Online research in philosophy

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.

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 paper provides close commentary on an important but generally neglected passage in "Prior Analytics" B.21 where, in the course of solving a logical puzzle concerning our knowledge of universal statements, Aristotle offers his only explicit treatment of the Platonic doctrine of Recollection. I show how Aristotle defends his solution to the "Paradox of Knowing Universals", as we might call it, and why he introduces Recollection into his discussion of the puzzle. The reading I develop undermines the traditional (...) view of the passage and lends fresh insight into Aristotle's conception of Plato's particular version of innatism; more specifically, when understood as I recommend, the passage strongly suggests that, on Aristotle's view, Plato's theory of Recollection is specifically designed to explain our apprehension of universal truths. The reading I propose also enables us to see how the allegedly non-standard use of the technical term ἐπαγω³ή in B.21 can be understood in a perfectly straightforward fashion to refer to an inductive inference from singular statements to the universal truth they exemplify. Owing to this last point in particular, the paper carries serious consequences for our understanding of the purported doublet in the problematic opening chapter to the "Posterior Analytics" where Aristotle offers his only explicit attempt to solve Meno's Paradox. (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)

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)

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)

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)

A study of the reception of Aristotle's Prior Analytics in the first half of the twelfth century. It is shown that Peter Abaelard was perhaps acquainted with as much as the first seven chapters of Book I of the Prior Analytics but with no more. The appearance at the beginning of the twelfth century of a short list of dialectical loci which has puzzled earlier commentators is explained by noting that this list formalises the classification of (...) extensional relations between general terms and that this classification had already be put forward by Boethius in his de Syllogismo Categorico and Introductio ad Syllogismos Categoricas . It is pointed out the kind of text referred to as an ` Introductio ' at the beginning of the twelfth-century follows very closely the structure of Boethius own Introductio and adds to it material drawn from his accounts of loci and the conditional propositions. It is argued that the reception of the Prior Analytics has to be understood against the background of this well developed tradition of treating together syllogisms, loci , and conditional propostions. Referring to a challenge to the formal validity of Darapti in the Ars Meliduna the paper concludes by illustrating that the theory of the syllogism presented in Prior Analytics was still controversial in the middle of the twelfth-century. (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)

This article is currently available as a free download on ingentaconnect.

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.

In this article, I shall consider medieval discussions of the principles of Aristotelian syllogistic which were called the dictum de omni et nullo and the expository syllogism. I am particularly interested in how theological questions contributed to the introduction of some influential new medieval ideas, such as the extensional sameness of the subject as the basis of predication, the interpretation of the expository syllogism from this point of view, and the explication of the logical subject of universal and particular syllogistic (...) premises with the phrase `Anything/something which is A. . .'. I end with some remarks about the increasing medieval awareness that these developments were beyond Aristotle's purview. (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.

Introduction -- Notes on translation and commentary -- Translation -- Commentary -- Notes on the text.

This is a revised and expanded edition of a seminal work in the logic and philosophy of time, originally published in 1968. Arthur N. Prior (1914-1969) was the founding father of temporal logic, and his book offers an excellent introduction to the fundamental questions in the field. Several important papers have been added to the original selection, as well as a comprehensive bibliography of Prior's work and an illuminating interview with his widow, Mary Prior. In addition, the (...) Polish logic which made Prior's writings difficult for many readers has been replaced by standard logical notation. This new edition will secure the classic status of the book. (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)

Abstract In Posterior Analytics II.19 Aristotle raises and answers the question, how do first principles become known? The usual view is that the question asks about the process or method by which we learn principles and that his answer is induction. I argue that the question asks about the original prior knowledge from which principles become known and that his answer is perception. Hence the aim of II.19 is not to explain how we get all the way to (...) principles but to defend the claim that our knowledge of them originates in perception. Aristotle explains how we learn principles earlier in book II, in his account of definitional inquiry. In II.19 he explains how we reach by induction the preliminary accounts necessary for such inquiries. (shrink)

In this paper I shall discuss the relationship between the two known Arabic translations of Aristotle’s Posterior Analytics and Avicenna’s Kitāb al-Burhān. I shall argue that Avicenna relies on both (1) Abū Bishr Mattā’s translation and (2) the anonymous translation used by Averroes in the Long Commentary as well as in the Middle Commentary (and also indirectly preserved by Gerard of Cremona’s Latin translation of Aristotle’s work). Although, generally speaking, the problem is relevant to the history of the transmission (...) of the Posterior Analytics from Greek through Syriac into Arabic, I do not intend to give a systematic presentation of the historical setting in which Aristotle’s work became readily available to the Arabo-Islamic culture. My aim here is rather to isolate and discuss some pieces of evidence concerning the texts that seem to have been available to Avicenna. In addition to that, I shall also provide evidence concerning the relationship with the Greek commentary tradition (in particular Philoponus and Themistius) that is likely to have influenced Avicenna in his discussion of Aristotle’s theory of demonstration and scientific knowledge. (shrink)

