The discussion of the Principle of Non-Contradiction (PNC) in Aristotle’s Metaphysics Γ is usually taken to include three ‘versions’ of the principle: an ontological, psychological, and logical one. In this article I develop an interpretation of Metaphysics Γ3 and a parallel text, De interpretatione 14, in order to show that these texts are concerned with two related but different principles: a version of the Principle of Identity, and a corollary to this, which concerns the ability to accept (...) two ‘opposite’ items at the same time. I argue that these principles must be considered separately in order to properly understand Aristotle’s remarks about PNC in Metaphysics Γ, and in order to defend his approach in these remarks against certain objections raised against the discussion in Metaphysics Γ by Jan Łukasiewicz in his "Über den Satz des Widerspruchs bei Aristoteles". The main result of my interpretation is to distinguish in the discussion of PNC in Metaphysics Γ three principles: one concerning linguistic items (words and statements), one concerning thoughts (δόξαι), and one concerning objects or states of affairs. (shrink)

Some forms of defining PNC in Aristotle’s works are as follows: a) Everything must be either affirmed or denied (φάναι ἢ ἀποφάναι). (Met., B, 996b28-29) or: it will not be possible to assert and deny the same thing truly at the same time. (Met., Γ, 1008a36-b1) In other words, ‘contradictory statements (ἀντικειμένας φάσεις) are not at the same time true. (Met., Γ, 1011b13-14) Also, ‘It is impossible that contradictories (ἀντίφασιν) should be at the same time true of the same thing.’ (...) (Met., Γ, 1011b15-16) Also, ‘Opposite statements (ἀντικειμένας φάσεις) can never be true of the same subjects.’ (Met., K, 1062a33-34; 1063b15-17) Also, ‘Of all affirmation or negation one is impossible. (PsA., A, 11, 77a22) b) A thing cannot at the same time be and not be. (Met., B, 996b30-31; Γ, 1006a3-5) This can also be extended to many other similar pairs of opposites: ‘The same thing cannot at the same time be and not be, or admit any other similar pair of opposites.’ (Met., K, 1061b34-1062a2) Also, ‘It will be possible for the same thing to be and not to be, except in virtue of an ambiguity.’ (Met., Γ, 1006b18-19) This is also asserted in another similar way: it is impossible that it should be at the same time true to say the same thing is a thing and is not a thing.’ (Met., Γ, 1006b33-34) c) ‘The same attribute cannot at the same time belong (ὑπάρχειν) and not belong to the same object in the same respect.’ (Met., Γ, 1005b19-21) d) Those positive and negative propositions are said to be contradictory which have the same subject and predicate. (OI, I, 7, 17a33-35) The opposition between an affirmation and a denial makes contradictories (ἀντίφασεως). (PsA., A, 2, 72a11-14) Based on Aristotle’s definition, ‘An affirmation is opposed to a denial in the sense which I denote by the term ‘contradictory’ (ἀντίφατικως), when, while the subject remains the same, the affirmation is of universal character and the denial is not.’ (OI., I, 7, 17b16-19) 1) Characteristics of PNC a) It is the most certain (Met., Γ, 1005b22-23 and b11) and the most indisputable (Met., Γ, 1006a5-6) of all principles. b) It is impossible: to believe its contrary (Met., Γ, 1005b24-30); to be really in that position (Met., Γ, 1008b11-13); and to defend it. (OI, I, 9, 18b17-19) Nonetheless, Aristotle thinks that many of the writers about nature assert the contrary of PNC and use a language opposite to it. (Met., Γ, 1005b35-1006a3) c) It is the starting point of all the other axioms. (Met., Γ, 1005b32-34) d) It is not hypothetical. (Met., Γ, 1005b13-17) e) Contradictories are extremely opposed to each other. (Met., Γ, 1007a1-4) f) Believing in PNC saves substance and essence and not believing in it makes all attributes accidents and there will be nothing as being essentially something. The reason is that something which essentially is a being cannot avoid being that thing. (Met., Γ, 1007a20-29 and b16-18) g) PNC supports plurality of things because otherwise all things will be one: ‘If all contradictories are true of the same subject at the same time, evidently all things will be one. For the same thing will be a trireme, a wall, and a man, if it is equally possible to affirm and deny anything of anything.’ (Met., Γ, 1007b18-22) In fact, PNC supports difference: ‘For if contradictories can be predicated alike of each subject, one thing will in no wise differ from another; for if it differs, this difference will be something true and peculiar to it.’ (Met., Γ, 1008a25-27) h) To accept truth and falsity, whether in an absolute sense (e.g. A is more true than B; or C is less true than D) entails PNC. (Met., Γ, 1008b2-7 and b31-35; 1009a2-5) In fact, PNC is entailed by accepting true affirmation. (Met., K, 1062b7-11) i) Judging and choosing between at least two things entails PNC: you cannot choose one as better than another without a previous judging that one is A and the other not A. (Met., Γ, 1008b18-24) The same is true about avoiding. (Met., Γ, 1008b24-29) j) PNC guarantees speaking and saying anything intelligible because otherwise e.g. saying ‘yes’ means both yes and no. (Met., Γ, 1008b7-13) k) Contradictories do not accept intermediates that means we must either affirm or deny a predicate on a subject and there is no third option. (Met., Γ, 1011b23-24; Met., I, 1055b1-2; PsA., A, 2, 72a11-14; Met., I, 1057a33-36) l) PNC is applicable also to the future time. (OI., I, 9, 19a28-29) m) PNC is presupposed by the least semantic of words. If we accept that each word has a meaning and, thus, signifies something definite, we cannot accept that it has the contradictory meaning and signies contradictory things and this approves PNC. Thus, Aristotle asks the opponent of PNC to say just one word, a significant word and takes this as the demonstration of PNC because by saying the word e.g. ‘man’ you have already signified man and not-man. (Met., Γ, 1005a11-13 and a18-22; 1006a28-31 and b13-15) Therefore, signification entails PNC: ‘He, then, who says this is and is not denies what he affirms, so that what the word signifies, he says it does not signify; and this is impossible. Therefore, if ‘This is’ signifies something, one cannot truly assert the contradictory.’ (Met., K, 1062a16-20) He says again: ‘If the word signifies something and this can be truly asserted of it, it necessarily is this; and it is not possible that that which is necessary should ever not be: it is not possible therefore to make the opposed assertions truly of the same subject.’ (Met., K, 1062a20-23; cf. Met., K, 1062a24-31) n) At Met., 4, 3, 1005b9-10 (check???) PNC is called as principle of things (ἀρχὰς τοῦ πράγματος). (quoted from B215, 517) . (shrink)

