Aristotle: Logic and Philosophy of Language

In In V Metaphysics, lec. 9, Aquinas distinguishes between “being by accident” (ens per accidens) and “being by itself” (ens per se) and includes the nine accidental categories under the latter. But isn’t substance a being per se while accidents are, by definition, accidental beings? Several authors—including Ralph McInerny, Paul Symington, and Greg Doolan—have offered explanations of this strange classification. Drawing on an overlooked parallel text in the Posterior Analytics commentary and on Aquinas’s critique of Avicenna’s understanding of accidental denominatives, (...) this paper presents an alternative explanation of the lecture. In the process, it clarifies how Aquinas views the relation of the ten categories to predication and suggests important implications for how we should understand the analogy of being and the phrase “substantial being” (esse substantiale). (shrink)

In this chapter I argue that writers on metaphor have misunderstood Aristotle on metaphor. Aristotle is not an elitist about metaphor and does not consider metaphors to be merely ornamental. Rather, Aristotle believes that metaphors are ubiquitous and believes that people can express themselves in a clearer and more attractive way through the use of metaphors and that people learn and understand things better through metaphor. He also distinguishes between the use of metaphor and the coinage of metaphor, and believes (...) that the ability to coin marvelous new metaphors is a form of literary genius, and he provided an entirely natural origin of metaphor coinage. (shrink)

L. Gazziero, « “Οἰκείως τῇ λογικῇ πραγματείᾳ” (Simplicii in Aristotelis categorias commentarium, 12.11). Contraintes disciplinaires – anciennes et modernes – de l’interprétation logique des Catégories d’Aristote », dans V. Brière et J. Lemaire (éd.), Qu’est-ce qu’une catégorie ? Interprétations d’Aristote, Leuven, Peeters, 2019, p. 9-59 [ISBN 9789042936621] -/- In addition to understanding the very notion of « category » according to its different Aristotelian contexts, the first order of business of an archaeology of Aristotle’s categories is to inquire into its (...) influential evolution at the hands of Late Ancient commentators. The essay retraces the origin and development of the « logical » interpretation which held sway both in ancient and modern times. It shows first that the key to understand the debate between Benveniste and Derrida over Aristotle’s categories is to be found in the Neoplatonic exegesis of the work of the same name. It shows next the powerful dynamic that led the commentators to dismiss more than a few hints in the text itself in order to build a remarkably consistent interpretation that understood the notion of category as the simplest and most fundamental element in a building block theory of linguistic expression and argumentation. -/- Face au foisonnement qui caractérise l’instruction contemporaine du dossier des « catégories » d’Aristote, il est encore et toujours utile de suivre le fil historique inauguré par Adolf Trendelenburg, réinventé par Emile Benveniste et élevé par Jacques Derrida au rang d’impératif méthodologique. Le geste inaugural d’une archéologie de la notion de « catégorie » consiste donc à se prémunir contre le risque d’évacuer le problème historique des catégories à la faveur d’une catégorialité anachronique ou passe-partout : ce qui n’est possible qu’à condition de replacer les « catégories » dans les différents contextes aristotéliciens où elles sont utilisées et d’interroger les contraintes disciplinaires qui ont structuré le débat autour de leur nature chez les commentateurs de l’Antiquité tardive. (shrink)

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

Boethius identifies God both with esse ipsum and esse suum. This paper explains Boethius's general semantic use of "esse" and the application of this use to God. It questions the helpfulness of attributing to Boethius "existence" words and argues for a more robust role in Boethius’s thought for Hilary of Poitiers’s and Augustine’s exegeses of Exodus 3:14-15 than has been acknowledged in recent scholarship.

