Prior Analytics Research Articles

Aristotle's Logical Works and His Conception of Logic

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.

The Logic of Necessity in Aristotle--an Outline of Approaches to the Modal Syllogistic, Together with a General Account of de dicto - and de re -Necessity

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.

Aristotle's Use of Examples in the Prior Analytics

AbstractThis 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.

The Development of Modus Ponens in Antiquity : From Aristotle to the 2nd Century AD

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.

“The Eminent Later Scholar” in Avicenna's Book of the Syllogism

Avicenna refers on a number of occasions in his Book of the Syllogism to “the eminent later scholar” (al-fā[ddotu]il min al-muta'a[hbrevu][hbrevu]irī). At least three recent studies have argued or assumed that this eminent later scholar is Alexander of Aphrodisias. It is argued in this article that Avicenna is in fact referring to Alfarabi. This has consequences for reconstructing the lost first part of Alfarabi's Great Commentary on the Prior Analytics, for highlighting certain aspects of Alfarabi's logical doctrines, and for understanding more about the relation between Avicenna and Alfarabi in matters logical.

Discrimination of aerobic endospore-forming bacteria via electrospray-lonization mass spectrometry of whole cell suspensions.

Direct injection electrospray ionization mass spectrometry (ESI-MS) without prior analyte separation was investigated for the analysis of whole cell suspensions of bacteria. Thirty-six strains of aerobic endospore-forming bacteria, consisting of six Bacillus species and one Brevibacillus species, were studied

Rhetoric Is a Counterpart of Dialectic (E retorike estin antistrophos te "dialektike"

Greek philosophers who preceded Aristotle, especially Gorgias, Plato, and Isocrates, developed their respective views on persuasive discourse (or rhetoric) based upon their larger philosophical projects. Similarly, I will argue in this essay, Aristotle developed his understanding of rhetoric as a part of his larger philosophical project. He not only equates rhetoric, in many respects, dialectic, but also treats it separately in the Rhetoric, perhaps as thoroughly as he treats dialectic in the Topics, In addition these two works, Aristotle addresses rhetorical issues in the Prior and Posterior Analytics, the Sophistical Refutation, the Politics, and the Nichomachean Ethics, perhaps in a similar manner as he addresses dialectic in the Prior Analytics (24a22-25, 68b8-14, 46a3-10), the Sophistical Refutation (165bl-4), the Posterior Analytics (81bl8-23), and the Metaphysics (995b21-25). Moreover, the parts that comprise both rhetoric and dialectic syllogism/enthymeme; induction/example; the respective audiences; and the purposes: inquire, argue, persuade all receive considerable discussion throughout his logical and nonlogical works. The similarities of the ways in which Aristotle discusses both rhetoric and dialectic and his repeated claims that rhetoric is a counterpart to or outgrowth of dialectic suggest that, for Aristotle, rhetoric is very closely related dialectic, that his understanding that rhetoric may be just as much a part of his larger project as is his dialectic understood within the purposes and intended audiences of each and further suggest that in order understand his view of rhetoric, it is first necessary understand his view of dialectic.1

Fallacies and formal logic in Aristotle

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.

Aristotle on Platonic Recollection and the Paradox of Knowing Universals: Prior Analytics B.21 67a8-30

AbstractThe 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 επαγωγη 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.

Aristotle's "De Interpretatione": Contradiction and Dialectic (review)

