Wittgenstein's Uniqueness Rule as an Elimination Rule of Inductive Types:

In the Context of Separating Arithmetic from Logic

Abstract

    We discuss the equational representations of the elimination rule of inductive types, with a focus on the type “natural number”, in the context of the series of approaches to separating an equational calculus from logic. We go back to a source of the purely equational representation of the elimination rule, Wittgenstein's uniqueness rule. We analyze Wittgenstein's argument, in comparison with others', which gives supplementary remarks to Marion-Okada (2018).