Many contemporary philosophers hold that comparison requires a common, monistic ‘covering value’, and Aristotle is often described as a forerunner of this view. This paper reconsiders that claim. First, its textual warrant is substantially weaker than has been thought. Philosophically, moreover, Aristotle’s theory of non-synonymous predication allows for comparisons to be made using the special kind of non-synonymous terms that he calls pros hen legomenon, literally those ‘said with reference to a single thing.’ His favourite example is ‘healthy’ as said (...) of food, organisms, and medical procedures: these various senses are not entirely synonymous, yet are not simply unconnected. This has significant implications. Aristotle famously holds that goodness is species-specific, and it would then seem that species cannot be ranked according to how good they are. Yet Aristotle does—frequently—rank species. The paper shows us that he is not, pace other scholars, thereby caught in a contradiction. -/- . (shrink)

Nos Segundos Analíticos II.8-10, Aristóteles apresenta um modelo investigativo de descoberta da essência pela causa a partir de uma estrutura triádica: a demonstração silogística. Esse modelo explanatório-causal é colocado em prática em casos de processos naturais (e.g. eclipse, trovão) e, apesar de mencionadas, as substâncias sensíveis (e.g. homem) não são concretamente analisadas – algo que só se consolida nos livros centrais da Metafísica (mais especificamente, em Z.17) a partir da análise hilemórfica. Além disso, em Segundos Analíticos II.9, Aristóteles apresenta uma (...) restrição quanto ao domínio de aplicação do modelo: apenas os itens que possuem “causa diferente” (ἕτερον αἴτιον) são passíveis de análise nesses termos. Se, por um lado, o capítulo parece ser uma restrição ao caso específico das substâncias, não são explicitados quais itens possuem e quais não possuem “causa diferente”. Desse modo, é suscitada a questão: teria Aristóteles previsto a aplicação do modelo explanatório-causal às substâncias hilemórficas quando da elaboração dos Segundos Analíticos, ou sua utilização na Metafísica representaria uma reformulação posterior? Neste cenário, temos pelo menos duas hipóteses interpretativas: (i) uma leitura restritiva (ou desenvolvimentista), em que as substâncias não teriam sido previstas; (ii) uma leitura não-restritiva, que se opõe à primeira ao defender que as substâncias já estariam previstas na elaboração dos Segundos Analíticos, e sua omissão se daria por economia argumentativa. O objetivo do presente trabalho é apresentar a hipótese não-restritiva como uma solução para o problema do ἕτερον αἴτιον, defendendo uma aproximação entre a Metafísica e os Segundos Analíticos. (shrink)

Relying on evidence from fifteen epigraphic collections and sixty-odd ancient sources as well as discussing a literature of over five hundred titles, the essay’s highly unorthodox conclusions are a case in point of the micrological ideal of achieving novelty on any given subject by way of transcribing and studying first-hand all relevant materials – edited and unedited alike. The paper’s ambition was to shed new light on one of the most intriguing analogies of the whole Aristotelian corpus, namely the comparison (...) between words and pebbles. A review of all material evidence and virtually all extant sources made short work of two related, albeit mutually exclusive, misconception about ancient reckoning boards and their workings: (1) the idea that – for all practical purposes – the abacus’ arrangement mirrored the decimal system, its columns and rows conveniently matching units, tens, hundreds, thousands, etc. (2) the idea that the inscriptions on several surviving counting boards were a nuisance to the extent that, being inconsistent to a fault with the decimal system itself, they made actual calculations harder than they already were (as opposed to making them easier, as one would expect). The paper demonstrated that the first assumption – the « decimal » bias – is simply mistaken and betrays little or no awareness of the epigraphic and archaeological evidence. The paper also demonstrated that the second assumption – the « abacus riddled with complications » bias – simply defeats the purpose of resorting to the abacus in the first place and betrays a poor understanding of its practical vocation which, most assuredly, was not to add to the very problem it was meant to solve. After bulldozing its way through both misunderstandings, the essay focused on the abacus most distinctive features, that is positionality (i.e. the abacus being a positional system through and through) and hybridity (i.e. the abacus’ place value system being monetary in nature and purpose, as opposed to it being abstract and homogeneous). The final result is an interpretation that moves away from the received views by showing that the prologue of the Sophistici elenchi offers no support to the notion that, when Aristotle referred to counters, he was leaning on a kinship of sorts – or any kinship, for that matter – between abstract calculation and speech. Once we turns the pebble’s simile on its head and set it back upon its feet (Aristotle’s pebble analogy is about pebbles, what else?), it becomes clear that it presupposed numeracy all right, but it was not about numeracy itself. Moreover its goal was not to explain why computational and linguistic symbolisms succeed, but to explain how they fail – failure being the whole point; in this particular instance, failure to detect and prevent abusive value shifts affecting words and counters alike. (shrink)

