The Discovery of Principles in Prior Analytics 1.30

Abstract

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 (1.30, 46a21–7). 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.

Abduction as Deductive Saturation: a Proof-Theoretic Inquiry

“…Moreover, the refutation-based approach presented in our work can, in theory, be extended to decidable fragments of predicate logic, with monadic first-order logic presenting an interesting case study, particularly in relation to the traditional topic of inventio medii (see e.g. [17]). A broader perspective could involve taming full first-order logic by utilizing an appropriate notion of approximated refutation and approximated deductive saturation.…”