Iterated reflection principles over full disquotational truth
Abstract
Iterated reflection principles have been employed extensively to unfold epistemic commitments that are incurred by accepting a mathematical theory. Recently this has been applied to theories of truth. The idea is to start with a collection of Tarski-biconditionals and arrive by finitely iterated reflection at strong compositional truth theories. In the context of classical logic it is incoherent to adopt an initial truth theory in which A and 'A is true' are inter-derivable. In this article we show how in the context of a weaker logic, which we call Basic De Morgan Logic, we can coherently start with such a fully disquotational truth theory and arrive at a strong compositional truth theory by applying a natural uniform reflection principle a finite number of times.
Cite
@article{arxiv.1703.02301,
title = {Iterated reflection principles over full disquotational truth},
author = {Martin Fischer and Carlo Nicolai and Leon Horsten},
journal= {arXiv preprint arXiv:1703.02301},
year = {2020}
}