Aristotle (d. 322 BC) was the first philosopher in the history of thought to examine all modes and types of belief acquisition such as knowledge, supposition, error and indirectly imagination. In his _Prior Analytics_, which he wrote primarily to clarify his theory of demonstration, Aristotle examined in detail the syllogism, which he saw as the most important form of reasoning, and his analysis was subject to interpretation by different traditions of thought for centuries. Aristotle’s _Prior Analytics_ was translated into (...) Arabic in the classical period and later interpreted by many Islamic logicians. This article aims to show how Aristotle’s definition of the syllogism in the _Prior Analytics_ was taken up and interpreted in the Peripatetic Islamic logical tradition. These interpretations of the definition of the syllogism will provide us with an idea about the unique features of the commentaries on the _Prior Analytics_ in the Islamic world. Here, introductory information about the translation of the _Prior Analytics_ into Arabic and its commentators in Arabic will be given, Aristotle’s definition of the syllogism and its versions in Peripatetic Islamic logicians will be indicated, and the interpretation of the basic terms in the definition by Peripatetic Islamic logicians will be revealed. (shrink)

Aristotle (b. 322 BC) was the first philosopher in the history of thought to examine all modes and types of belief acquisition such as knowledge, supposition, error and indirectly imagination. In his _Prior Analytics_, which he wrote primarily to clarify his theory of demonstration, Aristotle examined in detail the syllogism, which he saw as the most important form of reasoning, and his analysis was subject to interpretation by different traditions of thought for centuries. Aristotle’s _Prior Analytics_ was translated into (...) Arabic in the classical period and later interpreted by many Islamic logicians. This article aims to show how Aristotle’s definition of the syllogism in the _Prior Analytics_ was taken up and interpreted in the Peripatetic Islamic logical tradition. These interpretations of the definition of the syllogism will provide us with an idea about the unique features of the commentaries on the _Prior Analytics_ in the Islamic world. Here, introductory information about the translation of the _Prior Analytics_ into Arabic and its commentators in Arabic will be given, Aristotle’s definition of the syllogism and its versions in Peripatetic Islamic logicians will be indicated, and the interpretation of the basic terms in the definition by Peripatetic Islamic logicians will be revealed. (shrink)

In ancient philosophy, Logic was seen as the instrument and method of philosophy. However, sometimes detailed and profound discussions have been made about the demonstrativeness of philosophical sciences. Most philosophers have accepted that the mathematical sciences were especially demonstrative and likewise, most of the natural sciences are demonstrative for them. But can metaphysics be demonstrative or not? This is one of the fundamental issues around which the great debates were made in Islamic philosophy. While these issues are known to (...) specialists in this field, we can hardly find studies and research that deal with this issue to a sufficient degree and precise discussions in our day, I mean the issue of demonstrativeness of art of demonstration, art of dialectic, art of sophistry, art of rhetoric and art of poetry. It is clear that the peripatetic philosophers did not write a separate book or treatise on the issue of the demonstrativeness of the logical arts, but we can claim that they believed that all these arts were demonstrative and that they were extracted/abstracted using the art of demonstration. We can come across important phrases and statements that prove this claim between the lines of the books that these philosophers wrote in the science of logic. And while Aristotle is the founder of the science of logic, then how is it to be understood that there are practical particular examples and some easy rules of these arts? According to their texts, we can say that they believed that the actual performance of these arts by their actors in materials by particular and practical actions differs from extracting their universal rules by abstracting them from their materials through theoretical and analytical research. For example, the poems of the great poets; Homer and al-Mutanabbi, are particular works in the matter of the art of poetry performed by poets. The books written by Aristotle and Ibn Rushd in the art of poetry contain universal rules extracted abstractly from the materials of their particular poems. As for understanding the demonstrativeness of the remaining four arts, it is easier, but how should we understand the demonstrativeness of the art of demonstration itself? It seems that the peripatetic logicians also distinguished between applying demonstrative inferences to significant materials and extracting the universal rules of the art of demonstration from these materials. These five logical arts are not particular and practical things, but they are philosophical, demonstrative, and analytical studies for the peripatetic logicians in Islam. In this paper, we will try to draw attention to the issue of the demonstrativeness of the five arts and to open a new discussion about it based on some important sentences and phrases expressed by al-Fārābī, Ibn Zur‘a, Ibn Sīnā, Ibn Bājja and Ibn Rushd between the lines in their books, which they wrote in the field of logic and within different and multiple contexts. (shrink)