Reviewed by: Aristotle’s “De Interpretatione”: Contradiction and Dialectic by C. W. A. Whitaker Eugene Garver C. W. A. Whitaker, Aristotle’s “De Interpretatione”: Contradiction and Dialectic. Oxford: Clarendon Press, 1996. Pp. x + 235. Cloth, $60.00. Traditionally, the De Interpretatione is placed in the Organon between the Categories and the Prior Analytics. Where the Categories is about single terms and the Analytics about inferences, the De Interpretatione is about propositions. That traditional view is presupposed by most contemporary studies of the work, which “concentrate on a small number of passages, which have been treated as isolated oases of philosophical interest in an otherwise barren work,” highlights which include “Aristotle’s semantic theory of philosophy of language” in the first chapter, the first four “linguistic chapters,” and chapter 9 on the Sea Battle (1). I suppose that the square of opposition could be added to Whitaker’s list. Whitaker, in this republication of a doctoral dissertation, wants to challenge both the traditional view and the contemporary concentration by instead studying the work as a coherent whole, whose subject, it turns out, is not propositions after all but “contradictory pairs, which are central to the working of dialectic” (2). The book then proceeds through the De Interpretatione, chapter by chapter. If he succeeds, the De Interpretatione will henceforth be read as preparation for the Topics, rather than for the Analytics. There are also three appendices examining the use of such contradictory pairs in Metaphysics IV, the Topics, and the Posterior Analytics. Thus, the first five chapters of the De Interpretatione explain the nature of assertions, name and verb, and “before that, how language is related to thought and to the real world, and how it is that utterances can make claims about things which are true or false” (8). Where names, verbs, and propositions are part of our ordinary understanding of language, contradictory pairs are not, but are a philosophical understanding of a linguistic structure that has a specifically philosophical, dialectical, purpose. The rest of the De Interpretatione, from chapter 6 on, is the examination of contradiction. Chapters 7–9 classify contradictory pairs by different criteria. Each of these chapters isolates an exception to “the rule that, in every contradictory pair, one member is true and the other false” (79). Chapter 7 looks at the first exception to the rule, “non-universal statements about universals” (91). Whitaker’s project looks good here, since he then shows the dialectical uses of such propositions, and denies their value for the deductive logic of the Analytics. Similarly, in Chapter 8 Aristotle looks at “apparently simple assertions . . . which are not single” (105), which also have important uses in dialectic. Finally, chapter 9 looks at the third exception to the rule, future singular assertions. One payoff of this book is to place the sea battle discussion in its Aristotelian context. [End Page 459] Whitaker says that most discussions of the sea battle assume that what is at stake is what he calls the “Principle of Bivalence” in which every assertion is either true or false. He instead insists that it is contradictory pairs, not single assertions, that are being tested by future contingents. He thus concludes: “Dialectic is a universal discipline, and its questioning can cover any subject where a question can be posed which has a right and a wrong answer. Chapters 7 to 9 . . . demonstrate that there are limits to the universality of dialectic” (128). Whitaker follows the De Interpretatione chapter by chapter in the remainder of the book. He shows how the later chapters assist the dialectician in “sorting assertions into contradictory pairs” (181). And just as De Interpretatione begins with a consideration of the relation of language, thought, and the world, so it ends by showing the connection between contradictory propositions and opposed beliefs. Whitaker rarely strays from the De Interpretatione to show how our understanding of dialectic is improved by attention to this prerequisite. When he does, for example in a very short discussion of the relation of problems and propositions in the Topics, the results are illuminating. I would have liked more. This book should be useful to the growing numbers of scholars interested in Aristotle’s art of dialectic...

“Rational Diameters” and the Discovery of Incommensurability

1. The study of incommensurables and irrationals constituted a prominent part of early Greek geometry, stimulating efforts from the Pythagoreans, the key geometers Theaetetus and Eudoxus at the time of Plato, and extending to Euclid. [4] The Tenth Book of the Elements, by far the lengthiest and most imposing of the thirteen books, stands as the culmination of this inquiry. But before Euclid, we have only a few testimonies of the earliest work in this field, so that any attempt to describe the first discovery of the incommensurables is necessarily speculative. For Aristotle the existence of incommensurable magnitudes is already a familiar phenomenon, suitable as an example in his discussions of topics in logic and science. [1, pp. 295-297] In Prior Analytics I 23, for instance, he takes as his principal specimen of an indirect proof that of the incommensurability of the side and diameter* of the square and indicates its key feature: the hypothesis of commensurability entails that odd numbers equal even numbers. [3, pp. 22-23], [4, chap. 2] This manner of proof, which is still commonly used in elementary mathematics (see Section 8), has thus been supposed to represent the reasoning first adopted by the Pythagoreans. [2, Vol. III, p. 2]

Completion, reduction and analysis: three proof-theoretic processes in aristotle’s prior analytics

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

Averroes' Use of Examples in his Middle Commentary on the Prior Analytics, and Some Remarks on his Role as Commentator

Averroes wrote three kinds of commentaries on the books of Aristotle - epitomes, middle commentaries, and long commentaries - and each kind had its own purposes. His aims may have also differed from text to text. That is, it seems reasonable to assume that he would stick closer to Aristotle in the logical works than, for example, in the metaphysical works. The present study investigates what may be called the “theological aspects” of Averroes' commentaries, and explores the commentary of Averroes that appears least likely to contain such elements, the Middle Commentary on the Prior Analytics. The Prior Analytics is perhaps the most straightforward, even pedantic, of all of Aristotle's writings, and of Averroes' three kinds of commentaries, it is the middle commentaries which are least likely to diverge or digress from the text of Aristotle. The only trace of a religious hand in the commentary is Averroes' use of examples, and, in particular, examples that conclude that “the world is created” and the like. It is argued that Averroes chose these examples to show the traditionalist reading public the falsity of the theologians claims against the logic of the philosophers. The Appendix to the article shows that medieval commentators on Averroes' commentaries were also struck by his “creation of the world” examples.

