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SUPERVALUATION FIXED-POINT LOGICS OF TRUTH

PHILIP KREMER and ALASDAIR URQUHART
Journal of Philosophical Logic
Vol. 37, No. 5 (October 2008), pp. 407-440
Published by: Springer
Stable URL: http://www.jstor.org/stable/41217847
Page Count: 34
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SUPERVALUATION FIXED-POINT LOGICS OF TRUTH
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Abstract

Michael Kremer defines fixed-point logics of truth based on Saul Kripke's fixed point semantics for languages expressing their own truth concepts. Kremer axiomatizes the strong Kleene fixed-point logic of truth and the weak Kleene fixed-point logic of truth, but leaves the axiomatizability question open for the supervaluation fixed-point logic of truth and its variants. We show that the principal supervaluation fixed point logic of truth, when thought of as consequence relation, is highly complex: it is not even analytic. We also consider variants, engendered by a stronger notion of 'fixed point', and by variant supervaluation schemes. A 'logic' is often thought of, not as a consequence relation, but as a set of sentences - the sentences true on each interpretation. We axiomatize the supervaluation fixed-point logics so conceived.

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