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Abstract

This paper presents a defense of Epistemic Arithmetic as used for a formalization of intuitionistic arithmetic and of certain informal mathematical principles. First, objections by Allen Hazen and Craig Smorynski against Epistemic Arithmetic are discussed and found wanting. Second, positive support is given for the research program by showing that Epistemic Arithmetic can give interesting formulations of Church 's Thesis.

Informal Provability, First-Order BAT Logic and First Steps Towards a Formal Theory of Informal Provability

“…This idea comes from[Kripke, 1975].7 There are some alternative approaches to construct theories of informal provability[Flagg and Friedman, 1986;Horsten, 1994Horsten, , 1998Reinhardt, 1986;Shapiro, 1985;Stern, 2015]. We will not discuss them.…”