This paper is a critical exposition of Prior’s theory of truth as expressed by the following truth locutions: (1) ‘it is true that’ prefixed to sentences; (2) ‘true proposition’; (3) true belief’, ‘true assertion’, ‘true statement’, etc.; (4) ‘true sentence’.

This paper offers a novel reply to Prior’s dilemma (for the Is/Ought principle), advocating a so-called Weak Kleene framework motivated by two not uncommon thoughts in the debate, namely, that ought statements are identified as those that use ‘ought’, and that ought statements are ‘funny’ in ways that is statements aren’t (e.g., perhaps sometimes being ‘gappy’ with respect to truth and falsity).

This book says Prior claims: (1) that a sentence never names; (2) what a sentence says cannot be otherwise signified; and (3) that a sentence says what it says whatever the type of its occurrence; (4) and that quantifications binding sentential variables are neither eliminable, substitutional, nor referential. The book develops and defends (1)-(3). It also defends (4) against the sorts of strictures on quantification of such philosophers as Quine and Davidson.

Prior propounded a theory that, if correct, explains how it is possible for a statement about propositions to be true even if there are no propositions. The major feature of his theory is his treatment of sentence letters as bindable variables in non-referential positions. His theory, however, does not include a semantical account of the resulting quantification. The paper tries to fill that gap.

Bayesian epistemology tells us with great precision how we should move from prior to posterior beliefs in light of new evidence or information, but says little about where our prior beliefs come from. It offers few resources to describe some prior beliefs as rational or well-justified, and others as irrational or unreasonable. A different strand of epistemology takes the central epistemological question to be not how to change one’s beliefs in light of new evidence, but what reasons (...) justify a given set of beliefs in the first place. We offer an account of rational belief formation that closes some of the gap between Bayesianism and its reason-based alternative, formalizing the idea that an agent can have reasons for his or her (prior) beliefs, in addition to evidence or information in the ordinary Bayesian sense. Our analysis of reasons for belief is part of a larger programme of research on the role of reasons in rational agency (Dietrich and List, Nous, 2012a, in press; Int J Game Theory, 2012b, in press). (shrink)

A case against Prior’s theory of propositions goes thus: (1) everyday propositional generalizations are not substitutional; (2) Priorean quantifications are not objectual; (3) quantifications are substitutional if not objectual; (4) thus, Priorean quantifications are substitutional; (5) thus that Priorean quantifications are not ontologically committed to propositions provides no basis for a similar claim about our everyday propositional generalizations. Prior agrees with (1) and (2). He rejects (3), but fails to support that rejection with an account of quantification on (...) which there could be quantifications that are neither substitutional nor objectual. The paper draws from the work of Lorenzen an alternative conception of quantification in terms of which that needed account can be given. (shrink)

Let A, B, C stand for sentences expressing propositions; let A be a component of C; let C A/B be just like C except for replacing some occurrence of A in C by an occurrence of B; let = be a binary connective for propositional identity read as ‘the proposition that __ is the very same proposition as …’. Then authors defend adding ‘from C = C A/B infer A = B’ to Prior’s rules for propositional identity, appearing in (...) OBJECTS OF THOUGHT. (shrink)

Prior investigated a tense logic with an operator for ‘historical necessity’, where a proposition is necessary at a time iff it is true at that time in all worlds ‘accessible’ from that time. Axiomatisations of this logic all seem to require non-standard axioms or rules. The present paper presents an axiomatisation of a first-order version of Prior’s logic by using a predicate which enables any time to be picked out by an individual in the domain of interpretation.