In ancient philosophy, Logic was seen as the instrument and method of philosophy. However, sometimes detailed and profound discussions have been made about the demonstrativeness of philosophical sciences. Most philosophers have accepted that the mathematical sciences were especially demonstrative and likewise, most of the natural sciences are demonstrative for them. But can metaphysics be demonstrative or not? This is one of the fundamental issues around which the great debates were made in Islamic philosophy. While these issues are known to (...) specialists in this field, we can hardly find studies and research that deal with this issue to a sufficient degree and precise discussions in our day, I mean the issue of demonstrativeness of art of demonstration, art of dialectic, art of sophistry, art of rhetoric and art of poetry. It is clear that the peripatetic philosophers did not write a separate book or treatise on the issue of the demonstrativeness of the logical arts, but we can claim that they believed that all these arts were demonstrative and that they were extracted/abstracted using the art of demonstration. We can come across important phrases and statements that prove this claim between the lines of the books that these philosophers wrote in the science of logic. And while Aristotle is the founder of the science of logic, then how is it to be understood that there are practical particular examples and some easy rules of these arts? According to their texts, we can say that they believed that the actual performance of these arts by their actors in materials by particular and practical actions differs from extracting their universal rules by abstracting them from their materials through theoretical and analytical research. For example, the poems of the great poets; Homer and al-Mutanabbi, are particular works in the matter of the art of poetry performed by poets. The books written by Aristotle and Ibn Rushd in the art of poetry contain universal rules extracted abstractly from the materials of their particular poems. As for understanding the demonstrativeness of the remaining four arts, it is easier, but how should we understand the demonstrativeness of the art of demonstration itself? It seems that the peripatetic logicians also distinguished between applying demonstrative inferences to significant materials and extracting the universal rules of the art of demonstration from these materials. These five logical arts are not particular and practical things, but they are philosophical, demonstrative, and analytical studies for the peripatetic logicians in Islam. In this paper, we will try to draw attention to the issue of the demonstrativeness of the five arts and to open a new discussion about it based on some important sentences and phrases expressed by al-Fārābī, Ibn Zur‘a, Ibn Sīnā, Ibn Bājja and Ibn Rushd between the lines in their books, which they wrote in the field of logic and within different and multiple contexts. (shrink)

Aristotle’s modal syllogistic is his study of patterns of reasoning about necessity and possibility. Many scholars think the modal syllogistic is incoherent, a ‘realm of darkness’. Others think it is coherent, but devise complicated formal modellings to mimic Aristotle’s results. This volume provides a simple interpretation of Aristotle’s modal syllogistic using standard predicate logic. Rini distinguishes between red terms, such as ‘horse’, ‘plant’ or ‘man’, which name things in virtue of features those things must have, and green terms, such (...) as ‘moving’, which name things in virtue of their non-necessary features. By applying this distinction to the Prior Analytics, Rini shows how traditional interpretive puzzles about the modal syllogistic melt away and the simple structure of Aristotle’s own proofs is revealed. The result is an applied logic which provides needed links between Aristotle’s views of science and logical demonstration. The volume is particularly valuable to researchers and students of the history of logic, Aristotle’s theory of modality, and the philosophy of logic in general. (shrink)

Translation of the initial chapters of Aristotle’s Prior Analytics into Portuguese and introduction, which addresses interpretative disagreements and translation choices.

In Prior Analytics 1.15, Aristotle attempts to give a proof through the impossible of Barbara, Celarent, Darii, and Ferio with an assertoric first premiss, a contingent second premiss, and a possible conclusion. These proofs have been controversial since antiquity. I shall show that they are valid, and that Aristotle is able to explain them by relying on two meta-syllogistic lemmas on the nature of possibility interpreted as syntactic consistency. It will turn out that Aristotle's proofs are not of the (...) intended schemata. I shall investigate some of the results that the impact of this reconstruction on the modal syllogistic has: the relationship between Aristotle's syllogistic and the logics of relevance; the value of Aristotle's requirement that universal affirmative propositions be taken ‘absolutely’; the destruction of many Aristotelian proofs; the recovery of certain principles of modal opposition from a charge of inconsistency. (shrink)

In the first book of the Prior Analytics, Aristotle sets out, for the first time in Greek philosophy, a logical system. 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 between 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)

Three distinctly different interpretations of Aristotle’s notion of a sullogismos in Prior Analytics can be traced: (1) a valid or invalid premise-conclusion argument (2) a single, logically true conditional proposition and (3) a cogent argumentation or deduction. Remarkably the three interpretations hold similar notions about the logical relationships among the sullogismoi. This is most apparent in their conflating three processes that Aristotle especially distinguishes: completion (A4-6)reduction(A7) and analysis (A45). Interpretive problems result from not sufficiently recognizing Aristotle’s remarkable degree of (...) metalogical sophistication to distinguish logical syntax from semantics and, thus, also from not grasping him to refine the deduction system of his underlying logic. While it is obvious that Aristotle most often uses ‘sullogimos’ to denote a valid argument of a certain kind, we show that at Prior Analytics A4-6, 7, 45 Aristotle specifically treats a sullogismos as an elemental argument pattern having only valid instances and that such a pattern then serves as a rule of deduction in his syllogistic logic. By extracting Aristotle’s understanding of three proof-theoretic processes, this paper provides new insight into what Aristotle thinks reasoning syllogistically is and, moreover, it resolves three problems in the most recent interpretation that takes a sullogismos to be a deduction. (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)

