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 rediscovery of Aristotle’s works on syllogisms in the Latin world, especially the Sophistici Elenchi and then the Prior Analytics, gave rise to sophisticated views on the nature of syllogistic form and syllogistic matter in the thirteenth century. It led to debates on the ontology of the syllogism as studied in the Prior Analytics, i.e. the syllogism made of letters and the four logical constants a/e/i/o, with deep consequences on the definition of logic as a universal method for all sciences (...) and as a science itself. (shrink)

This paper contends that Stoic logic (i.e. Stoic analysis) deserves more attention from contemporary logicians. It sets out how, compared with contemporary propositional calculi, Stoic analysis is closest to methods of backward proof search for Gentzen-inspired substructural sequent logics, as they have been developed in logic programming and structural proof theory, and produces its proof search calculus in tree form. It shows how multiple similarities to Gentzen sequent systems combine with intriguing dissimilarities that may enrich contemporary discussion. Much of Stoic (...) logic appears surprisingly modern: a recursively formulated syntax with some truth-functional propositional operators; analogues to cut rules, axiom schemata and Gentzen’s negation-introduction rules; an implicit variable-sharing principle and deliberate rejection of Thinning and avoidance of paradoxes of implication. These latter features mark the system out as a relevance logic, where the absence of duals for its left and right introduction rules puts it in the vicinity of McCall’s connexive logic. Methodologically, the choice of meticulously formulated meta-logical rules in lieu of axiom and inference schemata absorbs some structural rules and results in an economical, precise and elegant system that values decidability over completeness. (shrink)

Peirce’s theory of the origin of abduction in Aristotle’s Prior Analytics II.25 is based on his account of abduction as a second-figure syllogism. Peirce read the difficult and (what he thought to be) corrupted passage of Prior Analytics II.25 and tried to amend its errors and explain its difficulties in order to argue that Aristotle was trying to present a syllogism in the second figure that infers a case, which is Peirce’s definition of abduction. “[H]e would not be Aristotle, to (...) have overlooked [the] question” whether such an inference sometimes occurs, said Peirce in his 1901 paper “The Logic of Drawing History from Ancient Documents” (CP 7.249). Several years after suggesting that Aristotle had described.. (shrink)

Avicenna’s ground-breaking view of logic as both a tool for other sciences and a science in its own right has already attracted scholars’ attention and has been studied in several different respects. The present paper aims to address a specific issue entailed by considering logic as a science in its own right: that is, assessing the relation in which logic as a science stands to the other sciences, and particularly to metaphysics and psychology. The inquiry will focus on a fundamental, (...) yet tricky, passage of chapter I.4 of Avicenna’s Kitāb al-Madḫal, the opening work of his most comprehensive philosophical summa, the Kitāb al-Šifāʾ (Book of Healing). Due to the obscurity of some of Avicenna’s references, chapter I.4 “on the subject-matter of logic” has stimulated numerous attempts at interpretation from the Middle Ages to today. In this paper, I will attempt to provide a new reading of the chapter in light of Avicenna’s definition of the epistemological status of science in Burhān II.7. (shrink)

It has been said that there is no scholarly consensus as to why Aristotle’s logics of proof and refutation would have borne the title _Analytics._ But if we consulted Tarski’s (Introduction to logic and the methodology of deductive sciences, Oxford University Press, New York, 1941) graduate-level primer, we would have the perfect title for them: _Introduction to logic and to the methodology of deductive sciences._ There are two strings to Aristotle’s bow. The methodological string is the founding work on the (...) epistemology of science, and the logical string sets down conditions on the proofs that bring this knowledge about. The logic of proof presents a difficulty whose solution exceeds its theoretical reach. The logic of refutation takes the problem on board, and advances a solution whose execution is framed by fallacy-avoidance at the beginning and fallacy-adoption at the end. But with a difference: the avoidance-fallacies are of Aristotle’s own conception, whereas the adoption-fallacies, so judged in the modern tradition, aren’t fallacies at all for Aristotle. The avoidance-fallacies are begging the question and _ignoratio elenchi_, and the adoption-fallacies, fallacies in name only, are the _ad hominem_ and _ad ignorantiam_, an inductive turning in the first instance, and an abductive finish in the second. (shrink)