Arthur Kaufmann is one of the most prominent figures among the contemporary philosophers of law in German speaking countries. For many years he was a director of the Institute of Philosophy of Law and Computer Sciences for Law at the University in Munich. Presently, he is a retired professor of this university. Rare in the contemporary legal thought, Arthur Kaufmann's philosophy of law is one with the highest ambitions — it aspires to pinpoint the ultimate foundations of law by explicitly (...) proposing an ontology, a general theory of knowledge and concept of a person. Kaufmann's work derives, first of all, from the thinking of Gustav Radburch, his teacher, and then from ideas of Karl Engish and Hans-Georg Gadamer. The philosophy undertakes to pursue the ultimate foundation of law, law which is understood by Kaufmann, first of all, as a "concrete judgement" that is, what is right in a concrete situation. Justice belongs to the essence of law and "unjust law" is contradictio in adiectio. Kaufmann opposes all those theories, which as the only foundation for establishing just law (Recht) adopt legal norms (Gesetz). In Kaufmann's opinion , such theories are powerless in the face of all types of distortions of law rendered by political forces. He suggests that the basic phenomenon which needs to be explained and which cannot be disregarded by a philosopher of law is so-called "legal lawlessness" ("Gestzliches Unrecht"). "Legal lawlessness" which forms a part of life experience for the people of twentieth century totalitarian states. It proved "with the accuracy of scientific experiment" that the reality of law consists of something more than bare conformity with legal norms. The existence of lex corrupta indicates that law contains something "non-dispositive" which requires acknowledgment of both law-maker and judge. Kaufmann, accepting the convergent concept of truth and cognition, assumes that "non-dispositive" content, emerging as the conformity of a number of cognitive acts of different subjects (inter-subjective communicativeness and verifiability), indicates the presence of being in this cognition. The questions "What is law?" and "What are the principles of a just solution?" lead straight to the ontology of law, to the question about the ontological foundations of law. Kaufmann discerns the ontological foundations of law in the specifically understood "nature of things" and, ultimately, in a "person". He proposes a procedural theory of justice, founded on a "person". In my work, I undertake to reconstruct the train of thought which led Kaufmann to the recognition of a "person" as the ontological foundation of law. In the first part, the conception of philosophy adopted by Kaufmann, initial characteristics of law — of reality which is the subject of analysis, as well as, the requirements for proper philosophical explanation of law posed by Kaufmann are introduced. In the second, Kaufmann's reconstruction of the process of the realisation of law is presented. Next, the conception of analogy which Kaufmann uses when explaining law is analyzed. In the fourth part, Kaufmann's conception of ontological foundations of law is discussed. A critical analysis is carried out in which I demonstrate that the theory of the ontological foundation of law proposed by Kaufmann and the concept of a person included in it do not allow a satisfac¬tory explanation of the phenomenon of "legal lawlessness" and lead to a number of difficulties in the philosophical explanation of law. Finally, the perspectives of a proper formulation of the issue of the ontological foundations of law are drafted in the context of the analyzed theory. My interest is centered on the conception of philosophy adopted by Kaufmann, according to which the existence of the reality is inferred on the basis of a certain configuration of the content of consciousness, whereas at the point of departure of philosophy of law, the data to be explained is a certain process, which is, basically, a process of cognition, while the reality appears only as a condition for the possibility of the occurrence of the process. I wish to argue that the difficulties which appear in the explanation of law are a consequence of the assumed fundamental philosophical solu¬tions, which seem to be characteristic, though usually not assumed explicitly, in philoso¬phy and theory of law dominant at present in continental Europe. Thereby, I wish to show the significance of ontological and epistemological solutions to the possibility of a proper formulation of the problems posed by philosophy and theory of law. Kaufmann proclaims himself in favour of a philosophy which poses questions about the ultimate foundations of understanding of the reality. In epistemology, he assumes that answers to the questions "What is reality like?" and ultimately "What is real?" are inferred on the basis of uniformity of a cognitive acts of different subjects. Cognition of the reality is accomplished exclusively through the content of conceptual material. The two fundamental questions posed by philosophy of law are "What is just law?" and "How is the just law enacted?" The latter is a question about the process of achieving a solution to a concrete case. Since, in Kaufmann's opinion, law does not exist apart from the process of its realisation, an answer to the question about the manner of realisation of law is of fundamental significance to answering the question: "What is law?" and to the explanation of the question about the ontological grounding of law, which is, as well, the foundation of justice. The proper solution has to take into account the moment of "non-dispositive" content of law; its positiveness understood as the reality and, at the same time, it has to point to the principles of the historical transformation of the content. Law, in the primary meaning of the word, always pertains, in Kaufmann's opinion, to a concrete case. A legal norm is solely the "possibility" of law and the entirely real law is ipsa res iusta, that which is just in a given situation. Determination of what is just takes place in a certain type of process performed by a judge (or by man confronted with a choice). Kaufmann aims to reconstruct this process. A question about the ontological foundation of law is a question about the ontological foundations of this process. In the analyzed theory it is formulated as a question about the transcendental conditions, necessary for the possibility of the occurrence of the process: how the reality should be thought to make possible the reconstructed process of the realisation of law. Kaufmann rejects the model for finding a concrete solution based on simple subsump¬tion and proposes a model in which concrete law ensues, based on inference by analogy, through the process of "bringing to conformity" that which is normative with that which is factual. Kaufmann distinguishes three levels in the process of the realisation of law. On the highest level, there are the fundamental legal principles, on the second legal norms, on the third — concrete solutions. The fundamental principles of law are general inasmuch as they cannot be "applied" directly to concrete conditions of life, however, they play an important part in establishing norms. A judge encounters a concrete situation and a system of legal norms. A life situation and norms are situated on inherently different levels of factuality and normativeness. In order to acquire a definite law both a norm (system of norms) and a life situation (Lebenssachverhalt) should undergo a kind of "treatment" which would allow a mutual conformity to be brought to them. Legal norms and definite conditions of life come together in the process of analogical inference in which the "factual state" ("Tatbestand") — which represents a norm, and in the "state of things" ("Sachverhalt") — which represents a specific situation are constructed. A "factual state" is a sense interpreted from a norm with respect to specific conditions of life. The "state of things" is a sense constructed on the basis of concrete conditions of life with respect to norms (system of norms). Legal norms and concrete conditions of life meet in one common sense established during the process of realisation of law. Mutatis mutandis the same refers to the process of composition of legal norms: as the acquisition of concrete law consists in a mutual "synchronization" of norms and concrete conditions of life, so acquisition of legal norms consists of bringing to conformity fundamental principles and possible conditions of life. According to Kaufmann, both of these processes are based on inference through analogy. As this inference is the heart of these processes it is simultaneously a foundation finding just law and justice. How does Kaufmann understand such an inference? As the basis for all justice he assumes a specifically interpreted distributive justice grounded on proportionality. Equality of relations is required between life conditions and their normative qualification. Concrete conditions of life are ascribed normative qualification not through simple application of a general norm. More likely, when we look for a solution we go from one concrete normative qualified case to another, through already known "applications" of norms to a new "application". The relation between life conditions and their normative qualifica¬tion has to be proportional to other, earlier or possible (thought of) assignments of that which is factual to that which is normative. Law as a whole does not consist of a set of norms, but only of a unity of relations. Since law is a, based on proportion, relative unity of a norm and conditions of life, in order to explain law in philosophical manner, the question about ontological base of this unity has to be asked. What is it that makes the relation between a norm and conditions of life "non-dispositive"? What is the basis for such an interpretation of a norm and case which makes it possible to bring a norm and conditions of life into mutual "conformity"? This is a question about a third thing (next to norms and conditions of life), with respect to which the relative identity between a norm and conditions of life occurs, about the intermediary between that which is normative and that which is factual and which provides for the process of establishing of norms, as well as, finding solutions. It is the "sense" in which the idea of law or legal norm and conditions of life have to be identical to be brought to mutual "conformity". In Kaufmann's opinion such a sense is nothing else but the "nature of things" which determines the normative qualification of the reality. Since establishment of this "sense" appears to be "non-dispositive" and controlled inter-subjectively (namely, other subjects will reach a similar result) so, in conformity with the convergent concept of truth, the "nature of things" must be assigned a certain ontological status. According to Kaufmann this is a real relation which occurs between being and obligation, between the conditions of life and normative quality. However, it should be underlined that from the point of view of the analyzed system the "nature of things" is a correlate of constructed sense, a result of a construction which is based on the principle of consistent understanding of senses ("non-normative" and "normative") and is not a reality which is transcendent against the arrangement of senses. In Kaufmann's theory, inference from analogy appears to be a process of reshaping the concepts (senses) governed by tendency to understand the contents appearing in relations between that which is factual and that which is normative in a consistent way. The analogical structure of language (concepts) and recognition of being as composed of an essence and existence is an indispensable requirement for the possibility of the realisation of law, based on specifically understood inference from analogy. It is necessary to assume a moment of existence without content which ensures unity of cognition. Existence emerges thus as a condition of the possibility of cognition. According to Kaufmann, the "nature of things" is the heart of inference through analogy and the basis for establishment of finding of law. Inference from the "state of things" to a norm or from a norm to the "state of things" always means inference through the "nature of things". The "nature of things" is the proper medium of objective legal sense sought in every cognition of law. In Kaufmann's view, the question whether the "nature of things" is ultima ratio of interpretation of law or is only a means of supplement gaps in law or whether it is one of the sources of law, is posed wrongly. The "nature of things" serves neither to supplement the gaps nor is it a source of law as, for example, a legal norm may be. It is a certain kind of "catalyst" necessary in every act of making law and solving a concrete case. Owing to "nature of things" it is possible to bring to a mutual conformity the idea of law and possible conditions of life or legal norms and concrete conditions of life. In Kaufmann's conception the "nature of things" is not yet the ultimate basis for understanding the "non-dispositiveness" of law. The relation between obligation and being is determined in the process of the realisation of law. Both the process itself and that which is transformed in this process are given. A question about the ontological bases of "material" contents undergoing "treatment" in the process of the realisation of law and about being which is the basis of regularity of the occurrence of the process arises. Only this will allow an explanation that the result of the process is not optional. Thus, a question about reality to which law refers and about the subject realising the law has to be formed. To this, Kaufmann gives the following answer: that which is missing is man but not "empirical man" but man as a "person". A "person" understood as a set of relations between man and other people and things. A "person" is the intermediary between those things which are different — norm and case are brought to conformity. A "person" is that which is given and permanent in the process of the realisation of law. It determines the content of law, is "subject" of law; this aspect is described by Kaufmann as the "what" of the process of realisation of law. A "person" consists of precisely just these relations which undergo "treatment" in the process. On the other hand, a "person" is "a place" in which the processes of realisation of law occur, it is the "how" of normative discourse, a "person" is that which determines the procedure of the process, being "outside" of it. This aspect of a "person" is connected with the formal moment of law. A "person" being, at the same time, the "how" and the "what" of the process of the realisation of law, is also, to put it differently, a structural unity of relation and that which constitutes this relation (unity of relatio and relata). According to this approach a "person" is neither an object nor a subject. It exists only "in between". It is not substance. Law is the relation between being and obligation. That which is obligatory is connected with that which is general. That which is general does not exist on its own, it is not completely real. Accordingly, a "person" as such is also not real. It is relational, dynamic and historical. A "person" is not a state but an event. In Kaufmann's opinion, such a concept of a "person" helps to avoid the difficulties connected with the fungibility of law in classical legal positivism. A "person" is that which is given, which is not at free disposal and secures the moment of "non-dispositiveness" of law. Kaufmann concludes: "The idea (»nature«) of law is either the idea of a personal man or is nothing". Theory points at the structure of realising law and explains the process of adoption of general legal norms for a concrete situation. The analysis has shown however, that in this theory a satisfactory answer to the question about the ultimate foundations of law is not given. It seems that in the analyzed theory the understanding of human being takes place through understanding of law. What is good for man as a "person", what is just, what a "person" deserves may be determined only against the existing system of law. A "per¬son" adopted as a basis of law is the reality postulated in the analysis of the process of the realisation of law. It is a condition of possibility of this process ( explaining, on one hand, its unity and, on the other hand, the non-dispositive moments stated in this process). A "person" in the discussed theory is entirely defined by the structure of law, it can be nothing more than that which is given in law, what law refers to, what law is about. Being, which is a "person", is constituted by relations between people and objects, the relations which are based on fundamental links between norms and conditions of life established in a process of bringing them to conformity. It has to be assumed that man as a "person" is a subject of law only as far as realising law "treats" given senses according to their current configuration. The system of law is a starting point and it describes in content what man is as a "person". Moreover, being a "person" is the condition for entering legal relations. Consistently, Kaufmann writes that "empirical man" is not the subject of law, man is not "out of nature" a "person". People become "persons" due to the fact that they acknowledge each other as "persons" — acknowledging, at the same time, law. This acknowledgement is a con¬dition of existence, of the possibility of the occurrence of process of realisation of law and of constituting legal relations which ultimately constitute a "person". Kaufmann assumes, that law tends towards a moral aim: it may and must create an external freedom, without which the internal freedom to fulfil moral obligations cannot develop. However, this postulate is not based on the necessary structure of human being. From the point of view of his system, it is nothing more than only a condition for the possibility of the occurrence of the process of the realisation of law — lack of freedom would destroy the "how" of this process. Thus, the postulate to protect the freedom of personal acts has to be interpreted, in accordance with the analyzed theory, as a postulate, the fulfilment of which aims ultimately at the accomplishment of the very same process of realisation of law itself and not the realisation of a given man. Kaufmann considers a "person" to be an element which unites the system of law as a whole. Law is a structure of relations, which are interdependent and inter-contingent. Consequently, a "person" which is to form the ontological basis of law has to be entity consisting of all relations. Being also the "how" of the process of realisation of law, if a "person" is to warrant its unity, it has to be a common source for all procedures. Hence, a single "person" would constitute a subject of law. Man appears to be only a moment of a certain entirety, realisation of which should be an aim of his actions. Law, creating a "person" as an object and subject of law becomes a primary entity. In the analyzed theory, the basis for determination of aims which law sets to man is not the allocation of man-subject to something which improves him but rather, such relation is only just constituted by law. A question appears, why should aims set in law also be the aims of "empirical man"? Why is this "empirical man" to be punished in the name of a "person" understood in such a way? If, however, it is assumed that what is man is determined by a system which is superior to him, then man has to be understood only as a part of a whole and there are no grounds to prohibit istrumental treatment of man and so the road to all aspects of totalitarianism might be opened. A problem of the application of created theory to the reality arises, the reality which the theory pretends to explain. Ultimately in his theory Kaufmann does not give any systemic grounds for a radical questioning of the validity of any legal norms. Every new norm becomes an equal part of system of norms. It is only its interpretation and application to given conditions of life that may be disputable, however, this refers to all norms without exception. Cohesive inter-pretation of norms and applications is necessary and sufficient for the acquisition of just law. New norms have to be interpreted in the light of others, correspondingly, the other norms require reinterpretation in the light of the new ones. Contradiction in interpretation of a norm does not form a basis for questioning norms but may serve only to question the manner of their interpretation (understanding). Therefore, no grounds exist to assume any legal norm as criminal or unjust, and in consequence, to question any consistently realised system based on formally, properly established norms, as "legal lawlessness". As law and a "person" do not exist without the process of realisation of law, the role of legal safety becomes crucial as the condition for the possibility of the occurrence of the process of realisation of law. Denying legal safety would be tantamount to negation of law in general (also of moral law) as negation of safety takes away, at the same time, the basis for occurrence of the process of realisation of law. Moreover, any lack of legal safety would also mean lack of a basis for the existence of man as a "person". Kaufmann's thesis, that civil disobedience is legalized only when it has a chance to lead to success, consistent with his concept of the foundations of law, seems to point directly to conclusions which deny the facts taken under consideration and doubtlessly Kaufmann's own intentions, since it would have to be assumed that accordingly there are no grounds to question a legal system in force based on violence which secures its operation. Force finally seems to determine which one of the mutually irreconcilable normative systems constitute law and which does not. A legitimate position is one which leads to success, it is the weaker system which is negated. If so, then basically violent imposition of law is not an act directed against the law in force but, to the contrary, realisation of law. In the context of the new system the former system of law may be talked about as unjust solely in the sense of being incapable of being consistently united with the new. However, at the base, ultimately, lies force which reaffirms differences and excludes from the process of realisation of law certain norms and their interpretations. Kaufmann was aiming at grounding of that which is "non-dispositive" in a certain given framework of interpretation. Nevertheless, he does not provide foundations for the understanding of phenomena, which he undertakes to explain at a point of departure. Instead of explaining them the theory negates the possibility of their existence. The reality postulated in regard to "non-dispositive" moments of the reconstructed process of acquiring law consist of a specifically understood "person", which appears in Kaufmann's conceptions as a condition of the possibility of the realisation of law. According to this approach understanding of a "person" may be only a function of law. To understand "legal lawlessness" and foundations of justice it is necessary to look for such theory of law in which understanding of man as a "person" and being is not a function of understanding of law (in which a "person" is not only a condition for possibility of reconstructed process of realisation of law; for possibility of cognition processes). It seems necessary to start from theory of being and a "person" based on broader experience than the one assumed by Kaufmann and reconstruct the ontological foundations of the process of realisation of law only in such perspective. Kaufmann points out that that to which law refers is ipsa res iusta a concrete relation of man to other people and things. This relation, in his theory, appears to be basically only just constituted by law (normative senses "applied" to conditions of life). Therefore, understanding the relation between a given man and other people and things which constitute the aim of his actions, that is understanding of good, is enacted against the background of constitution of senses; constitution which is a result of a process aiming towards consistent understanding of particular contents (of nor¬mative and non-normative senses). "Being" is secondary towards constructed senses it is only their correlate. The primary relation consists of relation of a man to law (system of norms), while the secondary relation is one of man to something which is the aim of his action (relation between man and good). Considering such approach it is difficult to envision a satisfying answer to the fundamental question: why does law put concrete man under any obligation to obey it? The source of this problem can be seen in reduction of the base for understanding good to content of obligation formulated in auto-reflection. Such reduction seems to be a consequence of Kaufmann's adoption of "convergent concept of truth" and in con¬sequence his recognition of indirect, essentialistic grasp of reality formulated in concepts as the basic and only foundation of theory of being and of law. In view of such an approach, analogy of law, concepts and being is the condition for the possibility of the process of transformation of senses which aims at consistent interpretation of all law. Existence is postulated with respect to the possibility of unity of experience and cognition. However, also a different approach to understanding of the problem of being and good is possible. In spontaneous cognition being is affirmed, first of all, not as a certain, non-contradictory, determined content, but as something existing. Together with a cer¬tain content (passed indirectly through notions) existence of being is co-given. The basis for unity of being is not formed by the consistence of content, as it is in the case of the theories departing from the analysis of cognition processes, but by an act of existence realising content (essence). Such an approach makes it also possible to go beyond the convergent concept of truth. It is worth mentioning that allocation of an agent to good is realised not only by the content of duty. A statement that something is good is primary with respect to determination of this good in content. The recognised good always bears some content, however, there are no reasons to base the concept of good exclusively on indirect, formulated in concepts cognition. As primary, can be adopted the relation of man to good and not of man to law. Determination in content appears to be only an articulation of aspectual cognition of being, as an object of action. In such a case the basis for relative unity of norm and conditions of life is not the "nature of things" understood as correlate of sense but it is relation to good based on internal constitution of man as potential, not self-sufficient being. It does not mean, that the moments of the process of realisation of law singled out by Kaufmann are not important to determination of what is just. He, quite rightly, points to significant role played by norms in the evaluation of concrete situations, in man's search for closer specification in content of good innate to him. The structure of process of determining law for a concrete situation, to a great degree corresponds to the processes of determining law which take place not only in the legal sciences. Kaufmann's analyses of the process of realisation of law show the complexity of the structure of these processes and point towards important moments allowing a better understanding of law and man. Nevertheless, these analyses cannot be a basis for construction of philosophical theory of law, theory which hopes to point out the ultimate, ontological foundations for understanding law. Kaufmann's results may become fully valid only in a more general perspective including broader experience at the point of departure. (shrink)