Quelque nombreuses et quelque influentes qu'elles soient par ailleurs, les vues d'Aristote sur le langage se caractérisent à la fois par leur hétérogénéité et par leur marginalité. Sans faire nulle part du langage et de la signification l'objet d'une investigation autonome et méthodique, Aristote multiplie les remarques et les digressions à leur sujet, que ce soit dans ses écrits d'éthique et de politique ou dans ses traités d'histoire et de philosophie naturelle, ou encore dans ses manuels de dialectique, de poétique (...) et de rhétorique. Face à l'abondance de ces matériaux et aux difficultés qu'ils présentent du fait de s'offrir au lecteur en ordre quelque peu dispersé, «Le langage. Lectures d'Aristote» fait le choix d'indexer l'étude du langage chez Aristote sur des passages précis du corpus en ne posant aux textes aristotéliciens d'intérêt linguistique que les questions auxquelles ces mêmes textes - tantôt pris isolément, tantôt mis en relation les uns avec les autres - apportent une réponse. (shrink)

I examine two startling claims attributed to some philosophers associated with Megara on the Isthmus of Corinth, namely: Ml. Something possesses a capacity at t if and only if it is exercising that capacity at t. M2. One can speak of a thing only by using its own proper A6yor;. In what follows, I will call the conjunction of Ml and M2 'Megaricism' .1 The lit­ erature on ancient philosophy contains several valuable discussions of Ml and M2 taken individually .2 (...) But there is no discussion of them together, much less of their logical relations. I intend to remedy that lack, and to show why it is a lack worth remedying. My aims are both philosophical and historical. Inevitably, in saying anything new and interesting about Megaric views, I will be adopting assumptions scarcely free from controversy, and indulging in quite a bit of charitable recon­ struction. But the resulting picture is of considerable interest. For it explains why, although Ml and M2 seem to have little to do with one another, it is in fact small wonder that anyone who held one would hold the other, for, as I attempt to show, they entail each other. It explains why the Megarics are associated in the primary literature with the names of such diverse philosophical ancestors as Parmenides and Protagoras. And it explains why, although they are both false, Ml and M2 were claims taken seriously by both Plato and Aristotle, who in developing their own views on modality and language saw reason to mention Megaricism, and to argue against it. (shrink)

In this paper I investigate Aristotle’s account of predication in Topics I 9. I argue for the following interpretation. In this chapter Aristotle (i) presents two systems of predication cutting across each other, the system of the so-called four ‘predicables’ and of the ten ‘categories’, in order to distinguish them and explore their mutual relationship. I propose a semantic interpretation of the relationship between them. According to this reading, every proposition formed through a predicable constitutes at the same time a (...) predication according to one of the ten categories, and, consequently, signifies one of them, expressing one of the predicative relationship conveyed by them. Further, Aristotle (ii) explains the predicative connection between these two systems and the ten items signified by the ‘things said without any combination’ enumerated in Chapter 4 of the Categories, whose list is almost identical with that of categories in Top. I 9, with the only exception of their first members. (shrink)

El siguiente artı́culo intenta defender la tesis de que la distinción aristotélica entre enérgeia y kı́nesis debe ser comprendida de modo intensional (en contraposición a una lectura extensional), tomando como punto de partida su célebre aparición en Met IX 6. Sobre la base de la identificación del problema acerca del cual trata dicho pasaje, se toma en consideración otras apariciones de la distinción en Met IX 8, en la EE, en la EN y en otros textos, en orden a documentar, (...) en primer lugar, la vinculación de la distinción con la noción de érgon y, en segundo lugar, de qué modo dicha vinculación permite una lectura intensional de la distinción. Por último, se ofrece un argumento adicional para dicha lectura considerando la estructura teleológica de la acciones presentada por Aristóteles en EN I 1. (shrink)

I argue there are two ways predication relations can hold according to the Categories: they can hold directly or they can hold mediately. The distinction between direct and mediated predication is a distinction between whether or not a given prediction fact holds in virtue of another predication fact’s holding. We can tell Aristotle endorses this distinction from multiple places in the text where he licenses an inference from one predication fact’s holding to another predication fact’s holding. The best explanation for (...) each such inference is that he takes some predication facts to be mediated by others. Once the distinction between direct and mediated predication has been explained and argued for, I show how it can help solve a persistent problem for the traditional view of non-substantial particulars in the Categories—that is, the view that non-substantial particulars are particular in the sense of being non-recurrent. Along with vindicating the traditional view, the direct/mediated predication distinction gives us a distinctive way of understanding what it is for something to be recurrent (or non-recurrent) as well as a better understanding of Aristotle’s broader commitments in the Categories as a whole. (shrink)