Two main claims are defended. The first is that negative categorical statements are not to be accorded existential import insofar as they figure in the square of opposition. Against Kneale and others, it is argued that Aristotle formulates his o statements, for example, precisely to avoid existential commitment. This frees Aristotle's square from a recent charge of inconsistency. The second claim is that the logic proper provides much thinner evidence than has been supposed for what appears to be the received (...) view, that is, for the view that insofar as they occur in syllogistic negative categoricals have existential import. At most there is a single piece of evidence in favor of the view?a special case of echthesis or the setting out of a case in proof. (shrink)

Le premier tractatus du commentaire d'Albert le Grand à l'Isagoge de Porphyre consiste en une manière de proème ou d'introduction à l'ensemble de la logique. Comme la plupart des textes d'Albert le Grand, ce traité est d'une très grande richesse, qu'atténuent toutefois son manque d'ordre et son obscurité d'expression. Étant donné que les aspects fondamentaux de la logique y sont touchés—son statut scientifique et philosophique, son utilité, son sujet, sa division, sa relation aux sciences du langage, etc.—, ce petit ouvrage (...) est du plus haut intérêt pour quiconque cherche à mieux comprendre la logique et la philosophie de la logique du XIIIe siècle. L'auteur présente ici une traduction annotée et expliquée de ce texte difficile, faite d'après la version provisoire de la nouvelle édition de Cologne. Le relevé des sources principales de l'ouvrage révèle, sur un fond aristotélicien permanent, une forte influence des traités logiques arabes nouvellement arrivés en Occident. The first tractatus of Albert the Great's commentary on Porphyry's Isagoge consists of a kind of proem or introduction to the whole of logic. As most of Albert the Great's texts, this tract is of great richness, though it lacks order and is sometimes obscure. Since the fundamental themes of logic are addressed therein—its scientific and philosophical status, its utility, its subject, its division, its relation to the linguistic arts, etc.—, this small work is of high interest for anyone trying to better understand thirteenth-century logic and philosophy of logic. The author presents a translation of this difficult text, made after a preliminary version of the new critical edition and enriched with an introduction and explanatory notes. The survey of the main sources of the tract reveals, apart from a permanent artistotelian background, the strong influence of the Arabic logical treatises which were then coming in the Western world. (shrink)

Le premier tractatus du commentaire d'Albert le Grand à l'Isagoge de Porphyre consiste en une manière de proème ou d'introduction à l'ensemble de la logique. Comme la plupart des textes d'Albert le Grand, ce traité est d'une très grande richesse, qu'atténuent toutefois son manque d'ordre et son obscurité d'expression. Étant donné que les aspects fondamentaux de la logique y sont touchés—son statut scientifique et philosophique, son utilité, son sujet, sa division, sa relation aux sciences du langage, etc.—, ce petit ouvrage (...) est du plus haut intérêt pour quiconque cherche à mieux comprendre la logique et la philosophie de la logique du XIIIe siècle. L'auteur présente ici une traduction annotée et expliquée de ce texte difficile, faite d'après la version provisoire de la nouvelle édition de Cologne. Le relevé des sources principales de l'ouvrage révèle, sur un fond aristotélicien permanent, une forte influence des traités logiques arabes nouvellement arrivés en Occident. Pour des exemples de ces auteurs contemporains, voir Lafleur ( 1988, p. 182, l.37–44, p. 321, l.284–294). The first tractatus of Albert the Great's commentary on Porphyry's Isagoge consists of a kind of proem or introduction to the whole of logic. As most of Albert the Great's texts, this tract is of great richness, though it lacks order and is sometimes obscure. Since the fundamental themes of logic are addressed therein—its scientific and philosophical status, its utility, its subject, its division, its relation to the linguistic arts, etc.—, this small work is of high interest for anyone trying to better understand thirteenth-century logic and philosophy of logic. The author presents a translation of this difficult text, made after a preliminary version of the new critical edition and enriched with an introduction and explanatory notes. The survey of the main sources of the tract reveals, apart from a permanent artistotelian background, the strong influence of the Arabic logical treatises which were then coming in the Western world. (shrink)

