or spatial sense or given the context of possible applicability of the set in different circumstances. This would obviously represent a dualism in itself as we would (for instance) posit and apply a full identity-equality-equivalence of x and y when applying Newtonian physics to certain observations we make (it would (...) be the case of neural correlates), and we would posit and apply a non - identity-equality-equivalence of x and y when applying Quantum mechanics to other observations. Following this dualism in and of theories, the same sate would need to be slightly modified: U2:(x~y)∪(x≈y); U3:(x~y)∩(x≈y); U4a:(x~y)⊆(x≈y) vs. U4b:(x~y)⊇(x≈y). (shrink)

Background If trials of therapeutic interventions are to serve society's interests, they must be of high methodological quality and must satisfy moral commitments to human subjects. The authors set out to develop a clinical - trials compendium in which standards for the ethical treatment of human subjects are integrated with standards for research methods. Methods The authors rank-ordered the world's nations and chose the 31 with >700 active trials as of 24 July 2008. Governmental and other authoritative entities of the (...) 31 countries were searched, and 1004 English-language documents containing ethical and/or methodological standards for clinical trials were identified. The authors extracted standards from 144 of those: 50 designated as ‘core’, 39 addressing trials of invasive procedures and a 5% sample of the remainder. As the integrating framework for the standards we developed a coherent taxonomy encompassing all elements of a trial's stages. Findings Review of the 144 documents yielded nearly 15 000 discrete standards. After duplicates were removed, 5903 substantive standards remained, distributed in the taxonomy as follows: initiation, 1401 standards, 8 divisions; design, 1869 standards, 16 divisions; conduct, 1473 standards, 8 divisions; analysing and reporting results, 997 standards, four divisions; and post-trial standards, 168 standards, 5 divisions. Conclusions The overwhelming number of source documents and standards uncovered in this study was not anticipated beforehand and confirms the extraordinary complexity of the clinical trials enterprise. This taxonomy of multinational ethical and methodological standards may help trialists and overseers improve the quality of clinical trials, particularly given the globalisation of clinical research. (shrink)

An interruption. Rethinking the first three chapters of this book, I have come to suspect that, not unlike Iris Murdoch and Emmanuel Levinas, the way I imagine ‘ethics’ floats on an idea that any ethical substantive position or ethical theory is always shaped through our existential condition and our embodied encounter with others. To Murdoch, existence is the disposition for our responses to the ways in which we perceive reality, and yet, although these responses are always part of who we (...) are, they are not always part of what we do, and so, we set ourselves ethical tasks when we desire to act ethically. As scholar Bridget Clarke argues, “to attend to something [for Murdoch] is to approach it with a just and loving eye, and therewith to perceive it in its unbounded particularity and complexity, and so, as it truly is.” Or as I argue, to attend to the other ‘justly and lovingly’, Murdoch would instruct, is not merely to accurately collect details about the other and then arrive at an approximation of its being, but also to apprehend the other as ‘distinctly singular’ and ‘distinctly foreign’ from oneself–which at once forgoes any assimilation of the other into oneself, incidentally. The recognition of the other as ‘one who embodies human otherness and dignity’ becomes the condition for and coherent way of imagining and accessing moral reality. Moreover, for Diane Davis, this “being-for-the-other names a pre-originary obligation to respond to the other [and] it is in this response that both the self and the other emerge as existents” whose ethical projects are each challenged by the markedly different and infinitely other being. This obligation, Levinas might also say, is an ‘authority’ that is experienced like the effect of the other upon me, so that I am subsequently motivated to enact ethical task-making. I am not, therefore, “pulling everything other into the same, the known, the comprehended,” nor am I looking to any normative theories as authoritative templates from which I act ethically. And so, unlike Husserl, I am not “joining the philosophical tradition in its fundamental disrespect for all things other,” but instead, by dispositioning myself between these theories in responsible Levinasian fashion, I will be tracking them in response to their confronting me, and not as normative theories that are applicable to real and lived experiences. (shrink)

The closing chapters of Aristotle’s Nicomachean Ethics x are regularly described as “puzzling,” “extremely abrupt,” “awkward,” or “surprising” to readers. Whereas the previous nine books described—sometimes in lavish detail—the multifold ethical virtues of an embodied person situated within communities of family, friends, and fellow-citizens, NE x 6-8 extol the rarified, god-like and solitary existence of a sophos or sage (1179a32). The ethical virtues that take up approximately the first half of the Ethics describe moral exempla who experience fear fighting for (...) their communities, are sensitive to the esteem and recognition of others, and feel love for a desire to live together with a wide variety of kinds of friends. Such good people take pleasure in prudently expending sums to improve their communities—communities in which they exchange goods and participate in ruling and being ruled in a cooperative fashion. The exemplum of x 7-8, by contrast, is a person whose activity consists almost entirely in exercising his or her mind (nous)—a part of one’s soul that Aristotle explicitly notes is disconnected from human emotions and that can be exercised, insofar as one as wise, in a wholly solitary fashion (1178a15-16, a19-20; 1177a33-34). Although Aristotle’s claim that a “life in accord with the mind” is best and most pleasant (1178a6-7) may jar the intuitions of many people—he himself endorses Anaxagoras’ claim that the happy person will appear as “someone who is absurd” (atopos, 1179a15) to most people—it is false to claim that his conclusions in NE x 6-8 are unexpected or unanticipated, or that the text is in any way discontinuous with what precedes it. The Nicomachean Ethics exhibits aspects of ring-composition both within the work as a whole and within book 10. In NE i 5 Aristotle introduces his rendition of a trope that he inherits (most immediately) from Plato, viz. that the problem of the good can be considered like a contest between three different kinds of life—the life of enjoyment (apolaustikos), the life of politics (politikos), and the life of contemplation (theôrêtikos). NE x 6-8 returns to that contest, rendering a verdict about which life takes first, second, and third place. As the opening lines of NE x 6 note, that verdict presupposes central claims articulated between the first and last books of the Ethics, specifically about the nature of the virtues, the nature of friendship, and the nature of pleasure. NE i 5 and x 6-8 thus serve as “bookends” which encase arguments and proposition located between them. Book 10 exhibits a similar ring-composition. NE x opens with methodological reflection on the gap between the theoretical positions that thinkers articulate and the way they live their lives (especially in the case of scolds who simultaneously criticize pleasure on a scientific level but seek it on a practical level [1172a33-b8]). Chapter 8 concludes with an explicit reiteration of the methodological point, a reiteration that underscores how Aristotle’s treatment of the contest of lives incorporates central aspects of the discussion of pleasure in NE x 1-5. Aristotle’s reiteration of the problem of a gap between theory and practice also draws attention to the centrality of his treatment of pleasure in his adjudication of the three lives. Although the life of pleasure takes a distant third in the contest of lives, the contemplative life wins the contest in part because it itself is the most pleasant form of life. The central philosophical problem looming behind Aristotle’s treatment of the contest of lives concerns the relationship between the notion of activity (energeia) and the notion of a way of life (bios). In the last four decades, much of the scholarship on NE x 6-8 has sought to address the question of what activities a certain way of life includes or excludes. “Monistic” or “dominant” end interpretations of the best life have viewed it as including only contemplative activities whereas “inclusivist” end interpretations of the best life have viewed it as including non-contemplative activities. Although this chapter largely side-steps this debate—partially because there are ample recent first-rate introductory treatments of the debate, partially because I have addressed the question elsewhere in my own writing —I argue that focusing solely on the contest between the two best ways of life overshadows the way that Aristotle incorporates insights from the third way of life into the best way of life. Although the notion of a contest among different kinds of lives presupposes that the lives are mutually exclusive, Aristotle has no problem saying that the contemplative life trumps the life of pleasure because the contemplative life is more pleasant. I proceed in two parts. In the first part I examine what I will call the “outer” ring of the Ethics, namely the relationship between the contest of lives proposed in NE i 5 and its overall resolution in x 6-8. I show how i 5 and x 6 establish the framework for the contest, how x 7 adjudicates that contest in large part by relying upon premises articulated in the interim between books 1 and 10, and how x 6 and x 8 determine the second and third place positions in the contest. In the second part I focus on what I will call the “inner” ring of NE x. More than half of NE x struggles with the nature of pleasure, its role in a happy life, and the methodological problems of examining pleasure within a practical science. I show how x 1 and x 8 are “bookends” that underscore the methodological problem of examining pleasure and how the contest of lives draws upon the proximate conclusions concerning the nature of pleasure in NE x 1-5. (shrink)