This book treats ancient logic: the logic that originated in Greece by Aristotle and the Stoics, mainly in the hundred year period beginning about 350 BCE. Ancient logic was never completely ignored by modern logic from its Boolean origin in the middle 1800s: it was prominent in Boole’s writings and it was mentioned by Frege and by Hilbert. Nevertheless, the first century of mathematical logic did not take it seriously enough to study the ancient logic texts. A renaissance in ancient (...) logic studies occurred in the early 1950s with the publication of the landmark Aristotle’s Syllogistic by Jan Łukasiewicz, Oxford UP 1951, 2nd ed. 1957. Despite its title, it treats the logic of the Stoics as well as that of Aristotle. Łukasiewicz was a distinguished mathematical logician. He had created many-valued logic and the parenthesis-free prefix notation known as Polish notation. He co-authored with Alfred Tarski’s an important paper on metatheory of propositional logic and he was one of Tarski’s the three main teachers at the University of Warsaw. Łukasiewicz’s stature was just short of that of the giants: Aristotle, Boole, Frege, Tarski and Gödel. No mathematical logician of his caliber had ever before quoted the actual teachings of ancient logicians. -/- Not only did Łukasiewicz inject fresh hypotheses, new concepts, and imaginative modern perspectives into the field, his enormous prestige and that of the Warsaw School of Logic reflected on the whole field of ancient logic studies. Suddenly, this previously somewhat dormant and obscure field became active and gained in respectability and importance in the eyes of logicians, mathematicians, linguists, analytic philosophers, and historians. Next to Aristotle himself and perhaps the Stoic logician Chrysippus, Łukasiewicz is the most prominent figure in ancient logic studies. A huge literature traces its origins to Łukasiewicz. -/- This Ancient Logic and Its Modern Interpretations, is based on the 1973 Buffalo Symposium on Modernist Interpretations of Ancient Logic, the first conference devoted entirely to critical assessment of the state of ancient logic studies. (shrink)

The reception history of Aristotle's Prior Analytics in the Islamic world began even before its ninth-century translation into Arabic. Three generations earlier, Arabic authors already absorbed echoes of the varied and extensive logical teaching tradition of Greek- and Syriac-speaking religious communities in the new Islamic state. Once translated into Arabic, the Prior Analytics inspired a rich tradition of logical studies, culminating in the creation of an independent Islamic logical tradition by Ibn Sina (d. 1037), Ibn (...) Rušd (d. 1098) and others. This article traces the translation and commentary tradition of the Prior Analytics in Syriac and Arabic in the sixth to ninth centuries and sketches its appropriation, revision and, ultimately, transformation by Islamic philosophers between the ninth and eleventh centuries. (shrink)

In this paper, we discuss the syllogisms from both fronts : Aristotle and Boethius. We mainly focus on the differences with respect to categorical and hypothetical syllogisms in Aristotle and Boethius. Regarding Aristotle’s works on logic, it is not unusual to claim that Aristotle extensively worked on categorical syllogisms. In Prior Analytics, Aristotle gave proofs for many valid moods. However we cannot find a similar treatment for hypothetical syllogism in his works. Thus, it might be a reason for his (...) students to improve Aristotle’s theory of syllogisms by filling the gaps in hypothetical syllogisms. As Boethius already emphasized in the Book I of De Hypotheticis Syllogismis, the Peripatetic School only initiated the start. The remaining and detailed treatise was due to Boethius himself. The impression we got from Boethius’s and Aristotle’s works on syllogisms is that the categorical syllogism is almost entirely developed by Aristotle himself, whereas the extensive and the detailed study of the hypothetical syllogism was carried out by Boethius, although he was not the first figure in the history who gave concise expositions on hypothetical syllogism. Boethius’s translations of syllogisms in medieval era were the primer resource and textbook for Aristotelian logic during the early Medieval ages. Therefore, the scholars of those times had no other chance but to work from Boethius’s commentaries. So, the evident properties of Aristotelian figures were not then visible. Boethius wrote several textbooks in logic. A detailed investigation might yield significant information on Boethius’s logic compared with the influence of Aristotle on Boethius. (shrink)

We propose a new modal logic endowed with a simple deductive system to interpret Aristotle's theory of the modal syllogism. While being inspired by standard propositional modal logic, it is also a logic of terms that admits a (sound) extensional semantics involving possible states-of-affairs in a given world. Applied to the analysis of Aristotle's modal syllogistic as found in the Prior Analytics A8-22, it sheds light on various fine-grained distinctions which when made allow us to clarify some ambiguities and (...) obtain a completely consistent system and prove all of the modal syllogisms considered valid by Aristotle. This logic allows us also to make a connection with the axioms of modern propositional modal logic and to perceive to what extent these are implicit in Aristotle's reasoning. Further work will involve addressing the question of the completeness of this logic (or variants thereof) together with an extension of the logic to include a calculus of relations (for instance the relational syllogistic treated in Galen's Introduction to Logic) which Slomkowsky has argued is already found in the Topics. (shrink)

The word pro-tasis is etymologically a near equivalent of pre-mise, pro-position, and ante-cedent—all having positional, relational connotations now totally absent in contemporary use of proposition. Taking protasis for premise, Aristotle’s statement (24a16) -/- A protasis is a sentence affirming or denying something of something…. -/- is not a definition of premise—intensionally: the relational feature is absent. Likewise, it is not a general definition of proposition—extensionally: it is too narrow. This paper explores recent literature on these issues.

