Unknown Truths and Unknowable Truths

TL;DR

This paper introduces a formal logic for unknowable truths, explores the relationship between unknown and unknowable truths, and provides an axiomatic system to understand their logical properties in epistemology.

Contribution

It is the first to develop a logical framework specifically for unknowable truths and analyze their connection with unknown truths in formal epistemology.

Findings

Proposed a new logic of unknowable truths

Analyzed the properties and relationships of unknown and unknowable truths

Axiomatized the logic to formalize their logical characteristics

Abstract

Notions of unknown truths and unknowable truths are important in formal epistemology, which are related to each other in e.g. Fitch's paradox of knowability. Although there have been some logical research on the notion of unknown truths and some philosophical discussion on the two notions, there seems to be no logical research on unknowable truths. In this paper, we propose a logic of unknowable truths, investigate the logical properties of unknown truths and unknowable truths, which includes the similarities of the two notions and the relationship between the two notions, and axiomatize this logic.