Aristotle determines eristic argument as argument which either operates upon the basis of acceptable premisses and merely give the impression of being deductive, or argument which truly is deductive but operates upon the basis of premisses which seem to be acceptable, but are not. I attempt to understand what Aristotle has in mind when he says that someone is deceived into accepting premisses which seem to be acceptable but which are really not, and how this disqualifies such arguments from being (...) dialectical. In the first section of the paper I interpret Aristotle’s notion of ἔνδοξα in terms of a relational concept of acceptability. Real ἔνδοα are propositions which are accepted by a qualified group or individual. False ἔνδοα may also be accepted by someone or some group, and may even be true, but they are used to serve the purposes of eristical argumentation, which departs from certain standards of dialectical argumentation articulated in the notion of ἔνδοξα as a norm for premiss-acceptance. In particular, eristic arguments may even be valid in the sense of a συλλογισμός while still failing to be proper dialectical arguments. In the second part of the paper I consider how this can be, in examining certain types of fallacies in the Sophistical Refutations and the relationship between fallacious argumentation and false ἔνδοξα. (shrink)

Un paralogisme semble commis dans la démonstration par Aristote du principe psychologique de non-contradiction : à partir d’un principe performatif d’assertion (dire quelque chose, c’est le croire), une approche moderne nous incline à prétendre qu’Aristote présuppose une transparence référentielle des contextes opaques de croyance afin de corréler les versions psychologique et logique. Nous tenterons de restituer la preuve du principe (I). Au moyen de la formalisation moderne, nous appliquerons cette explication à quelques paradoxes (II). Nous en conclurons la nature de (...) la non-contradiction (III), avant de proposer une "dissolution" syntaxique du problème d'opacité des contextes d'attitudes propositionnelles. Cette dissolution exprimera un certain scepticisme face aux approches formelles de l'intentionnalité. (shrink)

This paper considers the nature of the changes that took place in logic teaching at the University of Oxford from the beginning of the sixteenth century, when students attended university lectures on Aristotle’s texts as well as studying short works dealing with specifically medieval developments, to the beginning of the eighteenth century when teaching was centred in the colleges, the medieval developments had largely disappeared, and manuals summarizing Aristotelian logic were used. The paper also considers the reasons for these changes, (...) including changes in English society, and the effect of humanism and the more scholarly Aristotelianism that it produced. (shrink)

Aristotle draws what are, by our lights, two unusual relationships between predication and existence. First, true universal affirmations carry existential import. If ‘All humans are mortal’ is true, for example, then at least one human exists. And secondly, although affirmations with empty terms in subject position are all false, empty negations are all true: if ‘Socrates’ lacks a referent, then both ‘Socrates is well’ and ‘Socrates is ill’ are false but both ‘Socrates is not well’ and ‘Socrates is not ill’ (...) are true. In this paper, I conjecture that for Aristotle predications have mereological truth conditions: for example, ‘Socrates is pale’ is true just in case Socrates is a part of the mereological sum of pale things. The existential import of universal affirmations and the semantic profile of empty negations follow from this mereological semantics. (shrink)

Hermeneutics as we understand it today is an essentially modern phenomenon. The chapter presents observations that illustrate some of the central ways in which the modern and late modern phenomena of philosophical hermeneutics relate to the ancient philosophical legacy. First, the roots of hermeneutics are traced to ancient views on linguistic, textual, and sacral interpretation. The chapter then looks at certain fundamentally unhermeneutic elements of the Platonic, Aristotelian, and Augustinian “logocentric” theory of meaning that philosophical hermeneutics and its heirs sought (...) to call into question, reconsider, and deconstruct. Augustine's De doctrina christiana, can be regarded as an epitome and culmination of the ancient protohermeneutic heritage, theological as well as philological. Finally, Aristotle's practical philosophy, particularly the notion of phronesis, “practical insight”, is designated as an implicit ancient prototype of hermeneutic thinking, the reappropriation of which lay at the core of the Heideggerian and Gadamerian philosophical projects. (shrink)