This paper aims to achieve a better understanding of what Socrates means by “sumfvne›n” in the sections of the Phaedo in which he uses the word, and how its use contributes both to the articulation of the hypothetical method and the proof of the soul’s immortality. Section I sets out the well-known problems for the most obvious readings of the relation, while Sections II and III argue against two remedies for these problems, the first an interpretation of what the (...) sumfvne› n relation consists in, the second an interpretation of what sorts of thing the relation is meant to relate. My positive account in Section IV argues that we should take the musical connotations of the term seriously, and that Plato was thinking of a robust analogy between the way pitches form unities when related by certain intervals, and the way theoretical claims form unities when related by explanatory co-dependence. Section V surveys the work of IV from the point of view of the initial difficulties and suggests further consequences for the hypothetical method, including the logical relation between the sumfvne›n and diafvne›n relations, and the need for care in ordering the results of a hypothesis. -/- “But anyhow I proceeded in this way: on each occasion hypothesising the lÒgow which I judged to be strongest, I put down as true the things that seem to me to sumfvne›n with it – both about a causal account and any of the other things that are – but those things that did not I put down as false.” (Phaedo 100a3-7). -/- “But if someone clung to the hypothesis itself, you would bid him goodbye and wouldn’t answer him until you had examined its results, whether according to you they sumfvne› or diafvne› with one another.” (Phaedo 101d3-5). (shrink)

Cosmopolis A Review of Cosmopolitics -/- 2015/3-4 -/- Editorial Dominique de Courcelles & Paul Ghils -/- This issue addresses the general concept of “spirituality” as it appears in various cultural contexts and timeframes, through contrasting ideological views. Without necessarily going back to artistic and religious remains of primitive men, which unquestionably show pursuits beyond the biophysical dimension and illustrate practices seeking to unveil the hidden significance of life and death, the following papers deal with a number of interpretations covering a (...) wide field extending from belief to theory, from emotions to concepts, from the wisdom of personal experience to the most sophisticated doctrines. Spirit and spirituality are indeed many-faceted notions. They may refer to the intricate world of the interacting spirits which inhabit living beings in animistic traditions, without excluding a “grand force” linking human beings within a dynamic whole on which their very existence rely . They also bear upon more atomistic and either/or approaches of Western philosophy, which have become embodied in Cartesian dualism against a monotheist background, to the point of freezing the essence of individuals and culminating in the extreme individualism that characterizes our contemporaries. However, this equally refers to the opposite conception of materialism, across times and cultures, from ancient India and Greece (Cārvāka, originally known as Lokāyata, or some Buddhist doctrines for the former, Democritus or Lucretius for the latter) to more contemporary materialistic schools, whether modern or postmodern. -/- The following papers look at the contrasting forms of the philosophy and spirit of the human factor set into a whole, with no artificial disjoint between the psychical and the physical levels, as Wittgenstein put it: “And how can a body have a soul?”. This approach is not unrelated to the notion of anthropocene examined in a recent issue of Cosmopolis, with provides another comprehensive framework open to a spiritual life emerging from the very environment that generated it. -/- *** The first section of this issue was edited by Dominique de Courcelles, director at the National French Research Centre (CNRS), whom we wish to thank for collecting relevant studies relating to the religious and political questions, with a view to focusing on the war of ideas inevitably waged behind images, concepts and perceptions, taking an asymmetrical approach. To the extent that they are mindful of global/local interactions and include representations, opinions and beliefs, such disciplines as philosophy, philology, history and social sciences can provide useful studies accounting for new practices in geopolitics and a fair diplomacy. -/- In her introduction, Dominique de Courcelles first poses the question of how the religious and political spheres interrelate, with their corresponding religious demands and humanistic values. She then suggests that the right question today may be breaking with the philosophy of human rights concerned with the defense of human beings against the hazards of arbitrary politics or the instrumental use of religion, in favour of a fair philosophy of humankind, a new humanism. This would consist in recognizing a common loyalty of all towards one interhuman, not only interstate community, to protect it from both the autonomy demanded by individuals and the instrumental use of minorities. -/- Considering the fact of diversity, so important today in terms of both politics and religion, Abdelhai Azarkan looks at the conditions under which tolerance could obtain the double status of right and duty. He revisits to two philosophers, John Locke and Voltaire, who thought about it from the historical reality of religious wars. The former made tolerance into a right, basing his analysis on the political-legal level, while the latter saw tolerance as a duty, from an analysis based on ethical-political criteria. -/- Mathieu Guidère examines what he calls semantic denominationalism, a term which implies religious attributes and identities, whichever national loyalties or personal belonging they may have at the same time. Since the early 2000s, thie phenomenon has expanded tremendously, compounded by the “war on terror” and the over media-oriented terrorist actions. Denominational expressions act as formal names for ordinary and high-profile players in domestic and foreign policies of democratic states. These systems reveal a receding secularization, while the powerful comeback of religious identities signals the failure of nation-states and the weakening of the humanist spirit. -/- Barbara De Poli retraces the history of a contemporary jihadism claiming its Islamic essence and asserting the truth of genuine coranic principles via the war on infidels, with a view to restoring the Caliphate. After defining the term jihad, she shows that even if this contemporary jiadism is spreading in the Muslim world, it radically departs from Islamic law and the received use of the term jihad, in so far as it is rooted in the early radical thinking of Islamic ideologues in the 20th century, starting with with Hassan al-Banna, the founder of the Muslim Brotherhood. This current has been fueled by by international conflicts since the outbreak of the war in Afghanistan, in which the so-called Western countries bear a major responsibility. -/- Abderrazak Sayadi starts from the Tunisian experience to ask the question of humanist values and democracy within the relationships between the religious and political spheres. As a historian of religion, he is brought to demystify certain islamic principles and to paying attention to the reform of law, seeing the separation of religion and politics as a precondition to a successful democratic gamble and the establishment of a renewed humanism. -/- Dominique de Courcelles reminds us that getting a better knowledge of narrations and words makes it possible to better understand how logical and rhetorical thinking works for those who wage an asymetriccal war, re-enchanting and mystifying the world to better take control. As soon as 1932, an exchange of letters between Einstein and Freud made it clear that, in order to free man from fatality and war, education understood as culture was fundamental. Such illustrations as the exécution of Oussama ben Laden and the Caliph’s speech in Mossoul show that a premiminary analysis of images and words is essential to a fair diplomacy conducted by people from civil society, whose culture and wisdom allow justice and force to speak together and better resist war. -/- Marcel Boisard thinks that on the day the guns fall silent, exhausted by war, we will not return to the state borders that have prevailed for a century as an outcome of the Sykes-Picot agreement of 1916. It is time to prepare the “day after”, which will be a huge challenge. To this end, a summit of Middle-East nations is urgently needed to globally decide the fate of those peoples. On the condition that we know who the enemy is and accept to name it, to understand the history of the countries, groups and alliances, and to question any false or self-interested sense of certainty. -/- *** In the second section, Paul Schafer provides the author’s experiences to explain how culture, from the artistic to the biological, has the power to to open the doors to spirituality, from the inner self to the global environment. He asks himself whether a relative permanence of spirituality can arise from the specific moments that characterize it. Laurent Ledoux synthesizes the conclusion of a symposium held on 22 January 2015 on the links between philosophy and management, on the basis of the spiritual dimension conceived as “natural” and the answers it may suggest to the issues that face the organizations in a “contemporaniversal” world. Jacques Rifflet makes that question in a secular perspective, based on the wellsprings of personal commitment before it can be caught by any religious creed or scientific theory. In this sense spirituality, in alliance with reason, both inspires human consciousness and illuminates its destiny. Sami Aldeeb asks himself whether Islam can be reconciled with human rights. Caught between the belief in an absolute and final Word descended from the sky, and evidence showing that any religion is the creation of a given culture and a society situated in time and space, the Makkan and … contexts et médinois call for differentiated, if not opposite answers and exegeses. Bernard Carmona provides the outline of a dialogical framework, which is known to be a feature of debates between the various philosophical schools of classical India, exemplified here by the transdisciplinary perspective of debates within a Buddhist context. *** The articles not focused on the previous topic include a study by Landry Signé on China’s strategy, competing with the United States to control African resources. The author deals with the specific case of China’s rapprochement with Southern Sudan since Sudan was broken up. In the last paper, Goran Fejić and Rada Iveković, return to the essential role that women should play, and comments upon the role of some international legal instruments related in particular to the elimination of all forms of discrimination. The perspective is transnational and transethnic and is based on secular criteria, as regards nation-building and more generally society-building. Considering the persistence of widespread violence, whether in times of armed conflict or in times of peace, the question remains whether it is possible to fully implement rights and justice instruments. (shrink)

