Robin Smith

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

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?