how does one inquire into the truth of first principles? Where does one begin when deciding where to begin? Aristotle recognizes a series of difficulties when it comes to understanding the starting points of a scientific or philosophical system, and contemporary scholars have encountered their own difficulties in understanding his response. I will argue that Aristotle was aware of a Platonic solution that can help us uncover his own attitude toward the problem.Aristotle's central problem with first principles (...) arises from the fact that they cannot be demonstrated in the same way as other propositions. Since demonstrations proceed from prior and better-known principles, if the principles themselves were in need of... (shrink)

ABSTRACT: Alexander of Aphrodisias’ commentaries on Aristotle’s Organon are valuable sources for both Stoic and early Peripatetic logic, and have often been used as such – in particular for early Peripatetic hypothetical syllogistic and Stoic propositional logic. By contrast, this paper explores the role Alexander himself played in the development and transmission of those theories. There are three areas in particular where he seems to have made a difference: First, he drew a connection between certain passages from (...) class='Hi'>Aristotle’s Topics and Prior Analytics and the Stoic indemonstrable arguments, and, based on this connection, appropriated at least four kinds of Stoic indemonstrables as Aristotelian. Second, he developed and made use of a specifically Peripatetic terminology in which to describe and discuss those arguments – which facilitated the integration of the indemonstrables into Peripatetic logic. Third, he made some progress towards a solution to the problem of what place and interpretation the Stoic third indemonstrables should be given in a Peripatetic and Platonist setting. Overall, the picture emerges that Alexander persistently (if not always consistently) presented passages from Aristotle’s logical œuvre in a light that makes it appear as if Aristotle was in the possession of a Peripatetic correlate to the Stoic theory of indemonstrables. (shrink)

In the paper we examine the method of axiomatic rejection used to describe the set of nonvalid formulae of Aristotle's syllogistic. First we show that the condition which the system of syllogistic has to fulfil to be ompletely axiomatised, is identical to the condition for any first order theory to be used as a logic program. Than we study the connection between models used or refutation in a first order theory and rejected axioms for that theory. We show (...) that any formula of syllogistic enriched with classical connectives is decidable using models in the domain with three members. (shrink)

In Nicomachean Ethics VII Aristotle describes akrasia as a disposition. Taking into account that it is a disposition, I argue that akrasia cannot be understood on an epistemological basis alone, i.e., it is not merely a problem of knowledge that the akratic person acts the ways he does, but rather one is akratic due to a certain kind of habituation, where the person is not able to activate the potential knowledge s/he possesses. To stress this point, I focus on (...) the gap between potential knowledge and its activation, whereby I argue that the distinction between potential and actual knowledge is at the center of the problem of akrasia. I suggest that to elaborate on this gap, we must go beyond the limits of Nicomachean Ethics to Metaphysics IX, where we find Aristotle’s discussion of the distinction between potentiality and actuality. I further analyze the gap between potential and actual knowledge by means of Aristotle’s discussion of practical syllogism, where I argue that akrasia is a result of a conflict in practical reasoning. I conclude my paper by stressing that for the akratic person the action is determined with respect to the conclusion of the practical syllogism, where the conclusion is produced by means of a ‘conflict’ between the universal opinion which is potential and the particular opinion which is appetitive. (shrink)

Transformed RAVAL NOTATION solves Syllogism problems very quickly and accurately. This method solves any categorical syllogism problem with same ease and is as simple as ABC… In Transformed RAVAL NOTATION, each premise and conclusion is written in abbreviated form, and then conclusion is reached simply by connecting abbreviated premises.NOTATION: Statements (both premises and conclusions) are represented as follows: Statement Notation a) All S are P, SS-P b) Some S are P, S-P c) Some S are not P, S / (...) PP d) No S is P, SS / PP (- implies are and / implies are not) All is represented by double letters; Some is represented by single letter. No S is P implies No P is S so its notation contains double letters on both sides. -/- RULES: (1) Conclusions are reached by connecting Notations. Two notations can be linked only through common linking terms. When the common linking term multiplies (becomes double from single), divides (becomes single from double) or remains double then conclusion is arrived between terminal terms. (Aristotle’s rule: the middle term must be distributed at least once) -/- (2)If both statements linked are having – signs, resulting conclusion carries – sign (Aristotle’s rule: two affirmatives imply an affirmative) -/- (3) Whenever statements having – and / signs are linked, resulting conclusion carries / sign. (Aristotle’s rule: if one premise is negative, then the conclusion must be negative) -/- (4)Statement having / sign cannot be linked with another statement having / sign to derive any conclusion. (Aristotle’s rule: Two negative premises imply no valid conclusion) Syllogism conclusion by Tranformed Raval’s Notation is in accordance with Aristotle’s rules for the same. It is visually very transparent and conclusions can be deduced at a glance, moreover it solves syllogism problems with any number of statements and it is quickest of all available methods. By new Raval method for solving categorical syllogism, solving categorical syllogism is as simple as pronouncing ABC and it is just continuance of Aristotle work on categorical syllogism. It’s believed that Boole's system could handle multi-term propositions and arguments, whereas Aristotle could handle only two-termed subject-predicate propositions and arguments. For example, it’s claimed that Aristotle's system could not deduce: "No quadrangle that is a square is a rectangle that is a rhombus" from "No square that is a quadrangle is a rhombus that is a rectangle" or from "No rhombus that is a rectangle is a square that is a quadrangle". Above conclusion is reached at a glance with Raval's Notations (Symbolic Aristotle’s syllogism rules). Premise: "No (square that is a quadrangle) is a (rhombus that is a rectangle)" Raval's Representations: S – Q, S – Q / Rh – Re, Rh – Re Premise: "No (rhombus that is a rectangle) is a (square that is a quadrangle)". Raval's Representations: Rh – Re, Rh – Re / S – Q, S - Q Conclusion: "No (quadrangle that is a square) is a (rectangle that is a rhombus)" Raval’s Representations: Q – S, Q – S / Re – Rh, Re – Rh As “ Q – S” follows from “S – Q” and “Re – Rh” from “Rh – Re”. Given conclusion follows from the given premises. Author disregards existential fallacy, as subset of a null set has to be a null set. -/- . (shrink)

Yuri Matiyasevich's theorem states that the set of all Diophantine equations which have a solution in non-negative integers is not recursive. Craig Smoryński's theorem states that the set of all Diophantine equations which have at most finitely many solutions in non-negative integers is not recursively enumerable. Let R be a subring of Q with or without 1. By H_{10}(R), we denote the problem of whether there exists an algorithm which for any given Diophantine equation with integer coefficients, can (...) decide whether or not the equation has a solution in R. We prove that a positive solution to H_{10}(R) implies that the set of all Diophantine equations with a finite number of solutions in R is recursively enumerable. We show the converse implication for every infinite set R \subseteq Q such that there exist computable functions \tau_1,\tau_2:N \to Z which satisfy (\forall n \in N \tau_2(n) \neq 0) \wedge ({\frac{\tau_1(n)}{\tau_2(n)}: n \in N}=R). This implication for R=N guarantees that Smoryński's theorem follows from Matiyasevich's theorem. Harvey Friedman conjectures that the set of all polynomials of several variables with integer coefficients that have a rational solution is not recursive. Harvey Friedman conjectures that the set of all polynomials of several variables with integer coefficients that have only finitely many rational solutions is not recursively enumerable. These conjectures are equivalent by our results for R=Q. (shrink)

This paper intends to explain key differences between Aristotle’s understanding of the relationships between nous, epistêmê, and the art of syllogistic reasoning(both analytic and dialectical) and the corresponding modern conceptions of intuition, knowledge, and reason. By uncovering paradoxa that Aristotle’s understanding of syllogistic reasoning presents in relation to modern philosophical conceptions of logic and science, I highlight problems of a shift in modern philosophy—a shift that occurs most dramatically in the seventeenth century—toward a project of construction, (...) a pervasive desire for rational certainty, and a general insistence on the reducibility of the sciences. The major motivation of this analysis is my intention to show that modern attempts to reduce science/epistêmê to a single science/method of inquiry occlude dialectical and ethico-political dimensions of “reason” and, hence, also impoverish philosophy’s critical capacities. (shrink)

'Chance' is defined as an event on the time scale withour any cause before it appears. That means, that cause and effect is identical. This is the only way to integrate chance into a consistent theory of causality. The identity of cause and effect is called AHK theorem (Aristotle-Hegel-Kaiser).