Since the time of Aristotle's students, interpreters have considered Prior Analytics to be a treatise about deductive reasoning, more generally, about methods of determining the validity and invalidity of premise-conclusion arguments. People studied Prior Analytics in order to learn more about deductive reasoning and to improve their own reasoning skills. These interpreters understood Aristotle to be focusing on two epistemic processes: first, the process of establishing knowledge that a conclusion follows necessarily from a set of premises (that is, (...) on the epistemic process of extracting information implicit in explicitly given information) and, second, the process of establishing knowledge that a conclusion does not follow. Despite the overwhelming tendency to interpret the syllogistic as formal epistemology, it was not until the early 1970s that it occurred to anyone to think that Aristotle may have developed a theory of deductive reasoning with a well worked-out system of deductions comparable in rigor and precision with systems such as propositional logic or equational logic familiar from mathematical logic. When modern logicians in the 1920s and 1930s first turned their attention to the problem of understanding Aristotle's contribution to logic in modern terms, they were guided both by the Frege-Russell conception of logic as formal ontology and at the same time by a desire to protect Aristotle from possible charges of psychologism. They thought they saw Aristotle applying the informal axiomatic method to formal ontology, not as making the first steps into formal epistemology. They did not notice Aristotle's description of deductive reasoning. Ironically, the formal axiomatic method (in which one explicitly presents not merely the substantive axioms but also the deductive processes used to derive theorems from the axioms) is incipient in Aristotle's presentation. Partly in opposition to the axiomatic, ontically-oriented approach to Aristotle's logic and partly as a result of attempting to increase the degree of fit between interpretation and text, logicians in the 1970s working independently came to remarkably similar conclusions to the effect that Aristotle indeed had produced the first system of formal deductions. They concluded that Aristotle had analyzed the process of deduction and that his achievement included a semantically complete system of natural deductions including both direct and indirect deductions. Where the interpretations of the 1920s and 1930s attribute to Aristotle a system of propositions organized deductively, the interpretations of the 1970s attribute to Aristotle a system of deductions, or extended deductive discourses, organized epistemically. The logicians of the 1920s and 1930s take Aristotle to be deducing laws of logic from axiomatic origins; the logicians of the 1970s take Aristotle to be describing the process of deduction and in particular to be describing deductions themselves, both those deductions that are proofs based on axiomatic premises and those deductions that, though deductively cogent, do not establish the truth of the conclusion but only that the conclusion is implied by the premise-set. Thus, two very different and opposed interpretations had emerged, interestingly both products of modern logicians equipped with the theoretical apparatus of mathematical logic. The issue at stake between these two interpretations is the historical question of Aristotle's place in the history of logic and of his orientation in philosophy of logic. This paper affirms Aristotle's place as the founder of logic taken as formal epistemology, including the study of deductive reasoning. A by-product of this study of Aristotle's accomplishments in logic is a clarification of a distinction implicit in discourses among logicians--that between logic as formal ontology and logic as formal epistemology. (shrink)

How does Aristotle think about sentences like ‘Every x is y’ in the Prior Analytics? A recently popular answer conceives of these sentences as expressing a mereological relationship between x and y: the sentence is true just in case x is, in some sense, a part of y. I argue that the motivations for this interpretation have so far not been compelling. I provide a new justification for the mereological interpretation. First, I prove a very general algebraic (...) soundness and completeness result that unifies the most important soundness and completeness results to date. Then I argue that this result vindicates the mereological interpretation. In contrast to previous interpretations, this argument shows how Aristotle’s conception of predication in mereological terms can do important logical work. (shrink)

We can now recognize Aristotle's many accomplishments in logical theory, not the least of which is treating the deduction process itself as a subject matter and thus establishing the science of logic. Aristotle took logic to be that part of epistemolo gy used to establish knowledge of logical consequence. Prior Analytics is a metalogical treatise on his syllogistic system in which Aristotle modelled his deduction system to demonstrate certain logical relationships among its rules. Aristotle's n otion of substitution distinguishes (...) logical syntax from semantics and enabled him to distinguish validity from deducibility sufficiently to note the completeness of his logic. (shrink)

It has often been claimed that (i) Aristotle's expression 'protasis' means 'premiss' in syllogistic contexts and (ii) cannot refer to the conclusion of a syllogism in the Prior Analytics. In this essay we produce and defend a counter-example to these two claims. We argue that (i) the basic meaning of the expression is 'proposition' and (ii) while it is often used to refer to the premisses of a syllogism, in Prior Analytics 1.29, 45b4-8 it is used to refer (...) to the conclusion of a syllogism. In our view, the best explanation of Aristotle's use of the expression 'protasis' is that it means proposition throughout but is frequently used without change of meaning (in certain specific contexts) to refer to the premisses from which a conclusion follows. In Prior Analytics 1.29, 45b4-8 he uses 'protasis' to refer to the conclusion when he needs a single expression to refer to both the conclusion and one of the premisses of the syllogism that constitutes the core of a syllogism through the impossible. If we are correct, we have shown that the view that the expression 'the final protasis' in EN 7.3, 1147b9ff must mean 'the final premiss' and so cannot refer to the conclusion of the relevant syllogism is mistaken. (shrink)

To meet a dilemma between the axiomatic theory of demonstrative science in Posterior analytics and the non-axiomatic practice of demonstrative science in the physical treatises, Jonathan Barnes has proposed that the theory of demonstration was not meant to guide scientific research but rather scientific pedagogy. The present paper argues that far from contributing directly to oral instruction, the axiomatic account of demonstrative science is a model for the written expression of science. The paper shows how this interpretation accords with (...) related theories in the Organon, including the theories of dialectic in Topics and of deduction in Prior analytics. (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 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)

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)

The Prior Analytics marks the beginning of formal logic, and is one of the most influential works in the history of thought. It is here that Aristotle sets out his system of syllogistic reasoning. The first book, to which this volume is devoted, offers a coherent presentation of Aristotle's logic as a general theory of deductive argument.

