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ON CLASSICAL DETERMINATE TRUTH
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DOI：10.1017/S1755020325100968.png)
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Abstract
En 中文
The paper proposes and studies new classical, type-free theories of truth and determinateness with unprecedented features. The theories are fully compositional, strongly classical (namely, their internal and external logics are both classical), and feature a defined determinateness predicate satisfying desirable and widely agreed principles. The theories capture a conception of truth and determinateness according to which the generalizing power associated with the classicality and full compositionality of truth is combined with the identification of a natural class of sentences-the determinate ones-for which clear-cut semantic rules are available. Our theories can also be seen as the classical closures of Kripke-Feferman truth: their $\omega $ -models, which we precisely pin down, result from including in the extension of the truth predicate the sentences that are satisfied by a Kripkean closed-off fixed-point model. The theories compare to recent theories proposed by Fujimoto and Halbach, featuring a primitive determinateness predicate. In the paper we show that our theories entail all principles of Fujimoto and Halbach's theories, and are proof-theoretically equivalent to Fujimoto and Halbach's $\mathsf {CD}<^>{+}$ . We also show establish some negative results on Fujimoto and Halbach's theories: such results show that, unlike what happens in our theories, the primitive determinateness predicate prevents one from establishing clear and unrestricted semantic rules for the language with type-free truth.
Keywords:
formal theories of truth
axiomatic theories of truth
determinateness
liar paradox
fixed-point semantics
Journal
R
IF:
0.9
Papers:
19
Citations:
0