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)

Aristotle was the first thinker to devise a logical system. He drew upon the emphasis on universal definition found in Socrates, the use of reductio ad absurdum in Zeno of Elea, claims about propositional structure and negation in Parmenides and Plato, and the body of argumentative techniques found in legal reasoning and geometrical proof. Yet the theory presented in Aristotle’s five treatises known as the Organon—the Categories, the De interpretatione, the Prior Analytics, the Posterior Analytics, and the (...) Sophistical Refutations—goes far beyond any of these. (shrink)

Since the 1960's, work in the analytic tradition on the nature of mental and linguistic content has converged on the views that social facts about public language meaning are derived from facts about the thoughts of individuals, and that these thoughts are constituted by properties of the internal states of agents. I give a two-part argument against this picture of intentionality: first, that if mental content is prior to public language meaning, then a view of mental content much like (...) the causal-pragmatic theory presented by Robert Stalnaker in Inquiry must be correct; second, that the causal-pragmatic theory is false. I conclude with some positive suggestions regarding alternative solutions to the `problem of intentionality.'. (shrink)

Demonstrative logic, the study of demonstration as opposed to persuasion, is the subject of Aristotle's two-volume Analytics. Many examples are geometrical. Demonstration produces knowledge (of the truth of propositions). Persuasion merely produces opinion. Aristotle presented a general truth-and-consequence conception of demonstration meant to apply to all demonstrations. According to him, a demonstration, which normally proves a conclusion not previously known to be true, is an extended argumentation beginning with premises known to be truths and containing a chain of reasoning (...) showing by deductively evident steps that its conclusion is a consequence of its premises. In particular, 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 conception of deduction was meant to apply to all deductions. According to him, any deduction that is not immediately evident is an extended argumentation that involves a chaining of intermediate immediately evident steps that shows its final conclusion to follow logically from its premises. To illustrate his general theory of deduction, he presented an ingeniously simple and mathematically precise special case traditionally known as the categorical syllogistic. (shrink)

In his 1961 paper "Tithenai ta Phainomena",1 G. E. L. Owen addressed the problem of the relationship between science as preached in the Analytics and the practice of the Aristotelian treatises. However, he gave this venerable crux a novel twist by focusing on a different aspect of the issue. According to the Prior Analytics , it appears that the first premises of scientific demonstrations must be obtained from collections (historiai) of facts derived from empirical observation. However, many (...) of the treatises seem to make little use of empirical inquiry and instead concern themselves more with 'conceptual analysis.' This is especially true in the Metaphysics and the ethical treatises, but it is also very much characteristic of the Physics. How are these two kinds of inquiry related? (shrink)

I provide a survey of the contents of the works belonging to Aristotle's Organon in order to define their nature, in the light of his declared intentions and of other indications (mainly internal ones) about his purposes. No unifying conception of logic can be found in them, such as the traditional one, suggested by the very title Organon, of logic as a methodology of demonstration. Logic for him can also be formal logic (represented in the main by the De Interpretatione), (...) axiomatized syllogistic (represented in the main by the Prior Analytics) and a methodology of dialectical and rhetorical discussion. The consequent lack of unity presented by those works does not exclude that both the set of works called Analytics and the set of works concerning dialectic (Topics and Sophistici Elenchi) form a unity, and that a certain priority is attributed to the analytics with respect to dialectic. (shrink)

The Greek under the Latin and the Latin under the Greek -- Greek-Latin philosophical interaction -- The odyssey of semantics from the Stoa to Buridan -- The Chimera's diary -- Where were the stoics in the late Middle Ages? -- Theories of language in the Hellenistic age and in the twelfth and thirteenth centuries -- Late-ancient ancestors of medieval philosophical commentaries -- Boethius on Aristotle -- Boethius on the metaphysics of words -- Western and Byzantine approaches to logic -- Greek (...) and Latin medieval logic -- Philoponus, Alexander, and the origins of medieval logic -- Analyzing syllogisms or anonymus Aurelianensis III, the (presumably) earliest extant Latin commentary on the prior analytics, and its Greek model -- Fragments of Alexander's commentaries on Analytica posteriora and Sophistici elenchi. (shrink)

ABSTRACT: ‘Aristotelian logic’, as it was taught from late antiquity until the 20th century, commonly included a short presentation of the argument forms modus (ponendo) ponens, modus (tollendo) tollens, modus ponendo tollens, and modus tollendo ponens. In late antiquity, arguments of these forms were generally classified as ‘hypothetical syllogisms’. However, Aristotle did not discuss such arguments, nor did he call any arguments ‘hypothetical syllogisms’. The Stoic indemonstrables resemble the modus ponens/tollens arguments. But the Stoics never called them ‘hypothetical syllogisms’; nor (...) did they describe them as ponendo ponens, etc. The tradition of the four argument forms and the classification of the arguments as hypothetical syllogisms hence need some explaining. In this paper, I offer some explanations by tracing the development of certain elements of Aristotle’s logic via the early Peripatetics to the logic of later antiquity. I consider the questions: How did the four argument forms arise? Why were there four of them? Why were arguments of these forms called ‘hypothetical syllogisms’? On what grounds were they considered valid? I argue that such arguments were neither part of Aristotle’s dialectic, nor simply the result of an adoption of elements of Stoic logic, but the outcome of a long, gradual development that begins with Aristotle’s logic as preserved in his Topics and Prior Analytics; and that, as a result, we have a Peripatetic logic of hypothetical inferences which is a far cry both from Stoic logic and from classical propositional logic, but which sports a number of interesting characteristics, some of which bear a cunning resemblance to some 20th century theories. (shrink)

