Abstract: In 'Equivalences for Truth Predicates' (2017), Carlo Nicolai argues that mutual truth-definability is not sufficient for considering two axiomatic theories of truth conceptually the same. Furthermore, he argues that t-equivalence between two axiomatic theories of truth is a sufficient condition to consider them the same conceptual theory. The latter notion is strictly stronger than the former, and given elementary arithmetic as a background theory, t-equivalence entails synonymy.
If axiomatic theories of truth really are the way we want to formally discuss and compare different conceptual theories of truth, then it seems that we need a criterion for when two different axiomatic theories capture the same conceptual theory. This talk aims to put pressure on t-equivalence being this criterion. To do so, let KF_1 and KF_2 be two versions of a Kripke-Feferman theory of truth which differ only in the Gödel coding used in their arithmetisation of their syntax. More precisely, the only difference between the two theories is the Gödel code of their respective truth predicates. The talk motivates a conjecture that KF_1 and KF_2 are not synonymous, and hence not t-equivalent.
The talk further argues that KF_1 and KF_2 do capture the same conceptual theory. This is because the choice of Gödel encoding for a theory of truth, assuming it is reasonable, should not matter for the conceptual theory itself. Hence, if t-equivalence is sufficient but not necessary, and mutual truth-definability is necessary but not sufficient, then this suggests that a condition that is both sufficient and necessary lies strictly between the two notions.
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DPhil Seminar Convenor: Oscar Monroy Perez