At Topics 8.11 161b19–33 Aristotle lists five criticisms () which may be leveled against a dialectical argument ‘in itself’ (). The five criticisms correspond in many respects to the familiar conditions Aristotle places on syllogism and refutation. However, begging the question —the violation of the condition that the conclusion of a syllogism be something different () from the premises—seems not to appear on the list of five criticisms. That this omission is only apparent becomes clear once it is seen that (...) the five criticisms are not independent but rather amount to five successive filters through which an argument may be passed before its non-genuineness is exposed. This result sheds light on Aristotle's curious insistence, in the face of the heterogeneity of his examples of BTQ in Topics 8.13, that every question-begging refutation contains a premise that is ‘the same’ as the conclusion. The fact that the five criticisms expose BTQ as a defect in syllogistic reasoni.. (shrink)

This paper sets out to evaluate the claim that Aristotle’s Assertoric Syllogistic is a relevance logic or shows significant similarities with it. I prepare the grounds for a meaningful comparison by extracting the notion of relevance employed in the most influential work on modern relevance logic, Anderson and Belnap’s Entailment. This notion is characterized by two conditions imposed on the concept of validity: first, that some meaning content is shared between the premises and the conclusion, and second, that the premises (...) of a proof are actually used to derive the conclusion. Turning to Aristotle’s Prior Analytics, I argue that there is evidence that Aristotle’s Assertoric Syllogistic satisfies both conditions. Moreover, Aristotle at one point explicitly addresses the potential harmfulness of syllogisms with unused premises. Here, I argue that Aristotle’s analysis allows for a rejection of such syllogisms on formal grounds established in the foregoing parts of the Prior Analytics. In a final section I consider the view that Aristotle distinguished between validity on the one hand and syllogistic validity on the other. Following this line of reasoning, Aristotle’s logic might not be a relevance logic, since relevance is part of syllogistic validity and not, as modern relevance logic demands, of general validity. I argue that the reasons to reject this view are more compelling than the reasons to accept it and that we can, cautiously, uphold the result that Aristotle’s logic is a relevance logic. (shrink)

At APr 2.4 57a36–13, Aristotle presents a notorious reductio argument in which he derives the claim ‘If B is not large, B is large’ and calls that result impossible. Aristotle is thus committed to some form of connexivity and this paper argues that his commitment is to a strong form of connexivity which excludes even cases in which ‘B is large’ is necessary. It is further argued that Aristotle’s view of connexivity is best understood as arising from his analysis of (...) affirmation and negation in terms of combination and separation: a proposition that separates two terms cannot entail a proposition that combines the same two terms. In order to motivate this account of connexivity, this paper interprets Aristotle as emphasising the predicative structure, especially the copulae, of the argument’s component propositions. The arguments for this are based on a consideration of the larger context of APr 2.2–4. A reconstruction of the argument using propositional variables does not fully capture Aristotle’s intentions. (shrink)

Modern logicians have complained that Aristotelian logic lacks a distinction between predication and assertion, and that predication, according to the Aristotelians, implies assertion. The present paper addresses the question of whether this criticism can be levelled against Aristotle’s logic. Based on a careful study of the De interpretatione, the paper shows that even if Aristotle defines what he calls simple assertion in terms of predication, he does not confound predication and assertion. That is because, first, he does not understand compound (...) assertion in terms of predication, and secondly, he acknowledges non-assertive predicative thoughts that are truth-evaluable. Therefore, the implications of Aristotle’s ‘predication theory of assertion’ are not as devastating as the critics believe. (shrink)

Aristotle’s treatment of mixed, first-figure, problematic-assertoric syllogisms has generated a good deal of controversy among modern commentators.I argue that W.D.Ross’s criticism of A.Becker’s cr...

(1993). Alexander of aphrodisias and others on a controversial demonstration in aristotle’s modal syllogistic. History and Philosophy of Logic: Vol. 14, No. 2, pp. 201-214.