It is often said that an argument is valid if and only if it is impossible for its premises to be jointly true and its conclusion false. Usually there is little harm in saying this but it places the concept of truth at the very heart of logic and, given how complex and obscure that concept is, one might wonder if trouble arises from this.It does — in at least two contexts. One of these was explored in the first half (...) of the fourteenth century by Jean Buridan and by the mysterious figure known as the Pseudo-Scotus of the Questions on the Prior Analytics printed in the edition of Scotus's works edited by Luke Wadding. Buridan thought that the bearers of truth were particular sentence-tokens; he thought of truth as a .. (shrink)

I consider the proper interpretation of the process of ecthesis which Aristotle uses several times in the Prior analytics for completing a syllogistic mood, i.e., showing how to produce a deduction of a conclusion of a certain form from premisses of certain forms. I consider two interpretations of the process which have been advocated by recent scholars and show that one seems better suited to most passages while the other best fits a single remaining passage. I also argue (...) that ecthesis for Aristotle really means ?setting out? the case to be proved using letters. Aristotle?s remarks about the use of letters in mathematical proofs suggest that he had some understanding of rules equivalent to universal generalization and existential instantiation; the ?proofs through ecthesis? are so called because they rest on the latter rule, with which use of letters is involved in a special way. (shrink)

ABSTRACT: 'Aristotelian logic', as it was taught from late antiquity until the 20th century, commonly included a short presentation of the argument forms modus (ponendo) ponens, modus (tollendo) tollens, modus ponendo tollens, and modus tollendo ponens. In late antiquity, arguments of these forms were generally classified as 'hypothetical syllogisms'. However, Aristotle did not discuss such arguments, nor did he call any arguments 'hypothetical syllogisms'. The Stoic indemonstrables resemble the modus ponens/tollens arguments. But the Stoics never called them 'hypothetical syllogisms'; nor (...) did they describe them as ponendo ponens, etc. The tradition of the four argument forms and the classification of the arguments as hypothetical syllogisms hence need some explaining. In this paper, I offer some explanations by tracing the development of certain elements of Aristotle's logic via the early Peripatetics to the logic of later antiquity. I consider the questions: How did the four argument forms arise? Why were there four of them? Why were arguments of these forms called 'hypothetical syllogisms'? On what grounds were they considered valid? I argue that such arguments were neither part of Aristotle's dialectic, nor simply the result of an adoption of elements of Stoic logic, but the outcome of a long, gradual development that begins with Aristotle's logic as preserved in his Topics and Prior Analytics; and that, as a result, we have a Peripatetic logic of hypothetical inferences which is a far cry both from Stoic logic and from classical propositional logic, but which sports a number of interesting characteristics, some of which bear a cunning resemblance to some 20th century theories. (shrink)

Modern logicians have sought to unlock the modal secrets of Aristotle's Syllogistic by assuming a version of essentialism and treating it as a primitive within the semantics. These attempts ultimately distort Aristotle's ontology. None of these approaches make full use of tests found throughout Aristotle's corpus and ancient Greek philosophy. I base a system on Aristotle's tests for things that can never combine (polarity) and things that can never separate (inseparability). The resulting system not only reproduces Aristotle's recorded results for (...) the apodictic syllogistic in the Prior Analytics but it also generates rather than assumes Aristotle's distinctions among 'necessary', 'essential' and 'accidental'. By developing a system around tests that are in Aristotle and basic to ancient Greek philosophy, the system is linked to a history of practices, providing a platform for future work on the origins of logic. (shrink)

The taxonomy and analysis of fallacies in Aristotle's Sophistical Refutations pre-date the formal logic of his Prior Analytics A4-6. Of the 64 fully described examples of ?sophistical refutations? which are fallacious because they are only apparently valid, 49 have the wrong number of premisses or the wrong form of premiss or conclusion for analysis by the Prior Analytics theory of the categorical syllogism. The rest Aristotle either frames so that they do not look like categorical syllogisms (...) or analyses in a quite different way than by categorical syllogistic. (shrink)