The goals of this paper are two-fold: I wish to clarify the Aristotelian conception of the law of non-contradiction as a metaphysical rather than a semantic or logical principle, and to defend the truth of the principle in this sense. First I will explain what it in fact means that the law of non-contradiction is a metaphysical principle. The core idea is that the law of non-contradiction is a general principle derived from how things are in (...) the world. For example, there are certain constraints as to what kind of properties an object can have, and especially: some of these properties are mutually exclusive. Given this characterisation, I will advance to examine what kind of challenges the law of non-contradiction faces; the main opponent here is Graham Priest. I will consider these challenges and conclude that they do not threaten the truth of the law of non-contradiction understood as a metaphysical principle. (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)

Abstract. As a general theory of reasoning—and as a general theory of what holds true under every possible circumstance—logic is supposed to be ontologically neutral. It ought to have nothing to do with questions concerning what there is, or whether there is anything at all. It is for this reason that traditional Aristotelian logic, with its tacit existential presuppositions, was eventually deemed inadequate as a canon of pure logic. And it is for this reason that modern quantification theory, too, with (...) its residue of existentially loaded theorems and patterns of inference, has been claimed to suffer from a defect of logical purity. The law of non-contradiction rules out certain circumstances as impossible—circumstances in which a statement is both true and false, or perhaps circumstances where something both is and is not the case. Is this to be regarded as a further ontological bias? (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)

The argumentative structure of this article can be summarized as follows: 1) Spinoza was repeatedly accused of eleaticism; 2) there is a rupture with the eleaticism when one admits the ‘multivocity’ of the logical operators “is” and “is not”; as can be seen, for example, 2.1) in the discussion introducing the Great Genera in Plato’s Sophist, and 2.2) in a certain use made by Aristotle of the category’s doctrine in order to soften the Parmenidean version of the Principle of (...) Non-Contradiction. 3) Spinoza admits the ‘multivocity’ of “is” and “is not”. Hence, Spinoza should not be placed among the Eleatics but inside the brotherhood of the suspects of the so-called parricide against Parmenides. This reasoning, which almost sounds as a truism, will, however, suggest two interesting further considerations: one on how an important tradition of interpretation of Spinoza has misplaced the problem of the relationship of Spinoza’s ontology with the logical principles; and another on the type of logic that is implied by the theory of modes of perception or kinds of knowledge. (shrink)

This article has been written about the explanation of the scientific affair. There are the philosophical circles that a philosopher must consider their approaches. Postmodern thinkers generally refuse the universality of the rational affair. They believe that the experience cannot reach general knowledge. They emphasize on the partial and plural knowledge. Any human being has his knowledge and interpretation. The world is always becoming. Diversity is an inclusive epistemological principle. Naturally, in such a state, the scientific activity is a (...) non-sense process. The postmodern world is a post-scientific world. Another collection of approaches to science belongs to the analytical philosophy. The main part of analytical philosophy context centers around language. Language is the center of the world. We can study the world through language. Language is the possibility of knowledge. If we overcome the language games, we can study the world accurately. Generally, at present, it seems that the rational thoughts are marginal points in the sea of irrationality. We can probably talk about an anarchistic epistemological situation. Another issue is the role of observation to form a scientific activity. In this situation, the question is whether the observation is the technique of gathering information or the final reference of original scientific analysis. In relation to this issue, the confrontation of science with the families and the categories of the objects is the main problem. For more than two thousand years, the totalitarian heritage of the Aristotelian logic has been the guideline of categorizations for the human being. In order to reach an inclusive and applicable result, we should categorize everything; but it is not really known that if the method of the world categorization is the same or not. The accordance of the conceptual categories with their extensions in the world is one of the main problems which has malfunctioned the scientific system. It is better to say that it has deactivated science. Moreover, there are many interpretations for each event based on its occurrence conditions. For example, consider a fever; In order to diagnose its cause, the most significant factor is the role of a physician. There is no sense in saying that the observation has diagnosed the cause of the fever. This is the observer that plays a determinative role. Another problem is the disputes between realism and instrumentalism. Instrumentalists believe that to form a theory, the concepts are just the tools of scientific researches. Based on realism, but we confront the concepts in the original way. This chaos causes the scientific system to collapse. Now the question is what the solution is. I would like to propose my scheme that is constructed based on a main principle: there is no occurrence in the world unless we can trace the effect of consciousness back in that occurrence. In other words, there is no accident in the world. One can argue that it is the main problem that the effects of consciousness ---if there is such a concept--- is not traceable in the world. An immediate response to this problem is an inefficient technique . The observation is a technique . It is not the method of interpretation. Some people argue that the empirical approach cannot lead us to an authentic criterion to know the world. Because there is no criterion for truth, and if there is probably such a criterion, we can obtain it via several ways. The solution to the first problem is simple. Any occurrence is a truth; even we suppose it as a partial truth. Therefore we can say we face a multi-facial world. It can be the solution of the second problem: if consciousness is essentially the origin of the world and all occurrences, we face consciousness as a unique truth; even its creations contradict each other. If there is no consciousness as a creator of the world and we cannot trace it back in all existents, then what should we do? If there is consciousness, why its creations contradict each other. Since consciousness is a will, it is able to decide in any situation it intends. The issue of contradictory consciousness intentions has a teleological aspect. We cannot judge its teleological substance at present. If we are able to believe that there is no consciousness at all, it will contradict the main practical principle in our lives. Every action that we take in our lives is conjoined with consciousness. We learn many things from many sources. The substance of our instincts and emotions can be questioned. It is true that, infact we cannot analyze our instincts and emotions, but we can discuss explicitly about the rational elements of the instincts. What are these elements? These elements are the quality of their appearance. The quality of instinct appearance is different among beings. The strength and the depth and length of these irrational qualities are different in all beings. What factors or factor cause the differences among these aspects? There is certainly a determinative factor. The same factor which determines the occurrence of any event. Even if we believe in partial knowledge, we must accept the confrontation of the occurrences. Thus it is not possible to refuse the occurrences as the reference unit of knowledge. In spite of the difference, every occurrence, even as a single occurrence, happens and we can regard it as the reference unit of knowledge. Then we can consider every occurrence as an occurred object. When an occurrence happens, then it is a determined object. Everywhere there is a determination, there is certainly a determiner. Why do not we encounter a multi-determinative consciousness? Because there are a few aspects of the unique super-consciousness. These aspects are motion and growth and the amount of constituent material in every being. In all over the world, the difference in these factors creates all differences. Thus we do not encounter the plural consciousness. Is the world birth accidental? Infact, there is no accident. The accident has no meaning in the world. As explained above, the constructing element of the world is the occurrence. An occurrence can be analyzed. Therefore, we should not talk about the accident until we are not able to analyze all phenomena. We can look at every subject from different points of view at present. Thus there is theoretically no possibility to say that a certain matter is the consequence of the accident. The accident is a popular and inexact concept that has no philosophical content. Moreover, the definition of consciousness versus its contradiction causes the collapse of all epistemological axioms. We can ask why we must not define other logical principles against their contradictions. Thinkers who deny the role of logic usually ignore the role of logic. They have not been able to deny the logical function to form an epistemological system because it is not an easy task. In this article some other issues were discussed, such as the consideration of restriction as a stable and firm foundation of knowledge instead of the Descartes cogito. In addition to these philosophical points some other issues were propounded such as the role of instrumental mechanism to form the new science and the great alterations in philosophy and history of Europe. Many issues threaten human civilization. The only way to deal with such threats is certainly to use scientific facilities. The scientific possibilities undoubtedly come from a complete and inclusive scientific theory. The present article is an attempt to explain the scientific affair in order to develop human achievement, however small. -/- . (shrink)

Time was perceived by ancient philosophy as a cosmological enigma. The search for truth beyond time determined Greek thought. A true definition, says Aristotle (384-322 BC), expresses “the what-it-is-to-be” (τὸ τί ἦν εἶναι) of a thing, it is an account of the essence, and essence is identity. The principle of non-contradiction was considered by Aristotle as the first principle of the inquiry into Being. As such, it cannot be demonstrated, since this would lead to an infinite regress. Instead, (...) the noncontradiction principle is the first axiom of ontology. But time seems to question this tautology. Aristotle discusses time in the Physics. He begins with the questions about time’s existence which stem from his contemporaries’ conceptions. (shrink)

It will be shown in this article that an ontological approach for some problems related to the interpretation of Quantum Mechanics (QM) could emerge from a re-evaluation of the main paradox of early Greek thought: the paradox of Being and non-Being, and the solutions presented to it by Plato and Aristotle. More well known are the derivative paradoxes of Zeno: the paradox of motion and the paradox of the One and the Many. They stem from what was perceived by classical (...) philosophy to be the fundamental enigma for thinking about the world: the seemingly contradictory results that followed from the co-incidence of being and non-being in the world of change and motion as we experience it, and the experience of absolute existence here and now. The most clear expression of both stances can be found, again following classical thought, in the thinking of Heraclitus of Ephesus and Parmenides of Elea. The problem put forward by these paradoxes reduces for both Plato and Aristotle to the possibility of the existence of stable objects as a necessary condition for knowledge. Hence the primarily ontological nature of the solutions they proposed: Plato’s Theory of Forms and Aristotle’s metaphysics and logic. Plato’s and Aristotle’s systems are argued here to do on the ontological level essentially the same: to introduce stability in the world by introducing the notion of a separable, stable object, for which a ‘principle of contradiction’ is valid: an object cannot be and not-be at the same place at the same time. So it becomes possible to forbid contradiction on an epistemological level, and thus to guarantee the certainty of knowledge that seemed to be threatened before. After leaving Aristotelian metaphysics, early modern science had to cope with these problems: it did so by introducing “space” as the seat of stability, and “time” as the theater of motion. But the ontological structure present in this solution remained the same. Therefore the fundamental notion ‘separable system’, related to the notions observation and measurement, themselves related to the modern concepts of space and time, appears to be intrinsically problematic, because it is inextricably connected to classical logic on the ontological level. We see therefore the problems dealt with by quantum logic not as merely formal, and the problem of ‘non-locality’ as related to it, indicating the need to re-think the notions system, entity, as well as the implications of the operation ‘measurement’, which is seen here as an application of classical logic (including its ontological consequences) on the material world. (shrink)

This essay examines the role of non-existent objects in "epistemological ontology" — the study of the entities that make thinking possible. An earlier revision of Meinong's Theory of Objects is reviewed, Meinong's notions of Quasisein and Außersein are discussed, and a theory of Meinongian objects as "combinatorially possible" entities is presented.