The premise-fact confusion in Aristotle’s PRIOR ANALYTICS. -/- The premise-fact fallacy is talking about premises when the facts are what matters or talking about facts when the premises are what matters. It is not useful to put too fine a point on this pencil. -/- In one form it is thinking that the truth-values of premises are relevant to what their consequences in fact are, or relevant to determining what their consequences are. Thus, e.g., someone commits the premise-fact fallacy if (...) they think that a proposition has different consequences were it true than it would have if false. C. I. Lewis said that confusing logical consequence with material consequence leads to this fallacy. See Corcoran’s 1973 “Meanings of implication” [available on Academia. edu]. -/- The premise-fact confusion occurs in a written passage that implies the premise-fact fallacy or that suggests that the writer isn’t clear about the issues involved in the premise-fact fallacy. Here are some examples. -/- E1: If Abe is Ben and Ben swims, then it would follow that Abe swims. -/- Comment: The truth is that from “Abe is Ben and Ben swims”, the proposition “Abe swims” follows. Whether in fact Abe is Ben and Ben swims is irrelevant to whether “Abe swims” follows from “Abe is Ben and Ben swims”. -/- E1 suggests that maybe “Abe swims” wouldn’t follow from “Abe is Ben and Ben swims” if the latter were false. -/- E2: The truth of “Abe is Ben and Ben swims” implies that Abe swims. -/- E3: Indirect deduction requires assuming something false. -/- Comment: If the premises of an indirect deduction are true the conclusion is true and thus the “reductio” assumption is false. But deduction, whether direct or indirect, does not require true premises. In fact, indirect deduction is often used to determine that the premises are not all true. -/- Anyway, the one-page paper accompanying this abstract reports one of dozens of premise-fact errors in PRIOR ANALYTICS. In the session, people can add their own examples and comment on them. For example, is the one at 25b32 the first? What is the next premise-fact error after 25b32? Which translators or commentators discuss this? -/- . (shrink)

I argue, firstly, that the accounts of 'accident' in Aristotle's Met. V 30 and in Top. I 5 cannot be used to elucidate each other: the Metaphysics passage tries to disentangle the uses of a Greek word, the Topics passage introduces technical terms for Aristotle's semantics. I then argue that the positive definition in Top. I 5 is to be understood in the following way: X is an accident of Y iff X belongs to Y and if there is a (...) Z such that X can belong to Z and also not belong to Z. Thus, being white is an accident of snow. I finally argue that certain shortcomings in the Topics account lead Aristotle to redefine accident in the Posterior Analytics. (shrink)

A predicate logic typically has a heterogeneous semantic theory. Subjects and predicates have distinct semantic roles: subjects refer; predicates characterize. A sentence expresses a truth if the object to which the subject refers is correctly characterized by the predicate. Traditional term logic, by contrast, has a homogeneous theory: both subjects and predicates refer; and a sentence is true if the subject and predicate name one and the same thing. In this paper, I will examine evidence for ascribing to Aristotle the (...) view that subjects and predicates refer. If this is correct, then it seems that Aristotle, like the traditional term logician, problematically conflates predication and identity claims. I will argue that we can ascribe to Aristotle the view that both subjects and predicates refer, while holding that he would deny that a sentence is true just in case the subject and predicate name one and the same thing. In particular, I will argue that Aristotle's core semantic notion is not identity but the weaker relation of constitution. For example, the predication ‘All men are mortal’ expresses a true thought, in Aristotle's view, just in case the mereological sum of humans is a part of the mereological sum of mortals. (shrink)

ABSTRACT: In this paper I show that, contrary to the prevalent view, in his De Interpretatione chapter 8, Aristotle is concerned with a kind of ambiguity, i.e. with homonymy; more precisely, with homonymy of linguistic expressions as it may occur in dialectical argument. The paper has two parts. In the first part, I argue that in the Sophistici Elenchi 175b39-176a5 Aristotle indubitably deals with homonymy in dialectical argument; that De Interpretatione 8 is a parallel to Sophistici Elenchi 175b39-176a5; that De (...) Interpretatione 8 is concerned with dialectical argument; that, hence, De Interpretatione 8, too, deals with homonymy in dialectical argument. In the second part I discuss objections that have been put forward against the view that De Interpretatione 8 is about homonymy and demonstrate that they do not succeed. (shrink)

With regard to the importance of interrelations and interplays of topos and logos in ancient theory and practices, here I will appropriate Aristotle philosophizing of topos and logos and apply it for the ancient persian Empire as reflected in related inscriptions.