In this article, the author studies some central concepts in Avicenna's and sī's modal logics as presented in Avicenna's Al-Ish r t wa'l Tan īh t ( Pointers and Reminders ) and in sī's commentary. In this work, Avicenna introduces some remarkable distinctions in order to interpret Aristotle's modal syllogistic in the Prior Analytics . The author outlines a new interpretation of absolute sentences as temporally indefinite sentences and argues on the basis of this that Avicenna seems to (...) subscribe to the Principle of Plenitude. He also shows that he has no valid proof of the modal conversion rules and that he uses some rather ad hoc distinctions to show that Aristotle's modal syllogistic is correct. The author also notes some interesting differences between Avicenna's and sī's approaches to modal logic. (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)

To meet a dilemma between the axiomatic theory of demonstrative science in Posterior analyticsand the non-aximatic 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 Topicsand of deduction in Prior analytics. (shrink)

In an earlier article (s. J Gen Philos Sci 40:341–355, 2009), I have rejected an interpretation of Aristotle’s syllogistic which (since Patzig) is predominant in the literature on Aristotle, but wrong in my view. According to this interpretation, the distinguishing feature of perfect syllogisms is their being evident. Theodor Ebert has attempted to defend this interpretation by means of objections (s. J Gen Philos Sci 40:357–365, 2009) which I will try to refute in part [1] of the following article. I (...) want to show that (1) according to Aristotle’s Prior Analytics perfect and imperfect syllogisms do not differ by their being evident, but by the reason for their being evident, (2) Aristotle uses the same words to denote proofs of the validity of perfect and imperfect syllogisms („ apodeixis “, “ deiknusthai ” etc.), (3) accordingly, Aristotle defines perfect syllogisms not as being evident, but as “requiring nothing beyond the things taken in order to make the necessity evident“, i.e. as not “requiring one or more things that are necessary because of the terms assumed, but that have not been taken among the propositions” ( APr. I. 1), (4) the proofs by which the validity of perfect assertoric syllogisms can be shown according to APr. I. 4 are based on the Dictum de omni et nullo , (5) the fact that Aristotle describes these proofs only in rough outlines corresponds to the fact that his proofs of the validity of other fundamental rules are likewise produced in rough outlines, e.g . his proof of the validity of conversio simplex in APr. I. 2, which usually has been misunderstood (also by Ebert): (6) Aristotle does not prove the convertibility of E -sentences by presupposing the convertibility of I -sentences; only the reverse is true. (shrink)

This article investigates the prospect of giving de dicto- and de re-necessity a uniform treatment. The historical starting point is a puzzle raised by Aristotle's claim, advanced in one of the modal chapters of his Prior Analytics, that universally privative apodeictic premises simply convert. As regards the Prior and the Posterior Analytics, the data suggest a representation of propositions of the type in question by doubly modally qualified formulae of modal predicate logic that display a necessity (...) operator in two distinct positions. Can the N-operator occurring in these positions be given a unified semantical treatment (which would justify dispensing with a notational differentiation)? A positive answer, based on a suitably shaped truth condition for N-formulae, is given, and is supported in the final section with an alternative proof theoretically based conception of a property's essential belonging to an individual. (shrink)

In Prior Analytics A7 Aristotle points out that all valid syllogistic moods of the second and third figures as well as the two particular moods of the first figure can be reduced to the two universal first-figure moods Barbara and Celarent. As far as the third figure is concerned, it is argued that Aristotle does not want to say, as the transmitted text suggests, that only those two valid moods of this figure whose premisses are both universal statements (...) are directly reducible to Barbara and Celarent, but rather that it is those four valid moods of this figure whose respective minor premisses are universal statements of which this is true. It is shown that in order to carry this sense the transmitted text has to be corrected by inserting just one word, which seems to have dropped out. (shrink)

The first full-length study of Robert Kilwardby's commentary on Aristotle's Prior Analytics, based on a study of the medieval manuscripts.

Logic is the systematic study of patterns of correct inference. The first treatise on logic is Aristotle's Prior Analytics , written around 350 B.C. and there are remarkable similarities between the way he presented his theory of valid arguments and the way it is still taught today. He analyzes the form of various inferences and then illustrates them with concrete examples. He begins with very simple cases.

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.

This paper charts some early history of the possible worlds semantics for modal logic, starting with the pioneering work of Prior and Meredith. The contributions of Geach, Hintikka, Kanger, Kripke, Montague, and Smiley are also discussed.