Al-Farabi and Aristotelian Syllogistics: Greek Theory and Islamic Practices (review)

BOOK REVIEWS 135 unity of composite substances and their reproduction simply in physical terms (using the notion of vital heat), or whether Aristotle explains these phenomena in both physical terms (vital heat) and in terms of forms and ends. Hence, at the end of the book, where we learn how and why Aristotle's purely material explanation (vital heat) fails, it is unclear whether or not we are meant to conclude that Aristotle's natural philosophy simply lacks an adequate explanation of the unity and reproduction of substances. The strength and interest of this book lie in its systemic development of the roles of vital heat and connate pneuma in Aristotle's biological writings. What emerges is a picture of Aristotelian living substances that are primarily characterized by their internal heat; a vision of nature that is continuous, hierarchical, and organized by the principle of vital heat. This interpretation emphasizes the continuities between Aristotle's vision of nature with that of the Presocratics and the medical tradition, and Freudenthal provides informative and intelligent discussions of Aristotle's probable sources. Of course, as Freudenthal admits, vital heat cannot be both a material principle of unity and a principle that establishes a metaphysical hierarchy among natural beings. Vital heat is meant to explain why man is the most perfect animal, and why we walk upright, and it does so by means of its tendency to rise. But this explanation of how vital heat establishes a hierarchy and a value system in nature renders it unfit to act as a principle of material unity. For, the problem of material unity was generated by the idea that the four elements have natural tendencies to move apart. Because of Aristotle 's topological vision of matter, it seems futile for him to suggest a material solution to the problem of unity. With regard to reproduction, the prospects are brighter. For, it is clear that Aristotle bestows generative power on the male by virtue of the greater heat of his pneuma, and it is also clear that the pneuma bears the motions that convey the form to the offspring. Beyond those two facts, however, nothing is clear. Freudenthal attributes "informing" power to the pneuma; on his interpretation, it is both an efficient and a formal cause of the generation. Maybe so, but in light of the rich scholarly debate on this point in the past fifteen years, this interpretation requires argument and philosophical analysis rather than simple assertion. Freudenthal's Aristotle is engaged in a "global project" to provide a unified physiological account of soul-functions; vital heat is the central hypothesis of his research project. While I find this characterization of Aristotle's writing on nature unconvincing , Freudenthal does succeed in establishing that vital heat and pneuma are ubiquitous presences in Aristotle's biology that cannot be ignored by scholars. CHARLOTTE WITT Universityof New Hampshire Joep Lameer, AI-Farabi and Aristotelian Syllogistics: Greek Theory and Islamic Practices. Leiden: E.J. Brill, x994. Pp. xx + 352. Cloth, $74.5o. Joep Lameer's study, which focuses on Alfarabi's (d. 950-5 l) contribution to logic, serves as a prolegomena to any future study of logic in Islamic philosophy. Alfarabi's i36 JOURNAL OF THE HISTORY OF PHILOSOPHY 35: ~ JANUARY 1997 contribution to political philosophy and logic are well recognized. Recently, we have received a more complete view of his original ideas on analytic metaphysics, mostly due to the works of Muhsin S. Mahdi. A large number of Alfarabi's surviving texts are analyzed in this book. Lameer is very clear and applies first-order predicate logic to render some of Alfarabi's themes (22o-~2). He focuses on (i) primary sources needed to study Alfarabi's logic in Greek, Syriac, and Arabic, (ii) standard logic as covered in Aristotle's Prior Analytics and Topics, syllogisms, the logic of terms, induction , and paradigm, (iii) logic used in theological arguments (from the observable to the hidden), (iv) legal reasoning, and (v) metalogical issues in political philosophy and metaphysics. The text is full of insights, including: (a) Alfarabi was not influenced by any Latin philosophical tradition (xxi), (b) the Book of Agreement between the Views of the Divine Plato and...

