Hilbert’s Epsilon Calculus and its Successors

Hilbert’s epsilon calculus has been seen as a highbrow alternative to Fregean predicate logic, useful only for proving certain advanced meta-logical theorems. In this paper I show how it formalises natural language constructions, and validates natural language arguments which have not been traditionally treated, i.e. that it distinctly concerns a broader problematic than Fregean predicate logic. This arises out of one of the meta-logical theorems provable about the epsilon calculus - the Second Epsilon Theorem - which states that the epsilon calculus is a conservative extension of standard predicate logic. Any further theorems in the epsilon calculus, other than ones formalisable in predicate logic’s language, may therefore relate to further forms of speech, and argument, and in this paper I show that they do indeed do so.

Edgar Morscher

Papers

Problems in logic and ontology