This article identifies and formalizes the logical features of analogous terms that justify their use in deduction. After a survey of doctrines in Aristotle, Aquinas, and Cajetan, the criteria of “analogy of proper proportionality” are symbolized in first-order predicate logic. A common genus justifies use of a common term, but does not provide the inferential link required for deduction. Rather, the respective differentiae foster this link through their identical proportion. A natural-language argument by analogy is formalized so as to exhibit (...) these criteria, thereby showing the validity of analogical deduction. (shrink)

The article investigates the treatment of modality in chapters 12 and 13 of De Interpretatione and gives a new interpretation of the puzzling table of modals to be found at the beginning of chapter 13, as well as dealing with some of Aristotle’s puzzles. This is achieved by extending Aristotle’s distinction between two senses of possibility, which (following Ackrill) I call ‘one-sided’ and ‘two-sided’, to the two notions of necessity and impossibility. The conclusion is reached that, while the two notions (...) of necessity and impossibility are logically incompatible when both are taken as one-sided, in their two-sided senses they are in fact equivalent. (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)

AT POSTERIOR ANALYTICS 1.1.71B15 AND FOLLOWING, Aristotle identifies six characteristics of the first principles from which demonstrative science proceeds. These are traditionally grouped into two sets of three: group A: ex alêthôn, prôtôn, amêsôn; group B: gnôrimôterôn, proterôn, and aitiôn. The characteristic, which I believe has been underrated and somewhat misinterpreted by scholars and commentators from Philoponus to the present day, is the characteristic of truth. In this paper I propose to present a textually based interpretation of truth that shows (...) the following: that truth is necessarily linked to being. The example given of nonbeing, the commensurability of the diagonal with the sides of a square, suggests more than simple truth is required for first principles and premises of demonstrative science; and that Aristotle later in the APo changes this characteristic to necessary truth, for he recognizes that truth alone is an insufficient basis for scientific demonstration. The referents of necessary truth are eternal being, and the need for eternal being demands that universals exist extramentally for Aristotle. Finally, one of the important ways that universal genera and species exist for Aristotle are as real, causal principles. (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 begins "On Interpretation" with an analysis of the existence of linguistic entities as both physical and meaningful. Two things have been lacking for a full appreciation of this analysis: a more literal translation of the passage and an ample understanding of the distinction between symbols and signs. In this article, therefore, I first offer a translation of this opening passage (16a1-9) that allows the import of Aristotle's thinking to strike the reader. Then I articulate the distinction between symbol and (...) sign so crucial to understanding this passage. Aristotle employs this distinction, I argue, in order to show how the linguistic entities he defines later in "On Interpretation" (that is, name, verb, denial, affirmation, declaration, and articulation) are both conventional and natural, owing to their being both symbols and signs, respectively. Finally, I suggest why Aristotle's analysis of how linguistic entities exist as both physical and meaningful is fitting, since man himself, "the animal that has speech," lives at the boundary between nature and intelligence. (shrink)

This collection of essays is the product of a conference on Aristotle’s Posterior Analytics (Apo) held at the University of North Carolina at Chapel Hill in 2009. The essays address three main questions: (1) “How does the APo model of scientific knowledge, focused as it is on the construction of syllogisms, relate to the scientific accounts Aristotle presents elsewhere, especially in the biological treatises?’ (2) ‘How do the arguments and views presented in the APo relate to other aspects of Aristotle’s (...) philosophy?’ and (3) ‘How do the remarks in the concluding chapter of the APo concerning perception, memory, experience, and the grasp of the universal add up to an explanation of how we come to know first principles?’ The papers by J.G. Lennox, M. Leunissen and R. McKirahan address the first two questions, while those by M. Tuominen and G. Salmieri discuss the well-known passage in Apo II 19. (shrink)

