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|Title: ||On Wright’s Inductive Definition of Coherence Truth for Arithmetic|
|Authors: ||Ketland, Jeffrey|
|Issue Date: ||2000|
|Citation: ||Analysis 63/1, 6-15.|
|Abstract: ||In “Truth – A Traditional Debate Reviewed” (1999), Crispin Wright proposed an inductive definition of “coherence truth” for arithmetic relative to an arithmetic base theory B. Wright’s definition is in fact a notational variant of the usual Tarskian inductive definition, except for the basis clause for atomic sentences.
This paper provides a model-theoretic characterization of the resulting sets of sentences "cohering" with a given base theory B. These sets are denoted WB. Roughly, if B satisfies a certain minimal condition (for each term t, B proves an equation of the form t = n, where n is a numeral), then WB is the Th(M), where M is the canonical model of the set At(B) of atomic sentences provable in B.
The paper also shows that the disquotational T-scheme is provable (in a metatheory T) from Wright’s inductive definition just in case the base theory B is (provably in T) sound and complete for arithmetic atomic sentences.|
philosophy of mathematics
|Appears in Collections:||Philosophy research publications|
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