The Protagoras is the touchstone of Socrates’ moral intellectualist stance. The position in a nutshell stipulates that the proper reevaluation of a desire is enough to neutralize it.[1] The implication of this position is that akrasia or weakness of will is not the result of desire (or fear for that matter) overpowering reason but is due to ignorance. -/- Socrates’ eliminativist position on weakness of will, however, flies in the face of the common-sense experience regarding akratic action and thus Aristotle (...) was at pains to render Socrates’ account of moral incontinence intelligible. The key improvement Aristotle makes to Socrates’s model is to underscore that the conditioning of the akratic’s body plays a critical role in determining the power of one’s appetites and, accordingly, the capacity of one to resist the temptations these appetites present for rational evaluation. As Aristotle puts it, “For the incontinent man is like the people who get drunk quickly and on little wine, i.e., on less than most people.” (1151a 3-4). Aristotle presents what I shall call a somatic paradigm (i.e. the drunkard analogy) in order to tackle the problem of akrasia and it is this somatic solution that marks a significant improvement over Socrates’s intellectualist or informational model or so the tradition tells us. -/- In this paper, I wish to push back on the above Aristotelian explanation. I argue that when one fully examines Socrates’ account of weakness of will that Aristotle’s solution is less effective than is traditionally thought. In fact, Socrates can bring Aristotle’s model into his own; just as Aristotle absorbs what is right about Socrates’s model, namely, that akratic action utilizes reason but to a limited degree, Socrates in Meno (77C-78A) develops his own somatic model of weakness of will that connects to the intellectualist paradigm of the Protagoras. To achieve this rapprochement between the two models, I zero in on the description provided by Socrates of those individuals who desire bad things knowing they are bad as “ill-starred” or “bad spirited” (κακοδαίμων ). The “bad-spirited” is the coward and, in contrast to Aristotle’s drunkard, becomes fearful quickly from little danger. This additional somatic component, when connected to Socrates’s position on akrasia in Protagoras adds a new twist to Socrates’s model in the following way: while no one wishes to be ill-starred such that more harm than good will befall one, one may become so as a result of the bad choices one knowingly makes. -/- -/- [1] “After him came Socrates, who spoke better and further about this subject, but even he was not successful. For he used to make the virtues into sciences, and this is impossible. For the sciences all involve reason, and reason is to be found in the intellectual part of the soul. So that all the virtues, according to him arise in the rational part of the soul. The result is that in making the virtues into sciences he is doing away with the nonrational part of the soul and is thereby doing away with passion and character…” (Aristotle, Magna Moralia 1.1. 1182 a15-26). (shrink)

In recent decades, it has been argued that the modern concept of forgiveness is absent from Aristotle’s conception of συγγνώμη as it appears in his Rhetoric and Nicomachean Ethics. In this paper, I argue that Aristotle’s view is more modern than it might appear. I defend the idea that Aristotle’s treatment of συγγνώμη, when seen in conjunction with his theory of ethical decision, involuntary action, and character alteration, commits him to a cognitive and emotional theory of forgiveness (...) that is both well-grounded and thoroughly modern. I go on to claim that Aristotle’s view of συγγνώμη helps to solve at least four controversial problems about the nature of forgiveness raised by modern philosophers: how one can forgive a wrong without condoning it, whether forgiveness is a duty, whether moral luck requires us to forgive more widely, and whether forgiveness ought to be unconditional. (shrink)

