Kurt Gödel Research Center

Radically Type-free Logic, or Has First-order Logic Rested on a (or Maybe Several) Metaphysical Mistake(s)?

Talk held by Christopher Menzel (Texas A&M University, USA) at the KGRC Friday seminar on 2018‑06‑29.

Abstract

In this talk I will present a “radically” type-free logic – “Common Logic (CL)” – that evolved organically out of developments in knowledge representation (KR) necessitated by the need to share information on open networks like the World Wide Web. Basic CL syntax contains only a single lexical type – “names” – and there is only one semantic type – “things” – and any nonempty string of names/terms counts as both a term and an atomic formula. There are no restrictions on quantification so CL is also syntactically second-order. Its pragmatic origins notwithstanding, CL prompts us to reconsider the basic language and ontology of logic and, in particular, the linguistic and metaphysical assumptions built into the Fregean underpinnings of “traditional” first-order logic (TFOL). I will begin by spelling out the presuppositions of TFOL and will then lay out the KR phenomena that pushed the evolutionary revisions in CL. I will then define the syntax and semantics CL in formal detail and define a mapping from CL into TFOL. I will use that mapping to sketch a proof of the semi-decidability of CL validity. I will close with some reflections on CL’s implications for the language and ontology of logic.