Simultaneous quantitation of multiple cytokine mRNAs by RT-PCR utilizing plate based EIA methodology

Cytokines are small protein hormones produced during an immune response that are responsible for mediation and regulation of many aspects of immunity. Measurement of cytokines by several different methods has led to a broader understanding of the immune response. This paper describes a sensitive, reproducible, and quantitative RT-PCR assay for the simultaneous measurement of multiple cytokines. The main features of the methodology are: RNA competitors which control for all aspects of the process from RNA extraction, through reverse transcription (RT) and PCR amplification; a general cloning vector, pQPCR1, for building RNA competitors that does not require prior analyte cDNA cloning; and analysis by plate based EIA. This RT-PCR-EIA system is shown to be more sensitive than agarose gel electrophoresis followed by EtBr staining, measuring PCR product in the sub-nanogram range. It also extends the linear dynamic range of detection to a four log fold range of analyte concentration. The assay is reproducible, with coefficients of variation (CVs) in the 10–20% range. Moreover, the cloning vector is designed to accommodate multiple primer templates, thus allowing simultaneous quantitation of many different analytes from a single RT reaction. The described system is versatile and adapts to numerous analytes.

Ibn Rušd et lesPremiers Analytiquesd'Aristote: Aaperçu sur un problème de syllogistique modale

Ibn Rušd devoted a certain number of works to Aristotle'sPrior Analytics. In a series ofopusculeswritten over a period of twenty years and following upon hisMiddle Commentary on Aristotle's Prior Analytics, he faced a problem particular to the modal syllogism – that of the mood of the conclusion in mixed syllogisms.The problem can be stated as follows: At the beginning of thePrior Analytics, Aristotle established a formal deductive principle – that of universal attribution (Pr. An.I.1.24b26–30). Applied to the modal syllogism, this principle is inadequate as stated. It is too general to be applied in a univocal manner in all modal syllogisms. To preserve a sense of coherence in Aristotle's declarations, the commentators had to interpret it. Presenting the interpretations of the commentators, primarily al-Fārābī and Alexander, on the basis of al-Fārābī'sLarge Commentary on Aristotle's Prior Analytics, Averroes criticizes them. Applied according to Alexander's interpretation, the principle of universal attribution is valid only for modal syllogisms one of whose premises is necessary and the other assertoric; according to al-Fārābī's interpretation, it is verified only when the minor premise is possible. Averroes proposes two preliminary solutions. Either this formal deductive principle must be applied differently according to the modal differences of the minor premises in mixed syllogisms (first solution) or would be used in two ways, generally or in keeping with each mood (second solution). These solutions are not satisfactory, for they call into question the unity and universality of the principle of universal attribution as established by Aristotle. What is the utility, Averroes asks, of a principle which does not hold for all modalities or does not apply to all the premises when thePr. An.ought to furnish formal and universal principles of deduction? And why did Aristotle define the principle of universal attribution without distinguishing its application according to each of the three modal premises? Returning at the end of his career to a literal exegesis of Aristotle's propositions and without harkening back to the earlier solutions, he proposes a theory of making the terms modal (fourth solution) in order to save Aristotle's declarations with respect to the principle of universal attribution and the mood of the conclusion of mixed syllogisms (Pr. An.I. 9.30al5–20). Though formally inadequate, this solution, which had a continued history, proposes a new way of looking at the classification of modal propositions.

Le kitāb al-Taḥlīl d'Alfarabi

In a departure from the tradition of the Neoplatonic commentators of the Organon, the sequence of summaries in the “Bratislava series” insert two treatises between the Prior Analytics and the Posterior Analytics, namely the Resolution (kitāb al-Taḥlīl) and the Sophistical Refutations. And even though the Taḥlīl is concerned with Book 2 of the Topics, it does not deal with dialectic. Instead, it comments on the summary of the Topics that belongs to the Prior Analytics (I, 27–30), while “completing” it. The contents of kitāb al-Taḥlīl and the different titles that the fahāris give it (e.g., fīiktisăb al-muqaddimāt), lead one to realize that it is an addition to the Prior Analytics offering a theory concerning the generation of the premisses of the syllogism, something that may have appeared to Alfarabi as missing from Kitāb al-Qiyās.

Aristotle‘s axiomatic science:peripatetic notation or pedagogical plan?

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

Prior Analytics.

Prior Analytics.

From negation to “notion”: Cognitive processes and argumentative strategies

This article deals with the role of negation as a language and cognitive operation. Such a topic is treated here within the framework of the argumentative strategies which consist in making certain cognitive landmarks of the discourse ‘flip over’ with the intent of imposing the necessity to choose between two types of ‘notions’, aiming at the transformation of this choice into an ‘implication’. The reference here to the Aristotelian logic of Prior Analytics appears to be more efficient than any other contemporary logic and the author intends to give account of the role of negation as ‘contrary’ coming into play on an operational and cognitive basis in all the argumentative strategies which ‘oscillate’ reciprocally from universal to particular.