Aristotle classifies opposition (ἀντικεῖσθαι) into four groups: relatives (τὰ πρός τι), contraries (τὰ ἐναντία), privation and possession (στρέσις καὶ ἓξις) and affirmation and negation (κατάφασις καὶ ἀπόφασις). (Cat. , 10, 11b15-23) His example of relatives are the double and the half. Aristotle’s description of relatives as a kind of opposition is as such: ‘Things opposed as relatives are called just what they are, of their opposites (αὐτὰ ἃπερ ἐστι τῶν ἀντικειμένων λέγεται) or in some other way in relation to (...) them. For example, the double is called just what it is double of the other (οἷον τὸ διπλάσιον, αὐτὸ ὃπερ ἐστίν, ἑτέρου διπλάσιον λέγεται). Again, knowledge and the knowable are opposed as relatives, and knowledge is called just what it is, of the knowable, and the knowable too is called just what it is, in relation to its opposite, knowledge; for the knowable is called knowable by something-by knowledge.’ (Cat., 10, 11b24-30) 2) Senses of relatives In Met., Δ, 1020b26-32 Aristotle distinguishes three senses of relatives: i) That which contains something else many times to that which is contained many times in something else, and that which exceeds to that which is exceeded. E.g. double to half ii) The active to the passive; e.g. that which can heat to that which can be heated iii) The measurable to the measure, e.g. the knowable to knowledge and the perceptible to perception. 3) Relatives and contraries Aristotle’s discussion of relatives is unbelievably ambiguous. While he enumerates relatives besides contraries, privation-possession and affirmation-negation as four types of opposition (Cat., 10, 11b15-23), not only does not he restrict relatives to oppositions but he also does not totally differentiate it from contraries. Aristotle distinguishes between two senses of relatives one of which is contraries: ‘We have distinguished elsewhere the two senses in which relatives are so called-some as contraries (ὡς ἐναντία), others as knowledge to things known, a term being called relative because what is said one to the other is said by the other to itself (τῷ λέγεσθαί τι ἄλλο πρὸς αὐτό). (Met., I, 1056b34-1057a1) It seems that this differentiation is the same as, and maybe the one he himself refers to, the differentiation between the second and the third senses of relatives in Met., Δ, 1021a27-32: ‘Relative terms which imply number or capacity, therefore, are all relative because their very essence includes in its nature a reference to something else, not because something else is related to it (πρός τι πὰντα ἐστὶ πρός τι τῷ ὃπερ ἐστὶν ἄλλου λέγεσθαι αὐτὸ ὃ ἐστιν, ἀλλὰ μὴ τῷ ἄλλο πρὸς ἐκεινο); but that which is measurable or knowable or thinkable is called relative because something else is related to it. For the thinkable implies that there is thought of it, but the thought is not relative to that of which it is the thought; for we should then have said the same thing twice.’ Although Aristotle confirms contrariety in relatives (e.g. virtue to vice and knowledge to ignorance), he denies that there is a contrary ‘to every relative’ as there can be no contrary to what is double or treble. (Cat., 7, 6b15-19) The fact that Aristotle dedicates one sense of relatives to contraries means that the fourfold division of oppositions is not such a strict division without any kind of community between them. In his example of the first sense, however, Aristotle says: ‘One and number are in a sense opposed, not as contrary, but as we have said some relative terms are opposed; for inasmuch as one is measure and the other measurable, they are opposed.’ (Met., I, 1057a4-6) Now, the question is: Is Aristotle’s first sense of relative a contrary or not? Aristotle tells us that the opposition in this sense of relatives is the opposition of measure and measurable. The second sense has two differences with the first one: i) it is not a contrary and ii) what is said by one of the relatives to the other is also said by the latter to the former. To differentiate it from the first sense, when the one is the measure of the other, the latter will be the measure of the former as well: ‘But though knowledge is similarly spoken of as related to the knowable, the relation does not work out similarly for while knowledge might be thought to be the measure, and the knowable the thing measured, the fact is that all knowledge is knowable, but not all that is knowable is knowledge, because in a sense knowledge is measured by the knowable.’ (Met., I, 1057a7-12) Aristotle’s assertion at Met., I, 1057a36-37 that ‘of relative terms, those which are not contrary have no intermediate’ ensures us that we must take the first sense as contraries. Here he mentions a criterion of differentiation between two senses: while the first sense accepts intermediates (as, for example, great and small do), the second one does not. (Met., I, 1057a37-b1) It seems, however, that it is only the second sense that is the essential sense of relatives because the first sense, Aristotle says, is an accidental sense: ‘The one is opposed then to the many in numbers as measure to things measureable; and these are opposed as relatives which are not from their very nature relatives.’ (Met., I, 1056b32-34) 4) Definition of relative Aristotle’s first definition of the category of relative (πρός τι) is as such: ‘We call relative all such things as are said to be just what they are, of or than other things, or in some other way in relation to something else (Πρός τι δὲ τὰ τοιαῦτα λέγεται, ὃσα αὐτὰ ἃπερ ἐστὶν ἓτερων εἶναι λέγεται, ἢ ὁπωσοῦν ἄλλως πρὸς ἓτερον). (Cat., 7, 6a36-37; repeated almost without any change in: Cat., 7, 6b6-8) Aristotle’s examples are larger (because it is what it is than something else (τοῦθ᾿ ὃπερ ἐστὶν ἑτέρου λέγεται) that means it is called larger than something) and double. (Cat., 7, 6a37-b1) Aristotle’s aporia regarding relative is about their relation with substances: whether no substance is spoken of as a relative, or whether this is possible with regard to some secondary substances. (Cat., 7, 8a13-15) In the case of primary substances, it seems that he is confident, at least at first, that neither themselves nor their parts are spoken of in relation to anything: neither an individual man is called someone’s individual man nor an individual hand is called someone’s individual hand (but someone’s hand). (Cat., 7, 8a15-21) Although it is obvious that most of secondary substances are not spoken of as relatives (a man is not called someone’s man) (Cat., 7, 8a21-25), there are some with them there is room for dispute: a head is someone’s head and a hand is called someone’s hand, which seem to be relatives. (Cat., 7, 8a25-28) Aristotle thinks this must be due to the previous definition’s being problematic: with that definition ‘it is either exceedingly difficult or impossible to reach the solution that no substance is spoken of as a relative.’ (Cat., 7, 8a28-32) Thus, Aristotle changes his previous definition to a new one: ‘Those things are relatives for which being is the same as being somehow related to something’ (ἔστι τὰ πρός τι οἷς τὸ εἶναι ταὐτόν ἐστι τῷ πρός τί). (Cat., 7, 8a32-34) Although the first definition does indeed apply to all relations, its problem is that it does not take ‘their own being relative’ (τῷ πρός τι αὐτοῖς εἶναι) the same as ‘their being what they are of other things’ (ἃπερ ἐστὶν ἑτέρων λέγεσθαι). (Cat., 7, 8a34-37) Although this change of definition is to exclude all substances from being relative, what Aristotle says in Topics (To., Z, 8, 146a39- ), seems to ignore this: ‘For of everything relative the substance is relative to something else, seeing that the being of every relative term is identical with being in a certain relation to something.’ 5) Necessary knowledge of the related Knowledge of that in relation to which a relative is spoken of is necessary when one knows the relative: it is impossible to know a relative and at the same time not to know that in relation to which it is spoken of. (Cat., 7, 8a37-b3) To prove this, Aristotle adheres to the definition of relatives: ‘If someone knows of a certain ‘this’ that it is a relative, and being for relatives is the same as being somehow related to something, he knows that also to which this is somehow related.’ (Cat., 7, 8a37-b3; cf. 7, 8b3-15 for Aristotle’s examples) This necessary knowledge of the related, if we call it so, dedicates Aristotle an epistemological reason, besides the ontological one mentioned in his definition, for the exclusion of substances. As we noted in our discussion of Aristotle’s definition of relatives, he changed his first definition to exclude all substances from being relatives. Therefore, it is evident that for him relatives must not include substances, either primary or secondary. Aristotle does have no problem with primary substances simply because it is evident for him that they cannot be relatives. The same can be said about most of the secondary substances as well. The problem for which he changed the definition of substances was about some secondary substances like ‘head’ or ‘hand’: the fact that it is possible to know a hand or head without necessarily knowing definitely that in relation to which it is spoken of proves that they are not relatives. (Cat., 7, 8b15-21) 6) Reciprocation Aristotle regards reciprocation (ἀντιστρέφειν) necessary in all relations: ‘All relatives are spoken of in relation to correlatives that reciprocate.’ (Cat., 7, 6b28-29; cf. Cat., 10, 12b21-24) The sense of reciprocation is clear by his own examples: ‘The slave is called slave of a master and the master is called master of a slave; the double double of a half, and the half half of a double.’ (Cat., 7, 6b29-31) Reciprocation of relatives is so necessary that if there seems that we do not have reciprocation, it must necessarily be due to a mistake and that in relation to which something is spoken of must have not been given properly. (Cat., 7, 6b36-7a1) Aristotle’s example is this: If a wing is given as of a bird, ‘bird of a wing’ does not reciprocate because it has not been given properly: a wing is of a winged and not of a bird; a wing is wing of a winged and a winged is winged with a wing. (Cat., 7, 7a1-5) Even if we do not have a proper name to have a proper reciprocation, Aristotle points, we must invent names. (Cat., 7, 7a5-15 and 7b10-14) Thus, having proper names is the condition of necessary reciprocation: ‘All relatives are spoken of in relation to correlatives that reciprocate, provided they are properly given.’ (Cat., 7, 7a22-23) This condition is also said in another way: there is no reciprocation if a relation is given as related to some chance thing or to something that is accidentally the related thing like when, for example, a slave is given as of a man or a biped instead of being given as of a master. (Cat., 7, 7a25-31) 7) Simultaneity of relatives Aristotle believes that in most cases relatives are simultaneous: double and half or master and slave must exist at the same time: when there is a half, there is a double and when there is a slave, there is a master. (Cat., 7, 7b10-14) However, this receives some exceptions like knowable, which is prior and can, thus, exist before and without knowledge. (Cat., 7, 7b22-27) What approves this non-simultaneousness for Aristotle is that the destruction of knowledge does not carry the knowable to destruction. (Cat., 7, 7b27-31) The same is said about perception and perceptible. (Cat., 7, 7b35-8a9) Aristotle attaches simultaneity to reciprocation. This reciprocation, however, is not a simple reciprocation but ‘reciprocation as to implication of existence’ (ἀντιστρέφει μὲν κατὰ τὴν τοῦ εἶναι) with the condition that neither be in any way the cause of the other’s existence. (Cat., 13, 14b27-29; the same is said also at: Cat., 13, 15a4-11) Aristotle’s examples are the double and the half because when there is a double there is a half and when there is a half there is a double but neither is the cause of the other’s existence. (Cat., 13, 14b29-32) (We have ‘reciprocation as to implication of existence’ also in relation between genus and species but it seems that this has a totally different sense there. 8) Having no independent reality That a relative cannot be a substance, either a primary or a secondary substance, is discussed in our review of both the definition of relatives and their reciprocation. The differentiation of relatives and substances are so deep for Aristotle that after questioning the possibility of any common element or principle for substances and relatives (Met., Λ, 1070a33-36), he asserts that no substance, on the one hand, is the element of relatives and none of the relatives, on the other hand, is the element of substances. (Met., Λ, 1070b3-4) Aristotle does not, however, suffice to this. For him, relatives have the least substantiality, which is, for him, almost the same as reality: ‘The relative is least of all categories a real thing (φύσις τις) or substance, and less than quality and quantity; and the relative is an affection of quantity.’ (Met., M, 1088a22-25) Aristotle believes that an evidence of this least reality (ὄν) and substantiality is that relatives have no proper generation, destruction or movement while each of substance, quality and quantity have them. (Met., M, 1088a29-35) Moreover, neither motion (Phy., E, 1) nor any kind of change is applicable to relatives so that relatives are neither themselves alterations nor the subject of alterations (Phy., Z, 3) and the process of losing and acquiring states cannot be considered as alterations because these are the result of the alterations of non-relative things of which they are states. (Phy., Z, 3) Relative is not even matter but is something different. (Met., M, 1088a24-25) The reason is that the matter is potentially of a nature but relative is neither potentially nor actually of a nature. (Met., M, 1088b1-2) To understand the status of relatives in Aristotle’s world, we have to make a tripartite classification; a classification that though Aristotle himself did not make, his assertions approve it. Based on this division, there are three kinds of being in the world: i) Independent beings: This class includes only substances. ii) Dependent beings: This class includes qualities and quantities. Although they are real, they are ‘in’ substances and cannot exist without them. iii) Super dependent beings: This class includes at least relatives. The fact that relatives must be considered in a third class different from substances, on the one hand, and qualities and quantities, on the other hand, is obvious not only from the previously mentioned texts (Met., M, 1088a22-25, 29-35 and b1-2) in which relatives’ reality is considered less than all substances, qualities and quantities and different from matters but from this text: ‘For there is nothing either great or small, many or few, or, in general, relative which is not something (τι ὄν) different (ἓτερον) [that is also] many or few or great or small’. (Met, N, 1088a27-30) Therefore, super dependent beings are those beings that must necessarily be also something else, i.e. an independent or dependent being. Ackrill (1963, 99) points that some of the words used by Aristotle to exemplify relational entities, e.g. slave, are endowed with a complete sense and do not need to be supplemented by a correlate. (Thus, the linguist criterion of incompleteness would be deficient. Some other instances of relative entities like ‘state,’ ‘knowledge’ and perception are not necessarily followed by the genitive case. 9) Extent of relatives What is the extent of relatives? What are or are not included in relatives either among categories or among other concepts? Which concepts or things Aristotle regard as relative? i) Aristotle includes state (ἓξις) and position (θέσις) among relatives. (Cat., 7, 6b2-6; Cat., 7, 6b11-14; Cat., 8, 11a20-24) ii) Although relative is not matter but is something different (Met., M, 1088a24-25), matter is ‘non-being’ only in virtue of an attribute (Phy., A, 9) and is, thus, a relative term. (Phy., B, 2, 194b9) 10) Property and relativity Aristotle draws a contrast between two types of giving a property, absolute and relative: ‘A property is given either in its own right and for always or relative to something else and for a time.’ (To., E, 1, ^128b15-18) Being a civilized man, for example, is an absolute property for man while to command is a relative property for the soul. The absolute property, however, is considered not only potential to be discussed or observed in relation to many things or periods of time, it in fact ‘belongs to its subject relatively to every single thing that there is, so that if the subject is not distinguished relatively to everything else, the property will not have been given correctly.’ (To., E, 1, 129a18-20) Therefore, an absolute property is a property that ‘is ascribed to a thing in comparison with everything else and distinguishes it from everything else.’ (To., E, 1, 128b33- ) An absolute property is, then, absolutely relative and not conditionally relative, i.e. relative to a specific thing. This is what differentiates it from a relative property, which is relative to a certain thing: ‘A property relative to something else is one which separates its subject off not from everything else but from a particular definite thing.’ (To., E, 1, 128b33- ) One important difference between absolute and relative properties is that while an accident can be a relative property, it can never be an absolute property. (To., I, 5, ^102b20-36) For example, sitting, which is an accident, is also a property relatively to those who are not sitting. (To., I, 5, ^102b20-36) 11) Platonic theories as relatives At least three of Platonic theories Aristotle attaches to relatives: i) Forms ‘It seems that a Form is always spoken of in relation to a Form-this desire itself is for the pleasure itself, and wishing itself is for the good itself.’ (To., Z, 8, 147a^10) Moreover, the theory of Forms takes the relative prior to the absolute as, for example, it takes not the dyad but the number as first. (Met., A, 990b15-17) Aristotle believes that this is against not only the necessities of the case but only the Platonists’ opinion because Forms must be substances only, if they can be shared. (Met., A, 990b27-29) There are, however, things like ‘equal’ which are only relative: they are only in relation to something else. Now the theory that ideas are supposed to be substances only should entail the substantiality of merely relatives. The reason being that Forms are not shared incidentally but each thing shares in that which is not predicated of a subject. (Met., A, 990b29-31) ii) Unequal The Platonic theory of great and small or unequal, which we know more from Aristotle and has, in Platonic philosophy, a role like that of matter in Aristotelian philosophy, is also called relative by Aristole. (Met., M, 1089b4-15) iii) Potentiality Aristotle says that Platonists take what potentially is a ‘this’ and a substance but not actually so a relative because it is ‘neither potentially the one or being, nor the contradictory of the one nor of being, but one among beings.’ (Met., N, 1089b15-20) 12) All things as relative Aristotle attaches the theory that ‘everything is true’ to relativity and thinks the consequence of believing in this theory is that everything is true: ‘He who says all things that appear are true, makes all things relative.’ (Met., Γ, 1011a17-20) 13) Genera and species of relatives There are some genera, Aristotle hints, that are relative but their species are not relative. In such cases, the genera are spoken of in relation to something, but none of the particular cases are so spoken. (Cat., 8, 11a20-36) Aristole’s examples are knowledge and grammar of which the former is a relative but the latter is a quality. The consequence of this is that there is nothing absurd for a thing to be in both genera of relative and quality. (Cat., 8, 11a37- ) However, when the species is a relative, the genera will be a relative too. (To., Δ, 4, 124b15- ) Moreover, Aristotle asserts that ‘the differentiae of relative terms are themselves relative.’ (To., Z, 6, 145a14-16) Things that are called relative are called so, Aristotle says, ‘because the classes that include them are of this sort, e.g. medicine is thought to be relative bcs its genus, knowledge, is thought to be relative,’ (Met., Δ, 1021b4-6) 14) Relatives as indefinite? Fabio Morales takes 1088a29-b1 as a textual evidence supporting the assumption that Aristotle regarded relational terms as indefinite. (shrink)