The monograph contains three works on research on the concept of a rejected sentence. This research, conducted under the supervision of Prof. Jerzy Słupecki by U. Wybraniec-Skardowska (1) "Theory of rejected sentences" and G. Bryll (2) "Some supplements of theory of rejected sentences" and (3) "Logical relations between sentences of empirical sciences" led to the construction of a theory rejected sentences and made it possible to formalize certain issues in the methodology of empirical sciences. The concept of a rejected sentence (...) was introduced by J. Łukasiewicz in the course of his inquiry into Aristotelian Syllogistic. It was essentialy generelized by J. Słupecki who, with reference to Tarski's axiomatic theory of deductive systems (1930), gave the formal definition of the rejection function Cn' according to which a sentence y is rejected on the base of a set of sentences X iff at least one sentence which belongs to X can be deduced from the sentence y. Słupecki proved (1959) that the function Cn', which assignes to the set X the set of sentences rejected on the basis of X, is additive and satisfies the axioms of Tarski's general theory of deductive systems. Work (1) uses not only Tarski's general theory of systems but also his the so-called enlarged theory of systems (1930). It constructs a theory T of rejected sentences (propositions), which is created from Tarski's richer theory of systems by adding one axiom and a number of definitions; among them the definition of the rejection function Cn' is fundamental one. Cn' is a function which assignes to every set X of false sentences the set Cn'X whose members are exclusively false senteces. A number of theorems which describes properties of defined concepts have been proved in T. Some of them are necessary for conducting considertions of the concluding section of (1) devoted to the empirical sentences. Section 2 of (1) deals with the theory of the unit consequenses. It is characterized by an axiom from which follow all axioms of Tarski's general theory of deductive systems, additivity and the property that the unit consequence of the set X of sentences is a unit consequence only one sentence of X. An example of unit consequence is the rejection consequence Cn'. In section 3 of (1) the dual theory T' equivalent to T is presented. In T' the primitive concept is the rejection function Cn'. The fundamental axiom of T' states that Cn' is a unit consequence. The concluding section brings a few examples of applications of the definitions and theorems of T in the domain of the scientific methodology. Work (2) corresonds to J. Słupecki paper (1959) and the theory T of rejected propositions given in work (1). In this paper some suplements of the theory T are given. Work (3) is an extension of the theory of rejected propositios given in the paper (1). It is an attempt of formalization some problems of methodology of the empirical sciences which concern to such concepts as: empirical sentence, similar sentence, generalization, inductive conclusion etc. (shrink)

According to Cantor (Mathematische Annalen 21:545–586, 1883 ; Cantor’s letter to Dedekind, 1899 ) a set is any multitude which can be thought of as one (“jedes Viele, welches sich als Eines denken läßt”) without contradiction—a consistent multitude. Other multitudes are inconsistent or paradoxical. Set theoretical paradoxes have common root—lack of understanding why some multitudes are not sets. Why some multitudes of objects of thought cannot themselves be objects of thought? Moreover, it is a logical truth that such multitudes do (...) exist. However we do not understand this logical truth so well as we understand, for example, the logical truth $${\forall x \, x = x}$$ . In this paper we formulate a logical truth which we call the productivity principle. Rusell (Proc Lond Math Soc 4(2):29–53, 1906 ) was the first one to formulate this principle, but in a restricted form and with a different purpose. The principle explicates a logical mechanism that lies behind paradoxical multitudes, and is understandable as well as any simple logical truth. However, it does not explain the concept of set. It only sets logical bounds of the concept within the framework of the classical two valued $${\in}$$ -language. The principle behaves as a logical regulator of any theory we formulate to explain and describe sets. It provides tools to identify paradoxical classes inside the theory. We show how the known paradoxical classes follow from the productivity principle and how the principle gives us a uniform way to generate new paradoxical classes. In the case of ZFC set theory the productivity principle shows that the limitation of size principles are of a restrictive nature and that they do not explain which classes are sets. The productivity principle, as a logical regulator, can have a definite heuristic role in the development of a consistent set theory. We sketch such a theory—the cumulative cardinal theory of sets. The theory is based on the idea of cardinality of collecting objects into sets. Its development is guided by means of the productivity principle in such a way that its consistency seems plausible. Moreover, the theory inherits good properties from cardinal conception and from cumulative conception of sets. Because of the cardinality principle it can easily justify the replacement axiom, and because of the cumulative property it can easily justify the power set axiom and the union axiom. It would be possible to prove that the cumulative cardinal theory of sets is equivalent to the Morse–Kelley set theory. In this way we provide a natural and plausibly consistent axiomatization for the Morse–Kelley set theory. (shrink)

