Aristotle: Logic and Philosophy of Language

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)

The Divisio Aristotelea 67M/32DL establishes a distinction between two categories of beings, per se and relatives. I defend three main theses. First, the relation of dependence characterizing the members of the πρός τι category is modal and symmetrical in nature and, accordingly, the per se-relatives contrast cannot be equivalent to the substance-accidents contrast. Second, the type of relativity relevant to this divisio is both ontological and semantic in nature (but with different emphases depending on the version of the divisio considered). (...) I finally argue, against a widespread opinion, that the last line of the DL version of the divisio does not concern metaphysical principles. In so doing, I also compare the divisio to other Early Academic bicategorial schemes and show that they differ from one another significantly, especially as far as the alleged connection between categories and metaphysical principles is concerned. (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)

En este artículo pretendo echar luz sobre la distinción entre filosofía y erística en Platón y Aristóteles, dirigiendo la atención a la noción de aporía. En la sección I, sobre la base de un examen de las ocurrencias de eristikós en Menón, intento mostrar que Sócrates aparece estrechamente conectado al erístico, quien suele ser presentado como su oponente más peligroso. En la sección II, analizo la taxonomía de Aristóteles de los opositores al principio de no-contradicción en Metafísica IV, con el (...) fin de aclarar la distinción entre filósofos, genuinamente problematizados, y erísticos, que buscan la victoria verbal. En este punto, sostengo, Aristóteles sigue de cerca las enseñanzas de Platón en Menón. (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)

The subject of this paper is the issue of human speech in Aristotle, especially in his work Categories. Its primary goal is to elaborate an interpretation of Aristotle’s statements about human speech as a quantity (Cat. 4b20–b39, 5a15–b2) that would allow them to fit reasonably into the whole of Aristotle’s theory of language. The structure of the paper is as follows. In the first part a certain approach to the question of the reconstruction of Aristotle’s theory of language is proposed. (...) The second part, by means of the introduction of the criteria of separability and ontological priority of the first substance, creates a framework for the subsequent analysis of the two basic classifications, which constitute the main theme of Categories. The third part supplies its own interpretation of the ontological status of human speech in the context of the classification schemes in Categories, and this, in the fourth part, is inserted into the greater whole of Aristotle’s theory of language. (shrink)

AtCategories7, 6a36-7 Aristotle defines relatives, but at 8a13-28 worries that the definition may include some substances. Aristotle introduces a second account of relatives to solve the problem. Recent commentators have held that Aristotle intends to solve the extensional adequacy worry by restricting the extension of relatives. That is, R2 counts fewer items as relative than R1. However, this cannot explain Aristotle’s attitude to relatives, since he immediately returns to using R1. I propose a non-extensional reading. R1 and R2 do not (...) specify different sets of relatives, but rather different ways to understand each relative. (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)

At the beginning of Categories 5, Aristotle distinguishes between two kinds of substance: primary substance and secondary substance. Primary substances include particular living organisms, inanimate objects, and their parts. Secondary substances are the species and genera of these. This distinction is unique to the Categories, which raises the question of why Aristotle treats species and genera as substances. I argue that Aristotle has two distinct reasons for doing so, and contrast my interpretation with recent alternatives. On my view, species and (...) genera enjoy two kinds of fundamentality – ontological and epistemological – in virtue of which they warrant their status as substances. (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)

In Aristotle's biological treatise, On the Parts of Animals, one finds a rare and unexpected burst of rhetorical eloquence. While justifying the study of “less valued animals,” he erupts into praise for the study of all natural phenomena and condemns the small-mindedness of those who trivialize its worth. Without equal in Aristotle's remaining works for its rhetorical quality, it reveals the otherwise coolheaded researcher as a passionate seeker of truth and an unabashed lover of natural beauty. For Aristotle, rhetoric not (...) only discloses the truth of appearances by refuting counterarguments and defending one's claims within agonistic forums; rhetoric also defends and advances whole fields of study on the promise on wonder. By examining Aristotle's example in practice, this article seeks to elucidate a notion of the rhetoric for inquiry that calls lovers of wisdom to the empirical study of nature. (shrink)