In the present article we attempt to show that Aristotle's syllogistic is an underlying logiC which includes a natural deductive system and that it isn't an axiomatic theory as had previously been thought. We construct a mathematical model which reflects certain structural aspects of Aristotle's logic. We examine the relation of the model to the system of logic envisaged in scattered parts of Prior and Posterior Analytics. Our interpretation restores Aristotle's reputation as a logician of consummate imagination and skill. (...) Several attributions of shortcomings and logical errors to Aristotle are shown to be without merit. Aristotle's logic is found to be self-sufficient in several senses: his theory of deduction is logically sound in every detail. (His indirect deductions have been criticized, but incorrectly on our account.) Aristotle's logic presupposes no other logical concepts, not even those of propositional logic. The Aristotelian system is seen to be complete in the sense that every valid argument expressible in his system admits of a deduction within his deductive system: every semantically valid argument is deducible. (shrink)

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

Aristotle’s influence on D’Arcy Thompson was praised by Thompson himself and has been recognized by others in various respects, including the aesthetic and normative dimensions of biology, and the multicausal explanation of living forms. This article focuses on the relatedness of organic forms, one of the core problems addressed by both Aristotle’s History of Animals (HA), and the renowned chapter of Thompson’s On Growth and Form (G&F), “On the Theory of Transformations, or the Comparison of Related Forms.” We (...) contend that, far from being an incidental inspiration stemming from Thompson’s classicist background, his translation of HA played a pivotal role in developing his theory of transformations. Furthermore, we argue that Thompson’s interpretation of the Aristotelian method of comparison challenges the prevailing view of Aristotle as the founder of “typological essentialism,” and is a key episode in the revision of this narrative. Thompson understood that the method Aristotle used in HA to compare animal forms is better comprehended as a “method of transformations,” leading to a morphological arrangement of animal diversity, as opposed to a taxonomical classification. Finally, we examine how this approach to the relatedness of forms lay the foundation for a causal understanding of parts and their interconnections. Although Aristotle and Thompson emphasized distinct types of causes, we contend that they both differ in a fundamental sense from the one introduced by Darwin’s theory of natural selection, which was formulated as a solution to the species problem rather than the form problem. We conclude that Thompson’s interpretation of Aristotle’s approach to form comparison has not only impacted contemporary scholarship on Aristotle’s biology, but revitalized a perspective that has regained significance due to the resurgence of the problem of form in evo-devo. (shrink)

PHILOSOPHY OF HUMAN RIGHTS: HUMAN RIGHTS IN LIGHT OF THEIR INTERNATIONAL PROTECTION Summary The book consists of two main parts: in the first, on the basis of an analysis of international law, elements of the contemporary conception of human rights and its positive legal protection are identified; in the second - in light of the first part -a philosophical theory of law based on the tradition leading from Plato, Aristotle, and St. Thomas Aquinas is constructed. The conclusion contains an application (...) of the results of the analysis conducted in the second part. The first part comprises four chapters. The first aims at revealing characteristics of human rights on the basis of an analysis of historical conditioning of the inter-national law of human rights and its development. The historical context displays the practical, vindicative, and critical character of the positive legal protection of human rights. Moreover, the process of change of positive human rights law is distinguished from the process of change of human rights as such. In the second chapter the content of human rights - a topic which is only auxiliary to the conducted analysis - is discussed. Basic typology and catalogues of rights proclaimed in the Universal Declaration of Human Rights and protected in the International Covenants of Human Rights are presented. The review of the content of rights aims at a more precise limitation of the field of research. The examination shows a diversity of rights which poses a serious challenge to the coherence of every philosophical theory of human rights. In the third chapter, central in the first part, international law is analyzed with regard to the characteristics of rights and the foundations of them. The analysis of documents shows a number of solutions referring to the anthropological foundations of rights. The inherent dignity of the human person is the source of all human rights. Each human being is recognized as free, and endowed with both reason and conscience. In the propounded conception of man individuals are not rivals but create a community which is a condition for their development. International law characterizes the rights as universal, inherent, inalienable and inviolable. The reconstructed conception also comprises the following basic elements: on the level of the structure of rights, a recognition of their equality, interdependence, and comprehensiveness; in the grounding of these rights, a recognition of the anthropological foundations of law; in the conception of positive law, a recognition of the secondariness of the positive law of human rights to human rights themselves, and a recognition of human rights and justice as the basis for legal order; in the conception of state, a recognition of the well-being of the individual as the fundamental aim of actions undertaken by political institutions, and recogni¬tion of rights which form an impassable boundary to the power of the state, includ¬ing its legislative actions. The characterization of the international legal paradigm serving for the under¬standing of human rights is supplemented by analyses of the structure of their posi¬tive legal protection. Various meanings of the terms "right" and "freedom" are distinguished. Subjective right, as basic structure of the positive legal protection of human rights, is understood as a complex relation formed by various legal situations of the subject of a right which create a functional whole in respect of the subordi-nation of human person to its good. Subordinating person to a good proper for it, expressed usually in a proclamatory norm, is the central element of particular rights around which further elements aiming at the realization of this good are built. In the second part of the book a philosophical theory is developed which allows for the location of a coherent foundation for the presented characterization of human rights and their positive legal protection. This part consists of two chapters. The first includes a review of some - not entirely satisfactory - means of founding of human rights; the second presents philosophical conceptions of law and man which may form a basis for the constructed theory. The review of arguments contained in the first chapter does not aim at a detailed analysis of various specific ways of argumentation encountered in works on this subject but rather at a concise presentation of the main possible lines of argumentation. These analyses also serve to emphasize the positive solutions which are pro¬posed later and to underscore the explanatory power of the elaborated theory. This theory, retaining accurate intuitions contained in the presented types of argumenta¬tion, helps in avoiding their consequences which are difficult to reconcile with the reconstructed paradigm of human rights. Efforts to base human rights on the norms of international law rightly take into account the necessity of determining the content of the rights and their positive legal protection as a means for the realization of man's good. These attempts, how¬ever, do not properly take into account the inherent character of human rights, which are independent of positive law and provide grounds for applying specific legislative measures and not others. Founding human rights on freedom accurately points at the freedom of an indi¬vidual as a constitutive element of some rights; however, absolutization of freedom leads, to a loss of an important element of the contemporary paradigm of under¬standing human rights. This foundation undermines recognition of the fact that human rights may set limits to both the freedom of others and the freedom of the subject of rights itself. Additionally, attempts at the so-called axiological justification of human rights are discussed. This type of justification has a few variants depending on the as¬sumed conception of value. Subjectivistic conceptions have similar advantages and disadvantages to the conceptions basing human rights on freedom; objectivistic conceptions while providing for the universality of human rights place, the fundamental aim of human rights protection beyond the individual human being - in the idealistically existing world of values; finally, conceptions rooting values and human rights in culture, while accurately noting that human rights are learned through the medium of culture, place the source of human rights beyond a concrete individual - in culture and processes which take place in it - which leads to difficulties in finding a basis for the universality of rights. Furthermore, attempts to ground human rights in specific characteristics of the human being are presented. This type of approach points to an important problem of dependence of the content of rights on what man is. However, recognition of specific characteristics of a human being as an ontic foundation of the existence of rights poses a danger to their universality since one has to accept that it is not enough to be a man to be a subject of rights, but a man possessing specific charac¬teristics. The second chapter aims at outlining solutions worked out by Saint Thomas Aquinas. For a fuller understanding of his propositions selected elements of Plato's and Aristotle's philosophy are presented. It was them who formulated the founda¬tions for reflection on law and justice in the ontological context. A qualification is made that Stoicism is not be analysed in depth. Although Thomas' concept of law was undoubtedly developed under the influence of the Stoic doctrine as well, it is not in this that one should look for the tools to understand the ontic foundations of human rights and law in general since the Stoic moral philosophy and philosophy of law were developed in the context of a theory of being which assumed monistic and pantheistic premises as foundations, leading to the recognition of a total subor¬dination of the human individual to a larger unity of which man is only a part. The analysis of Plato's and Aristotle's texts concentrates on problems of justice. Plato seems to be the first philosopher who reflected on the formula basic in the history of European thought: to render to each his due. It appears that justice as both a characteristic of man and his acts is understood in the perspective of that which is just, that which is a good for another man - the recipient of the act. The basis for determining what is just is the relation of correspondence between some¬one and something. While in the case of Plato this relation is based on something beyond its terms, namely on ideas, in the case of Aristotle the relation occurs on account of the elements of the relation itself. Something is just when it contributes to the develop¬ment of the recipient of an act realizing that which is just. At the same time, the realization of that which is just is a good for the agent. In the analysis of the just two types of relation are revealed: the relation of due-to-recipient occurring on account of the compatibility of that which is due, with the recipient of the act; and - a "superstructure" - a relation of obligation-of-subject occurring on account of the compatibility of the acting subject with the thing which should be done. The basis for being that which is due is formed by various potentialities of development of man - the recipient of agency; the basis of being that which is an obligation is the possibility of development of the subject of action. Aristotle distinguishes various types of freedom and points to the necessity of taking them into account in the discussion of justice. Among other things, as the core of man's freedom, he considers life for its own sake, which can be seen as his expression of the basic indices of the autotelic character of man - which is funda¬mental for later conceptions of dignity. The freedom which is described by him is not, however, inherent and inalienable; being free is conditioned by a factual possi¬bility of undertaking actions, which are not solely means to the realization of aims set by others. Thomas Aquinas takes over the Aristotelian research perspective both in his conception of man and of law. At the same time, however, he significantly enriches it. In anthropology he develops a conception of personal being. Drawing upon his distinction between existence ("that something is") and essence ("what something is"), he sees the basis for being a person in the dignity of personal being which is a certain way of existence of a rational being more perfect than that of non-personal beings. The person is a being which, by virtue of its act of existence, is individual¬ized in a specific way. It is an aim in itself. Expressing it in a negative way, one may say that it does not exist as a means for the realization of the aims of others and, in this sense, that it is free. As distinct from Aristotelian conclusions, being a person is not conditioned by the specific actions of a being. Dignity is inherent, based on that which is the foundation of the factual existence of every rational being. Although freedom requires that a being is rational, dignity still encompasses all being, all its properties and potentialities. Thus an act conforming with dignity has to take into account a whole human being. Among different types of that which is just, ius, the first place, from the point of view of understanding law, falls to "the just thing itself ("ipsa res justa"), which is right in the full meaning of the word. On the one hand, it is that which is due; on the other hand, it determines the way of acting in the utmost degree, since the course of every act is determined in the fullest extent by its aim. The content of ius may be determined both by elements independent of free decisions - ius naturale - and by free decisions taking into account the state of things - ius positivum. Recognition of the objective structure of being as the basis of law does not entail that it is possible or desirable to determine unequivocally "the only right" patterns of conduct. This concept is very well justified within the system proposed by Saint Thomas. Individualization of being is a significant element of the develop¬ment of a person as a person. It is attained by the realization of individual aims which are not unequivocally determined by circumstances and the nature common to all people. By virtue of free choices made in the sphere of that which is not by its nature unjust, the object of action becomes ius. Since in the realization of the person the individualization of human being is central, Aquinas clearly sees the need for the protection of the sphere of "dominion of will". This sphere itself constitutes ius naturale, something which is due to man independently of the acts of will. Therefore "law should forbid nothing which is not unjust" ("nihil debet lege prohiberi quod licite fieri potest", In 3 Sent., dist. 40, q. I, a. 1, 3). Besides the relation of due-to-recipient, ius also includes the relation of obligation-of-subject which is superimposed on the relation of due-to-recipient. As far as the ontic foundations of obligation are concerned, in explaining why man is subordinated to realization of the good of others, Aquinas generally follows Aristotle in accepting that this basis is the subordination to moral good - to actions conforming with the learned truth about reality. Aquinas' systemic solutions allow, however, to reach deeper and understand why moral development is also a development of the whole human being. This was difficult within Aristotle's system, since he was reluc¬tant to decide whether precedence should be given to intellectual or moral develop¬ment. The inclination to realise good of another appears to be a transcendental characteristic of being, based on its very existence. Morality understood as rational and free subordination to realize the good of another is a specifically personal way of the realization of this inclination. Thus just actions contribute to the actualization of being in the aspect of its existence and therefore to the actualization of being as a whole. Thomas' conception of natural law (lex naturalis) as participation in eternal law (lex aeterna), offers possibilities for grasping that which is just as something which is basically accessible cognition, independently of Revelation and independently of faith in God, and at the same time as something based in eternal law, understood as a design of God's wisdom. Eternal law, embracing all particular actions, is not, from the human perspective, accessible cognition directly. It is enacted in the struc-ture of the created being and - in case of human beings - in free choices taking this structure into account. In the concluding remarks, the results obtained earlier are applied directly to the contemporary conception of human rights. Human rights are understood in the first place as "just things" - concrete goods of man; as that which is due because of subordination, based on dignity, to the personal development of man. That which is just is understood as a relational - actual or potential - state of things, which exists by virtue of existing relations. Evaluations referring to that which is right are true when respective relations of due-to-recipient take place; norms of conduct are true when respective relations of obligation-of-subject take place. Examples of the application of the sketched theory outside the field of human rights are also presented. Procedural consequences of the developed theory are shown, such as the discrimination of two types of legislative procedures which differ significantly in the structure of argumentation: the first aims at recognition of that which is just independently of the will of the legislator, and the second, at making individual or collective "projects" of development compatible. Finally the possibilities of applying the theory to the increasingly important problems of the protection of the environment and the "rights" of animals are mentioned. The central issue is a philosophical conception of man and his freedom and a conception of law. It is also indispensable to turn to a general theory of being. The search for a comprehensive theory of human rights requires attention to the Abso¬lute Being - God - as well. This is important for at least two reasons. First, a conception of the Absolute Being is integral to philosophy of the systemic type -of which the present book is a piece. A conception of the Absolute Being is signifi¬cant for understanding all being, including, first of all, man as a personal being. Second, every theory of human rights which does not comprise the problem of the Absolute may be questioned as to whether solutions adopted in it do not lead, in consequence, to eliminating God from the perspective of the understanding of law. It is desirable that a philosophical theory should deal with this problem directly. A theory which eliminates God from the perspective of the understanding of rights will be unacceptable for all those who, for philosophical reasons or relying on faith, consider God as the author of inherent rights. Nevertheless, a theoretical approach to rights from the perspective of the Absolute Being should only be a possible extension of a philosophical approach which bases rights on something which is cognizable independently of the acceptance of the existence of God so that the theory is also acceptable for those who reject the existence of God or suspend their judgment on this subject. The pursued theory should therefore contain, on the one hand, reference to natural, faith-independent foundations of human rights, but on the other hand, point to a possible extension accounting for the Absolute Being. The analyses contained in this chapter have undoubtedly some historical value since they are based on source texts. Nevertheless, the use of these texts and not critical works was dictated, first of all, by a conviction that analyses embrace a given theory in the aspect selected by the interests of the researcher. Therefore to find out what past thinkers say on the subject characterized in the first part it is simpler to reach to the sources than to adopt the existing critical works. The pre¬sented reconstruction of Aquinas' views on philosophy of law incorporates proposi¬tions of supplementing and developing some of the ideas undertaken by him. Obligation to act in this and not an other way arises because human actions are subordinated to the conformity, on the one hand, of aims realized by these actions and, on the one hand, the order of being determining that which is favourable to man or destroys him. The content of the order of being is, on the one hand, determined by the structure of being independent from man's will and, on the other, by free decisions of man. (shrink)