This volume examines the entire logical and philosophical production of Nikolai A. Vasil’ev, studying his life and activities as a historian and man of letters. Readers will gain a comprehensive understanding of this influential Russian logician, philosopher, psychologist, and poet. The author frames Vasil’ev’s work within its historical and cultural context. He takes into consideration both the situation of logic in Russia and the state of logic in Western Europe, from the end of the 19th century to the beginning of (...) the 20th. Following this, the book considers the attempts to develop non-Aristotelian logics or ideas that present affinities with imaginary logic. It then looks at the contribution of traditional logic in elaborating non-classical ideas. This logic allows the author to deal with incomplete objects just as imaginary logic does with contradictory ones. Both logics are objects of interesting analysis by modern researchers. (shrink)

Non-commuting quantities and hidden parameters – Wave-corpuscular dualism and hidden parameters – Local or nonlocal hidden parameters – Phase space in quantum mechanics – Weyl, Wigner, and Moyal – Von Neumann’s theorem about the absence of hidden parameters in quantum mechanics and Hermann – Bell’s objection – Quantum-mechanical and mathematical incommeasurability – Kochen – Specker’s idea about their equivalence – The notion of partial algebra – Embeddability of a qubit into a bit – Quantum computer is not Turing machine – (...) Is continuality universal? – Diffeomorphism and velocity – Einstein’s general principle of relativity – „Mach’s principle“ – The Skolemian relativity of the discrete and the continuous – The counterexample in § 6 of their paper – About the classical tautology which is untrue being replaced by the statements about commeasurable quantum-mechanical quantities – Logical hidden parameters – The undecidability of the hypothesis about hidden parameters – Wigner’s work and и Weyl’s previous one – Lie groups, representations, and psi-function – From a qualitative to a quantitative expression of relativity − psi-function, or the discrete by the random – Bartlett’s approach − psi-function as the characteristic function of random quantity – Discrete and/ or continual description – Quantity and its “digitalized projection“ – The idea of „velocity−probability“ – The notion of probability and the light speed postulate – Generalized probability and its physical interpretation – A quantum description of macro-world – The period of the as-sociated de Broglie wave and the length of now – Causality equivalently replaced by chance – The philosophy of quantum information and religion – Einstein’s thesis about “the consubstantiality of inertia ant weight“ – Again about the interpretation of complex velocity – The speed of time – Newton’s law of inertia and Lagrange’s formulation of mechanics – Force and effect – The theory of tachyons and general relativity – Riesz’s representation theorem – The notion of covariant world line – Encoding a world line by psi-function – Spacetime and qubit − psi-function by qubits – About the physical interpretation of both the complex axes of a qubit – The interpretation of the self-adjoint operators components – The world line of an arbitrary quantity – The invariance of the physical laws towards quantum object and apparatus – Hilbert space and that of Minkowski – The relationship between the coefficients of -function and the qubits – World line = psi-function + self-adjoint operator – Reality and description – Does a „curved“ Hilbert space exist? – The axiom of choice, or when is possible a flattening of Hilbert space? – But why not to flatten also pseudo-Riemannian space? – The commutator of conjugate quantities – Relative mass – The strokes of self-movement and its philosophical interpretation – The self-perfection of the universe – The generalization of quantity in quantum physics – An analogy of the Feynman formalism – Feynman and many-world interpretation – The psi-function of various objects – Countable and uncountable basis – Generalized continuum and arithmetization – Field and entanglement – Function as coding – The idea of „curved“ Descartes product – The environment of a function – Another view to the notion of velocity-probability – Reality and description – Hilbert space as a model both of object and description – The notion of holistic logic – Physical quantity as the information about it – Cross-temporal correlations – The forecasting of future – Description in separable and inseparable Hilbert space – „Forces“ or „miracles“ – Velocity or time – The notion of non-finite set – Dasein or Dazeit – The trajectory of the whole – Ontological and onto-theological difference – An analogy of the Feynman and many-world interpretation − psi-function as physical quantity – Things in the world and instances in time – The generation of the physi-cal by mathematical – The generalized notion of observer – Subjective or objective probability – Energy as the change of probability per the unite of time – The generalized principle of least action from a new view-point – The exception of two dimensions and Fermat’s last theorem. (shrink)

This essay examines the role of non-existent objects in "epistemological ontology"--the study of the entities that make thinking possible. An earlier revision of Meinong's Theory of Objects is reviewed, Meinong's notions of Quasisein and Aussersein are discussed, and a theory of Meinongian objects as "combinatorially possible" entities is presented.

TWENTIETH-CENTURY ETHICS. AFTER NIETZSCHE -/- Preface This book tells the story of twentieth-century ethics or, in more detail, it reconstructs the history of a discussion on the foundations of ethics which had a start with Nietzsche and Sidgwick, the leading proponents of late-nineteenth-century moral scepticism. During the first half of the century, the prevailing trends tended to exclude the possibility of normative ethics. On the Continent, the trend was to transform ethics into a philosophy of existence whose self-appointed task was (...) that of describing the human condition as consisting of choices, as unavoidable as arbitrary, without any attempt at providing criteria for making such choices. In the Anglo-Saxon countries, the heir of ethics was a philosophy of morality, that is, an analysis of the language of morality that intended to clarify valuations without trying to justify them. 1958 was the year of the normative turn that led to the Rehabilitation of practical philosophy, a turn followed by decades of controversies between distinct kinds of normative ethics: utilitarian, Kantian, virtue ethics. While the controversy was raging, a quiet revolution took place, that of applied ethics which surprisingly dissolved the controversy's very subject matter by providing methods for making convergence possible on intermediate principles even when no agreement was available about first principles. The normative turn and the revolution of applied ethics have led us, at the turn of the century, to a goal that was quite far from the starting point. Instead of scepticism and relativism that was the fashion at the beginning of the century, at the beginning of the third millennium impartial and universal moral arguments seem to hold the spot being supported, if not by a final rational foundation, at least by reasonableness, the most precious legacy of the Enlightenment. -/- ● TABLE OF CONTENTS -/- ● I Anglo-Saxon philosophy: naturalism 1. Dewey beyond evolutionism and utilitarianism 2. Dewey and anti-essentialist moral epistemology 3. Dewey and naturalist moral ontology 4. Dewey and normative ethics of conduct and function 5. Perry and semantic naturalism -/- ● II Anglo-Saxon philosophy: ideal utilitarianism and neo-intuitionism 1. Moore's critique of utilitarian empiricism 2. Moore on the naturalistic fallacy 3. Moore on the nature of intrinsic value 4. Moore on ideal utilitarianism 5. Prichard on the priority of the right over the good 6. Ross's coherentist moral epistemology 7. Ross's moral ontology: realism, pluralism, and non-naturalism 8. Ross's normative ethics of prima facie duties -/- The chapter reconstructs the background of ideas, concerns and intentions out of which Moore's early essays, the preliminary version, and then the final version of Principia Ethica originated. It stresses the role of religious concerns, as well as that of the Idealist legacy. It argues that PE is more a patchwork of somewhat diverging contributions than a unitary work, not to say the paradigm of a new school in Ethics. -/- ●III Anglo-Saxon philosophy: non-cognitivism 1. The Scandinavian School, the Vienna circle and proto-emotivism 2. Wittgenstein and the ineffability of ethics 3. Russell's and Ayer's radical emotivism 4. Stevenson and moderate emotivism 5. Stevenson and the pragmatics of moral language 6. Stevenson and the methods for solving ethical disagreement 7. Hare and prescriptivism The chapter reconstructs first the discussion after Moore. The naturalistic-fallacy argument was widely accepted but twisted to prove instead that the intuitive character of the definition of 'good', its non-cognitive meaning, in a first phase identified with 'emotive' meaning. Alfred Julius Ayer is indicated as a typical proponent of such non-cognitivist meta-ethics. More detailed discussion is dedicated to Bertrand Russell's ethics, a more nuanced and sophisticated doctrine, arguing that non-cognitivism does not condemn morality to arbitrariness and that the project of rational normative ethics is still possible, heading finally to the justification of a kind of non-hedonist utilitarianism. Stevenson's theory, another moderate version of emotivism is discussed at some length, showing how the author comes close to the discovery of the role of a pragmatic dimension of language as a basis for ethical argument. A section reconstructs the discussion from the Forties about Hume's law, mentioning Karl Popper's argument and Richard Hare's early non-cognitivist but non-emotivist doctrine named prescriptivism. -/- ●IV Anglo-Saxon philosophy: critics of non-cognitivism 1. Neo-naturalism and its objections to the naturalistic fallacy argument 2. Objections to Hume's law 3. Clarence Lewis and the pragmatic contradiction 4. Toulmin and the good reasons approach 5. Baier and moral reasons 5. Baier, social moralities and the absolute morality 6. Baier and the moral point of view 7. Baier and the contents of absolute ethics -/- ● V Continental philosophy: the philosophy of values 1. Max Weber and the polytheism of values 2. Phenomenology against psychologism and rationalism 3. Reinach and the theory of social acts 4. Scheler and the material ethics of values 5. Hartmann and the ontology of values 6. Plessner, Gehlen and the Philosophische Anthropologie -/- The chapter illustrates first the idea of phenomenology and the Husserl's project of a phenomenological ethic as illustrated in his 1908-1914 lectures. The key idea is dismissing psychology and trying to ground a new science of the apriori of action, within which a more restricted field of inquiry will be the science of right actions. Then the chapter illustrates the criticism of modern moral philosophy conducted in the 1920 lectures, where the main target is naturalism, understood in the Kantian meaning of primacy of common sense. The third point illustrate is Adolph Reinach's theory of social acts as a key the grounding of norms, a view that sketches the ideas 'discovered' later by Clarence I. Lewis, John Searle, Karl-Otto Apel and Jürgen Habermas. A final section discusses Nicolai Hartman, who always refused to define himself a phenomenologist and yet developed a more articulated and detailed theory of 'values' – with surprising affinities with George E. Moore - than philosophers such as Max Scheler, who claimed to be Husserl's legitimate heirs. -/- ● VI Continental philosophy: the critics of the philosophy of values 1. Freud, the Superego and Civilization 2. Heidegger on original ethos against ethics 3. Sartre and de Beauvoir on authenticity and ambiguity 4. Adorno and Horkheimer on emancipation and immoralism -/- ●VII Post-liberal theologians and religious thinkers 1. Barth on the autonomy of faith from ethics 2. Developments of Reformed moral theology after Barth 3. Bonhoeffer on the concrete divine command and ethics of penultimate realities 4. Developments of Reformed and Catholic moral theology after world war II 5. Baeck and the transformation of liberal Judaism 6. Rosenzweig against liberal Judaism 7. Buber and religion as the vital lymph of morality 8. Heschel and Judaism as a science of actions -/- The chapter examines the main protagonists of Christian theology and Jewish religious thinking in the twentieth century. It stresses how the main dilemmas of contemporary philosophical ethics lie at the root of the various path of inquiry taken by these thinkers. -/- ● VIII Normative ethics: neo-Utilitarianism 1. The discussion on act and rule utilitarianism 2. Hare on two-tiered preference utilitarianism 3. Harsanyi, Gauthier and rational choice ethics 4. Parfit, utilitarianism and the idea of a person 5. Brandt and indirect conscience utilitarianism -/- The chapter addresses the issue of the complex process of self-transformation Utilitarianism underwent after Sidgwick's and Moore's fatal criticism and the unexpected Phoenix-like process of rebirth of a doctrine refuted. Two examples give the reader a glimpse at this uproarious process. The first is Roy Harrod Wittgensteinian transformation of utilitarianism in pure normative ethics depurated from hedonism as well as from whatsoever theory of the good. This transformation results in preference utilitarianism combined with a 'Kantian' version of rule utilitarianism. The second is Richard Hare's two-level preference utilitarianism, where act utilitarianism plays the function of the eventual rational justification of moral judgments and rule-utilitarianism that of an action-guiding practical device. -/- ● IX Normative ethics: neo-Aristotelianism and virtue ethics 1. Hannah Arendt, action and judgement 2. Hans-Georg Gadamer and phronesis 3. Alasdair MacIntyre on practices, virtues, and traditions 5. Stuart Hampshire on deliberation 6. Bernard Williams and moral complexity 7. Feminist ethics -/- Sect 1 reconstructs the post-war rediscovery of ethics by many German thinkers and its culmination in the Sixties in the movement named 'Rehabilitation of practical philosophy' is described. Heidegger's most brilliant disciples were the promoters of this Rehabilitation. Hans-Georg Gadamer is a paradigmatic example. His reading of Aristotle's lesson I reconstructed, starting with Heidegger's lesson but then subtly subverting its outcome thanks to the recovery of the significant role of the notion of phronesis. Sect 3 discusses the three theses defended by Anscombe in 'Modern Moral Philosophy'. It argues that: a) her answer to the question "why should I be moral?" requires a solution of the problem of theodicy, and ignores any attempts to save the moral point of view without recourse to divine retribution; b) her notion of divine law is an odd one more neo-Augustinian than Biblical or Scholastic; c) her image of Kantian ethics and intuitionism is the impoverished image manufactured by consequentialist opponents for polemical purposes and that she seems strangely accept it; d) the difficulty of identifying the "relevant descriptions" of acts is not an argument in favour of an ethics of virtue and against consequentialism or Kantian ethics, and indeed the role of judgment in the latter is a response to the difficulties raised by the case of judgment concerning future action. The chapter gives a short look at further developments in the neo-naturalist current trough a reconstruction of Philippa Foot's and Peter Geach's critiques to the naturalist-fallacy argument and Alasdair MacIntyre's grand reconstruction of the origins and allegedly inevitable failure of the Enlightenment project of an autonomous ethic. -/- ● X Normative ethics: Kantian and rights-based ethics 1. Dialogical constructivism 2. Apel, Habermas and discourse ethics 3. Gewirth and rights-based ethics 4. Nagel on agent-relative reasons 5. Donagan and persons as ends in themselves Parallel to the neo-Aristotelian trend, there was in the Rehabilitation of practical philosophy a Kantian current. This current started with the discovery of the pragmatic dimension of language carried out by Charles Peirce and the Oxford linguistic philosophy. On this basis, Karl-Otto Apel singled out as the decisive proponent of the linguistic and Kantian turn in German-speaking ethics, worked out the performative-contradiction argument while claiming that this was able to provide a new rational and universal basis for normative ethics. The chapter offers an examination of his argument in some detail, followed by a more cursory reconstruction of Jürgen Habermas's elaboration on Apel's theory. -/- ● XI The applied ethics renaissance 1. Elisabeth Anscombe on the atom bomb 2. From medical ethics to bioethics 3. Rawls and public ethics 3. Nozick, Dworkin and further developments of public ethics 5. Sen and the revival of economic ethics -/- The chapter presents the revolution of applied ethics while stressing its methodological novelty, exemplified primarily by Beauchamp and Childress principles approach and then by Jonsen and Toulmin's new casuistry. The chapter argues that Rawls's distinction between a "political" and a "metaphysical" approach to the theory of justice, one central part of ethical theory, is a formulation of the same basic idea at the root of both the principles approach and the new casuistry, both discussed in the following chapter. The idea is that it is possible to reach an agreement concerning positive moral judgments even though the discussion is still open – and in Rawls' view never will be close – on the essential criteria for judgment. -/- ● XII Fin-de-siècle metaethics 1. Deontic logics 2. Anti-realism 3. External realism 4. Internal realism 5. Kantian constructivism -/- The chapter illustrates the fresh start of meta-ethical discussion in the Eighties and Nineties and the resulting new alignments: metaphysical naturalism, internal realism, anti-realism, and constructivism. (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)

