Iterated reflection over full disquotational truth

Martin Fischer, Carlo Nicolai, Leon Horsten

Research output: Contribution to journalArticle (Academic Journal)peer-review

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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.
Original languageEnglish
Pages (from-to)2631–2651
Number of pages21
JournalJournal of Logic and Computation
Volume27
Issue number8
Early online date8 Aug 2017
DOIs
Publication statusPublished - 1 Dec 2017

Keywords

  • Truth
  • semantic paradoxes
  • basic de Morgan logic
  • Reflection principles

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