Compare two conceptions of validity: under an example of a modal conception, an argument is valid just in case it is impossible for the premises to be true and the conclusion false; under an example of a topic-neutral conception, an argument is valid just in case there are no arguments of the same logical form with true premises and a false conclusion. This taxonomy of positions suggests a project in the philosophy of logic: the reductive analysis of the modal conception (...) of logical consequence to the topic-neutral conception. Such a project would dispel the alleged obscurity of the notion of necessity employed in the modal conception in favour of the clarity of an account of logical consequence given in terms of tractable notions of logical form, universal generalization and truth simpliciter. In a series of publications, John Etchemendy has characterized the model-theoretic definition of logical consequence as truth preservation in all models as intended to provide just such an analysis. In this paper, I will argue that Aristotle intends to provide an account of a modal conception of logical consequence in topic-neutral terms and so is engaged in a project comparable to the one described above. That Aristotle would be engaged in this sort of project is controversial. Under the standard reading of the Prior Analytics, Aristotle does not and cannot provide an account of logical consequence. Rather, he must take the validity of the first figure syllogisms (such as the syllogism known by its medieval mnemonic ‘Barbara’: A belongs to all B; B belongs to all C; so A belongs to all C) as obvious and not needing justification; he then establishes the validity of the other syllogisms by showing that they stand in a suitable relation to the first figure syllogisms. I will argue that Aristotle does attempt to provide an account of logical consequence—namely, by appeal to certain mereological theorems. For example, he defends the status of Barbara as a syllogism by appeal to the transitivity of mereological containment. There are, as I will discuss, reasons to doubt the success of this account. But the attempt is not implausible given certain theses Aristotle holds in semantics, mereology and the theory of relations. (shrink)

This paper examines the relevance and importance of the large number of examples which Aristotle uses in his "Prior Analytics." In the first part of the paper three preliminary issues are raised: First, it investigates what counts as an example in Aristotle's syllogistic, and especially whether only examples expressed in concrete terms should be considered as examples or maybe also propositions and arguments with letters of the alphabet. The second issue concerns the kinds of examples Aristotle actually uses from (...) everyday life as well as from various scientific and philosophical forms of discourse; among these, it seems that biological examples, rather than mathematical ones, have a predominant place. Finally, I discuss what Aristotle himself has to say about the use of examples, and in particular about the similarity between the use of an example and the use of induction. The second part of the paper focusses on the functions of Aristotle's logical examples. It is of course obvious that some of the examples in the Prior Analytics are used to illustrate, and thus to clarify, a definition, a logical rule, a type of argument. However, I think that Aristotle's logical examples have another function, which is philosophically more interesting, namely as integral parts of the procedure of proving something. To support this claim, I analyse three passages from the "Prior Analytics" in which examples are used either in order to prove that something is not the case, i.e. as counter-examples, or in order to prove positively that it is possible for something to be the case. At the end, I argue that for such uses of examples Aristotle uses the notion of 'ekthesis', which seems to have a wider sense than usually suggested; that is to say, it is used to refer to any proof by means of an example, and not only for the procedure which Aristotle uses to reduce imperfect to perfect syllogisms. (shrink)

This chapter contains sections titled: Knowledge and Analysis The Relation Between Prior and Posterior Analytics Syllogistic Interpretations of Aristotle's Syllogistic Logic Knowledge of Facts Aristotelian Causes Demonstration Principles Definitions and Demonstrations Necessity Science and Dialectic Fallibility Applicability Readings of Aristotle's Theory of Science Epistemological Status of the Analytics Bibliography.

This expository paper on Aristotle’s prototype underlying logic is intended for a broad audience that includes non-specialists. It requires as background a discussion of Aristotle’s demonstrative logic. Demonstrative logic or apodictics is the study of demonstration as opposed to persuasion. It is the subject of Aristotle’s two-volume Analytics, as its first sentence says. Many of Aristotle’s examples are geometrical. A typical geometrical demonstration requires a theorem that is to be demonstrated, known premises from which the theorem is to be deduced, (...) and a deductive logic by which the steps of the deduction proceed. Every demonstration produces knowledge of its conclusion for every person who comprehends the demonstration. Aristotle presented a general truth-and-consequence theory of demonstration meant to apply to all demonstrations: a demonstration is an extended argumentation that begins with premises known to be truths and that involves a chain of reasoning showing by deductively evident steps that its conclusion is a consequence of its premises. In short, a demonstration is a deduction whose premises are known to be true. Aristotle’s general theory of demonstration required a prior general theory of deduction presented in the Prior Analytics. His general immediate-deduction-chaining theory of deduction was meant to apply to all deductions: any deduction that is not immediately evident is an extended argumentation that involves a chaining of immediately evident steps that shows its final conclusion to follow logically from its premises. His deductions, both direct and indirect, were rule-based and not tautology-based. The idea of tautology-based deduction, which dominated modern logic in the early years of the 1900s, is nowhere to be found in Analytics. Rule-based deduction was rediscovered by modern logicians. To illustrate his general theory of deduction, Aristotle presented a prototype: an ingeniously simple and mathematically precise special case traditionally known as the categorical syllogistic. With reference only to propositions of the four so-called categorical forms, he painstakingly worked out exactly what those immediately evident deductive steps are and how they are chained to complete deductions. In his specialized prototype theory, Aristotle explained how to deduce from a given categorical premise set, no matter how large, any categorical conclusion implied by the given set. He did not extend this treatment to non-categorical deductions, thus setting a program for future logicians. The prototype, categorical syllogistic, was seen by Boole as a “first approximation” to a comprehensive logic. Today, however it appears more as the first of the dozens of logics already created and as the first exemplification of a family that continues to expand. (shrink)

ABSTRACT: English translation of the 2nd/3rd century Peripatetic Philosopher's Alexander of Aphrodisias commentary on Aristotle's non-modal syllogistic, i.e. on one of the most influential logical texts of all times. -/- Volume includes introduction on Alexander of Aphrodisias and the early commentators, translation with notes and comments, appendices with a new translation of Aristotle's text, a summary of Aristotle's non-modal syllogistic and textual notes.