As a first stab, call a property recurrent if it can be possessed by more than one object, and nonrecurrent if it can be possessed by at most one object. The question whether Aristotle holds that there are nonrecurrent properties has spawned a lively and ongoing debate among commentators over the last forty-five years. One source of textual evidence in the Categories, drawn on in this debate, is Aristotle’s claim that certain properties are inseparable from what they are in. Here (...) the point of contention is whether this commits Aristotle to holding that these properties are inseparable from individuals, since it is commonly held that a property is nonrecurrent, if it is inseparable from an individual. I argue that this evidence is neutral on the question whether there are nonrecurrent properties in Aristotle. One of my aims here is to disentangle the question of recurrence from local issues of individuality and universality in the Categories. But another aim is to turn from the textual considerations, which have dominated the debate, to broader methodological considerations. It is a shared assumption among all those who look to textual evidence from the Categories, so to decide whether Aristotle believes there are nonrecurrent properties, that in this work Aristotle is engaged in a project where the question of recurrence is relevant. I argue that Aristotle’s concerns in the Categories are disjoint from the question of recurrence, and so this shared assumption is false. (shrink)

The reintroduction of Aristotle's Analytics to the Latin West—in particular, the reintroduction of the Posterior Analytics—forever altered the course of medieval epistemological discussions. Although the Analytics fell decidedly from grace in later centuries, the sophisticated account of human cognition developed in the Posterior Analytics appealed so strongly to thirteenth-century European scholars that it became one of the two central theories of knowledge advocated in the later Middle Ages. Robert Grosseteste's 'Commentarius in Posteriorum Analyticorum Libro', written in the 1220s, is most (...) likely the first complete Latin commentary on the Posterior Analytics. As the thirteenth century wore on, Aristotle’s account of human cognition was generally set in opposition to the Augustinian-influenced theory of divine illumination that was de rigueur in the early thirteenth century. Although common consensus holds that this pattern of opposition was set already in Grosseteste’s CPA, I argue that the story of the Posterior Analytics’s early reception is, in fact, quite different. In particular, I maintain that, rather than seeing himself as forced to choose between his earlier theory of divine illumination and the “new” Aristotelian epistemology, Grosseteste is perfectly content to blend and bring together the diverse elements of these systems and to present a consciously synthetic rather than adversarial picture of these differing accounts of human cognition. (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)

Prior Analytics by the Greek philosopher Aristotle (384 – 322 BCE) and Laws of Thought by the English mathematician George Boole (1815 – 1864) are the two most important surviving original logical works from before the advent of modern logic. This article has a single goal: to compare Aristotle’s system with the system that Boole constructed over twenty-two centuries later intending to extend and perfect what Aristotle had started. This comparison merits an article itself. Accordingly, this article does not discuss (...) many other historically and philosophically important aspects of Boole’s book, e.g. his confused attempt to apply differential calculus to logic, his misguided effort to make his system of ‘class logic’ serve as a kind of ‘truth-functional logic’, his now almost forgotten foray into probability theory, or his blindness to the fact that a truth-functional combination of equations that follows from a given truth-functional combination of equations need not follow truth-functionally. One of the main conclusions is that Boole’s contribution widened logic and changed its nature to such an extent that he fully deserves to share with Aristotle the status of being a founding figure in logic. By setting forth in clear and systematic fashion the basic methods for establishing validity and for establishing invalidity, Aristotle became the founder of logic as formal epistemology. By making the first unmistakable steps toward opening logic to the study of ‘laws of thought’—tautologies and laws such as excluded middle and non-contradiction—Boole became the founder of logic as formal ontology. (shrink)

Discussion of the Aristotelian syllogistic over the last sixty years has arguably centered on the question whether syllogisms are inferences or implications. But the significance of this debate at times has been taken to concern whether the syllogistic is a logic or a theory, and how it ought to be represented by modern systems. Largely missing from this discussion has been a study of the few passages in the Prior Analytics where Aristotle provides explicit guidance on how to individuate syllogisms. (...) I argue that syllogisms are individuated by unordered premise pairs and so may be fruitfully thought of as multi-succedent sequents. I conclude by drawing a few consequences for the representation of the syllogistic. (shrink)