Aristotle’s De Interpretatione has been referred to as the most influential text to be written in the history of semantics. I argue, however, that it is Plato who lays the foundation for subsequent reflection on signification. In the Cratylus, Plato confronts the two prevalent views of his time on the nature of the relationship between a name and a thing named: conventionalism, which holds that there is an arbitrary, imposed relationship between names and what they name; and naturalism, which holds (...) that there is a natural relationship between names and what they name. The true originality of Plato’s line of reasoning consists in arguing that whether we begin with naturalism or conventionalism, we are soon forced to introduce a third, mediating term between word and thing into the relation of signification. Plato thus establishes the tertiary nature of the sign-relation, a position that Aristotle takes for granted. (shrink)

Journal Name: Apeiron Issue: Ahead of print.

I examine the treatment of metaphor by medieval logicians and how it stemmed from their reception of classical texts in logic, grammar, and rhetoric. I consider the relation of the word 'metaphor' to the notions of translatio and transumptio, and show that it is not always synonymous with these. I also show that in the context of commentaries on the Sophistical Refutations metaphor was subsumed under equivocation. In turn, it was linked with the notion of analogy not so much in (...) the Greek sense of a similarity between two proportions or relations as in the new medieval sense of being said secundum prius et posterius. Whether or not analogy could be reduced to metaphor, or the reverse, depended on the controversial issue of the number of acts of imposition needed to produce an equivocal term. A spectrum of views is canvassed, including those found in the logic commentaries of John Duns Scotus. (shrink)

This article considers three medieval approaches to the problem of future contingent propositions in chapter 9 of Aristotle's _De interpretatione_. While Boethius assumed that God's atemporal knowledge infallibly pertains to historical events, he was inclined to believe that Aristotle correctly taught that future contingent propositions are not antecedently true or false, even though they may be characterized as true-or-false. Aquinas also tried to combine the allegedly Aristotelian view of the disjunctive truth-value of future contingent propositions with the conception of all (...) things being timelessly present to God's knowledge. The second approach was formulated by Peter Abelard who argued that in Aristotle's view future contingent propositions are true or false, not merely true-or-false, and that the antecedent truth of future propositions does not necessitate things in the world. After Duns Scotus, many late medieval thinkers thought like Abelard, particularly because of their new interpretation of contingency, but they did not believe, with the exception of John Buridan, that this was an Aristotelian view. (shrink)

On the unity of modal syllogistics in Aristotle. The goal of this paper is an interpretation of Aristotle's modal syllogistics closely oriented on the text using the resources of modern modal predicate logic. Modern predicate logic was successfully able to interpret Aristotle's assertoric syllogistics uniformly, that is, with one formula for universal premises. A corresponding uniform interpretation of modal syllogistics by means of modal predicate logic is not possible. This thesis does not imply that a uniform view is abandoned. However, (...) it replaces the simple unity of the assertoric by the complex unity of the modal. The complexity results from the fact that though one formula for universal premises is used as the basis, it must be moderated if the text requires.Aristotle introduces his modal syllogistics by expanding his assertoric syllogistics with an axiom that links two apodictic premises to yield a single apodictic sentence. He thus defines a regular modern modal logic. By means of the regular modal logic that is thus defined, he is able to reduce the purely apodictic syllogistics to assertoric syllogistics. However, he goes beyond this simple structure when he looks at complicated inferences.In order to be able to link not only premises of the same modality, but also premises with different modalities, he introduces a second axiom, the T-axiom, which infers from necessity to reality or - equivalently - from reality to possibility. Together, the two axioms, the axiom of regularity and the T-axiom, define a regular T-logic. It plays an important role in modern logic. In order to be able to account for modal syllogistics adequately as a whole, another modern axiom is also required, the so-called B-axiom. It is very difficult to decide whether Aristotle had the B-axiom. Each of the two last named axioms is sufficient to achieve the required contextual moderation of the basic formula for universal propositions. (shrink)