When faced with the charge that a given concept of God is contradictory, the standard move among philosophers and theologians has been to try to explain away the contradiction and show that the concept of God in question is consistent. This has to do, of course, with the Law of Non-Contradiction (LNC). Another option, which has recently generated interest among logicians and analytic philosophers of religion, is to reject such a move as unnecessary and defend what might be called the (...) contradictory God thesis. To be sure, something close to that can be found in philosophers such as Pseudo-Dionysius, Thomas Aquinas and Nicolaus de Cusa. However, it is only recently that this approach has gained momentum, certainly driven by the contemporary advance of dialetheism and glut theoretic approaches in general, and paraconsistent logic. Needless to say, a standard move among defenders of the contradictory God thesis is to challenge the LNC. The argumentation, however, is seldomly framed in conceptual terms. Instead, it is mostly framed in ontological terms, as God being a contradictory entity. From this perspective, the contradictory God thesis is the thesis that God is a contradictory object. My goal in this paper is to provide a conceptual assessment of the discussion surrounding the contradictory God thesis. To achieve this, I make use of a general and hopefully non-controversial meta-theory of concepts and adopt a semantic approach rather than a metaphysical one. Within this framework, I address the following questions: What are the different ways we can understand the contradictory God thesis? What grounds are there for rejecting a contradictory concept of God? What standard moves are available to defend oneself from such criticisms and how do they relate to the LNC? What challenges do they present? As a secondary goal, the paper introduces a novel defense of the contradictory God thesis, drawing on a specific interpretation of the theology of the 16th-century Indian thinker Jīva Gosvāmī, which avoids the need to challenge the LNC. I term this approach ‘non-dialetheic mystical contradictory theism.’. (shrink)

In this paper we present a philosophical motivation for the logics of formal inconsistency, a family of paraconsistent logics whose distinctive feature is that of having resources for expressing the notion of consistency within the object language in such a way that consistency may be logically independent of non- contradiction. We defend the view according to which logics of formal inconsistency may be interpreted as theories of logical consequence of an epistemological character. We also argue that in order to (...) philosophically justify paraconsistency there is no need to endorse dialetheism, the thesis that there are true contradictions. Furthermore, we argue that an intuitive reading of the bivalued semantics for the logic mbC, a logic of formal inconsistency based on classical logic, fits in well with the basic ideas of an intuitive interpretation of contradictions. On this interpretation, the acceptance of a pair of propositions A and ¬A does not mean that A is simultaneously true and false, but rather that there is conflicting evidence about the truth value of A. (shrink)

My object is Aristotle's discussion of principle of non-contradiction in the first stretch of Metaphysics IV.4. My main focus rests on the connections between Aristotle's discussion of the principle and some key notions of his (explicit or implied) semantics.

In this thesis I argue against unrestricted mereological hybridism, the view that there are absolutely no constraints on wholes having parts from many different logical or ontological categories, an exemplar of which I take to be ‘mixed fusions’. These are composite entities which have parts from at least two different categories – the membered (as in classes) and the non-membered (as in individuals). As a result, mixed fusions can also be understood to represent a variety of cross-category summation such as (...) the abstract with the concrete, the physical with the non-physical, and the possible with the impossible, just to name a few. -/- Proposed by David Lewis (1991) alongside his defence of classical mereology (the major theory of parthood which permits such transcategorial composites through its principle of unrestricted composition) it is my contention that mixed fusions are an under-examined consequence of indiscriminate mereological fusion which harbour a multitude of complications. In my attempt to discern their substantive character, throughout this thesis I make a case study of mixed fusions and uncover several problematic consequences which I think follow from their most plausible assessment. -/- These include: (1) that mixed fusions’ probable membership relations may lead to dubious foundational loops in the mereological Universe, or (2) otherwise that mixed fusions oblige an implausible ontological priority of the mereological Universe as a whole; (3) that mixed fusions contradict the reductive account of set theory they are proposed within, by plausibly being seen to have the same members as their class parts, and (4) that mixed fusions therefore confound a mereological thesis of Composition as Identity, which some (including Lewis) use to support classical mereology – a consequence which is potentially self-defeating; (5) that mixed fusions as sums of abstract and concrete entities both subvert Lewis’s (1986) system of modal realism, while (6) also undermining less expansive theories of possible worlds; and finally, (7) that even where some of the foregoing is resisted, it remains implausible that mixed fusions are ontologically innocent, because their supposed distinction from their parts in this case ensures that they need to be counted as additional entities in one’s ontology. -/- To be clear, I do not advance a theory of mereological hybrid nihilism in the sense of denying all cases of transcategorial composition. (I only cover a few select instances of mereological hybridism via mixed fusions after all.) Rather, I deny that mereological hybridism is plausible in full generality, by demonstrating that any cases of it are at least limited by the constraints that I identify. This in turn vindicates a call for a restriction on parthood theories and composition principles which allow certain types of categorially mixed entities – including restricting classical mereology with its principle of unrestricted composition. -/- Although theories of parthood like the standard classical mereology are not ordinarily developed for the sake of mereological hybrids like mixed fusions, these and other transcategorial composites are still among the logical consequences of such parthood systems operating with sufficient generality. The significance of my thesis, then, comes from showcasing how some of these kinds of entities do not conform to the systems in which they are included as required, and hence I argue for the rejection of unrestricted mereological hybridism as well as any mereological principles which support it. (shrink)

The book is a collection of papers and aims to unify the questions of syntax and semantics of language, which are included in logic, philosophy and ontology of language. The leading motif of the presented selection of works is the differentiation between linguistic tokens (material, concrete objects) and linguistic types (ideal, abstract objects) following two philosophical trends: nominalism (concretism) and Platonizing version of realism. The opening article under the title “The Dual Ontological Nature of Language Signs and the Problem of (...) Their Mutual Relations” provides a broad introduction into the problem area connected with this differentiation, while the logic-formal characteristics of the distinction are framed in the work entitled “On the Type-Token Relationships” (Chapter 1). The basic part of the book deals with issues relating to syntax (Chapters 2-4) and semantics of language (Chapters 5-6), as well as pertaining to syntactic-semantic pragmatic questions (Chapters 7-13). Throughout the book, language, categorial language, is characterized syntactically as generated by classical categorial grammar (Chapter 2) and formalized on two opposing levels: as language of expression-tokens (level of tokens) and language of expression-types (level of types). The author’s considerations contained in Chapters 2 and 4 lead to the important philosophical conclusion that in formal-logical syntactic studies on language the assumption that expression-types constitute the primary language layer while expression-tokens make the secondary one, can be neglected; thus, this speaks in favour of the opposing standpoint—the concretistic one—in the ontology of language syntax. In the works “Meaning and Interpretations”, Parts I and II (Chapters 5 and 6), it is underlined, however, that such semantic concepts as: meaning, denotation and interpretation are defined on the types level, yet their formal definitions require making use of notions of the tokens level. The semantic notions introduced in the above-mentioned articles are also used in the following works of the present selection, under the titles: “Three Principles of Compositionality” and “On Metaknowledge and Truth” (Chapters 7 and 8). They formalize two principles of compositionality that are well known in the literature on the subject, deriving from Frege, i.e. those of meaning and of denotation; they are related to the syntactic principle of compositionality which was introduced by the author. All the three principles are, at the same time, three conditions of homomorphism of categorial language algebra into three kinds of non-standard models of language (one syntactic and two semantic ones: intensional and extensional), which allows introducing three definitions of truthfulness into these models. The next two works in the collection, entitled: “On Language Adequacy” and “What is the Sense in Logic and Philosophy of Language” (Chapters 9 and 10) concern adequacy of categorial language syntax along with its dual semantics: intensional and extensional, and categorial compatibility of any of its syntactic categories with two corresponding semantic categories: intensional and extensional, based on the compatibility the syntactic category of each language expression with the ontological category assigned to its denotatum. The well-known problem of categorial compatibility for first-order quantifiers finds its solution in the paper “Categories of First-Order Quantifiers” (Chapter 11). In the work “Logic and Ontology of Language” (Chapter 12), being in a sense a summary of the considerations presented in the preceding chapters of the book, language is treated as an ontological being, characterized in compliance with the logical conception of language proposed by Ajdukiewicz. Application—like throughout the book—of tools of classical logic and set theory has resulted in emergence of a general formal logical theory of syntax, semantics and pragmatics of language, which takes into account duality in the understanding of linguistic expressions as tokens (concretes) and types (abstract objects). In terms that take into account a functional approach to language itself, there comes out an ontological neutrality of logic with respect to existential assumptions relating to the ontological nature of linguistic expressions and their extra-linguistic ontological counterparts. The issues connected with applying logic while explaining the manner of using linguistic tokens and linguistic types to determine notions of language communication are raised and illustrated in the last chapter of the work, bearing the title “A Logical Conceptualization of Knowledge on the Notion of Language Communication”. (shrink)

This paper defends the possibility of admitting occurrents in a presentist ontology. Two ways of doing so are proposed, the first one involves Meinongian presentism. By using the notion of non-existent object and coherently modifying some mereological principle, it is argued, the presentist can allow for occurrents. The second proposal involves ex-concrete objects. Ex-concrete objects, i.e. objects that are contingently not concrete, have been used by Linsky and Zalta, 431-458, 1994), Williamson in the modal metaphysics debate, by Orilia, (...) 589-607, 2016) in the presentism-eternalism debate, and by Longenecker, 5091-5111, 2018) in the debate about material constitution. I argue that, just by admitting ex-concrete objects, it is possible to have occurrents even for the presentist. Of course, in order to do so we must modify our definitions of occurrent and continuant. Nevertheless, I argue that my theory is metaphysically sound, at least for the presentist persuaded by the intuitive claim that there are occurrents, which otherwise she must reject. (shrink)

