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)

In Prior Analytics 1.27–30, Aristotle develops a method for finding deductions. He claims that, given a complete collection of facts in a science, this method allows us to identify all demonstrations and indemonstrable principles in that science. This claim has been questioned by commentators. I argue that the claim is justified by the theory of natural predication presented in Posterior Analytics 1.19–22. According to this theory, natural predication is a non-extensional relation between universals that provides the metaphysical basis for demonstrative (...) science. (shrink)

In Posterior Analytics 1.3, Aristotle advances three arguments against circular proof. The third argument relies on his discussion of circular proof in Prior Analytics 2.5. This is problematic because the two chapters seem to deal with two rather disparate conceptions of circular proof. In Posterior Analytics 1.3, Aristotle gives a purely propositional account of circular proof, whereas in Prior Analytics 2.5 he gives a more complex, syllogistic account. My aim is to show that these problems can be solved, and that (...) Aristotle’s third argument in 1.3 is successful. I argue that both chapters are concerned with the same conception of circular proof, namely the propositional one. Contrary to what is often thought, the syllogistic conception provides an adequate analysis of the internal deductive structure of the propositional one. Aristotle achieves this by employing a kind of multiple-conclusion logic. (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)

In the Posterior Analytics, Aristotle imposes some requirements on scientific propositions: (i) they must be susceptible of syllogistic articulation, (ii) they must have universal terms as subjects of predication and (iii) their subjects must be primary, i.e. they cannot “be said of a distinct underlying subject”. However, it is problematic to meet those three requirements together. If associated with the theory of predication in Categories, the requirement (iii) shall prescribe names or descriptions of individuals within the category of substance as (...) subjects of predication, which are primary insofar as they cannot play the logical role of predicate. Nevertheless, if the requirement (i) is satisfied, then the terms of scientific proposition would be able to perform the function of subject as well as of predicate since the rules of conversion and syllogistic moods presuppose the interchangeability among terms of predication. The requirement (ii), by its turn, withdraws all particular subjects from scientific propositions and a fortiori individual substances. We offer as a solution for the aforementioned dilemma the association of theses from the Posterior Analytics, not with the treatise Categories, but with the new ontology of predication emerged in the Metaphysics, which, by introducing the hylomorphic analysis of compound substances, admits primary and notwithstanding universal subjects of predication: the specific forms. (shrink)