Most interpretations of Aristotle’s Posterior Analytics believe that the term ‘ameson’ is used to describe the principles or foundations of a given system of justification or explanation as epistemically prior to or more fundamental than the other propositions in the system. Epistemic readings (as I shall call them) arguably constitute a majority in the secondary literature. This predominant view has been challenged by Robin Smith (1986) and Michael Ferejohn (1994; 2013), who propose interpretations that should be classified as non-epistemic (...) according to the definition above. My aim in this article is purely negative. I intend to show that these non-epistemic interpretations are liable to serious objections and are in conflict with some important features of Aristotle’s theory of demonstration. (shrink)

Compare two conceptions of validity: under an example of a modal conception, an argument is valid just in case it is impossible for the premises to be true and the conclusion false; under an example of a topic-neutral conception, an argument is valid just in case there are no arguments of the same logical form with true premises and a false conclusion. This taxonomy of positions suggests a project in the philosophy of logic: the reductive analysis of the modal conception (...) of logical consequence to the topic-neutral conception. Such a project would dispel the alleged obscurity of the notion of necessity employed in the modal conception in favour of the clarity of an account of logical consequence given in terms of tractable notions of logical form, universal generalization and truth simpliciter. In a series of publications, John Etchemendy has characterized the model-theoretic definition of logical consequence as truth preservation in all models as intended to provide just such an analysis. In this paper, I will argue that Aristotle intends to provide an account of a modal conception of logical consequence in topic-neutral terms and so is engaged in a project comparable to the one described above. That Aristotle would be engaged in this sort of project is controversial. Under the standard reading of the Prior Analytics, Aristotle does not and cannot provide an account of logical consequence. Rather, he must take the validity of the first figure syllogisms (such as the syllogism known by its medieval mnemonic ‘Barbara’: A belongs to all B; B belongs to all C; so A belongs to all C) as obvious and not needing justification; he then establishes the validity of the other syllogisms by showing that they stand in a suitable relation to the first figure syllogisms. I will argue that Aristotle does attempt to provide an account of logical consequence—namely, by appeal to certain mereological theorems. For example, he defends the status of Barbara as a syllogism by appeal to the transitivity of mereological containment. There are, as I will discuss, reasons to doubt the success of this account. But the attempt is not implausible given certain theses Aristotle holds in semantics, mereology and the theory of relations. (shrink)

This study contributes substantially to research on Aristotelian logic in Byzantium. It includes a critical edition of the commentary by Leo Magentenos, the Metropolitan of Mytilene (twelfth c.?) on Book II of the Prior Analytics along with an edition of the syllogism diagram attributed to this work in the manuscript tradition of this work.

Studies of Aristotle’s syllogistic system, since Corcoran’s deductionist interpretation supplanted Łukasiewicz’ axiomaticist interpretation, misrepresent Aristotle’s logic in two important respects. Following Corcoran, they take indirect deduction to occur only once in a deduction discourse; they then obviate the system having a reductio rule. Second, they represent reduction as a deductive process for deriving ‘imperfect’ syllogisms from ‘perfect’ syllogisms to impose an axiomatic interpretation on the logic. Denying that Aristotle's logic admits of a reductio rule results from this (...) misrepresentation of reduction. This discussion shows that the defects imputed to Aristotle's logic, and systems devised to resolve them, result from misunderstanding reduction, which itself results from misapprehending Prior Analytics expressly to identify in a metadiscourse deduction rules and not deductions per se. (shrink)

The purpose of this paper is to give an account and a rational reconstruction of the heuristic advice provided by Aristotle in the Topics and Prior Analytics in regard to the difficulty or ease of strategic planning in the context of a dialectical dialogue. The general idea is that a Questioner can foresee what his refutational syllogism would have to look like given the character of the thesis defended by the Answerer, and therefore plan accordingly. A rational reconstruction of (...) this advice will be attempted from three perspectives: strategic planning based on the acceptability of Answerer’s thesis, strategic planning based on the predicational form of the thesis, strategic planning based on the logical form of the thesis. In addition, we will provide an illustration of the potential of this heuristic advice as we apply it to the interpretation of a fragment from Plato, presuming that, in a similar way, a reading of this kind might be more generally applicable in the interpretation of the Platonic dialogues. (shrink)

In this volume Mueller and Gould present the translation of Alexander’s commentary on chapters 14–22 of the first book of the Prior Analytics. These chapters deal with modal logic as applied to contingent propositions and to combinations of unqualified premises and of one assertoric proposition. In the 58 page introduction Professor Mueller presents first a survey of Aristotle’s assertoric syllogistic to turn next to combinations with a contingent premise in the three figures. He then passes to modal syllogistic without (...) contingency. Modal syllogistic can be understood as an extension of assertoric syllogistic. Aristotle seeks to determine which modal propositions related to first figure assertoric syllogisms are true syllogisms. The translation of Alexander’s text is excellent. (shrink)