This article aims to provide a structural analysis of the problems related to the easy knowledge problem. The easy knowledge problem is well known. If we accept that we can have basic knowledge via a source without having any prior knowledge about the reliability or accuracy of this source, then we can acquire knowledge about the reliability or accuracy of this source too easily via information delivered by the source. Rejecting any kind of basic knowledge, however, leads into an (...) infinite regress and, plausibly, to skepticism. The article argues that the third alternative, accepting basic knowledge but rejecting easy knowledge, entails closure failure. This is obviously the case for deductive bootstrapping, but, notably, the problem also arises for inductive bootstrapping. Hence, the set of problems related to the easy knowledge problem has the structure of a trilemma. We are forced to accept easy knowledge, closure failure, or skepticism. (shrink)

The Shadow of God in the Philosopher’s Garden. The Parc de La Villette in Paris in the context of the philosophy of chôra I Bernard Tschumi’s project of the Parc de La Villette could have won the competition and was implemented thanks to the political atmosphere that accompanied the victory of the left-wing candidate in the French presidential elections in 1981. François Mitterand’s revision of the political programme and the replacement of radical reforms with the construction of prestigious architectural objects (...) and urban assumptions in the French capital gave Tschumi a unique opportunity to realise ideas that polemicised with traditional forms of social life, questioned the basic principles of architecture and included architectural work in the philosophical disputes over the issues of metaphysics. Tschumi’s theoretical assumptions put forward during the design of the Parc de La Villette highlighted the questions of conflict between the main components of the project and suggested that the intensification of differences was analogous to Jacques Derrida’s creation of the concept of différance. It was this philosopher who in a special commentary to Derrida’s project also introduced the concept of maintenant, which aimed at demonstrating that the architect’s polemical inclinations remain in a hidden balance with his inclinations to affirmation of architectural principles. During the discussion between Derrida and Peter Eisenman, who was to take part in the design of the Parisian park, the concept of the chôra was also put forward, which in the course of the debate led to an additional confusion of architectural and philosophical problems. II In the period from the Antiquity to the Renaissance, the dialogue Timaeus was the most frequently commented work of Plato. At present, the most frequently discussed is the issue of the chôra included in it, which aroused fascination among philosophers, researchers of rhetoric, religion, feminism, but also architecture. The work on the chôra also influenced the development of the interpretation of the Parc de La Villette, among which the topics related to the beginning and the change were highlighted. In early uses of the word chôra in Greek, as in Homer’s 18th Book of Iliad, it meant both dancing and a place to dance. On this occasion, it can be seen that it is not possible to determine which phenomenon took precedence in the creation of the name. It cannot be denied, however, that the word concerned a specific movement, as if circular and returning to an indefinable beginning. Despite gaining more and more general meanings, the word chôra has retained its connection with the dance of people on the threshing floor, the dance of bees (choros meliton) or the dance of stars (choros astron). In Timaeus, the chôra is a space filled with movement with an effect similar to shaking the sieve to husk the grain: it separates similar elements from the dissimilar ones. The juxtaposition of the Parc de La Villette and the chôra already at this stage leads to the suggestion that the park was treated by the architect as a place of dynamic changes leading to the establishment of new social solutions. In his statements, the architect confirmed that the park was to be a space of new politics and ethics. The book by Julia Kristeva La Révolution du langage poétique contributed to the spread of the belief that works of art can play a role as factors of political revolution. In this work, the author put forward the thesis that the chôra is a kind of space, the character of which has a destructive influence on attempts to conclude language games. The chôra gives beginning to words, but at the same time, by leaving a trace of this beginning it forces us to renew their meanings. The chôra understood in this way, turns out to be an irremovable beginning, to which one has to return all the time. Kristeva found manifestations of the chôra’s activity in avant-garde French poetry, to which she attributed the role of a mediator between criticism of metaphysics and aspirations for social change. The chôra, violating the language, introduces some voids into it, as if traces of the abyss, which direct the consciousness towards understanding the necessity of political changes. The Parc de La Villette was to pursue similar objectives in the city space. In his essays, Tschumi considered the problems of creating spaces that would give rise to a radical democracy. The proposed rebellious spaces should have the characteristics of a void, in which contradictory forces would occur as forms of pure activity. The means of achieving this goal was to concentrate contradictions and make them visible. The Parc de La Villette was supposed to collect differences as indelible and at the same time by showing them it was supposed to raise awareness of the social world as a conglomerate of differences. Saturation of the space of the park with subversive values results from the character of this space suppressed in the consciousness, as well as from the social diversity which has not been taken into account so far. The main contradictions contained in space relate to the division that exists between its presentation as a mental problem and a sensual one. The park was the deliberate creation of a place that transcends such a division and creates a separate space for negotiation between architectural theories and its practical applications. The purpose of the park was to become a place of future events, which would not hide their conflicting character coming from diversity of both space and society. The method of composition usually aimed at achieving a harmonious whole has been replaced by Tschumi with a system of juxtaposition of non-coherent elements or those resulting from variations and transformations. Tschumi did not seek direct influence on politics in the Parc de La Villette, but made room for thinking about the possibilities of the future. He introduced problems rather than showed solutions to them. The task of the park was to put the principles of architecture into a kind of vibration that would inspire users to participate in the new community. III Tschumi believes that the quality of architecture depends on the theoretical factor it contains. Such a view led to the creation of architecture that would achieve visibility and comprehensibility only after its interpretation. On his way to creating such an architecture he took on a purely philosophical reflection on the basic building block of architecture, which is space. In 1975, he wrote an essay entitled Questions of Space, in which he included several dozen questions about the nature of space. The questions he formulated could be regarded as analogous to the situation in the philosophy of the time, in which the interest in questioning the most obvious forms of understanding the world and intellectual categories increased. The research on space is an area common to many fields of natural sciences, humanities and artistic creation, but it also deals with other problems, such as issues of experience. The concept of space-time continuum proposed by Hermann Minkowski drew attention to the identity of time and space with the events taking place. Probably regardless of the postulates of physicists commenting on Albert Einstein’s discoveries, also in philosophy it increased the importance of the concept of the event which became dominant in Martin Heidegger’s latest work Contributions of Philosophy: Of the event. Furthermore, Tschumi’s reflections on space entered into relation with the problem of experience, which aroused the interest of a group of French philosophers trying to assimilate Georges Bataille’s concept of “inner experience”. Both Tschumi and Derrida referred to Bataille because his views could be used not only to modify the concept of the subject, but also to change the understanding of what constitutes the area of architecture. The discussion on experience has led to the recognition that the subject is not sovereign, but actually a form of what is on their outside. Such insights make it possible to treat the area of the Parc de La Villette as existing mainly when it is organised by its users. The decisive features of the park are its assumptions, according to which it is a variety of active void that leads to agreeing new social relations with it. The park does not force to participate in already existing moral or political communities, but tries to move into an unknown future in which the scope of free functioning of individuals will be increased. Doubts about the principles of functioning of the individual self and its discovery as a whole composed of non-coherent parts, as well as its dependence on its own depth full of disordered forces, influenced the understanding of architecture as a set of contradictions whose source is a fundamental void anticipating the empty phenomenal space. The use of this phenomenal void in architecture, as well as the rejection of the whole and unity, had a specific political purpose and drew its inspiration from political analyses. In the Parc de La Villette, metaphysics and politics were brought closer together because the philosophy of void was used to create new conditions for community action. It can be argued that the source of this philosophy was the perception of errors in existing societies dependent on the shortcomings of traditional metaphysics. Spacing (espacement) was one of the key terms in Derrida’s philosophy, which was also combined with the concepts of différance and chôra. The study of the nature of space, especially its transition from the level of pure possibility to the level of sensual phenomenon, also contributes to understanding how well designed space can have an impact on its audience. This explanation is based on Tschumi’s assumption that the space of the Parc de La Villette contradicts the integrating approaches and instead exposes contradictions, but it does so in a way that combines incompatible properties into a single piece of architecture. The specificity of such integration is similar to the invention of a musical phrase, which is an ideological message: moral and political. Such a thesis may raise doubts, however, if both the clearly adopted assumptions and those deduced from the work allow for their logically ordered presentation then to a limited extent it may be assumed that the work has achieved a connection between a specific philosophy of space and its practical application. Derrida combined the problem of spatiality with the problem of transcendental imagination in the philosophy of Immanuel Kant, who in the first version of Critique of Pure Reason assumed that pure imagination precedes the appearance of time and space, even in their transcendental forms. The imagination in such a situation can be described as a factor activating time and space, which indicates what function is played by movement in this activity. This leads us to recognize that the ultra originary source of pure forms of sensual intuition is movement, which in early Greek philosophy was identified with void and its lack of resistance to phenomena occurring in it. Derrida’s philosophy in search of a certain super-transcendental source of time and space pointed to différance which, like void or the chôra, does not have material features or even any other form of being. Différance is the primary cause of the disruption of motionlessness and the introduction of activity into motionless time and space, thus its activity can be described as spacing (espacement). Derrida’s discoveries in this respect are not entirely original, because Georg Wilhelm Friedrich Hegel already pointed out when examining the present that it is primarily a differential relation (differente Beziehung), which, being seemingly neutral, influences the present with supernatural force and makes it unidentifiable with itself. Differente Beziehung must similarly influence the originary space, negating its initial character by multiplying its divisions and expanding its boundaries. Différance acts by revealing contradictions wherever there is apparent undifferentiation. Tschumi, composing the Parc de La Villette as a variety of void and a set of incompatible layers, followed the rules of différance or the chôra: he made void visible together with its saturation with contradictions. If space can be considered to be the result of the activity of difference, such