• It would be a moral disgrace for God (if he existed) to allow the many evils in the world, in the same way it would be for a parent to allow a nursery to be infested with criminals who abused the children. • There is a contradiction in asserting all three of the propositions: God is perfectly good; God is perfectly powerful; evil exists (since if God wanted to remove the evils and could, he would). • The religious believer (...) has no hope of getting away with excuses that evil is not as bad as it seems, or that it is all a result of free will, and so on. Piper avoids mentioning the best solution so far put forward to the problem of evil. It is Leibniz’s theory that God does not create a better world because there isn’t one — that is, that (contrary to appearances) if one part of the world were improved, the ramifications would result in it being worse elsewhere, and worse overall. It is a “bump in the carpet” theory: push evil down here, and it pops up over there. Leibniz put it by saying this is the “Best of All Possible Worlds”. That phrase was a public relations disaster for his theory, suggesting as it does that everything is perfectly fine as it is. He does not mean that, but only that designing worlds is a lot harder than it looks, and determining the amount of evil in the best one is no easy matter. Though humour is hardly appropriate to the subject matter, the point of Leibniz’s idea is contained in the old joke, “An optimist is someone who thinks this is the best of all possible worlds, and a pessimist thinks.. (shrink)

St. Thomas’s Third Way to prove the existence of God, “Of Possibility and Necessity” (ST 1, q.2, art. 3, response) is one of the most controverted passages in the entire Thomistic corpus. The central point of dispute is that if there were only possible beings, each at some time would cease to exist and, therefore, at some point in time nothing would exist, and because something cannot come from nothing, in such an eventuality, nothing would exist now—a reductio ad absurdum (...) conclusion. Therefore, at least one necessary being must exist. Generations of critics and defenders have contended over St. Thomas’s proof. This article argues that the principle of pros hen analogy is implicit in the Third Way and that once identified explains the ontological dependency of possible beings, as secondary analogates, on the first necessary being, as primary analogate. Thus, without the necessary being as primary analogate, possible beings simply could not exist. The fact that they do exist is evidence for the existence of the necessary being. St. Thomas makes synthesizes the principle of pros hen analogy, as found in Aristotle’s Metaphysics, with the Neoplatonic principle of participation. Aristotle develops pros hen analogy in contradistinction to univocal and equivocal predication as well as to genus in Metaphysics 4.2, 11.3, 12.3-5. Since Scotus and re-enforced by modern analytic logic, philosophers have almost universally regarded any kind of analogical predication as a sub-category of equivocal predication and, thus, implicitly occlude the possibility of considering pros hen analogy in their readings of the Third Way. Distinction of per se and per accidens infinite regress and of radical and natural contingency are also central to understanding the Third Way. While resolving apparent problems in the Third Way, the article also seeks to rehabilitate the doctrine of pros hen analogy as a basic principle in Thomistic and, indeed, Aristotelian metaphysics. (shrink)

During 17th century a scientific controversy existed on the derivation of Snell’s laws of reflection and refraction. Descartes gave a derivation of the laws, independent of the minimality of travel time of a ray of light between two given points. Fermat and Leibniz gave a derivation of the laws, based on the minimality of travel time of a ray of light between two given points. Leibniz’s calculus method became the standard method of derivation of the two laws. We demonstrate in (...) this article that Snell’s law of reflection follows from simple results of geometry. We do not use the concept of motion or the time of travel in our demonstration. That is, time plays no role in our demonstration. (shrink)

I use the Corcoran–Smiley interpretation of Aristotle's syllogistic as my starting point for an examination of the syllogistic from the vantage point of modern proof theory. I aim to show that fresh logical insights are afforded by a proof-theoretically more systematic account of all four figures. First I regiment the syllogisms in the Gentzen–Prawitz system of natural deduction, using the universal and existential quantifiers of standard first-order logic, and the usual formalizations of Aristotle's sentence-forms. I explain how the (...) syllogistic is a fragment of my system of Core Logic. Then I introduce my main innovation: the use of binary quantifiers, governed by introduction and elimination rules. The syllogisms in all four figures are re-proved in the binary system, and are thereby revealed as all on a par with each other. I conclude with some comments and results about grammatical generativity, ecthesis, perfect validity, skeletal validity and Aristotle's chain principle. (shrink)

This book presents a (new) attempt to apply the notion of an underlying logic to Aristotle’s Organon and certain passages of the Metaphysics. The author situates his approach as part of a ‘deductio...