At the beginning of the Posterior Analytics, Aristotle says that “all learning and all rational teaching arises from previously existing knowledge”. How, then, can we have any knowledge? If all our knowledge is acquired by learning that depends on previously existing knowledge, then we would have an infinite regress of still prior knowledge, with the result that we cannot learn anything without having learned something else first. If we reject this possibility, then the only one that remains is (...) that we have some knowledge that we did not learn. This might happen in two ways: either we have some knowledge that we never acquired at all, or we have some knowledge that we acquired but without learning it. We would have knowledge that we never acquired if there was never a time at which we did not have it (which would entail, of course, that we were born with it). Plato held that we do have such knowledge, and indeed that all the genuine knowledge that we have is innate in this way. Aristotle, however, denies that we have innate knowledge (for instance at An. Post. II.19, 100a10). Since he nevertheless does think that we have knowledge, he must think that we have some knowledge which we did not acquire by learning. In fact, he does present such a view in Posterior Analytics II.19, where he claims that our knowledge of the principles ( ¢¡¤£¦¥¨§ ) of sciences comes to us through perception and induction and that the state of knowledge of them is “intelligence” or “thought” ( © ). Aristotle says explicitly that in this process the mind is passive; therefore, it is reasonable for us to regard it as not being a kind of learning (or at any rate as a kind of rational learning). Thus, Aristotle’s overall position is consistent. (shrink)

A Linguistic Analysis of Prior, Quine, and Searle on Propositional Attitudes, Martinich on Fictional Reference, Taglicht on the Active/Passive Mood Distinction in English, etc.

The first book of NE is organised on the model of investigating definitions described in the second Book of the Posterior Analytics , although, of course, with some adaptation due to the subject matter. It first establishes if the object exists and looks for the meaning of the terms used in common language to indicate it, next considers some necessary qualities of the object and then concludes with a definition of the object. We find there a dialectical syllogism of (...) definition, and not the procedure in three steps described in NE VII 1, sometimes called `the method of ethics'. In fact, the method described in NE VII 1 does not apply to the first book of the NE . Its relevance for the NE has been somehow exaggerated. (shrink)

In this paper we examine Prior’s reconstruction of Master Argument [4] in some modal-tense logic. This logic consists of a purely tense part and Diodorean definitions of modal alethic operators. Next we study this tense logic in the pure tense language. It is the logic K t 4 plus a new axiom ( P ): ‘ p Λ G p ⊃ P G p ’. This formula was used by Prior in his original analysis of Master Argument. ( (...) P ) is usually added as an extra axiom to an axiomatization of the logic of linear time. In that case the set of moments is a total order and must be left-discrete without the least moment. However, the logic of Master Argument does not require linear time. We show what properties of the set of moments are exactly forced by ( P ) in the reconstruction of Prior. We make also some philosophical remarks on the analyzed reconstruction. (shrink)

b>. According to the standard and largely traditional interpretation, Aristotle’s conception of nous, at least as it occurs in the Posterior Analytics, is geared against a certain set of skeptical worries about the possibility of scien- tific knowledge, and ultimately of the knowledge of Aristotelian first princi- ples. On this view, Aristotle introduces nous as an intuitive faculty that grasps the first principles once and for all as true in such a way that it does not leave any room (...) for the skeptic to press his skeptical point any further. Thus the tradi- tional interpretation views Aristotelian nous as having an internalist justifica- tory role in Aristotelian epistemology. In contrast, a minority (empiricist) view that has emerged recently holds the same internalist justificatory view of nous but rejects its internally certifiable infallibility by stressing the connection be- tween nous and Aristotelian induction. I argue that both approaches are flawed in that Aristotle’s project in the Posterior Analytics is not to answer the skeptic on internalist justificatory grounds, but rather lay out a largely externalist explica- tion of scientific knowledge, i.e. what scientific knowledge consists in, without worrying as to whether we can ever show the skeptic to his satisfaction that we do ever possess knowledge so defined. (shrink)

Hume’s celebrated argument concerning miracles, and an 18th century criticism of it put forward by Richard Price, is here interpreted in terms of the modern controversy over the base-rate fallacy. When considering to what degree we should trust a witness, should we or should we not take into account the prior probability of the event reported? The reliability of the witness (’Pr’(says e/e)) is distinguished from the credibility of the testimony (’Pr’(e/says e)), and it is argued that Hume, as (...) a good proto-Bayesian, argued that the credibility of the testimony should be calculated in terms of both the reliability of the witness and the prior probability of the event reported. (shrink)

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; the second discusses a cluster of problems raised by the axioms or principles of such a 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. There is an additional glossary and the bibliography has been extended. (shrink)