activity has a certain regularity, which influences the behaviour of its observers. Differences or contradictions fall into a certain rhythm, which can be considered a manifestation of transcendent order. The problem is that what can be considered the source of such order, namely the logos or God, is partly disorder and error. According to descriptions contained in Timaeus, the world is a combination of forces that drive to order with forces of erroneous necessity that resounds in every order and forces it to return to disorder. Derrida denied the possibility of understanding différance as a theological value, even if it were a negative or apophatic theology, but no categorical denial could be perfect. The assumption that différance or the chôra are not endowed with any substance properties cannot deny their activity, and thus a certain force. Already since Democritus, philosophy has multiplied the names of such a force and the contradictory variety of its manifestations, never forgetting also the necessity for reason to withdraw from the possibility of giving its correct characteristics. Such a withdrawal may be interpreted as an expression of respect and, in certain situations, as a cult of the force that precedes reasonableness. The Parc de La Villette, which is an artistic divagation about the contradictions and forces behind them, can be considered as a place of their sublimation, and therefore as a variation of the temple of what differs from order and disorder. IV In the texts that presented the theoretical assumptions of the Parc de La Villette, Tschumi used a large number of terms that contradicted not only the traditional principles of composing architecture, but also negated the rules of social order and the foundations of Western metaphysics. Tschumi’s statements, which are a continuation of his leftist political fascinations from the May 1968 revolution, as well as his interest in the philosophy of French poststructuralism and his collaboration with Derrida, prove that terms such as “disruption”, “dissociation”, “disfunction”, “disjunction” and “dispersion” not only referred to architectural problems but also applied to political criticism and the deepest foundations of thinking itself. His collaboration with Derrida manifested itself primarily in the publication La Case Vide: La Villette 1985, in which the architect’s design drawings and texts explaining his concepts related to the Parc de La Villette were accompanied by an extensive essay by Derrida, which included theoretical problems taken up by Tschumi in a philosophical context. Architectural and philosophical issues were also combined during seven discussion meetings organised by Eisenman, invited by Tschumi to collaborate on the design of the Parc de La Villette. Eisenman, who, like Tschumi, invited Derrida to participate in the design of the park and also led to the publication of Chora L Works: Jacques Derrida and Peter Eisenman, in which his ideas were confronted with Derrida’s philosophical text. In this case, Derrida’s essay was not a direct commentary on the architect’s concepts, but rather a reflection on the question of the chôra presented by Plato in Timaeus. During the discussion and in his essay, Derrida pointed out that the chôra is a component of the created world, yet it does not belong to it, but precedes it. The originality of the chôra is so radical that she also precedes all the factors of creating the world, including ideas and the Demiurge. Thus athesis appeared in the metaphysics of the West that the chôra is a form of active abyss, in relation to which all beings are secondary, both those perfect (as ideas or God) and those created, such as the world, things, people or language. This leads to the conclusion that the chôra does not exist, because all existence is a derivative of the chôra. Nor could the chôra be described, since it is a form of developing a space that is preceded by a lack of space characteristic of the chôra. Derrida intended the chôra to be an instance with an exceptional degree of transcendentalism, an anti-metaphysical instance, but also an a-theological one. However, this attempt failed, both in the field of secular philosophy and in the field of theology. Derrida’s characteristics of the chôra to strengthen its transcendentalism and negation of metaphysics had to be expressed in a language that immediately produces new concepts and a new metaphysics that reproduces the categories of the beginning, the origin or the foundation known from earlier philosophical traditions. All forms of criticism of metaphysics are also inspired by negative, apophatic and mystical theology. The undermining of many concepts of permanent meaning and the introduction of new concepts of unstable meaning, characteristic of the philosophy of deconstruction, had many features of originality, but it was directed towards problems whose solutions repeat, with the use of new vocabulary, the findings known in culture since Democritus. Thus, if apophatic philosophy can be regarded as deconstruction avant la lettre, then deconstruction itself in its late versions began to take on the features of a new religion. The exchange of inspiration between theology and deconstruction was manifested in a series of scientific conferences and publications in which Derrida’s philosophical concepts were interpreted within the scope of religious thought. Theological threads began to be found in such concepts of deconstruction as différance or the chôra, while at the same time Derrida himself undertook in his philosophy to study problems such as the Other (L’Autre) or the Impossible (Impossible), which belonged to newer theological traditions. As a consequence of the new problems, the deconstruction became closer to the features of a new religion. Philosophy, at least from Kant’s time, has tried to create a system that would take over from religion the tasks of setting moral and political goals. Similarly, Derrida has directed his interest towards the problems of democracy and ethics, which would enable their renewal. Attempts to create a new religion (cleared of old metaphors), a new community or a new democracy bring problems and threats which may be no less troublesome than the previous systems. All promises of freedom carry with them threats, the greater the more they strive for perfection. The renewal of existential orders, sometimes carried out by means of violent changes, is a certain repetitive feature of human cultures. Deep changes, however, do not protect against the return of both old gods and old demons. Tschumi and Derrida were shaped in their youth by the atmosphere of leftist rebellion against the moral and political limitations of ossified communities and the imperfections of democracy. The ethical theme distinguishes many of their works, including the Parc de La Villette. The opposition to the metaphysical traditions of philosophy and architecture contained in this park was prompted by specific political situations and resulted from bringing political issues to the level of philosophical considerations. Achievements made at the level of pure concepts were then subject to elevation, to a kind of sacralization, which made them religious concepts. The deconstruction reached for the status of the new religion especially when it found its followers and began to generate moral obligations. In the new situation, terms such as the chôra, l’Autre or the Impossible were absolutized and in relation to them a cult and attitude of adoration emerged. The Parc de La Villtette then gained new post-secular meanings, which allow it to be assigned the function of a Temple of Otherness (L’Autre) and Impossible. V In the traditional sense, a work of art creates an illustration of the outside world, or of a certain text or doctrine. Sometimes it is considered that such an illustration is not literal, but is an interpretation of what is visible, or an interpretation of a certain literary or ideological message. It can also be assumed that a work of art creates its own visual world, a separate story or a separate philosophical statement. Parc de La Villette represents the last of these possibilities: it is a philosophical statement that develops the premises derived from poststructuralist philosophies and the philosophy of deconstruction. The uniqueness of its being status, however, is that it does so not only at the level of the theoretical assumptions, but also through its functioning as an active philosophical work. This means that a park is a happening philosophy. Its activity, however, does not refer only to the present tense, but is also an attempt to penetrate the future, all otherness and impossibility. This kind of activity assumes that the work, in a sense, does not yet fully exist, but is also still produced in the processes of its interpretation. The theoretical foundations of the park included texts by Tschumi, in which he questioned traditional ways of creating a work of architecture, postulating in return the use of a long series of negations, which were comparable to the crisis of metaphysics characteristic of contemporary philosophy. It is therefore no coincidence that the publication containing Tschumi’s theoretical text on Parc de La Villette was accompanied by an essay by Derrida developing some of the architect’s concepts. The next step in integrating philosophy into the process of park design was a series of discussions between Eisenman and Derrida, who completely moved the creation of the park into the world of thoughts, without accentuating the need for their realization in the material reality. The main topic of these discussions was the problem of the chôra, which was taken up by later commentators and used to interpret the park as a work in which the philosophy of the beginning is manifested relating to issues of politics, morality and religion. The park was therefore interpreted as a space of invention within the scope of creating new rules of functioning of the community and democracy. Thinking about the political future may, however, exceed the horizon of ordinary expectations. Although philosophical thought is always connected with contemporary problems and metaphysics sometimes intertwines with current politics, yet at the same time the customs of philosophy also include crossing horizons and thinking about absolute otherness and impossibility. Initially, the chôra, différance, absolute otherness (tout autre) and the Impossible were concepts of pure philosophy of atheistic character, but with the further development of the discussion, more and more theological motifs began to emerge. One of the reasons for this phenomenon was the fact that radical negations of all being, which were contemplated in contemporary philosophy (by Heidegger and Derrida, among others), had previously been manifested in negative and apophatic theologies (by Master Eckhart, among others).Also the category of the “Other”, taken from Emmanuel Levinas, was clearly connected with the thought about God. A further reason for connecting the chôra with the theological thought was the interest in the philosophy of deconstruction expressed by some theologians. John Caputo in particular managed to persuade Derrida to participate in discussions on the current status of religion. In the late period of Derrida’s writing, further statements on religious topics appeared. All these reasons led to posing a question about the identity of the chôra and God. Although there were no satisfactory conclusions on this issue, the discussion was also important to create an interpretation of the park as a place of worship. The chôra, representing, according to Plato, the preoriginal emptiness is the place of every beginning, but it turns out that it is not neutral to the being created in it. The chôra deposits itself in every being as an irremovable beginning that interferes with its stability. The chôra, therefore, forces us into a palintropical movement, but it also turns out to be a pure compulsion, an erring necessity and a fundamental force from which, in the human perception, motifs useful to the individual and to the community are extracted. All definitions of this force, including its anthropomorphisation, are formulated in such a way that they allow for building private and collective morality upon them. Such definitions are changed depending on variable political situations. It is difficult to determine whether in the processes of changes in the formulation of “God’s names” any essential value is retained, which is not subject to change. The current definitions of the chôra (God?), which can be found, for example, in the philosophy of Caputo, stress that she is a combination of various and contradictory forces. This characteristic inherits much of Plato’s concept, reminds us of Master Eckhart’s views on Gottheit and, at the same time, is not unfamiliar to Tschumi, whose essays were an apologia of contradictions. The current concept of chôra, transferred into the sphere of politics, is the praise of social diversity and the protection of the difference from the forces of order. In the Parc de La Villette, the future community and democracy were elevated as a system of safe existence of individuals in all their singularity. The park is a temple of a future community in which individual beings have nothing in common. (shrink)