In the center of the fifth book of the Nicomachean Ethics, Aristotle elliptically characterizes political justice as a form of reciprocal rule that exists between free and equal persons pursuing a common life directed toward self-sufficiency under the rule of law. My dissertation analyzes Aristotle's thematic treatments of political justice in the Nicomachean Ethics and Politics in order to elucidate its meaning, clarify its relationship to the other forms of justice that he also discusses, and compare it to contemporary neo-Aristotelian (...) accounts of justice. ;The first chapter examines the unclear and disputed passages of Ethics V.6--7 and explains why Aristotle discusses political justice in his ethical treatise. The second chapter makes use of Aristotle's juxtaposition of political justice to household justice on the one hand and despotic justice on the other hand in order to explicate the necessary conditions of political justice, namely, freedom, equality, commonality, self-sufficiency, and the rule of law. To make sense of these concepts, the chapter explores such topics as Aristotle's understanding of the household, his notion of the self and his political criticisms of Socrates. The third chapter examines political justice or reciprocal rule in the Politics in order to understand how political justice can be both a human virtue and an institutional arrangement of offices. The fourth chapter offers a critique of Fred Miller's reconstruction of Aristotelian natural rights. Although Miller is correct to say that Aristotle recognized and understood "rights claims," he is mistaken in claiming that they are an integral part of Aristotle's practical philosophy. Aristotle understood the problems for political compromise posed by rights conceived as "trumps," and he rejects rights as philosophically fundamental on the grounds that they are an inadequate solution to both the political problem of justice and the stability of flourishing political institutions. (shrink)

The relationship between nature and normativity in Aristotle’s practical philosophy is problematic. On the one hand, Aristotle insists that ethical virtue arises through the habitual repetition of ethically good actions, and thus no one is good or virtuous by nature. Phusikê aretê or “natural virtue” is more like cleverness (demotes) than prudence (phronêsis) and it can result in wrong actions. Yet on the other hand, at times Aristotle appears to use nature to justify normative claims. Thus the problem (...) with Aristotle’s use of the notion of nature in his practical philosophy is that in some instances what is natural seems to be ethically neutral, but in other instances it seems to set the standard for human perfection. Modern Aristotle exegetes have sometimes argued that Aristotle must, consciously or not, be using the term “nature” in at least two different senses here. To use the language of Julia Annas, when Aristotle talks about “natural virtue” in the sense of the talents or abilities which one possesses from birth, he has in mind the notion of “mere nature,” but when he discusses the perfections which a virtuous individual enjoys by his or her nature, Aristotle has in mind the notion of nature as an “ethical ideal.” I would like to suggest an alternative solution to the problem of reconciling Aristotle’s different senses of nature in his Ethics. In Nicomachean Ethics V.7, Aristotle claims that political justice {to dikaion politikon) possesses a “natural” {phusikon) part and a “conventional” {nomikori) part. Aristotle claims that both nature and convention admit of variation, and his language suggests that the two are ultimately parts which need to be interwoven or combined. Scholars who have struggled with Aristotle’s apparently disparate senses of the idea of nature have assumed that nature is an ethical ideal which can be separated from and serve as a guide for that which is merely conventional. I argue that when Aristotle invokes what is “natural” as a norm, he does so under the assumption that the natural component of a norm is ultimately separable from its conventional part only in abstraction. Just like the syllable “BA” is not reducible to the letters “b” and “a,” but instead is a whole greater than its two parts, political justice is a composite unity of nature and convention which, in unifying the two parts, transforms them. (shrink)

Aristotle, in Chapter 7 of his Categories, classifies habits and dispositions, as well as knowledge, among relatives. However, in Chapter 8 of the Categories, he affirms that habits, including knowledge, and dispositions, including unstable knowledge, are qualities. Thus, habits and dispositions in general, and knowledge in particular, seem to be subject to a ‘dual categorization’. At the end of Chapter 8 of the treatise, the issue of the dual categorization is explicitly raised. How can one and the same thing be (...) a quality and a relative? Aristotle gives two distinct solutions to this problem. Both have been criticized by some modern commentators : these solutions would amount to a rejection of the basic principles of the categorial system and, as such, to a sort of philosophical suicide. However, Aristotle’s early commentators, notably the Greek Neoplatonists and Boethius, made attempts to render both solutions plausible and compatible with the rest of the doctrine. Their attempts are not only of exegetical interest, they also contain some significant philosophical analyses concerning the categories. In what follows, I will present the abovementioned problem of dual categorization in Aristotle and the two solutions offered to it in Categories, 8, 11a20-38. I will then turn to the early reception of this text, and focus on the way the Greek Neoplatonists and Boethius tried to make Aristotle’s solutions more plausible. Throughout, I will try to establish in what sense habits and dispositions in general, and knowledge in particular, are relative. I will conclude with some remarks on the later reception of Categories, 8, 11a20-38 and on the problem of the ontological status of mental acts and states. (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)

"It is difficult not to notice a curious unrest in the philosophic atmosphere of the time, a loosening of old landmarks, a softening of oppositions, a mutual borrowing from one another on the part of systems anciently closed, and an interest in new suggestions, however vague, as if the one thing sure were the inadequacy of extant school-solutions. The dissatisfactions with these seems due for the most part to a feeling that they are too abstract and academic. Life is confused (...) and superabundant, and what the younger generation appears to crave is more of the temperament of life in its philosophy, even though it were at some cost of logical rigor and formal purity." - William James (1904). -/- Abstract: The study of model-based reasoning (MBR) is one of the most interesting recent developments at the intersection of psychology and the philosophy of science. Although a broad and eclectic area of inquiry, one central axis by which MBR connects these disciplines is anchored at one end in theories of internal reasoning (in cognitive science), and at the other, in C.S. Peirce’s semiotics (in philosophy). In this paper, we attempt to show that Peirce’s semiotics actually has more natural affinity on the psychological side with ecological psychology, as originated by James J. Gibson and especially Egon Brunswik, than it does with non-interactionist approaches to cognitive science. In particular, we highlight the strong ties we believe to exist between the triarchic structure of semiotics as conceived by Peirce, and the similar triarchic stucture of Brunswik’s lens model of organismic achievement in irreducibly uncertain ecologies. The lens model, considered as a theory of creative abduction, provides a concrete instantiation of at least one, albeit limited, interpretation of Peirce’s semiotics, one that we believe could be quite fruitful in future theoretical and empirical investigations of MBR in both science an philosophy. (shrink)

Sometimes, in the Nicomachean Ethics (NE), Aristotle describes virtuous actions as the sorts of actions that are ends; it is important for Aristotle to do so if he wants to maintain, as he seems to at least until NE 10.7-8, that virtuous actions are a constituent of eudaimonia. At other times, he claims that virtuous actions are the sorts of actions that are for the sake of ends beyond themselves; after all, no one would choose to go into battle or (...) give away a significant portion of their wealth if it did not realize some good end. In this paper, I review the familiar problem raised by Aristotle's discussion of the nature of virtuous actions, propose a solution to this problem by appealing to a distinction between virtuous actions and 'acting virtuously', and sketch the significance of this solution for understanding the relationship between virtue and human happiness. (shrink)

Abstract -/- The indistinction between repose and uniform movement exposed in the principle of inertia marks one of the most famous dissertations: the discussion between Newton and Leibniz. Through their respective conceptions of space, both seek to solve the problem of indistinction. The relational space of Leibniz, supported by the principle of sufficient reason and the identity of indiscernibles leads to the kinematic solution of the problem of inertia. The objective of this paper is to show the (...) contribution of Leibniz, in terms of relations of order, by distinguishing between equality by identity and equality by equivalence. Under a philosophical approach we link identity, equivalence and equality as relations of order with the indiscernibility between different states of movement. We expose first the principle of sufficient reason and the identity of indiscernibles. Under Bernoulli's principle of indifference, we argue that we distinguish between equality in abstract and equality in concrete. As a third part, we present the relationship between the identity of the indiscernibles and the predicate of equality under logical analysis. Finally we present the conclusions. -/- . (shrink)

Plato recognizes faction as a serious threat to any political community. The Republic’s proposed solution to faction relies on bringing citizens into a relation of ὁμόνοια. On the dominant line of interpretation, ὁμόνοια is understood along the lines of “explicit agreement” or “consensus.” Commentators have consequently thought that the καλλίπολις becomes resistant to faction when all or most of its members explicitly agree with one another about certain fundamentals of their political association—for example, they agree regarding who should govern (...) in the καλλίπολις.We argue that ὁμόνοια in Plato’s political philosophy has been under-analyzed and misunderstood. We show that, in Alcibiades I, rendering ὁμόνοια simply as agreement results in confusion about how expertise, political friendship, and civic unity are compossible in a well-ordered political community. In our view, Plato refines and adds philosophical depth to the concept of ὁμόνοια in the Republic. We claim that ὁμόνοια is a relation of psychological “like-mindedness” that obtains among members of different occupational classes in a political community. A community is rendered resistant to faction, then, when its members are, in some significant way, psychologically alike. Additionally, while Platonic ὁμόνοια can naturally be expected to result in substantive agreement among citizens, we argue that Platonic ὁμόνοια does not consist solely in agreement. (shrink)