In previous issues of The Review of Metaphysics attention has been drawn to the project of Professor Richard Sorabji to publish the English translations of the ancient Greek commentators of Aristotle. We are happy to present a new volume of this series which contains the English translation of the commentary by Alexander of Aphrodisias on Aristotle’s Prior Analytics, I, chapters 8–13. In his preface Professor Sorabji underlines the importance of Alexander’s commentary on these chapters, in which Aristotle invented modal (...) syllogistic. This volume comprises the commentary on chapters 8 to 13. Chapters 1, 2, and 4 to 7 contain Aristotle’s assertoric syllogistic. For Alexander’s commentary on these chapters the translators refer to the excellent edition of Jonathon Barnes, et al. In chapters 8 to 13 Aristotle studies syllogisms which consist of two necessary propositions and those which are composed of one necessary proposition and a second which is modally unqualified. The central question is which modal syllogisms, analogous to assertoric syllogisms of the first figure, are true syllogisms. The translators have added Alexander’s commentary on chapter 17, where it is argued that a privative contingent proposition cannot be converted into a syllogism of the first figure. (shrink)

During the years 800-1200 A.D., Arabic scholars studied many of the works of Greek philosophy, and recorded their interpretations. Significant Arabic interpretations of Aristotle's Prior Analytics, the key work of his logical Organon, however, have remained largely unavailable in the West. The recent discovery of several Arabic manuscripts in Istanbul revealed the “Short Commentary on Prior Analytics” by the medieval Arabic philosopher al-Farabi. Nicholas Rescher here presents the first translation of this work in English, and supplements this with (...) an informative introduction and numerous explanatory footnotes. (shrink)

In this chapter, Hankinson examines Aristotle's philosophy of science, or the logical structure of explanation as set out in the Posterior Analytics, and which is based on the theory of the syllogism worked out in the Prior Analytics. For Aristotle, definition is fundamental to the project of exhibiting science in its appropriate explanatory form, i.e. proceeding deductively from fundamental principles and axioms about the structure of things. Science and scientific explanation are for Aristotle construed realistically: science must mirror (...) reality, and therefore theory always must cohere with observation and empirical investigation. Hankinson discusses Aristotle's qualitative physics of motion, on the basis of the doctrine of natural places, his account of chemical combination, and his cosmology, which is at once teleological in character, while being empirically adequate. Hankinson also discusses Aristotle's successors Theophrastus and Strato of Lampsacus: Theophrastus developed and refined Aristotle's methodology while bringing some scepticism to the ubiquitous application of teleology; Strato also tends more towards mechanistic explanations. (shrink)

At Prior Analytics II 22.68a16–21, Aristotle argues that if A is predicated of all B and C and nothing else, and B is predicated of all C, then A and B convert. In justifying his argument, however, he appears to claim that B is not predicated of all A. This claim has long been a cause of puzzlement to commentators. A widespread view is that the kind of conversion discussed in the passage at issue should be explained in both (...) extensional and intensional terms. After providing some textual evidence that Aristotle only apparently claims that B is not predicated of all A, I give a purely extensional account of Aristotle’s argument. This account is plausible, conservative and simpler than any of the intensional accounts that have been proposed so far. (shrink)

"During the years 800-1200 A.D., Arabic scholars studied many of the works of Greek philosophy, and recorded their interpretations. Significant Arabic interpretations of Aristotle's Prior Analytics, the key work of his logical Organon, however, have remained largely unavailable in the West. The recent discovery of several Arabic manuscripts in Istanbul revealed the "Short Commentary on Prior Analytics" by the medieval Arabic philosopher al-Farabi. Nicholas Rescher here presents the first translation of this work in English, and supplements this with (...) an informative introduction and numerous explanatory footnotes." --. (shrink)

This mainly historical paper provides a comprehensive discussion of the (heretoforth neglected) evidence of Peripatetic syllogistic in Sextus Empiricus. The paper sets out to show that it is likely that in Sextus (and Apuleius) there is valuable evidence of a transitional period in later ancient logic that is marked out as such by a number of characteristics, which include the following: (i) A Peripatetic term ‘categorical syllogism’ is newly in use, but no term ‘hypothetical syllogism’ has been established (...) yet. (ii) Stoic and Peripatetic logic are treated as complementing each other. (iii) The reversion of quantified propositions from predicate-subject to subject-predicate formulation is still fairly new. (iv) The so-called crocodile example is used to show that induction lacks the feature of concluding by necessity that is a defining mark of Aristotelian syllogisms. (v) The use of the expression katholikê protasis for categorical universal premise-propositions is distinctive of the period. (vi) The argument forms displayed by Sextus’ three examples appear to be indirectly related to the soon-to-appear Platonist hypothetical syllogistic. (vii) There are parallels that suggest that Sextus’ source belongs to the same historical period of logic as Apuleius’ source and as some probably recent source of Alexander of Aphrodisias’ Prior Analytics commentary (that is presented along with some later views and arguments, which may include Alexander’s own). Small differences between the three authors show that Sextus did not draw from the Greek handbook that was Apuleius’ source. (shrink)

Since at least late antiquity, Aristotle’s Prior Analytics B 23 has been misread. Aristotle does not think that an induction is a syllogism made good by complete enumeration. The confusion can be eliminated by considering the nature of the surviving text and watching very closely Aristotle’s moving back and forth between “induction” and “syllogism from induction.” Though he does move freely between them, the two are not synonyms.

