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

The Posterior Analytics contains some of Aristotle's most influential thoughts in logic, epistemology, metaphysics, and the philosophy of science. The first book expounds and develops the notions of a demonstrative argument and of a formal, axiomatized science, and investigates in particular the theory of definition. For the second edition of this volume, the translation has been completely rewritten; and the commentary, which is done with the needs of philosophical readers in mind, has been thoroughly revised in the light (...) of the scholarship of the last twenty years. (shrink)

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)

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)

What is meant under the genuine title of Aristotle’s ta Analytika is rarely properly understood. Presumably, his analytics was inspired by the method of geometric analysis. For Aristotle, this was a regressive or heuristic procedure, departing from a proposed conclusion and asking which premises could be found in order to syllogize, demonstrate or explain it. The terms that form categorical and modal propositions play a fundamental role in analytics. Aristotle introduces letters in lieu of the triples of terms (...) constitut­ing the propositions and the three syllogistic figures that schematize them. His formulation of the three syllogistic figures refers to a syntacti­cal and predicative order and position of the triples of terms, arranged in some diagrammed schemata, which, regrettably, are missing from the extant text of the Prior Analytics. Considering planar and graphic arrangements, both vertical and horizontal orders as well as the posi­tion of the three terms involved, we propose a reconstruction, at least to some extent, of these probable lettered diagrams. In such reconstructed diagrams, we can appropriately capture the definition of syllogism as a predicative connexion of terms, and easier survey a synoptic account of all valid predicative relations and transpositions, and also reduce the imperfect syllogisms into the moods of the first figure. Aristotle’s syllogistic is an analytical calculation of terms, understood as predicates and subjects within the categorical propositions, and more precisely of three terms schematized in three figures in predicative links such that, by means of a middle, follows from necessity a conclusion of the extreme terms. The necessity of the consequence is not based on the implication or inference of the propositions, but on a predictive transi­tivity through the middle term within the syllogistic figures. Syllogism must draw its conclusion through the way its terms are predicated of one another. Aristotle in his Prior Analytics developed also a complex account of modal syllogisms within necessity and possibility of belonging. This account involves also such an analyti­cal reduction to the syllogistic figures. In this analytical perspective, we try to throw some light on his modal syllogisms, although this difficult and nowadays thoroughly discussed topic would require a much wider treatment. (shrink)

Aristotle contrasts episteme and doxa through the key notions of universal and necessary. These notions have played a central role in Aristotle’s characterization of scientific knowledge in the previous chapters of APo. They are not spelled out in APo I.33, but work as a sort of reminder that packs an adequate characterization of scientific knowledge and thereby gives a highly specified context for Aristotle’s contrast between episteme and doxa. I will try to show that this context introduces a contrast in (...) terms of explanatory claims: on the one hand, episteme covers those claims which capture explanatory connections that are universal and necessary and thereby deliver scientific understanding; on the other hand, doxa covers the explanatory attempts that fail at doing so. (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)

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.

Prior Analytics by the Greek philosopher Aristotle and Laws of Thought by the English mathematician George Boole are the two most important surviving original logical works from before the advent of modern logic. This article has a single goal: to compare Aristotle's system with the system that Boole constructed over twenty-two centuries later intending to extend and perfect what Aristotle had started. This comparison merits an article itself. Accordingly, this article does not discuss many other historically and philosophically (...) important aspects of Boole's book, e.g. his confused attempt to apply differential calculus to logic, his misguided effort to make his system of ‘class logic’ serve as a kind of ‘truth-functional logic’, his now almost forgotten foray into probability theory, or his blindness to the fact that a truth-functional combination of equations that follows from a given truth-functional combination of equations need not follow truth-functionally. One of the main conclusions is that Boole's contribution widened logic and changed its nature to such an extent that he fully deserves to share with Aristotle the status of being a founding figure in logic. By setting forth in clear and systematic fashion the basic methods for establishing validity and for establishing invalidity, Aristotle became the founder of logic as formal epistemology. By making the first unmistakable steps toward opening logic to the study of ‘laws of thought’—tautologies and laws such as excluded middle and non-contradiction—Boole became the founder of logic as formal ontology.… using mathematical methods … has led to more knowledge about logic in one century than had been obtained from the death of Aristotle up to … when Boole's masterpiece was published.Paul Rosenbloom 1950. (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)