The text was originally a conference speech. In principle, it was prepared for teachers of philosophy and people interested in philosophy, therefore it has the character of an essay and only to a small extent refers to the literature of the subject. However, I am deeply convinced of the validity of the thesis that I propose in it, even if they may seem only to a small extent supported by references to the state of research. -/- Synthetical studies take a (...) special place in the research on the history of ancient philosophy. They demonstrate the existing perspective by performing a selection and arrangement of the material, presenting the periodisation, accentuating and determining what is “philosophically significant.” This article points out that despite the great progress made in detailed research that has taken place over the last few decades, the general framework of development of philosophy, derived from Hegel’s thought, has remained unchanged for two centuries. Hegel’s perspective has instilled a certain pattern that encompasses a whole series of debatable solutions. These include (1) development of a certain understanding of what “philosophy” is and thus separating it from a wide spectrum of literature, rhetoric, medicine, and religion; (2) introduction of a dubious periodisation (e.g. the distinction between the Presocratic period and Socrates’ breakthrough in the form of a departure from the philosophy of nature and return to ethical considerations; (3) adoption of philosophy of Plato and Aristotle as the apex of thought. The author highlights the need to change the approach to the history of ancient philosophy and modify the existing paradigm. He calls for paying greater attention to the intertextual element and to the fact that the assessment of originality and relevance of preserved works is falsified due to the disappearance of comparative material. The proposal to establish a new reconstructive paradigm is based on the belief that during further research on ancient philosophy it would be advisable (1) to expand the research perspective and enrich it with the fields of education, medicine, the great sphere of literature, the spheres of fine arts and music, (2) to focus more on the issue of transmission and reception of texts thanks to which it is possible to deepen and extend the reconstructed context of philosophical discussions, (3) to come to the realisation that the abstract character of description, connected with all the syntheses of the philosophical thought in antiquity lead to its oversimplification and impoverishment by presenting it out of the context and depriving of what is individual and specific for a particular thinker. (shrink)

This paper defends Aristotle’s project of deriving the order of time from the order of change in Physics 4.11, against the objection that it contains a vicious circularity arising from the assumption that we cannot specify the direction of a change without invoking the temporal relations of its stages. It considers and rejects a solution to this objection proposed by Ursula Coope, and proposes an alternative solution. It also considers the related problem of how the temporal (...) orders and directions derived from individual changes can together constitute a single, globally consistent order and direction of time. (shrink)

It is uncontroversial that artifacts like statues and tables are mind-dependent. What is controversial is whether and how this mind-dependence has implications for the ontology of artifacts. I argue the mind-dependence of artifacts entails that there are no artifacts or artifact joints in the extra-mental world. In support of this claim, I argue that artifacts and artifact joints lack any extra-mental grounding, and so ought not to have a spot in a realist ontology. I conclude that the most plausible story (...) about artifacts is that they are in minds of suitably intelligent creatures, and not the extra-mental world. Artifacts and their joints are merely mental projections onto a world of ‘indifferent materials’. With this established, I show how many cases of object coincidence, the view that more than one material object can be located in the same exact region of space-time, cannot occur. (shrink)

I discuss a contemporary solution to the dynamic problem of old evidence (POE), as proposed by Sprenger. Sprenger’s solution combines the Garber–Jeffrey–Niiniluoto (GJN) approach with Howson’s suggestion of counterfactually removing the old evidence from scientists’ belief systems. I argue that in the dynamic POE, the challenge is to explain how an insight under beliefs in which the old evidence E is known increased the credence of a scientific hypothesis. Therefore, Sprenger’s counterfactual solution, in which E has (...) been artificially removed, does not resolve the problem. I consider several potential responses. (shrink)

We re-examine the problem of existential import by using classical predicate logic. Our problem is: How to distribute the existential import among the quantified propositions in order for all the relations of the logical square to be valid? After defining existential import and scrutinizing the available solutions, we distinguish between three possible cases: explicit import, implicit non-import, explicit negative import and formalize the propositions accordingly. Then, we examine the 16 combinations between the 8 propositions having the first two (...) kinds of import, the third one being trivial and rule out the squares where at least one relation does not hold. This leads to the following results: (1) three squares are valid when the domain is non-empty; (2) one of them is valid even in the empty domain: the square can thus be saved in arbitrary domains and (3) the aforementioned eight propositions give rise to a cube, which contains two more (non-classical) valid squares and several hexagons. A classical solution to the problem of existential import is thus possible, without resorting to deviant systems and merely relying upon the symbolism of First-order Logic (FOL). Aristotle’s system appears then as a fragment of a broader system which can be developed by using FOL. (shrink)

The paper defends three claims about Aristotle’s theory of uncontrolled actions (akrasia) in NE 7.3. First, I argue that the first part of NE 7.3 contains the description of the overall state of mind of the agent while she acts without control. Aristotle’s solution to the problem of uncontrolled action lies in the analogy between the uncontrolled agent and people who are drunk, mad, or asleep. This analogy is interpreted as meaning that the uncontrolled agent, while (...) acting without control, is still in possession of her knowledge but she is unable to use it as knowledge due to the temporary disablement of her reason by appetite. Due to this disablement, the uncontrolled agent is temporarily unable to be motivated to act by her knowledge and acts merely on her appetite. Second, I argue that the second part of NE 7.3 provides an analysis of the particular mental state from which the uncontrolled action issues. Its central passage is a description of the uncontrolled agent’s state of mind before the uncontrolled action and not, as it has been traditionally understood, a description of her state of mind during the uncontrolled action. Third, I argue that, on Aristotle’s view, the transition from the state before the uncontrolled action to the state in which the agent already acts without control does not involve any psychological state that would constitute the agent’s choice to abandon her decision and give in to her desires but proceeds on a purely physiological level. (shrink)

According to the “paradox of knowability”, the moderate thesis that all truths are knowable – ... – implies the seemingly preposterous claim that all truths are actually known – ... –, i.e. that we are omniscient. If Fitch’s argument were successful, it would amount to a knockdown rebuttal of anti-realism by reductio. In the paper I defend the nowadays rather neglected strategy of intuitionistic revisionism. Employing only intuitionistically acceptable rules of inference, the conclusion of the argument is, firstly, not ..., (...) but .... Secondly, even if there were an intuitionistically acceptable proof of ..., i.e. an argument based on a different set of premises, the conclusion would have to be interpreted in accordance with Heyting semantics, and read in this way, the apparently preposterous conclusion would be true on conceptual grounds and acceptable even from a realist point of view. Fitch’s argument, understood as an immanent critique of verificationism, fails because in a debate dealing with the justification of deduction there can be no interpreted formal language on which realists and anti-realists could agree. Thus, the underlying problem is that a satisfactory solution to the “problem of shared content” is not available. I conclude with some remarks on the proposals by J. Salerno and N. Tennant to reconstruct certain arguments in the debate on anti-realism by establishing aporias. (shrink)

Although the theory of the assertoric syllogism was Aristotle's great invention, one which dominated logical theory for the succeeding two millenia, accounts of the syllogism evolved and changed over that time. Indeed, in the twentieth century, doctrines were attributed to Aristotle which lost sight of what Aristotle intended. One of these mistaken doctrines was the very form of the syllogism: that a syllogism consists of three propositions containing three terms arranged in four figures. Yet another was that a syllogism is (...) a conditional proposition deduced from a set of axioms. There is even unclarity about what the basis of syllogistic validity consists in. Returning to Aristotle's text, and reading it in the light of commentary from late antiquity and the middle ages, we find a coherent and precise theory which shows all these claims to be based on a misunderstanding and misreading. (shrink)

In this paper, I argue that one approach to normative political theory, namely contextualism, can benefit from a specific kind of historical inquiry, namely genealogy, because the latter provides a solution to a deep-seated problem for the former. This problem consists in a lack of critical distance and originates from the justificatory role that contextualist approaches attribute to contextual facts. I compare two approaches to genealogical reconstruction, namely the historiographical method pioneered by Foucault and the hybrid method (...) of pragmatic genealogy as practiced by Bernard Williams, arguing that they both ensure an increase in critical distance while preserving contextualism’s distinctiveness. I also show, however, that only the latter provides normative action-guidance and can thus assist the contextualist theorist in the crucial task of discerning how far certain contextual facts deserve their justificatory role. I prove this point by showing how a pragmatic genealogy of the practice of punishment can inform the contextualist’s reflection about the role this practice should play in a transitional scenario, i.e. in the set of circumstances societies go through in the aftermath of large-scale violence and human rights violations. (shrink)

Alexander of Aphrodisias picks up Aristotle’s insufficient treatment of simultaneous perception and develops an adequate solution for the problem, thereby offering an account of the unity of perceptual consciousness—the single mental activity of a single subject with complex content. I show the adequacy of the solution by using as criteria the requirements that have been identified by Aristotle and approved (and explained) by Alexander. I analyze Alexander’s solution in two turns. First, with respect to heterogeneous (...) perceptibles, Alexander adopts and reformulates Aristotle’s metaphorical account invoking the analogy with a point. Second, with respect to homogeneous opposites, accordingly, perception is judgement, but it involves physical changes in diverse parts of the primary sense-organ. By this account Alexander resolves the issue of the unity of the subject on the level of the capacity of the soul, and coordinates the complexity of content with the complexity on the physical level. In addition to being adequate, the solution is faithful to Aristotle. I suggest that the interpretative decisions Alexander makes (the clarification of the analogy; the reference he finds to the analogy; the two components of the solution, judgement and parts of the organ) form an ingenious extension of Aristotle’s treatment. Interestingly, even though many elements in Alexander’s interpretation are taken up by modern commentators, no one has followed it in its entirety, nor even treated it in its own right. (shrink)

