Since Peter Geach coined the phrase in 1966 there has been much discussion among scholars of the "Socratic fallacy." No consensus presently exists on whether Socrates commits the "Socratic fallacy"; almost all scholars agree, however, that the "Socratic fallacy" is a bad thing and that Socrates has good reason to avoid it. I think that this consensus of scholars is mistaken. I think that what Geach has labeled a fallacy is no fallacy at all, but a perfectly innocent consequence of (...) Platonic epistemology. The "Socratic fallacy" arises from the "Priority of Definition" principle (PD). Plato is committed to (PD) in the "Meno." The "Meno" also contains a famous discussion of the difference between episteme and doxa (97a ff.). If we understand what Plato meant by episteme we can see that he must be committed to (PD); but we can also see that (PD) has none of the harmful consequences Geach attributes to it. Geach's view is indebted to Wittgenstein's philosophy of language. (PD) is implausible on this reading of the verb "to know," but not on Plato's. Plato claims that a demand for an explanation is appropriate wherever a claim to knowledge is made. Plato links the concept of episteme explicitly with the concept of logos; the connection between the terms may have been analytic. It does not follow from the Platonic conception of knowledge, as Geach argues, that it is "no use" using examples to establish general definitions. All that follows is that one cannot know that an alleged example of a term T is a genuine example until one has a general account of what it is to be T. Without the stronger conclusion, Geach cannot establish that the "Socratic fallacy" is a fallacy. (shrink)

1. Lemmon’s stratification. By a “tense logic” I mean a system with the following features: it contains sentential variables which stand for sentences which in some cases are true at some times and false at others; it contains the usual truth-functions, whose truth-conditions are given the obvious modifications, e.g. Np is true when and only when p is false, Kpq is true when and only when both its conjuncts are; and it contains two additional functions which may be interpreted as (...) ‘It will be the case that p’ and ‘It has been the case that p’, the former being true when and only when the plain p will be true later on and the latter when and only when the plain p has been true at some earlier time. (shrink)

This is a brief review of Silverman's study of Plato's ontology, in particular his theory of Forms. Silverman writes from an analytic viewpoint. He accepts the developmentalist picture of Plato's thought, but holds that the development is gradual. He focuses on the issue of predication, and especially self-predication. He tends to treat Plato's ontology as a free-standing subject. All of these features are controversial. I wondered in particular whether the analytic approach required more precision than can be found in the (...) dialogues. (shrink)

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

WE must first state the subject of our inquiry and the faculty to which it belongs: its subject is demonstration and the faculty that carries it out demonstrative science.

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.

Die Quellen der Aristoteles-Rezeption bzw. der aristotelischen Logik im byzantinischen Mittelalter sind nur teilweise oder gering erforscht. Eine der wichtigen Autoritäten dieser Tradition stellt Leon Magentenos (12. Jh.?) dar. Magentenos war Metropolit von Mytilene sowie ein Gelehrter, der Kommentare zu allen sechs Traktaten des aristotelischen Organon (Categoriae, De Interpretatione, Analytica Priora, Analytica Posteriora, Topica, Sophistici Elenchi) verfasst hat. Hier wird die kritische Edition des Kommentars zum zweiten Buch der Ersten Analytik zusammen mit seiner Übersetzung ins Englische vorgelegt. Untersucht werden auch (...) die dem Kommentar angehängten syllogistischen Diagramme. Kommentare zu Analytica Priora II nach der Spätantike und vor Magentenos waren eher eine Rarität, daher ist sein Kommentar eine wichtige Quelle für alle Forscher, die sich mit der Geschichte der byzantinischen Logik und der aristotelischen Kommentierung befassen. (shrink)

This study contains three parts. The first tries to follow the spread of the study of the Prior Analytics in the first two centuries during which it was at all studied in Western Europe, providing in this connection a non-exhaustive list of extant commentaries. Part II points to a certain overlap between commentaries on the Prior Analytics and works from the genre of sophismata . Part III lists the questions discussed in a students' compendium from about (...) the 1240s and in six commentaries per modum quaestionis from the 1270s through the 1290s. (shrink)

The last 14 chapters of book 1 of Aristotle's "Prior Analytics" are concerned with the representation in the formal language of syllogistic of propositions and arguments expressed in more or less everyday Greek. In his commentary on those chapters, Alexander of Aphrodisias explains some of Aristotle's more opaque assertions and discusses post-Aristotelian ideas in semantics and the philosophy of language. In doing so he provides an unusual insight into the way in which these disciplines developed in the Hellenistic (...) era. He also shows a more sophisticated understanding of these fields than Aristotle himself, while remaining a staunch defender of Aristotle's emphasis on meaning as opposed to Stoics concern with verbal formulation. In his commentary on the final chapter of book 1 Alexander offers a thorough discussion of Aristotle's distinction between denying that something is, e.g., white and asserting that it is non-white. (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)

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)

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)

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)

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.

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

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.

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)

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)

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’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)

It has often been claimed that Aristotle’s expression ‘protasis’ means ‘premiss’ in syllogistic contexts and 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 the basic meaning of the expression is ‘proposition’ and 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 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)

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)

All the way through An.Pr. A9 11, Aristotle gives a new and separate proof of each modal syllogism. He does not take the mixed syllogisms as entirely trivial and obvious. He tries to explain them and to establish their validity. And that is where ...

I argue that, in the Prior Analytics, higher and above the well-known ‘reduction through impossibility’ of figures, Aristotle is resorting to a general procedure of demonstrating through impossibility in various contexts. This is shown from the analysis of the role of adunaton in conversions of premises and other demonstrations where modal or truth-value consistency is indirectly shown to be valid through impossibility. Following the meaning of impossible as ‘non-existent’, the system is also completed by rejecting any invalid combinations (...) of terms in deductions or conversions. The notion of impossibility reaches the core of Aristotle's system in the Prior Analytics. On the one hand, the use of adunaton shows that he is following one of the two requisites for demonstrative science formulated in the Posterior Analytics, i.e. to demonstrate that it is impossible for things to be otherwise than stated. On the other hand, that demonstrations through impossibility are rooted in the notion of contradiction supp.. (shrink)

I reconstruct Aristotle’s analytical procedure in Prior Analytics I.45 and its metalogical implications. Aristotle’s analysis unfolds three groups of syllogisms: symmetrically analysable, asymmetrically analysable, and non-analysable syllogisms. From the first and the third group could be extracted 27 combinations of the two mutually non-derivable deductive rules. Aristotle’s reduced deductive system in APr. I.7 with the two moods in the first figure (traditionally called Barbara and Celarent) follows this pattern. I demonstrate that the deductive system with Barbara and Celarent (...) is just one of 27 possible complete deductive systems with the two mutually non-derivable syllogistic rules. On top of that, given the fact that there are two combinations of mutually non-derivable conversion rules, I conclude that Prior Analytics hides in itself 54 complete deductive systems with a minimal number of mutually non-derivable rules. Finally, it is commented what might be the role of analysis; to what extent Aristotle could be aware of possibilities presented here; why he still prefers only one deductive system to many others with the same deductive power. (shrink)

This is a brief note that looks at the problem presented by the traditional rendering of the modal syllogism Disamis XLL. In two recent articles, I argue that we should not attribute Disamis XLL to Aristotle. The purpose of this note is to provide textual support for my claim.