We examine some of Connes’ criticisms of Robinson’s infinitesimals starting in 1995. Connes sought to exploit the Solovay model S as ammunition against non-standard analysis, but the model tends to boomerang, undercutting Connes’ own earlier work in functional analysis. Connes described the hyperreals as both a “virtual theory” and a “chimera”, yet acknowledged that his argument relies on the transfer principle. We analyze Connes’ “dart-throwing” thought experiment, but reach an opposite conclusion. In S , all definable sets of reals (...) are Lebesgue measurable, suggesting that Connes views a theory as being “virtual” if it is not definable in a suitable model of ZFC. If so, Connes’ claim that a theory of the hyperreals is “virtual” is refuted by the existence of a definable model of the hyperreal field due to Kanovei and Shelah. Free ultrafilters aren’t definable, yet Connes exploited such ultrafilters both in his own earlier work on the classification of factors in the 1970s and 80s, and in Noncommutative Geometry, raising the question whether the latter may not be vulnerable to Connes’ criticism of virtuality. We analyze the philosophical underpinnings of Connes’ argument based on Gödel’s incompleteness theorem, and detect an apparent circularity in Connes’ logic. We document the reliance on non-constructive foundational material, and specifically on the Dixmier trace −∫ (featured on the front cover of Connes’ magnum opus) and the Hahn–Banach theorem, in Connes’ own framework. We also note an inaccuracy in Machover’s critique of infinitesimal-based pedagogy. (shrink)

In Metaphysics Γ, Aristotle argues against those who seem to accept contradictions. He distinguishes between the Sophists, who deny the principle of non-contradiction through arguments, and the Natural Philosophers, whose physical investigations lead to the acceptance of objective contradictions. Heraclitus’ name appears throughout the discussion. Usually, he is associated with the discussion against the Sophists. In this paper, I explore how the discussion with the Natural Philosophers may illuminate both the interpretation of Heraclitus by Aristotle and Heraclitus’ own worldview. (...) To refute the Natural Philosophers, Aristotle proposes a general reconstruction of their reasoning. Roughly, relying on sensory evidence (A1), they see that the same thing changes from one opposite to another (A2). Such a change appears to characterize a generation out of non-being, which a Natural Philosopher does not accept (A3). To solve the problem, despite their different worldviews, Natural Philosophers hint at a state in which opposites co-occur, characterizing an objective contradiction (C). Looking at the discussion in Metaphysics Γ and Heraclitus fragments, sections 1–3 show how assumptions A1, A2, and A3 easily apply to Heraclitus. The case of the conclusion is more challenging. In the case of the Pluralists, the co-existence of opposites characterizes a state in which there is no generation. Such a view does not fit Heraclitus’ mobilism. To argue that Aristotle’s argument is general enough to encompass dynamic views, I examine his problematization of accepting the change of change in Metaphysics K and Physics V. There, after re-stating several points that appear in Metaphysics Γ, Aristotle argues that accepting the becoming of another becoming leads to a state of contradiction in which the becoming is perishing. Heraclitus’ B8, cited in Nicomachean Ethics, gives evidence that, for Aristotle, Heraclitus puts a process at the origin of an opposite process. Moreover, after examining the expression ‘living the death/dying the life’ in B62, I argue that Heraclitus was aware that his worldview implied a dynamic objective contradiction. Finally, an analysis of elemental changes in B36 proves that accepting objective contradictions does not make Heraclitus’ worldview less attractive. (shrink)

Katerina Kolozova is a Macedonian philosopher whose publications from last two decades aim to analyze various topics using François Laruelle’s “non-philosophy” or “non-standard philosophy.” Non-philosophy could be roughly described as radicalized deconstruction: Laruelle claims that not everything can be grasped by a philosophy: for Laruelle, “philosophy is too serious an affair to be left to the philosophers alone.”1 Non-philosophy opposes the “principle of sufficient philosophy” through which philosophy determines and decides what is real. According to Laruelle, the ultimate limit (...) of philosophical thought and its self-proclaimed sufficiency lies in its inherent tendency to close itself in a transcendental system of autofetishist conceptions, which presume that one can grasp the Real (“The Real is neither capable of being known or even ‘thought,’ but can be described in axioms. [...] Even ‘immanence’ only serves to name the Real which tolerates nothing but axiomatic descriptions or formulations.”) by a philosophical thought, or that the Real could be mediated only through human thought. Laruelle criticizes this tendency of philosophy, which is usually expressing itself through the structure of “philosophical Decision.” (“To philosophize is to decide Reality and the thoughts that result from this, i.e. to believe to be able to order them in the universal order of the Principle of Reason [Logos].”) Katerina Kolozova use Laruelle’s non-philosophy to explore more explicitly political topics. In the Cut Of Th e Real (2014), she criticized certain dogmatism of poststructuralist philosophy and feminist theory, namely their symptomatic rejection of the Real and the One. In Toward a Radical Metaphysics of Socialism (2015) and The Lived Revolution (2016) Kolozova presented a rereading of Marx, whose work she found relevant for the critique of speculative philosophical dimension of the capitalist economy, embodied in the 2008 global finance crisis, and in the latter book, she explored the possibility of a new political solidarity, based on “bodies in pain.” Kolozova doesn’t call to philosophically reconstruct Marx’s thought for the current situation, but she goes back to Marx with the help of Laruelle’s non-Marxism, contrary to the usual approach of Marxist philosophers, who often try to create certain philosophical system of Marx’s work. Together with Eileen A. Joy, Kolozova edited the anthology After the “Speculative Turn” (2016), which addressed recent realist and materialist tendencies in feminist philosophy. In her most recent book, Capitalism’s Holocaust of Animals (2019), Kolozova aimed to explore broader philosophical foundations of neoliberal capitalism, and its dealing with nonhuman animals and their suffering. According to Kolozova, “We have to start by coming to terms with what we did to the animals in the constitutive act of philosophy and via proxy to all those dehumanised that belong to the species of man ‘by courtesy’ only.” . (shrink)

The topic of this paper may be introduced by fast zooming in and out of the philosophy of information. In recent years, philosophical interest in the nature of information has been increasing steadily. This has led to a focus on semantic information, and then on the logic of being informed, which has attracted analyses concentrating both on the statal sense in which S holds the information that p (this is what I mean by logic of being informed in the rest (...) of this article) and on the actional sense in which S becomes informed that p. One of the consequences of the logic debate has been a renewed epistemological interest in the principle of information closure (henceforth PIC), which finally has motivated a revival of a skeptical objection against its tenability first made popular by Dretske. This is the topic of the paper, in which I seek to defend PIC against the skeptical objection. If I am successful, this means – and we are now zooming out – that the plausibility of PIC is not undermined by the skeptical objection, and therefore that a major epistemological argument against the formalization of the logic of being informed based on the axiom of distribution in modal logic is removed. But since the axiom of distribution discriminates between normal and non-normal modal logics, this means that a potentially good reason to look for a formalization of the logic of being informed among the non-normal modal logics, which reject the axiom, is also removed. And this in turn means that a formalization of the logic of being informed in terms of the normal modal logic B (also known as KTB) is still very plausible, at least insofar as this specific obstacle is concerned. In short, I shall argue that the skeptical objection against PIC fails, so it is not a good reason to abandon the normal modal logic B as a good formalization of the logic of being informed. (shrink)

This article offers a novel, conservative account of material constitution, one that incorporates sortal essentialism and features a theory of dominant sortals. It avoids coinciding objects, temporal parts, relativizations of identity, mereological essentialism, anti-essentialism, denials of the reality of the objects of our ordinary ontology, and other departures from the metaphysic implicit in ordinary ways of thinking. Defenses of the account against important objections are found in Burke 1997, 2003, and 2004, as well as in the often neglected six paragraphs (...) that conclude section V of this article. (shrink)

Metamorphosis seems problematic for our occidental point of view. Becoming in general is viewed as an error or exception by our classic standpoint. In fact, it is strongly against identity and law of non-contradiction: A is fundamentally something different from B and for A it is impossible to be at the same time B. We need to think A as what-becomes-B in order to make metamorphosis possible. Anyway, how can A become B? As a matter of fact, this very claim (...) has been historically the most common critic opposed to becoming. Deleuze and Guattari in their monumental work had tried to offer an enormous contribution to a few related problems. Redefining the subject as an event described by movement and affect can exceed the metamorphosis’ aporia. This new principle of individuation provides a new look upon arisen questions primarily because affects and movements are constant coordinates that define how metamorphosis is experienced. The paper tries to show how the betweenness in action in the encounter with people, human beings, things, animals, plants and minerals defines the logic field of metamorphosis. This is shown in dialogue with the ontological turn in anthropology that is particularly focused on this affective and lively dimension of encounter especially among Amazonian populations. Actually this is also what happens in our – occidental and classical but live – relation with things and objects, as long as we try to think a real conceptualisation of experience. (shrink)

This study will examine the ontological dependency between the thinking act of the intellect and the intelligibility of the objects of thought. Whereas the intellectual tradition prior to Duns Scotus grounds the formation of the objects of thought and our ability to understand them with certainty in different forms of participation in the divine intellect, Scotus shows that the intelligibility of the objects of thought is internal to them alone and is not dependent on participation.

