The Significance of Aristotle's Particularisation in the Foundations of Mathematics, Logic and Computability: Rosser and Formally Undecidable Arithmetical Propositions

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 review Rosser’s claim that Gödel’s reasoning can be recast to arrive at his intended result without the assumption of ω-consistency, since Rosser’s argument appeals to a fundamental tenet of this logic, namely Aristotlean particularisation, which implies ω-consistency.