Andrea Libero Carbone

Two of Aristotle’s major legacies, namely, the theory of scientific syllogism and teleology seem to conflict on several planes. Indeed, an array of formal limitations prevents him from formalizing teleological explanations into scientific syllogisms, which are entirely absent from his works. To achieve this, Aristotle resorts to a different tool, the logic of ‘consequence’. This governs both the teleological relation between an end and a means that underlies necessity ‘from a hypothesis’—which is the necessity proper to living things—and a different form of syllogisms, namely, syllogisms ‘from a hypothesis’. His guidelines in the first chapter of his Parts of Animals on the proper form of demonstration to be adopted in biology should be read as laying out the rules of inference for translating teleological explanations into syllogisms ‘from a hypothesis’.

Aristotle’s biology is based on his method of division of animal kinds by multiple differentiae. This results in complex clusters of non-subordinate terms, between which Aristotle seeks to establish universal correlations. The form of these, however, does not correspond to that prescribed by his theory of syllogism. Mereological relations between terms are not linear and quantification is far more complex than the distinction between universal and particular propositions. Thus the axiomatisation of Aristotle’s biology requires a tool designed for analysing such complex universal correlations into valid syllogistic premises. Prosleptic-like premises turn out to be the solution outlined by Aristotle. They make it possible to handle both the logic of consequence which translates from and into mereological relations between term clusters, and the complex quantification required by division based on multiple differentiæ, through the instantiation of a variable ideally consisting of indivisible groups of animals.