When Aristotle introduces the perfect moods, he refers back to the dictum de omni et nullo, a semantic condition for universal affirmations and negations. There recently has been renewed interest in the question whether the dictum validates the assertoric syllogistic. I rehearse evidence that Aristotle provides a mereological semantics for universal affirmations and negations, and note that this semantics entails a nonstandard reading of the dictum, under which the dictum, in the presence of a minimal logical apparatus, indeed validates the (...) assertoric syllogistic. I argue that this mereological validation offers advantages over recent discussions in Morison, Malink, Ebert and Vlasits. (shrink)

The purpose of this paper is an attempt to delimitate what the dialectical syllogism looks like in Aristotle’s Topics. Aristotle never gave an example of a dialectical syllogism, but we have some clues spread over books I and VIII of the Topics which make it possible to understand at least what within a dialectical debate is a dialectical syllogism. The interpretation advanced here distinguishes the logical order of the dialectical argumentation from the order of the debate. This distinction enables us (...) to have a better understand of what is and how the dialectical syllogism is identified in the debate. In addition, we can solve some interpretative difficulties other interpretations could not solve, and have a more solid grasp of how endoxa are used in a dialectical debate. (shrink)

This paper discusses the following question: why was the term “dunatos” (“possible”) employed by Aristotle as an alternative label for imperfect syllogisms in his discussion of assertoric syllogistic? My answer ascribes to Aristotle a bottom up perspective, in which he stresses what is necessary in the premise-pairs to attain target conclusions of a given form within a given figure. I argue that “dunatos” is employed by Aristotle to stress that an imperfect syllogism is always one of the possible options to (...) attain a conclusion of a given form within a given figure. I also argue that this picture sheds some light on Aristotle’s clarifications of the final clause in his definition of syllogism. (shrink)

El objetivo principal de este trabajo es presentar el sistema lógico que resulta de extender, de una manera natural, a la Silogística con la Lógica proposicional, y demostrar que tal extensión se puede caracterizar como un sistema axiomático. Los axiomas que se utilizan son los de Jan Łukasiewicz , y la completitud de tal sistema de axiomas se prueba utilizando un método análogo al método del conjunto maximal consistente con testigos de Henkin, siguiendo algunas ideas que utiliza John Corcoran para (...) probar que su sistema de reglas de inferencia para la Silogística es completo. (shrink)

The aim of this paper is to show how the invention of imaginary logic by Nikolaj A. Vasil’ev, forerunner of various logical and metaphysical theories appeared in the 20th century, is grounded on a revaluation of Aristotelian ontology. I shall introduce the reason why Aristotle believes that the study of the principle of contradiction is part of ontology (§ 2); I shall explain why Vasil’ev considers the law of contradiction an empirical law, and not a logical one (§ 3.1). I (...) will show his conception of contradiction (§ 3.2) and I will discuss how he believes that it’s possible to renounce this law; (§ 3.3). I shall then explain the fundamental features of imaginary logic (§ 4.1 and § 4.2); and, finally I shall claim how, in spite of a convergence from the logical point of view (§ 5.1), the incompatibility of the two authors takes place on an ontological level (§ 5.2). In order to do so, I shall implement the analysis of the Aristotelian syllogistic conducted by the Polish logician and philosopher Jan Łukasiewicz, together with a crucial distinction between two concepts: the one of ‘law’ and the one of ‘principle’. -/- . (shrink)

In the first book of the Prior Analytics, Aristotle sets out, for the first time in Greek philosophy, a logical system. It consists of a deductive system (I.4-22), meta-logical results (I.23-26), and a method for finding and giving deductions (I.27-29) that can apply in “any art or science whatsoever” (I.30). After this, Aristotle compares this method with Plato’s method of division, a procedure designed to find essences of natural kinds through systematic classification. This critical comparison in APr I.31 raises an (...) interpretive puzzle: how can Aristotle reasonably juxtapose two methods that differ so much in their aims and approach? What can be gained by doing so? Previous interpreters have failed to show how this comparison is legitimate or what important point Aristotle is making. The goal of this paper is to resolve the puzzle. In resolving this puzzle we not only learn more about the relationship be- tween division and the syllogistic in Aristotle. We will also learn something about the motivation for the syllogistic itself, by seeing the role that it plays in his philosophy of science. (shrink)