Gödel's Philosophical Legacy Kurt Gödel's contributions to philosophy extend beyond his incompleteness theorems. He engaged deeply with the work of other philosophers, including Immanuel Kant and Edmund Husserl, and explored topics such as the nature of time, the structure of the universe, and the relationship between mathematics and reality. Gödel's philosophical writings, though less well-known than his mathematical work, offer rich insights into his views on the nature of existence, the limits of human knowledge, and the interplay between the finite (...) and the infinite. His work continues to inspire and challenge philosophers, mathematicians, and scientists, inviting them to explore the profound and often enigmatic questions at the heart of human understanding. -/- Kurt Gödel's Broader Contributions to Philosophy Kurt Gödel, while primarily known for his monumental incompleteness theorems, made significant contributions that extended beyond the realm of mathematical logic. His philosophical pursuits deeply engaged with the works of eminent philosophers like Immanuel Kant and Edmund Husserl. Gödel's explorations into the nature of time, the structure of the universe, and the relationship between mathematics and reality reveal a profound and multifaceted intellectual legacy. -/- Engagement with Immanuel Kant Gödel held a deep interest in the philosophy of Immanuel Kant. He admired Kant's critical philosophy, particularly the distinction between the noumenal and phenomenal worlds. Kant posited that human experience is shaped by the mind’s inherent structures, leading to the conclusion that certain aspects of reality (the noumenal world) are fundamentally unknowable. Gödel’s incompleteness theorems echoed this Kantian theme, illustrating the limits of formal systems in capturing the totality of mathematical truth. Gödel believed that mathematical truths exis t independently of human thought, akin to Kant's noumenal realm. This philosophical alignment provided a robust foundation for Gödel's Platonism, which asserted the existence of mathematical objects as real, albeit abstract, entities. -/- Influence of Edmund Husserl Gödel was also profoundly influenced by Edmund Husserl, the founder of phenomenology. Husserl's phenomenology emphasizes the direct investigation and description of phenomena as consciously experienced, without preconceived theories about their causal explanation. Gödel saw Husserl's work as a pathway to bridge the gap between the abstract world of mathematics and concrete human experience. Husserl's ideas about the structures of consciousness and the intentionality of thought resonated with Gödel's views on mathematical intuition. Gödel believed that human minds could access mathematical truths through intuition, a concept that draws on Husserlian phenomenological methods. -/- The Nature of Time and the Universe Gödel's philosophical inquiries extended to the nature of time and the structure of the universe. His collaboration with Albert Einstein at the Institute for Advanced Study led to the development of the "Gödel metric" in 1949. This solution to Einstein's field equations of general relativity described a rotating universe where time travel to the past was theoretically possible. Gödel's model challenged conventional notions of time and causality, suggesting that the universe might have a more intricate structure than previously thought. Gödel's exploration of time was not just a mathematical curiosity but a profound philosophical statement about the nature of reality. He questioned whether time was an objective feature of the universe or a construct of human consciousness. His work hinted at a timeless realm of mathematical truths, aligning with his Platonist view. -/- Mathematics and Reality Gödel's philosophical outlook extended to the broader relationship between mathematics and reality. He believed that mathematics provided a more profound insight into the nature of reality than empirical science. For Gödel, mathematical truths were timeless and unchangeable, existing independently of human cognition. This perspective led Gödel to critique the materialist and mechanistic views that dominated 20th-century science and philosophy. He argued that a purely physicalist interpretation of the universe failed to account for the existence of abstract mathematical objects and the human capacity to understand them. Gödel's philosophy suggested a more integrated view of reality, where both physical and abstract realms coexist and inform each other. -/- Gödel's Exploration of Time Kurt Gödel, one of the most profound logicians of the 20th century, ventured beyond the confines of mathematical logic to explore the nature of time. His inquiries into the concept of time were not merely theoretical musings but were grounded in rigorous mathematical formulations. Gödel's exploration of time challenged conventional views and opened new avenues of thought in both physics and philosophy. -/- Gödel and Einstein Gödel’s interest in the nature of time was significantly influenced by his friendship with Albert Einstein. Both were faculty members at the Institute for Advanced Study in Princeton, where they engaged in deep discussions about the nature of reality, time, and space. Gödel's exploration of time culminated in his solution to Einstein's field equations of general relativity, known as the Gödel metric. -/- The Gödel Metric In 1949, Gödel presented a model of a rotating universe, which became known as the Gödel metric. This solution to the equations of general relativity depicted a universe where time travel to the past was theoretically possible. Gödel’s rotating universe contained closed timelike curves (CTCs), paths in spacetime that loop back on themselves, allowing for the possibility of traveling back in time. The Gödel metric posed a significant philosophical challenge to the conventional understanding of time. If time travel were possible, it would imply that time is not linear and absolute, as commonly perceived, but rather malleable and subject to the geometry of spacetime. This raised profound questions about causality, the nature of temporal succession, and the very structure of reality. -/- Philosophical Implications Gödel’s exploration of time extended beyond the mathematical implications to broader philosophical inquiries: Nature of Time: Gödel questioned whether time was an objective feature of the universe or a construct of human consciousness. His work suggested that our understanding of time as a linear progression from past to present to future might be an illusion, shaped by the limitations of human perception. -/- Causality and Free Will: The existence of closed timelike curves in Gödel’s model raised questions about causality and free will. If one could travel back in time, it would imply that future events could influence the past, potentially leading to paradoxes and challenging the notion of a deterministic universe. -/- Temporal Ontology: Gödel's work contributed to debates in temporal ontology, particularly the debate between presentism (the view that only the present exists) and eternalism (the view that past, present, and future all equally exist). Gödel’s rotating universe model seemed to support eternalism, suggesting a block universe where all points in time are equally real. Philosophy of Science: Gödel’s exploration of time had implications for the philosophy of science, particularly in the context of understanding the limits of scientific theories. His work underscored the importance of considering philosophical questions when developing scientific theories, as they shape our fundamental understanding of concepts like time and space. -/- Legacy Gödel’s exploration of time remains a significant and controversial contribution to both physics and philosophy. His work challenged established notions and encouraged deeper inquiries into the nature of reality. Gödel’s rotating universe model continues to be a topic of interest in theoretical physics and cosmology, inspiring new research into the nature of time and the possibility of time travel. In philosophy, Gödel’s inquiries into time have prompted ongoing debates about the nature of temporal reality, the relationship between mathematics and physical phenomena, and the limits of human understanding. His work exemplifies the intersection of mathematical rigor and philosophical inquiry, demonstrating the profound insights that can emerge from such an interdisciplinary approach. The Temporal Ontology of Kurt Gödel Kurt Gödel's profound contributions to mathematics and logic extend into the realm of temporal ontology—the philosophical study of the nature of time and its properties. Gödel's insights challenge conventional perceptions of time and suggest a more intricate, layered understanding of temporal reality. This essay explores Gödel's contributions to temporal ontology, particularly through his engagement with relativity and his philosophical reflections. -/- Gödel's Rotating Universe One of Gödel’s most notable contributions to temporal ontology comes from his work in cosmology, specifically his solution to Einstein’s field equations of general relativity, known as the Gödel metric. Introduced in 1949, the Gödel metric describes a rotating universe with closed timelike curves (CTCs). These curves imply that, in such a universe, time travel to the past is theoretically possible, presenting a significant challenge to conventional views of linear, unidirectional time. -/- Implica tions for Temporal Ontology Gödel's rotating universe model has profound implications for our understanding of time: Eternalism vs. Presentism: Gödel’s model supports the philosophical stance known as eternalism, which posits that past, present, and future events are equally real. In contrast to presentism, which holds that only the present moment exists, eternalism suggests a "block universe" where time is another dimension like space. Gödel’s rotating universe, with its CTCs, reinforces this view by demonstrating that all points in time could, in principle, be interconnected in a consistent manner. Non-linearity of Time: The possibility of closed timelike curves challenges the idea of time as a linear sequence of events. In Gödel’s universe, time is not merely a straight path from past to future but can loop back on itself, allowing for complex interactions between different temporal moments. This non-linearity has implications for our understanding of causality and the nature of temporal succession. Objective vs. Subjective Time: Gödel’s work invites reflection on the distinction between objective time (the time that exists independently of human perception) and subjective time (the time as experienced by individuals). His model suggests that our subjective experience of a linear flow of time may not correspond to the objective structure of the universe. This raises questions about the relationship between human consciousness and the underlying temporal reality. -/- Gödel and Philosophical Reflections on Time Gödel’s engagement with temporal ontology was not limited to his cosmological work. He also reflected deeply on philosophical questions about the nature of time and reality, drawing on the ideas of other philosophers and integrating them into his own thinking. Kantian Influences: Gödel was influenced by Immanuel Kant’s distinction between the noumenal world (things as they are in themselves) and the phenomenal world (things as they appear to human observers). Gödel’s views on time echoed this distinction, suggesting that our perception of time might be a phenomenon shaped by the limitations of human cognition, while the true nature of time (the noumenal aspect) might be far more complex and non-linear. Husserlian Phenomenology: Gödel’s interest in Edmund Husserl’s phenomenology also informed his views on time. Husserl’s emphasis on the structures of consciousness and the intentionality of thought resonated with Gödel’s belief in the importance of intuition in accessing mathematical truths. Gödel’s reflections on time incorporated a phenomenological perspective, considering how temporal experience is structured by human consciousness. Mathematical Platonism: Gödel’s Platonist views extended to his understanding of time. Just as he believed in the independent existence of mathematical objects, Gödel saw time as an objective entity with a structure that transcends human perception. His work on the Gödel metric can be seen as an attempt to uncover this objective structure, revealing the deeper realities that underlie our experience of time. (shrink)

A principle, according to which any scientific theory can be mathematized, is investigated. Social science, liberal arts, history, and philosophy are meant first of all. That kind of theory is presupposed to be a consistent text, which can be exhaustedly represented by a certain mathematical structure constructively. In thus used, the term “theory” includes all hypotheses as yet unconfirmed as already rejected. The investigation of the sketch of a possible proof of the principle demonstrates that it should be (...) accepted rather a metamathematical axiom about the relation of mathematics and reality. The main statement is formulated as follows: Any scientific theory admits isomorphism to some mathematical structure in a way constructive. Its investigation needs philosophical means. Husserl’s phenomenology is what is used, and then the conception of “bracketing reality” is modelled to generalize Peano arithmetic in its relation to set theory in the foundation of mathematics. The obtained model is equivalent to the generalization of Peano arithmetic by means of replacing the axiom of induction with that of transfinite induction. The sketch of the proof is organized in five steps: a generalization of epoché; involving transfinite induction in the transition between Peano arithmetic and set theory; discussing the finiteness of Peano arithmetic; applying transfinite induction to Peano arithmetic; discussing an arithmetical model of reality. Accepting or rejecting the principle, two kinds of mathematics appear differing from each other by its relation to reality. Accepting the principle, mathematics has to include reality within itself in a kind of Pythagoreanism. These two kinds are called in paper correspondingly Hilbert mathematics and Gödel mathematics. The sketch of the proof of the principle demonstrates that the generalization of Peano arithmetic as above can be interpreted as a model of Hilbert mathematics into Gödel mathematics therefore showing that the former is not less consistent than the latter, and the principle is an independent axiom. The present paper follows a pathway grounded on Husserl’s phenomenology and “bracketing reality” to achieve the generalized arithmetic necessary for the principle to be founded in alternative ontology, in which there is no reality external to mathematics: reality is included within mathematics. That latter mathematics is able to self-found itself and can be called Hilbert mathematics in honour of Hilbert’s program for self-founding mathematics on the base of arithmetic. The principle of universal mathematizability is consistent to Hilbert mathematics, but not to Gödel mathematics. Consequently, its validity or rejection would resolve the problem which mathematics refers to our being; and vice versa: the choice between them for different reasons would confirm or refuse the principle as to the being. An information interpretation of Hilbert mathematics is involved. It is a kind of ontology of information. The Schrödinger equation in quantum mechanics is involved to illustrate that ontology. Thus the problem which of the two mathematics is more relevant to our being is discussed again in a new way A few directions for future work can be: a rigorous formal proof of the principle as an independent axiom; the further development of information ontology consistent to both kinds of mathematics, but much more natural for Hilbert mathematics; the development of the information interpretation of quantum mechanics as a mathematical one for information ontology and thus Hilbert mathematics; the description of consciousness in terms of information ontology. (shrink)

Bertrand Russell’s _Principles of Mathematics_ (1903) gives rise to several interpretational challenges, especially concerning the theory of denoting concepts. Only relatively recently, for instance, has it been properly realised that Russell accepted denoting concepts that do not denote anything. Such empty denoting concepts are sometimes thought to enable Russell, whether he was aware of it or not, to avoid commitment to some of the problematic non-existent entities he seems to accept, such as the Homeric gods and chimeras. In this paper, (...) I argue first that the theory of denoting concepts in _Principles of __Mathematics_ has been generally misunderstood. According to the interpretation I defend, if a denoting concept shifts what a proposition is about, then the aggregate of the denoted terms will also be a constituent of the proposition. I then show that Russell therefore could not have avoided commitment to the Homeric gods and chimeras by appealing to empty denoting concepts. Finally, I develop what I think is the best understanding of the ontology of _Principles of __Mathematics_ by interpreting some difficult passages. (shrink)

While there is considerable disagreement on the precise nature of material objecthood, it is standardly assumed that material objects must be spatial. In this paper, I provide two arguments against this assumption. The first argument is made from largely a priori considerations about modal plenitude. The possibility of non-spatial material objects follows from commitment to certain plausible principles governing material objecthood and plausible principles regarding modal plenitude. The second argument draws from current philosophical discussions regarding theories of quantum gravity and (...) the emergence of spacetime. When it is appreciated what possible worlds these current theories commit us to, the possibility of non-spatial material objects will follow. Thus, either route will lead us to the possibility of non-spatial material objects. The significance of this result is that we need to revise our accounts of material objecthood to both accommodate these possibilities and the theories that lead to them. (shrink)

This article explores the usefulness of interdisciplinarity as method of enquiry by proposing an investigation of the concept of information in the light of semiotics. This is because, as Kull, Deacon, Emmeche, Hoffmeyer and Stjernfelt state, information is an implicitly semiotic term (Biological Theory 4(2):167–173, 2009: 169), but the logical relation between semiosis and information has not been sufficiently clarified yet. Across the history of cybernetics, the concept of information undergoes an uneven development; that is, information is an ‘objective’ entity (...) in first order cybernetics, and becomes a ‘subjective’ entity in second order cybernetics. This contradiction relegates the status of information to that of a ‘true’ or ‘false’ formal logic problem. The present study proposes that a solution to this contradiction can be found in Deely’s reconfiguration of Peirce’s ‘object’ (as found in his triadic model of semiosis) into ‘thing’ and ‘object’ (Deely 1981). This ontology allows one to argue that information is neither ‘true’ nor ‘false’, and to suggest that, when considered in light of its workability, information can be both true and false, and as such it constitutes an organism’s purely objective reality (Deely 2009b). It is stated that in the process of building such a reality, information is ‘motivated’ by environmental, physiological, emotional (including past feelings and expectations) constraints which are, in turn, framed by observership. Information is therefore found in the irreducible cybersemiotic process that links at once all these conditions and that is simultaneously constrained by them. The integration of cybernetics’ and semiotics’ understanding of information shows that history is the analytical principle that grants scientific rigour to interdisciplinary investigations. As such, in any attempt to clarify its epistemological stance (e.g. the semiotic aspect of information), it is argued that biosemiotics does not need only to acknowledge semiotics (as it does), but also cybernetics in its interdisciplinary heritage. (shrink)

This brief brochure is intended to present a philosophical theory known as re- lational materialism. We introduce the postulates and principles of the theory, ar- ticulating its ontological and epistemological content using the language of category theory. The identification of any existing entity is primarily characterized by its relational, finite, and non-static nature. Furthermore, we provide a categorical con- struction of particularities within the relational materialist onto-epistemology. Our objective is to address and transform a specific perspective prevalent in scientific communities (...) into a productive network of philosophical commitments. (shrink)

This brief brochure is intended to present a philosophical theory known as relational materialism. We introduce the postulates and principles of the theory, articulating its ontological and epistemological content using the language of category theory. The identification of any existing entity is primarily characterized by its relational, finite, and non-static nature. Furthermore, we provide a categorical construction of particularities within the relational materialist onto-epistemology. Our objective is to address and transform a specific perspective prevalent in scientific communities into a productive (...) network of philosophical commitments. (shrink)