Aristotle presents a formal logic in the Prior Analytics in which the premises and conclusions are never conditionals. In this paper I argue that he did not simply overlook conditionals, nor does their absence reflect a metaphysical prejudice on his part. Instead, he thinks that arguments with conditionals cannot be syllogisms because of the way he understands the explanatory requirement in the definition of a syllogism: the requirement that the conclusion follow because of the premises. The key passage (...) is Prior Analytics I.32, 47a22–40, where Aristotle considers an argument with conditionals that we would consider valid, but which he denies is a syllogism. I argue that Aristotle thinks that to meet the explanatory requirement a syllogism must draw its conclusion through the way its terms are predicated of one another. Because arguments with conditionals do not, in general, draw their conclusions through predications, he did not include them in his logic. (shrink)

In this paper I examine two passages in Aristotle's 'Analytics' that deal with the topics of inductive knowledge, in general, and with the specific issue of "simultaneous learning", the grasping of two distinct, new pieces of information in a single act of thought. Interpreters have generally followed the treatment of these passages by Ross and Barnes, but difficulties have recently been raised for this interpretation, especially by Gifford. I attempt to deal with these difficulties and to show that the (...) problems with the received interpretation are not so great as to render it untenable. In doing so I develop an account of Aristotelian epagoge that Lesher, Hamlyn, and McKirahan originated, and show how this account enhances our understanding of the process by which, according to Aristotle, knowledge is acquired and applied. (shrink)

Aristotle's Prior Analytics marks the beginning of formal logic. For Aristotle himself, this meant the discovery of a general theory of valid deductive argument, a project that he had described as either impossible or impracticable, probably not very long before he actually came up with syllogistic reasoning. A syllogism is the inferring of one proposition from two others of a particular form, and it is the subject of the Prior Analytics. The first book, to which this volume is (...) devoted, offers a fairly coherent presentation of Aristotle's logic as a general theory of deductive argument. (shrink)

Aristotle was the founder not only of logic but also of modal logic. In the Prior Analytics he developed a complex system of modal syllogistic which, while influential, has been disputed since antiquity--and is today widely regarded as incoherent. Combining analytic rigor with keen sensitivity to historical context, Marko Malink makes clear that the modal syllogistic forms a consistent, integrated system of logic, one that is closely related to other areas of Aristotle's philosophy. Aristotle's modal syllogistic differs significantly from (...) modern modal logic. Malink considers the key to understanding the Aristotelian version to be the notion of predication discussed in the Topics--specifically, its theory of predicables and the ten categories. The predicables introduce a distinction between essential and nonessential predication. In contrast, the categories distinguish between substantial and nonsubstantial predication. Malink builds on these insights in developing a semantics for Aristotle's modal propositions, one that verifies the ancient philosopher's claims of the validity and invalidity of modal inferences. While it acknowledges some limitations of this reconstruction, Aristotle's Modal Syllogistic brims with bold ideas, richly supported by close readings of the Greek texts. (shrink)

In Prior Analytics I.30, Aristotle seems too much optmistic about finding out the principles of sciences. For he seems to say that, if our empirical collection of facts in a given domain is exhaustive or sufficient, it will be easy for us to find out the explanatory principles in the domain. However, there is a distance between collecting facts and finding out the explanatory principles in a given domain. In this paper, I discuss how the key expression in the (...) sentence at 46a25 should be interpreted: “the true characteristics of things” (“τῶν ἀληθῶς ὑπαρχόντων τοῖς πράγμασιν”). I argue that, on a more accurate interpretation of the expression, Aristotle’s point would cease to look like a piece of naïve or even silly optimism. (shrink)

Aristotle studies syllogistic argumentation in Sophistical Refutations and Prior Analytics. In the latter he focuses on the formal and syntactic character of arguments and treats the sullogismoi and non-sullogismoi as argument patterns with valid or invalid instances. In the former Aristotle focuses on semantics and rhetoric to study apparent sullogismoi as object language arguments. Interpreters usually take Sophistical Refutations as considerably less mature than Prior Analytics. Our interpretation holds that the two works are more of a piece (...) than previously believed and, indeed, that Aristotle's treatment of fallacious reasoning presupposes the results of the formal theory. (shrink)

This paper discusses the possible classification of Aristotle’s syllogistic as a non-classical logical system, positing Aristotle himself as a non-classical logician. Initially, we find compelling arguments for this thesis, particularly regarding the expressive power and the rules governing logical inference inherent in Aristotle’s approach. My analysis nevertheless addresses two significant counterarguments. The first, the special case objection, posits that Aristotle’s syllogistic can be framed as a classical logic which deals with canonical syllogistic forms. I argue that this objection is insufficient, (...) as it is possible to point cases in which his system seems to differ from classical logic. The second counterargument, the formalisation gap objection, highlights that Aristotle’s syllogistic resists straightforward modern logical interpretations. This latter objection is evaluated as more compelling and substantial. In particular, a distinction between two concepts is proposed which could help us understand what Aristotle was aiming at in his theory of inference: the notions of ‘to follow from’ and ‘to be a conclusion of’. While the former aligns with the usual sense formal validity, the second requires an inferential structure connecting the premises to the conclusion, explaining why Aristotle excluded inferences like from A ⊢ A syllogisms despite acknowledging that A follows from A. (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)