Amongst the entities making up social reality, are there necessary relations whose necessity is not a mere reflection of the logical connections between corresponding concepts? We distinguish three main groups of answers to this question, associated with Hume and Adolf Reinach at opposite extremes, and with Searle who occupies a position somewhere in the middle. We first set forth Reinach’s views on what he calls ‘material necessities’ in the realm of social entities. We then attempt to show that Searle (...) has not identified a sustainable position somewhere between the Humean and the Reinachian extremes. This is because Searle’s position is threatened by circularity, and to steer clear of that danger it must incorporate at least some elements of Reinach’s essentialism. (shrink)

Suppose one has a system, the infinite set of positive integers, P, and one wants to study the characteristics of a subset (or subsystem) of that system, the infinite subset of odd positives, O, relative to the overall system. In mathematics, this is done by pairing off each odd with a positive, using a function such as O=2P+1. This puts the odds in a one-to-one correspondence with the positives, thereby, showing that the subset of odds and the original set of (...) positives are the same size, or have the same cardinality. This counter-intuitive result ignores the “natural” relationship of one odd for every two positives in the sequence of positive integers, which would suggest that O is one-half the size of P. However, in the set of axioms that constitute mathematics, it is considered valid. Fair enough. In the physical universe (i.e., the starting system), though, relationships between entities matter. In biochemistry, if you start with an organism, say a rat, and you want to study its heart, you can do this by removing some heart cells and studying them in isolation in a cell culture system. But, the results often differ compared to what occurs in the intact animal because studying the isolated cultured cells ignores the relationships in the intact body between the cells, the rest of the heart tissue and the rest of the rat. In chemistry, if a copper atom were studied in isolation, it would never be known that copper atoms in bulk can conduct electricity because the atoms share their electrons. In physics, the relationships between inertial reference frames in relativity, and observer and observed in quantum physics can't be ignored. Relationships matter in the physical world, but the mathematics of infinite sets is still used to describe it. Does this matter? It seems to, at least in physics. Infinities cause numerous problems in theoretical physics such as non-renormalizability and problems in unifying quantum mehanics and general relativity . This suggests that the pairing off method and the mathematics of infinite sets based on it are analogous to a cell culture system or studying a copper atom in isolation if they are used in studying the physical universe because they ignore the inherent relationships between entities. In the real, physical world, the natural, inherent, relationships between entities can't be ignored. Said another way, the set of axioms that constitute abstract mathematics may be similar but not identical to the set of physical axioms by which the real, physical universe runs. This suggests that the results from abstract mathematics about infinities may not apply to or should be modified for use in physics. (shrink)