I defend an interpretation of Aristotle’s _Posterior Analytics _Book I which distinguishes between two projects in different passages of that work: to explain what a given science is and to explain what properly scientific knowledge is. I present Aristotle’s theory in answer to ii, with special attention to his definition of scientific knowledge in 71b9-12 and showing how this is developed on chapters 1.2-9 and 1.13 into a solid Theory of Scientific Demonstration. The main point of this theory is (...) that demonstrations need to capture relevant explanations. Some formal requirements of the demonstration are unfoldings of the main project, 1.e., to capture and present properly relevant causal-explanatory relations. (shrink)

This volume collects Late Ancient, Byzantine and Medieval appropriations of Aristotle's Posterior Analytics, addressing the logic of inquiry, concept formation, the question whether metaphysics is a science, and the theory of demonstration.

At the end of Republic 5, Plato distinguishes epistêmê from doxa, knowledge from belief. In Posterior Analytics 1.33, Aristotle provides his own distinction between epistêmê and doxa. I explore his way of distinguishing them and compare it with Plato's.

I discuss an important feature of the notion of cause in Post. An. 1. 13, 78b13–28, which has been either neglected or misunderstood. Some have treated it as if Aristotle were introducing a false principle about explanation; others have understood the point in terms of coextensiveness of cause and effect. However, none offers a full exegesis of Aristotle's tangled argument or accounts for all of the text's peculiarities. My aim is to disentangle Aristotle's steps to show that he (...) is arguing in favour of a logical requirement for a middle term's being the appropriate cause of its explanandum. Coextensiveness between the middle term and the attribute it explains is advanced as a sine qua non condition of a middle term's being an appropriate or primary cause. This condition is not restricted either to negative causes or to middle terms in second‐figure syllogisms, but ranges over all primary causes qua primary. (shrink)

I intend to show that Aristotle follows some of the main guidelines of the Analytics in his investigation about the nature of the city in Politics I. I assume that Pol. I sets out the causes of the city and that the book responds to the four questions presented in APo. II.1. I demonstrate that Aristotle’s methodology follows a φυσικῶς standard. In addition, I assume that dialectic plays a secondary – refutative – role, as opposed to the opinion of (...) Owen (1961) and Barnes (1980) that dialectic was the main methodology applied in practical philosophy. (shrink)

Aristotle, great Greek philosopher, researcher, reasoner, and writer, born at Stagirus in 384 BCE, was the son of Nicomachus, a physician, and Phaestis. He studied under Plato at Athens and taught there ; subsequently he spent three years at the court of a former pupil, Hermeias, in Asia Minor and at this time married Pythias, one of Hermeias's relations. After some time at Mitylene, in 343?2 he was appointed by King Philip of Macedon to be tutor of his teen-aged son (...) Alexander. After Philip's death in 336, Aristotle became head of his own school, the Lyceum at Athens. Because of anti-Macedonian feeling there after Alexander's death in 323, he withdrew to Chalcis in Euboea, where he died in 322. Nearly all the works Aristotle prepared for publication are lost; the priceless ones extant are lecture-materials, notes, and memoranda. They can be categorized as follows: I Practical: Nicomachean Ethics; Great Ethics ; Eudemian Ethics; Politics; Economics ; On Virtues and Vices. II Logical: Categories; Analytics ; Interpretation; Refutations used by Sophists; Topica. III Physical: Twenty-six works including astronomy, generation and destruction, the senses, memory, sleep, dreams, life, facts about animals, etc. IV Metaphysics: on being as being. V Art: Rhetoric and Poetics. VI Other works including the Constitution of Athens; more works also of doubtful authorship. VII Fragments of various works such as dialogues on philosophy and literature; and of treatises on rhetoric, politics and metaphysics. The Loeb Classical Library edition of Aristotle is in twenty-three volumes. (shrink)

