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.

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)

This chapter contains sections titled: Necessity and Predication “Through Itself” Demonstrations, Universals, and the Objects of Scientific Knowledge The Route to the Principles Axioms, Common Principles, and Self‐evidence Demonstration and Analysis Bibliography.

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

In 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 argue that Prior analyticsII.5?7, 8?10, and 1.45 actually contain studies of processes for transforming arguments into other arguments which Aristotle carried out before having completed the theory of perfecting syllogisms by reduction to first-figure moods as presented in Prior analytics1.4?7. This position rejects Ross's opinion that these passages are ?mental gymnastics?, and Patzig's view that some of these texts contain studies of alternative axiomatizations or other logical studies posterior to the completion of the basic theory of syllogisms.

Scholars of classical philosophy have long disputed whether Aristotle was a dialectical thinker. Most agree that Aristotle contrasts dialectical reasoning with demonstrative reasoning, where the former reasons from generally accepted opinions and the latter reasons from the true and primary. Starting with a grasp on truth, demonstration never relinquishes it. Starting with opinion, how could dialectical reasoning ever reach truth, much less the truth about first principles? Is dialectic then an exercise that reiterates the prejudices of one's times and at (...) best allows one to persuade others by appealing to these prejudices, or is it the royal road to first principles and philosophical wisdom? In From Puzzles to Principles? May Sim gathers experts to argue both these positions and offer a variety of interpretive possibilities. The contributors' thoughtful reflections on the nature and limits of dialectic should play a crucial role in Aristotelian scholarship. (shrink)

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)

Modern interpreters have often regarded Aristotle’s Posterior Analytics as a mystery, or even a bit of an embarrassment. In his treatises on natural science and ethics, Aristotle is constantly concerned to review the opinions of his predecessors and of people in general; where appropriate, he also takes note of experiential observations, some of them highly specialized. However, the traditional view of the Posterior Analytics is that it advances an almost Cartesian picture of sciences as deductive systems founded on intuitively evident (...) first premises. How are these to be reconciled? (shrink)

This chapter contains sections titled: The Origins: Parmenides and Zeno Dialectic and the Beginnings of Logical Theory Aristotle and the Theory of Demonstration The Regress Argument of Posterior Analytics I.3 Time and Modality: The Sea‐Battle and the Master Argument Sentential Logic in Aristotle and Afterwards.

MEDIEVAL LOGICS LAMBERT MARIE DE RIJK (ed.), Die mittelalterlichen Traktate De mod0 opponendiet respondendi, Einleitung und Ausgabe der einschlagigen Texte. (Beitrage zur Geschichte der Philosophie und Theologie des Mittelalters, Neue Folge Band 17.) Miinster: Aschendorff, 1980. 379 pp. No price stated. THE SEVENTEENTH CENTURY MARTA FATTORI, Lessico del Novum Organum di Francesco Bacone. Rome: Edizioni dell'Ateneo 1980. Two volumes, il + 543, 520 pp. Lire 65.000. VIVIAN SALMON, The study of language in 17th century England. (Amsterdam Studies in the Theory (...) and History of Linguistic Science, Series 111: Studies in theHistory of Linguistics, Volume 17.) Amsterdam: John Benjamins B.V., 1979.x + 218 pp. Dfl. 65. Theoria cum Praxi. Zum Verhaltnis von Theorie und Praxis im 17. und 18. Jahrhundert. (Akten des 111. Internationalen Leibnizkongress, Hannover, 12. bis 17.November 1977, Band 111: Logik, Erkenntnistheorie, Wissenschaftstheorie, Metaphysik, Theologie.) Wiesbaden: Franz Steiner Verlag, 1980. vii + 269 pp. DM 48. CLASSICAL AND NON-CLASSICAL LOGICS MICHAEL CLARK, The place of syllogistic in logical theory. Nottingham: University of Nottingham Press, 1980. ix + 151 pp. £3.00. A.F. PARKER-RHODES, The theory of indistinguishables. Dordrecht, Boston and London: D. Reidel Publishing Company, 1981. xvii + 216 pp. Dfl.90.00/$39.50. NICHOLAS RESCHER and ROBERT BRANDOM, The logic of inconsistency. Oxford:Basil Blackwell, 1980. x + 174 pp. f 11.50. MISCELLANEOUS J. ZELENY, The logic of Marx. Translated from the German by T. Carver. Oxford: Basil Blackwell, 1980. xcii + 247 pp. £12.50. FELIX KAUFMANN, The infinite in mathematics. Edited by Brian McGuinness. Introduction by E. Nagel. Translation from the German by Paul Foulkes. Dordrecht: Reidel, 1978. xvii + 235 pp. Dfl 85/$39.50 (cloth); Dfl 45/$19.95 (paper). PAMELA MCCORDUCK, Machines who think. San Francisco: W.H. Freeman and Company, 1979. xiv + 275 pp. $14.95. J. MITTELSTRASS (ed.), Enzyklopadie Philosophie und Wissenschaftstheorie Bd. 1 : A-G. Mannheim, Wien, Ziirich: Bibliographisches Institut, 1980. 835 pp. DM 128. (shrink)