A non-relativistic quantum mechanical theory is proposed that describes the universe as a continuum of worlds whose mutual interference gives rise to quantum phenomena. A logical framework is introduced to properly deal with propositions about objects in a multiplicity of worlds. In this logical framework, the continuum of worlds is treated in analogy to the continuum of time points; both “time” and “world” are considered as mutually independent modes of existence. The theory combines elements of Bohmian mechanics and (...) of Everett’s many-worlds interpretation; it has a clear ontology and a set of precisely defined postulates from where the predictions of standard quantum mechanics can be derived. Probability as given by the Born rule emerges as a consequence of insufficient knowledge of observers about which world it is that they live in. The theory describes a continuum of worlds rather than a single world or a discrete set of worlds, so it is similar in spirit to many-worlds interpretations based on Everett’s approach, without being actually reducible to these. In particular, there is no splitting of worlds, which is a typical feature of Everett-type theories. Altogether, the theory explains (1) the subjective occurrence of probabilities, (2) their quantitative value as given by the Born rule, and (3) the apparently random “collapse of the wavefunction” caused by the measurement, while still being an objectively deterministic theory. (shrink)

The present first part about the eventual completeness of mathematics (called “Hilbert mathematics”) is concentrated on the Gödel incompleteness (1931) statement: if it is an axiom rather than a theorem inferable from the axioms of (Peano) arithmetic, (ZFC) set theory, and propositional logic, this would pioneer the pathway to Hilbert mathematics. One of the main arguments that it is an axiom consists in the direct contradiction of the axiom of induction in arithmetic and the axiom of infinity in set theory. (...) Thus, the pair of arithmetic and set are to be similar to Euclidean and non-Euclidean geometries distinguishably only by the Fifth postulate now, i.e. after replacing it and its negation correspondingly by the axiom of finiteness (induction) versus that of finiteness being idempotent negations to each other. Indeed, the axiom of choice, as far as it is equivalent to the well-ordering “theorem”, transforms any set in a well-ordering either necessarily finite according to the axiom of induction or also optionally infinite according to the axiom of infinity. So, the Gödel incompleteness statement relies on the logical contradiction of the axiom of induction and the axiom of infinity in the final analysis. Nonetheless, both can be considered as two idempotent versions of the same axiom (analogically to the Fifth postulate) and then unified after logicism and its inherent intensionality since the opposition of finiteness and infinity can be only extensional (i.e., relevant to the elements of any set rather than to the set by itself or its characteristic property being a proposition). So, the pathway for interpreting the Gödel incompleteness statement as an axiom and the originating from that assumption for “Hilbert mathematics” accepting its negation is pioneered. A much wider context relevant to realizing the Gödel incompleteness statement as a metamathematical axiom is consistently built step by step. The horizon of Hilbert mathematics is the proper subject in the third part of the paper, and a reinterpretation of Gödel’s papers (1930; 1931) as an apology of logicism as the only consistent foundations of mathematics is the topic of the next second part. (shrink)

Logics based on weak Kleene algebra (WKA) and related structures have been recently proposed as a tool for reasoning about flaws in computer programs. The key element of this proposal is the presence, in WKA and related structures, of a non-classical truth-value that is “contaminating” in the sense that whenever the value is assigned to a formula ϕ, any complex formula in which ϕ appears is assigned that value as well. Under such interpretations, the contaminating states represent occurrences of a (...) flaw. However, since different programs and machines can interact with (or be nested into) one another, we need to account for different kind of errors, and this calls for an evaluation of systems with multiple contaminating values. In this paper, we make steps toward these evaluation systems by considering two logics, HYB1 and HYB2, whose semantic interpretations account for two contaminating values beside classical values 0 and 1. In particular, we provide two main formal contributions. First, we give a characterization of their relations of (multiple-conclusion) logical consequence—that is, necessary and sufficient conditions for a set Δ of formulas to logically follow from a set Γ of formulas in HYB1 or HYB2 . Second, we provide sound and complete sequent calculi for the two logics. (shrink)

Peter Godfrey-Smith writes in the section 3.3 “The Ravens Problem” of his book “Theory and Reality” [chapter “Induction and Confirmation”]: “First, the logical empiricists were concerned to deal with the case where generalizations cover an infinite number of instances. In that case, as we see each raven we are not reducing the number of ways in which the hypothesis might fail”. Infinite sets and finite sets have different properties and follow different rules. For example: let’s call “bag X” a specific (...) bag that contains 90 marbles; the generalization A “All marbles in bag X are red” covers a finite number of instances. By contrast, the generalization AE “All things that are not red are not marbles in bag X” covers an infinite number of instances. The propositions A and AE are logically equivalent, but there is an asymmetry due to the fact that A can only have a finite number of instances (since the set of the marbles contained in bag X is a finite set). Because of the aforementioned asymmetry, even though A and AE are logically equivalent propositions, it is wrong to equate an instance of A with an instance of AE. Another example involving a finite set: let’s call “barrique X” a certain 205-liter (54.1553 US gal) barrique. In the following generalization, the expression "all minerals" should not be understood as "all types of minerals", but should be understood literally as "all minerals". B “All minerals are in barrique X”. BE “All objects that are not in barrique X are not minerals”. Of course, a 205-litre barrique cannot contain an infinite number of minerals; the set of objects contained in barrique X is a finite set: therefore in the generalization B we refer to a set that is assumed to be an infinite set (the set of minerals) and to a set (the finite set of minerals contained in barrique X) that is not assumed to be an infinite set. By contrast, in the generalization BE we refer to two sets that are assumed to be infinite sets (the set of all objects that are not contained in barrique X and the set of all objects that are not minerals). Therefore, although B and BE are logically equivalent propositions, an instance of BE cannot be equivalent to an instance of B. Now, let’s analyze the following generalizations. C “All the elements of the set of ravens are elements of the set of black ravens”. CE “All the things that are not elements of the set of black ravens are not elements of the set of ravens”. It is assumed that the number of ravens is infinite, but it is not assumed that the number of black ravens is infinite: that the number of black ravens is infinite is only a hypothesis (for which confirmation is sought), it cannot be assumed as true that the number of black ravens is infinite. Therefore, in the generalization C we refer to a set that is assumed to be an infinite set (the set of ravens) and to a set (the set of black ravens) that is not assumed to be an infinite set. By contrast, in the generalization CE we refer to two sets that are assumed to be infinite sets (the set of all objects that are not elements of the set of black ravens and the set of all objects that are not elements of the set of ravens). Someone could argue that in the generalizations C “All the elements of the set of ravens are elements of the set of black ravens” and CE “All the things that are not elements of the set of black ravens are not elements of the set of ravens” only the set of ravens is assumed to be infinite: but even in this case an asymmetry would remain because C “ All the elements of the set of ravens are elements of the set of black ravens” refers to a set (the set of ravens) that is assumed to be an infinite set and to a set (the set of black ravens) that is not assumed to be infinite; by contrast, CE “All the things that are not elements of the set of black ravens are not elements of the set of ravens” in this case would refer to two sets that are not assumed to be infinite sets. Because of the aforementioned asymmetries, an instance of C cannot be equivalent to an instance of CE. -/- -/- . (shrink)

