The significance of Aristotle's particularisation in the foundations of mathematics, logic and computability IV - Turing and a sound, finitary, interpretation of PA

摘要

The logic underlying our current interpretations of all first-order formal languages - which provide the formal foundations for all computing languages - is Aristotle's logic of predicates. I show, first, that the 'standard' model of PA - which appeals to Aristotlean particularisation under Tarski's definitions of what constituted an interpretation of the language - is not sound. I then define a sound, finitary, interpretation of PA and show that PA is categorical.