Logic and Knowledge -/- Editor: Carlo Cellucci, Emily Grosholz and Emiliano Ippoliti Date Of Publication: Aug 2011 Isbn13: 978-1-4438-3008-9 Isbn: 1-4438-3008-9 -/- The problematic relation between logic and knowledge has given rise to some of the most important works in the history of philosophy, from Books VI–VII of Plato’s Republic and Aristotle’s Prior and Posterior Analytics, to Kant’s Critique of Pure Reason and Mill’s A System of Logic, Ratiocinative and Inductive. It provides the title of an important collection (...) of papers by Bertrand Russell (Logic and Knowledge. Essays, 1901–1950). However, it has remained an underdeveloped theme in the last century, because logic has been treated as separate from knowledge. -/- This book does not hope to make up for a century-long absence of discussion. Rather, its ambition is to call attention to the theme and stimulating renewed reflection upon it. The book collects essays of leading figures in the field and it addresses the theme as a topic of current debate, or as a historical case study, or when appropriate as both. Each essay is followed by the comments of a younger discussant, in an attempt to transform what might otherwise appear as a monologue into an ongoing dialogue; each section begins with an historical essay and ends with an essay by one of the editors. -/- Carlo Cellucci is Emeritus Professor of Philosophy at the University of Rome ‘La Sapienza,’ Italy. He is currently completing a book entitled, Remaking Logic: What is Logic Really? -/- Emily Grosholz is Professor of Philosophy at the Pennsylvania State University, USA. She is the author of Representation and Productive Ambiguity in Mathematics and the Sciences (Oxford University Press, 2007). -/- Emiliano Ippoliti is a Research Fellow at the University of Rome ‘La Sapienza,’ Italy. His main interests are heuristics, the logic of discovery, and problem-solving. He is currently working on a book, Ampliating Knowledge: Data, Hypotheses and Novelty. -/- TABLE OF CONTENTS -/- Foreword .................................................................................................... ix Acknowledgements ................................................................................. xxv -/- Section I: Logic and Knowledge -/- Chapter One................................................................................................. 3 The Cognitive Importance of Sight and Hearing in Seventeenthand Eighteenth-Century Logic (Mirella Capozzi) Discussion .............................................................................................. 26 (Chiara Fabbrizi) Chapter Two .............................................................................................. 33 Nominalistic Content (Jody Azzouni) Discussion ............................................................................................... 52 (Silvia De Bianchi) Chapter Three ............................................................................................ 57 A Garden of Grounding Trees (Göran Sundholm) Discussion.......................................................................................... .. 75 (Luca Incurvati) Chapter Four .............................................................................................. 81 Logics and Metalogics (Timothy Williamson) Discussion.......................................................................................... 101 (Cesare Cozzo) Chapter Five ............................................................................................ 109 Is Knowledge the Most General Factive Stative Attitude? (Cesare Cozzo) Discussion.......................................................................................... 117 (Timothy Williamson) Chapter Six .............................................................................................. 123 Classifying and Justifying Inference Rules (Carlo Cellucci) Discussion.......................................................................................... 143 (Norma B. Goethe) -/- Section II: Logic and Science -/- Chapter Seven.......................................................................................... 151 The Universal Generalization Problem and the Epistemic Status of Ancient Medicine: Aristotle and Galen (Riccardo Chiaradonna) Discussion.......................................................................................... 168 (Diana Quarantotto) Chapter Eight........................................................................................... 175 The Empiricist View of Logic (Donald Gillies) Discussion.......................................................................................... 191 (Paolo Pecere) Chapter Nine............................................................................................ 197 Artificial Intelligence and Evolutionary Theory: Herbert Simon’s Unifying Framework (Roberto Cordeschi) Discussion.......................................................................................... 216 (Francesca Ervas) Chapter Ten ............................................................................................. 221 Evolutionary Psychology and Morality: The Renaissance of Emotivism? (Mario De Caro) Discussion.......................................................................................... 232 (Annalisa Paese) Chapter Eleven ........................................................................................ 237 Between Data and Hypotheses (Emiliano Ippoliti) Discussion.......................................................................................... 262 (Fabio Sterpetti) -/- Section III: Logic and Mathematics -/- Chapter Twelve ....................................................................................... 273 Dedekind Against Intuition: Rigor, Scope and the Motives of his Logicism (Michael Detlefsen) Discussion.......................................................................................... 290 (Marianna Antonutti) Chapter Thirteen...................................................................................... 297 Mathematical Intuition: Poincaré, Polya, Dewey (Reuben Hersh) Discussion.......................................................................................... 324 (Claudio Bernardi) Chapter Fourteen ..................................................................................... 329 On the Finite: Kant and the Paradoxes of Knowledge (Carl Posy) Discussion.......................................................................................... 358 (Silvia Di Paolo) Chapter Fifteen ........................................................................................ 363 Assimilation: Not Only Indiscernibles are Identified (Robert Thomas) Discussion.......................................................................................... 380 (Diego De Simone) Chapter Sixteen ....................................................................................... 385 Proofs and Perfect Syllogisms (Dag Prawitz) Discussion.......................................................................................... 403 (Julien Murzi) Chapter Seventeen ................................................................................... 411 Logic, Mathematics, Heterogeneity (Emily Grosholz) Discussion.......................................................................................... 427 (Valeria Giardino) -/- Contributors........................................................................................ ..... 433 Index............................................................................................... ......... 437 -/- Price Uk Gbp: 49.99 Price Us Usd: 74.99 -/- Website: http://www.c-s-p.org/Flyers/Logic-and-Knowledge1-4438-3008-9.htm. (shrink)