The main thesis of this work is as follows: there are versions of Yablo’s paradox that, if Cook is right about the non-circular character of his version of it, are truly paradoxical and genuinely non-circular, and Cook’s version of Yablo’s paradox is one of them. Here I will not evaluate the"circular" or"non-circular" side to Cook’s proposal. In fact, I think that he is right about it, and that his version of Yablo’s list is non-circular. But is it paradoxical? In order (...) to be so, the principles that lead to (i) the derivation of a contradiction, or (ii) the impossibility to give a stable assignment of truth values to the relevant set of sentences, must be acceptable. I will explore two ways to argue that they are not. I will conclude that these attempts lead to a very narrow conception of a theory of truth, or to deny that a paradigmatic case of paradox, such as the"Old-Fashioned Liar," is truly paradoxical. La tesis principal de este trabajo es la siguiente: hay versiones de la paradoja de Yablo tales que, si Cook está en lo cierto acerca del carácter no-circular de su propia versión de ella, son genuinamente paradójicas y auténticamente no-circulares, y la versión de Cook en cuestión es una de ellas. Aquí no voy a evaluar su carácter circular o no-circular. Creo, de hecho, que Cook está en lo correcto sobre el punto. Pero, ¿es su versión auténticamente paradójica? Para que lo fuera, los principios que llevan a (i) derivar una contradicción, o (ii) la imposibilidad de dar una asignación de valores de verdad estables al conjunto relevante de oraciones, deben ser aceptables. Voy a explorar dos modos de argumentar que no lo son. voy a concluir que estos intentos llevan a una concepción de la teoría de la verdad muy estrecha, o a negar que un caso paradigmático de paradoja, como el"mentiroso Tradicional", sea auténticamente paradójica. (shrink)

It is possible that the world contains infinitely many agents that have positive and negative levels of well-being. Theories have been developed to ethically rank such worlds based on the well-being levels of the agents in those worlds or other qualitative properties of the worlds in question, such as the distribution of agents across spacetime. In this thesis I argue that such ethical rankings ought to be consistent with the Pareto principle, which says that if two worlds contain the (...) same agents and some agents are better off in the first world than they are in the second and no agents are worse off than they are in the second, then the first world is better than the second. I show that if we accept four axioms – the Pareto principle, transitivity, an axiom stating that populations of worlds can be permuted, and the claim that if the ‘at least as good as’ relation holds between two worlds then it holds between qualitative duplicates of this world pair – then we must conclude that there is ubiquitous incomparability between infinite worlds. I show that this is true even if the populations of infinite worlds are disjoint or overlapping, and that we cannot use any qualitative properties of world pairs to rank these worlds. Finally, I argue that this incomparability result generates puzzles for both consequentialist and non-consequentialist theories of objective and subjective permissibility. (shrink)

According to Humean theories of objective chance, the chances reduce to patterns in the history of occurrent events, such as frequencies. According to non-Humean accounts, the chances are metaphysically fundamental, existing independently of the "Humean Mosaic" of actually-occurring events. It is therefore possible, by the lights of non-Humeanism, for the chances and the frequencies to diverge wildly. Humeans often allege that this undermines the ability of non-Humean accounts of chance to rationalize adherence to David Lewis' Principal Principle (PP), which (...) states that an agent's degrees of belief should match what they take to be the objective chances. In this paper, I propose two approaches to justifying (PP) for non-Humean chance, hence defusing the Humean objection. The first approach justifies (PP) via the role it plays in informing outright beliefs about long-run frequencies. The second approach justifies (PP) by showing that adherence to (PP), even for non-Humean chance, maximizes expected epistemic utility according to the actual objective chance function. I then address an objection to this approach, concerning the alleged circularity of the derivations. (shrink)

Why is there something rather than nothing? This paper explores one particular argument in favor of the answer that 'the existence of nothing' would amount to a logical contradiction. This argument consists of positing the existence of a novel entity, called a bion, of which all contingent things can be composed yet itself is non-contingent. First an overview of historical attempts to compile a systematic and exhaustive list of answers to the question is presented as context. Then follows an analysis (...) of how the antropic principle would manifest itself in a world that consists of information and at the same time conforms to modal realism. Next, a thought experiment introduces bions as the foundation of such a world, showing how under these circumstances the ultimate origin of all existing things would be explained. The non-contingent nature of bions themselves is subsequently argued via a discussion of the principle of non-contradiction. Finally, this theory centered on the existence of bions is integrated into the worldview of Popperian metaphysics. According to the latter's criteria, I conclude that bion theory provides an integral answer to why there is something rather than nothing. (shrink)

One of the still unsolved problems in liberal anarchism is a definition of social constituency in positive terms. Partially, this had been solved by the advancements of liberal discourse ethics. These approaches, built on praxeology as a universal framework for social formation, are detached from the need of any previous or external authority or rule for the discursive partners. However, the relationship between action, personal identity, and liberty within the process of a community becoming solely generated from the praxeological a (...) priori remains largely disputed. In order to develop a testable constitutional model, this study revises how the “ontological turn” was introduced into liberal theories and redefines the concept of liberty. Liberty is usually understood as a moral goal or measurement for just actions, as the generative principle of all social existence - individual and interpersonal. For this purpose, the function of performative contradiction within the mechanism of interpersonal “encounter”, as part of the co-generative process of the individual becoming and social formation was explored through the production of a game-based narrative historiography grounded on 19th century life writings. This narrative historiography was developed in the context of Swiss history, with a “design-based” research approach, and resulted in a prototype for networked storytelling through which the transformative learning process could be visible and the negotiation of competing individual visions of the future could be re-enacted. (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)

In its strongest, unqualified form the principle of wholistic reference is that each and every proposition refers to the whole universe of discourse as such, regardless how limited the referents of its non-logical or content terms. Even though Boole changed from a monistic fixed-universe framework in his earlier works of 1847 and 1848 to a pluralistic multiple-universe framework in his mature treatise of 1854, he never wavered in his frank avowal of the principle of wholistic reference, possibly in (...) a slightly weaker form. Indeed, he took it as an essential accompaniment to his theory of concept formation and proposition formation. Similar views are found in later logicians, and some of the most recent formulations of standard, one-sorted first-order logic seem to be in accord with a form of it, if they do not actually imply the principle itself. (shrink)

In its strongest, unqualified form the principle of wholistic reference is that each and every proposition refers to the whole universe of discourse as such, regardless how limited the referents of its non-logical or content terms. Even though Boole changed from a monistic fixed-universe framework in his earlier works of 1847 and 1848 to a pluralistic multiple-universe framework in his mature treatise of 1854, he never wavered in his frank avowal of the principle of wholistic reference, possibly in (...) a slightly weaker form. Indeed, he took it as an essential accompaniment to his theory of concept formation and proposition formation. Similar views are found in later logicians, and some of the most recent formulations of standard, one-sorted first-order logic seem to be in accord with a form of it, if they do not actually imply the principle itself.Em sua forma mais forte e geral, o princípio da referência universalista afirma que toda proposição refere-se ao universo completo do discurso propriamente dito, independentemente de quão limitados sejam os referentes de seus termos não-lógicos ou com conteúdo. Embora Boole mudasse de um modelo monístico de universo-fixo nos seus trabalhos iniciais de 1847 e 1848 para um modelo pluralista de universo-múltiplo no seu tratado maduro de 1854, ele nunca hesitou em sua aceitação franca do princípio da referência universalista, possivelmente em uma forma ligeiramente mais fraca. De fato, ele considerou este princípio como um acompanhamento essencial para a sua teoria de formação de conceitos e de proposições. Visões semelhantes são encontradas em lógicos posteriores, e algumas das mais recentes formulações da lógica clássica de primeira ordem parecem estar de acordo com uma forma deste, se é que elas não implicam, de fato, o próprio princípio. (shrink)

The aim of this paper is to show that topology has a bearing on Leibniz’s Principle of the Identity of Indiscernibles (PII). According to (PII), if, for all properties F, an object a has property F iff object b has property F, then a and b are identical. If any property F whatsoever is permitted in PII, then Leibniz’s principle is trivial, as is shown by “identity properties”. The aim of this paper is to show that (...) topology can make a contribution to the problem of giving criteria of how to restrict the domain of properties to render (PII) non-trivial. In topology a wealth of different Leibnizian principles of identity can be defined - PII turns out to be just the weakest topological separation axiom T0 in disguise, stronger principles of can be defined with the aid of higher separation axioms Ti, i > 0. Topologically defined properties have a variety of nice features, in particular they are stable in a natural sense. Topologically defined properties do not have a monopoly on defining “good” properties. In the final section of the paper it is show that the topological approach is closely related to Gärdenfors’s approach of conceptual spaces based on the concept of convexity. (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)

The well-known Principle of Plenitude has it that everything that exists in some possible world exists in the actual world. I argue for an amended version of this principle: If there’s a possible world in which something lacks some positive property, then there’s an object in the actual world that lacks that property. That is, all positive universally held properties in the actual world are necessarily universally held. This rules out that for some positive property, everything in (...) the actual world merely happens to have it. After having presented and defended the argument, I show that it has a wide range of corollaries, such as that there are mereologically simple and composite things, physical and non-physical things, caused and uncaused things, and contingent and necessarily existing things. The argument has three premises. The first premise is the thesis that there are no things that do not exist. The second premise is a Fregean theory of linguistic meaning. According to the third premise, two meanings coincide if and only if their reference sets coincide. The notion of a reference set is defined in the paper. (shrink)

Nelson's Proof of the Impossibility of the Theory of Knowledge -/- In addressing the possibility of a theory of knowledge, Leonard Nelson noted the contradiction of an epistemological criterion that one would require in order to differentiate between valid and invalid knowledge. Nelson concluded that the inconsistency of such a criterion proves the impossibility of the theory of knowledge. -/- Had the epistemological criterion had a perception, then it would presume to adjudicate on its own truth (thus epistemological circular argument). (...) However, if one were to assume that the criterion is not knowledge, one would then have to justify how this is a criterion for truth - yet this would only be possible when it may be considered as an object of knowledge. One would equally have had to predetermine the criterion in order to determine the truth of this knowledge, thereby providing another circular argument. Ostensibly, every criterion of truth fails at its very own test since it cannot guarantee its own truth, just as Munchausen, contrary to his assertion, could not draw himself out of the swamp by tugging on a tuft of his own hair. -/- Nelson proposed a solution of the epistemological problem (the question of the differentiation between valid and invalid knowledge), that based on Jakob Friedrich Fries' differentiation between proof and deduction. Proof, according to Nelson (in reference to Fries), can be defined as derivation of truth from one statement from another statement. Thus, from the truth in the statement that "all men are mortal", one is then able to say that "Socrates is a man" and thence extrapolate from the truth of the statement that "Socrates is mortal." If knowledge were to be considered somewhat judgmental (in a statement), then an attempt at proof (i.e. recourse to previous judgments) would inevitably lead to an infinite regression in justification, since each judgment would necessitate a further justification from another judgment. Every attempt to prove an epistemological criterion is thus also confronted by this regression in justification. -/- Nelson's attempt at a solution rests on the assumption of the existence of an immediate knowledge as a justification of the truth (mediate) of knowledge. Nelson considers immediate knowledge to be non-judgmental knowledge. These include intuitions (e. g. seeing-the-red-roof) and also philosophical knowledge that pre-exists in his opinion before a judgmental reflexion (immediate) in our reason (e. g. the principle of causality). -/- Proof of the truth of mediate knowledge can be effected by showing its compliance with attendant immediate knowledge (rational truth = correspondence of mediate knowledge with their immediate knowledge). Nelson considered this as a resolution of the circular epistemological argument. In regard to philosophical knowledge, Nelson sees these as subject to deduction and not proof. The following example illustrates the goal of deduction: -/- An approach for deducing the principle of causality: A) Every change has a cause. (The principle of causality) A´) A is a reiteration of an immediate knowledge. (Meta-assertion following A) -/- "A" may not be provable, but A´ may justified, and thus Nelson identified it as a deduction following from A. // reference: http://www.friesian.com/nelproof.htm. (shrink)

Hume’s Treatise, with its celebrated bundle theory of the self, is a significant contribution to the embryonic Newtonian experimental philosophy of the enlightenment. But the theory is inadequate as it stands, as the appendix to the Treatise makes clear. For this account of the self, apparently, rests on contradictory principles — propositions, fortunately, that can be reconciled, according to Hume. My paper is a critical exploration of Hume’s argument for this intriguing suggestion.