Aristotle’s theory of human happiness in the Nicomachean Ethics explicitly depends on the claim that contemplation (theôria) is peculiar to human beings, whether it is our function or only part of it. But there is a notorious problem: Aristotle says that divine beings also contemplate. Various solutions have been proposed, but each has difficulties. Drawing on an analysis of what divine contemplation involves according to Aristotle, I identify an assumption common to all of these proposals and argue for (...) rejecting it. This allows a straightforward solution to the problem and there is evidence that Aristotle would have adopted it. (shrink)

In ancient philosophy, there is no discipline called “logic” in the contemporary sense of “the study of formally valid arguments.” Rather, once a subfield of philosophy comes to be called “logic,” namely in Hellenistic philosophy, the field includes (among other things) epistemology, normative epistemology, philosophy of language, the theory of truth, and what we call logic today. This entry aims to examine ancient theorizing that makes contact with the contemporary conception. Thus, we will here emphasize the theories of the “syllogism” (...) in the Aristotelian and Stoic traditions. However, because the context in which these theories were developed and discussed were deeply epistemological in nature, we will also include references to the areas of epistemological theorizing that bear directly on theories of the syllogism, particularly concerning “demonstration.” Similarly, we will include literature that discusses the principles governing logic and the components that make up arguments, which are topics that might now fall under the headings of philosophy of logic or non-classical logic. This includes discussions of problems and paradoxes that connect to contemporary logic and which historically spurred developments of logical method. For example, there is great interest among ancient philosophers in the question of whether all statements have truth-values. Relevant themes here include future contingents, paradoxes of vagueness, and semantic paradoxes like the liar. We also include discussion of the paradoxes of the infinite for similar reasons, since solutions have introduced sophisticated tools of logical analysis and there are a range of related, modern philosophical concerns about the application of some logical principles in infinite domains. Our criterion excludes, however, many of the themes that Hellenistic philosophers consider part of logic, in particular, it excludes epistemology and metaphysical questions about truth. Ancient philosophers do not write treatises “On Logic,” where the topic would be what today counts as logic. Instead, arguments and theories that count as “logic” by our criterion are found in a wide range of texts. For the most part, our entry follows chronology, tracing ancient logic from its beginnings to Late Antiquity. However, some themes are discussed in several eras of ancient logic; ancient logicians engage closely with each other’s views. Accordingly, relevant publications address several authors and periods in conjunction. These contributions are listed in three thematic sections at the end of our entry. (shrink)

This article investigates a tension that arises in Hegel’s aesthetic theory between theoretical and practical forms of reason. This tension, I argue, stems from Hegel’s appropriation of an Aristotelian framework for a historically unfolding social teleology which puts practical reason to work for the aims of theoretical reason. Recognizing that this aspect of Hegel’s dialectic is essential in overcoming problems left in Kant’s transcendental idealism, the appearance of incongruence does not lessen. Grouped together with absolute spirit, Hegel positions art as (...) a transitory mode of mind, a vehicle, which aims to raise spirit to the higher cognition of philosophy. When the unfolding absolute concept becomes too complex for articulation in the material, art must end, as spirit’s message can be expressed only through the non-material form of philosophy. This study focuses on the ambivalence found in Hegel’s writings regarding his account of historical completion. Though Hegel sees in the Absolute a metaphysical solution to the unity of subject and object, the practical aspects of the unity appear to falter when philosophy becomes the dominant mode of expression at the close of a historical cycle. In Lectures on the History of Philosophy, Hegel links his notion of the Absolute, albeit with modification, to Aristotle’s nous. As described in De Anima, this entails a progression in which active and possible intellect rise to the level of the eternal, while passive intellect, the imaginative element, passes on with the body. Because the architecture of Aristotle’s nous, which is not in line with his defense of poetry, is integrated into the blueprint of Hegel’s absolute, an unresolved tension emerges in the spirit of art. A divergence of aims is forced to the surface through Hegel’s application of a template for achievement of theoretical knowledge, with an end in the universal, to a form of practical knowing which has an end in the particular. (shrink)

In this paper I defend the eternity solution to the problem of human freedom and divine foreknowledge. After motivating the problem, I sketch the basic contours of the eternity solution. I then consider several objections which contend that the eternity solution falsely implies that we have various powers (e.g., to change God’s beliefs, or to affect the past) which, according to the objector, we do not in fact have.

This paper aims to suggest a new arrangement of Plato’s dialogues based on a different theory of the ontological as well as epistemological development of his philosophy. In this new arrangement, which proposes essential changes in the currently agreed upon chronology of the dialogues, Parmenides must be considered as criticizing an elementary theory of Forms and not the theory of so-called middle dialogues. Dated all as later than Parmenides, the so-called middle and late dialoguesare regarded as two consecutive endeavors to (...) resolve the problems drawn out in there; an effort in the theory of knowledge through Theaetetus, Meno and Phaedo and another in ontology through the second part of Parmenides, Sophist and Republic. -/- Key Words: Plato; chronology; development; ontology; epistemology -/- Introduction There are many determinative factors regarding the chronology of the dialogues about which our informationis terribly deficient. There is no certain evidence about the date of each of the dialogues, nor any reliable information about the beginning and ending time of Plato’s writing. The most determinative issue among all chronological matters, I am inclined to insist, is the question that if did Plato use to manipulate or, as Dionysius of Halicarnassus said (1808, 406), polish, comb and curl his previously written dialogues and, if so, to what extent? That there is almost no answer to this most crucial issue shows how far deficient, indefinite and inconclusive the chronological plans can be. The fact that we do not even have enough information to decide, in case of Socratic dialogues, to what extent they are reporting or reflecting the actual dialogues of historical Socrates, and to what extent they are Plato-made stories so that even now we have a schizophrenic character between Socrates and Plato, can be good evidence for this deficiency. There are, nevertheless, somemore certain informations that can be contributive in case of the arrangement of some dialogues. a) The only external evidence provided by Aristotle that Lawswas written after Republic (Politics, II, 6) which was repeated by others . b) Few internal evidences provided by references in dialogues themselves including: i) the cross references in the Sophist 217a and Politicus 257a and 258b which indicate the prior composition of Sophist; ii) Timaeus 27 which hints to Critias as its sequel; iii) Theaetetus 183e where Socrates says he met Parmenides when he was young which has been taken as a reference to Parmenides; iv) a similar reference to the discussion of young Socrates with Parmenides this time in Sophist 217c; v) Sophist 216a refers to a previous discussion which has been thought to be referring to Theaetetus, and vi) the Timaeus 17b-19b in which Socrates tries to summarize his previous dialogue about the structure of cities, and the kind of men these cities must bring up to become the best people and so on which, among the dialogues we have now, must refer to Republic. (shrink)

This review places this translation and commentary on Book A of Prior Analytics in historical, logical, and philosophical perspective. In particular, it details the author’s positions on current controversies. The author of this translation and commentary is a prolific and respected scholar, a leading figure in a large and still rapidly growing area of scholarship: Prior Analytics studies PAS. PAS treats many aspects of Aristotle’s Prior Analytics: historical context, previous writings that influenced it, preservation and transmission of its manuscripts, (...) editions of its manuscripts, interpretations, commentaries, translations, and its influence on subsequent logic, philosophy, and mathematics. All this attention is warranted because Prior Analytics marks the origin of logic: the field that, among other things, asks of a given proposition whether it follows from a given set of propositions; and, if it follows, how we determine that it follows; and, if it does not follow, how we determine that it does not follow. This translation and commentary is not suitable for use in an undergraduate course. It has too many quirks that the teacher would want to warn against. A copy editor should have dealt with these things and with other matters such as incorrect punctuation and improper end-of-line divisions. The prose is heavily laden with glaring clichés. The one-page preface contains “longer than I care to remember”, “more than I can possibly list here”, “first and foremost”, and “last and by no means least”—a sentence later is devoted to thanking the “incredibly meticulous and helpful copy-editor”. A few pages later the translator reveals the need “to find a path between the Scylla … and the Charybdis …”. Moreover, the index is far from meeting the needs of undergraduate students. The attention to scholarly detail is not what one hoped for from Oxford University Press. At 26b10-15, this translation reads “let swan and white be chosen as white things” for what Smith correctly translates “let swan and snow be selected from among those white things”. At 41b16, “angles AB and CD” should read “angles AC and BD”. Despite this book’s flaws, it will be found useful if not indispensable for those currently engaged in Prior Analytics studies. The alternatives suggested to Robin Smith’s translation choices are often worth consideration. It is to be emphasized, however, that this book is unsuitable for those entering Prior Analytics studies. (shrink)

In these pages the author intends to examine the idea, quite widespread among Aristotle’s recent scholars, that the method of metaphysics were mainly dialectical. This problem is investigated in Aquinas, who decidedly denies that metaphysics uses dialectics because it just provides probability. Metaphysics, unlike dialectics, is not only based on the being of reason but also on the natural being. Therefore, it does not simply constitute a rational game about quiddities, but it studies things in their real actuality (...) and must therefore be supported by evidence. Although Aquinas agrees with Aristotle in affirming that not every science enjoys the same certainty, this fact is due to different reasons. First, all things do not possess the same stability and constancy. Secondly, there is not always a perfect match between the studied matter and the human faculty to ascertain. This match between the object and the subject is the most decisive factor for the certainty of sciences. (shrink)