Although Bayesian methods are widely used in phylogenetic systematics today, the foundations of this methodology are still debated among both biologists and philosophers. The Bayesian approach to phylogenetic inference requires the assignment of prior probabilities to phylogenetic trees. As in other applications of Bayesian epistemology, the question of whether there is an objective way to assign these prior probabilities is a contested issue. This paper discusses the strategy of constraining the prior probabilities of phylogenetic trees by means (...) of the Principal Principle. In particular, I discuss a proposal due to Velasco (Biol Philos 23:455–473, 2008) of assigning prior probabilities to tree topologies based on the Yule process. By invoking the Principal Principle I argue that prior probabilities of tree topologies should rather be assigned a weighted mixture of probability distributions based on Pinelis’ (P Roy Soc Lond B Bio 270:1425–1431, 2003) multi-rate branching process including both the Yule distribution and the uniform distribution. However, I argue that this solves the problem of the priors of phylogenetic trees only in a weak form. (shrink)

Contemporary hybrid logic is based on the idea of using formulas as terms, an idea invented and explored by Arthur Prior in the mid-1960s. But Prior’s own work on hybrid logic remains largely undiscussed. This is unfortunate, since hybridisation played a role that was both central to and problematic for his philosophical views on tense. In this paper I introduce hybrid logic from a contemporary perspective, and then examine the role it played in Prior’s work.

The aim of this paper is to draw attention to a conflict between two popular views about time: Arthur Prior’s proposal for treating tense on the model of modal logic, and the ‘Platonic’ thesis that some objects (God, forms, universals, or numbers) exist eternally.1 I will argue that anyone who accepts the former ought to reject the latter.

Galileo claimed inconsistency in the Aristotelian dogma concerning falling bodies and stated that all bodies must fall at the same rate. However, there is an empirical situation where the speeds of falling bodies are proportional to their weights; and even in vacuo all bodies do not fall at the same rate under terrestrial conditions. The reason for the deficiency of Galileo’s reasoning is analyzed, and various physical scenarios are described in which Aristotle’s claim is closer to the truth than is (...) Galileo’s. The purpose is not to reinstate Aristotelian physics at the expense of Galileo and Newton, but rather to provide evidence in support of the verdict that empirical knowledge does not come from prior philosophy. (shrink)

Bayesian methods have become among the most popular methods in phylogenetics, but theoretical opposition to this methodology remains. After providing an introduction to Bayesian theory in this context, I attempt to tackle the problem mentioned most often in the literature: the “problem of the priors”—how to assign prior probabilities to tree hypotheses. I first argue that a recent objection—that an appropriate assignment of priors is impossible—is based on a misunderstanding of what ignorance and bias are. I then consider different (...) methods of assigning prior probabilities to trees. I argue that priors need to be derived from an understanding of how distinct taxa have evolved and that the appropriate evolutionary model is captured by the Yule birth–death process. This process leads to a well-known statistical distribution over trees. Though further modifications may be necessary to model more complex aspects of the branching process, they must be modifications to parameters in an underlying Yule model. Ignoring these Yule priors commits a fallacy leading to mistaken inferences both about the trees themselves and about macroevolutionary processes more generally. (shrink)

A consideration of some basic problems that arise in the attempt to provide an adequate characterization of statistical explanation is taken to show that an understanding of the nature of scientific explanation requires us to deal with the philosophical problems connected with the nature of prior probabilities.