In the second half of Book One of the Prior Analytics, Aristotle reflects on the application of the formalized logic has developed in the first half, focusing particularly on the non-modal or assertoric syllogistic developed in the first seven chapters. These reflections lead Alexander of Aphrodisias, who was a great exponent of Aristotelianism in the late second century, to explain and sometimes argue against subsequent developments of Aristotle's logic and alternatives and objections to it, ideas associated mainly with (...) his colleague Theophrastus and with the Stoics. The other main topic of this part of the Prior Analytics is the specification of a method for discovering true premises needed to prove a given proposition. Aristotle's presentation is sometimes difficult to follow, and Alexander's discussion is extremely helpful to the uninitiated reader. In his commentary on the final chapter translated in this volume, Alexander provides an insightful account of Aristotle's criticism of Plato's method of division. (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)

Revision of the author's thesis (Ph. D.)--Laval University, 1999.

This paper revisits Aristotle’s discussion of akrasia in NE VII. 1–10. I try to offer a scientific reading of the book, according to which NE VII. 1–10 closely instantiates the main guidelines of Aristotle’s Posterior Analytics. I propose that NE VII. 1–2, which aims to establish the fact that akrasia exists, corresponds to the ὅτι-stage of an Aristotelian scientific inquiry, and NE VII. 3–10, which aims to explain both the cause and the object of akrasia, corresponds to the διότι-stage (...) of the inquiry. (shrink)

Aristotle described the scientific explanation of universal or general facts as deducing them through scientific demonstrations, that is, through syllogisms that met requirements he first formulated of logical validity and explanatoriness. In Chapters 19-23, he adds arguments for the further logical restrictions that scientific demonstrations can neither be indefinitely long nor infinitely extendible through the interposition of new middle terms. Chapters 24-26 argue for the superiority of universal over particular demonstration, of affirmative over negative demonstration, and of direct negative demonstration (...) over demonstration to the impossible. Chapters 27 34 discuss different aspects of sciences and scientific understanding, allowing us to distinguish between sciences, and between scientific understanding and other kinds of cognition, especially opinion. Philoponus' comments on these chapters are interesting especially because of his metaphysical analysis of universal predication and his understanding of the notion of subordinate sciences. We learn from his commentary that Philoponus believed in Platonic Forms as inherent in, and posterior to, the Divine Intellect, but ascribed to Aristotle an interpretation of Plato's Forms as independent substances, prior to the Demiurgic Intellect. A very important notion from Aristotle's Posterior Analytics is that of the 'subordination' of sciences, i.e. the idea that some sciences depend on 'higher' ones for some of their principles. Philoponus goes beyond Aristotle in suggesting a taxonomy of sciences, in which the subordinate science is the same in genus as the superordinate, but different in species. (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)

I present three critical points against G.E.R. Lloyd's ‘The Fortunes of Analogy’. First, I argue that Lloyd unduly criticises Aristotle's view of analogies. Second, I argue that Lloyd needs to discuss the means of limiting the semantic stretch of terms, for instance through the distinction between fiat and bona fide boundaries. Third, I point out some terminological issues in Lloyd's account, especially concerning the applicability of validity, soundness, and fallaciousness to analogies.

In 1928, Friedrich Solmsen argued that Aristotle'sPosterior Analyticswas largely composed before thePrior Analytics. Ross rejected Solmsen's position in 1939, and a rather lengthy series of rebuttals and counter-attacks between the two scholars followed. Quite recently, Jonathan Barnes has revived this issue with arguments in favour of something very close to Solmsen's thesis: that Aristotle first developed a theory of demonstration (‘apodeictic’) before he had worked out the syllogistic, and that thePosterior Analyticswas originally conceived against this background. Subsequently, when Aristotle (...) formulated a syllogistic, he is supposed by Barnes to have revised or added to the contents of thePosterior Analyticsso as to make syllogistic the logic of Aristotelian science. Thus, Barnes says: ‘the syllogism is in fact an incidental adjunct to the theory of demonstration: the theory can be formulated without reference, explicit or implicit, to Syllogistic, and itcould havebeen discovered by someone who knew nothing whatever about the Syllogism’ (pp. 33–4). (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)