Abstract: Fruits are a rich source of energy, minerals and vitamins. They also contain fiber. There are many fruits types such as: Apple and pears, Citrus, Stone fruit, Tropical and exotic, Berries, Melons, Tomatoes and avocado. Classification of fruits can be used in many applications, whether industrial or in agriculture or services, for example, it can help the cashier in the hyper mall to determine the price and type of fruit and also may help some people to determining whether a (...) certain type of fruit meets their nutritional requirement. In this paper, machine learning based approach is presented for classifying and identifying 10 different fruit with a dataset that contains 6847 images use 4793 images for training, 1027 images for validation and 1027 images for testing. A deep learning technique that extensively applied to image recognition was used. We used 70% from image for training and 15% from image for validation 15% for testing. Our trained model achieved an accuracy of 100% on a held-out test set, demonstrating the feasibility of this approach. (shrink)

This article seeks to justify the claim that Thomas Aquinas proposed a concept of natural law which is immune to the argument against the recognition of an objective grounding of the good formulated by a well-known representative of the liberal tradition, Isaiah Berlin, in his famous essay “Two Concepts of Freedom.” I argue that Aquinas’s concept of freedom takes into account the very same values and goals that Berlin set out to defend when he composed his critique of natural (...) law. In particular, the article suggests that Aquinas recognizes freedom as a greater perfection of man than rationality, and that this freedom is realized, among other things, through the co-construction of the good that gives a goal and a shape to human action and to the whole of a person’s life. I argue that the co-construction of such a good involves the co-construction of natural law in the strict sense of the term. Indeed, the content of natural law can be understood as a set of goods which are goals that inform human action. From a human perspective, natural law is not a pre-existing recipe which has merely to be “read.” Defining the concrete content of natural law is an ongoing process. The process of defining natural law’s content takes humanly knowable, objective elements into account, and so draws on knowledge. Yet free choice also plays an important part in this process. When speaking of the process of defining the content of natural law, therefore, and in determining what here-and-now is to be done, it is reasonable to describe man as a creator of the natural law, or as a legislator, just as the members of a parliament are the creators of civil law — bearing in mind that only a just law is truly law and therefore the creation of both civil and natural law reaches only as far is the scope of just actions directed by these laws. From the perspective of human action, we may speak of each person’s free choice to establish a given good as the end of a specific act, and in so doing to declare that action proper under natural law in the strict sense of the term (which differs from the rules of natural law). An appreciation of what is particular and individual (particulare et individuum), and an appreciation of free choice that goes hand-in-hand with this, is deeply embedded in Thomas’s system of thought. Particularity and individuality has its basis in an especially excellent way of human existence. (shrink)

Autonomous and automatic weapons would be fire and forget: you activate them, and they decide who, when and how to kill; or they kill at a later time a target you’ve selected earlier. Some argue that this sort of killing is always wrong. If killing is to be done, it should be done only under direct human control. (E.g., Mary Ellen O’Connell, Peter Asaro, Christof Heyns.) I argue that there are surprisingly many kinds of situation where this is false (...) and where the use of Automated Weapons Systems would in fact be morally required. These include cases where a) once one has activated a weapon expected then to behave lethally, it would be appropriate to let it continue because this is part of a plan whose goodness one was best positioned to evaluate before activating the weapon; b) one expects better long-term consequences from allowing it to continue; c) allowing it to continue would express a decision you made to be resolute, a decision that could not have advantaged you had it not been true that you would carry through with it; d) the weapon is mechanically not recallable, so that, to not allow it to carry through, you would have had to refrain from activating it in the first place, something you expected would have disastrous consequences; e) you must deputize necessary killings to autonomous machines in order to protect yourself from guilt you shouldn’t have to bear; f) it would be morally better for the burden of responsibility for the killing to be shared among several agents, and the agents deputizing killing to machines can do this, especially where it’s not predictable which machine will be successful; g) a killing would be morally better done with elements of randomness and lack of deliberation, and a (relatively stupid) machine could do this where a person could not; h) the machine would be acting as a Doomsday Device, so that it could not have had its hoped for deterrent effect had you not ensured that you would be unable to recall it if enemy action activated it; i) letting it carry through is a necessary part of its own learning process, and you expect that this learning will have salutary effects later on; j) human intervention in the machine’s operation would disastrously impair its precision, or its speed and efficiency; k) using non-automated methods would require human resources you just don’t have in a task that nevertheless must be done (e.g., using land-mines to protect remote installations); l) the weapon has such horrible and indiscriminate power that it is doubtful whether it could be actually used in ways compatible with International Humanitarian Law and the Laws of War, which require that weapons be used only in ways respecting distinctness, necessity and proportionality, but its threat of use could respect these principles in affording deterrence provided human error cannot lead to their accidental deployment, this requiring that they be controlled by carefully designed autonomous and automatic systems. I then consider objections based on conceptions of human dignity and find that very often dignity too is best served by autonomous machine killing. Examples include saving your village by activating a robot to kill invading enemies who would inflict great indignity on your village, using a suicide robot to save yourself from a less dignified death at enemy hands, using a robotic drone to kill someone otherwise not accessible in order to restore dignity to someone this person killed and to his family, and using a robot to kill someone who needs killing, but the killing of whom by a human executioner would soil the executioner’s dignity. I conclude that what matters in rightful killing isn’t necessarily that it be under the direct control of a human, but that it be under the control of morality; and that could sometimes require use of an autonomous or automated device. (This paper was formerly called "Fire and Forget: A Defense of the Use of Autonomous Weapons in War" on Philpapers; the current title is the title of the published version.). (shrink)

Buddhist philosophers have investigated the techniques and methodologies of debate and argumentation which are important aspects of Buddhist intellectual life. This was particularly the case in India, where Buddhism and Buddhist philosophy originated. But these investigations have also engaged philosophers in China, Japan, Korea and Tibet, and many other parts of the world that have been influenced by Buddhism and Buddhist philosophy. Several elements of the Buddhist tradition of philosophy are thought to be part of this investigation. -/- There (...) are interesting reasoning patterns discernible in the writings of Buddhist philosophers. For instance, the Mādhyamika philosopher Nāgārjuna presents arguments for the emptiness of all things in terms of catuṣkoṭi (four ‘corners’: roughly speaking, truth, false, both, neither). There are also the Indian vāda (debate) literature and Tibetan bsdus grwa (collected topics) that list techniques of debates. -/- The main interest here is the tradition of Buddhist philosophy, sometimes referred to as Pramāṇavāda, whose central figures are Dignāga (approx. 480–540 CE) and Dharmakīrti (6th– 7th CE). This philosophy is understood to be the Buddhist school of logic-epistemology. ‘Pramāṇavāda’ is not a doxographical term traditionally used to refer to a recognised school of Buddhist philosophy. It is a conventional term that is sometimes used in modern literature. Nevertheless, in what follows, we think of it as a tradition within Buddhist philosophy and ‘Buddhist logic’ refers to what is developed in this tradition. -/- Buddhist logicians have systematically analysed the kind of reasoning involved in acquiring knowledge. They hold that there are valid ways to reason that are productive of knowledge. In what follows, some of the main elements of their analyses will be described. Note, however, that, while exegetical studies of Buddhist texts are important, we must step back from them and consider what is involved in taking a Buddhist approach to logic in light of modern formal logic. This analysis will be done against the backdrop of the contemporary literature on logic and related subjects in contemporary philosophy to make sense of the logical studies by Buddhist logicians. (shrink)