A Co-inductive Language and Truth Degrees

Abstract

Abstract.We investigate what happens if PA LTr2, a co-inductive language, formalizes itself. We analyze the truth concept in fuzzy logics by formalizing truth degree theory in the framework of truth theories in fuzzy logics. Hájek-Paris-Shepherdson's paradox [HPS00] involves that so called truth degrees do not represent the degrees of truthhood (defined by the truth predicate) correctly in Lukasiewicz infinite-valued predicate logic ∀ L, therefore truth degree theory fails there.

Truth without standard models: some conceptual problems reloaded

“…Therefore, in both systems we have the same consequence: there will always be a non-standard number in the extension of T . Yatabe [31] acknowledges the problem:…”

“…Many theorists have argued that, since these objects satisfy the predicate Sent(x), though they are not sentences in the usual sense, they are nonstandard sentences and, thus, still sentences. In this sense, one of the most important contributions to this topic is the famous Abraham Robinson's paper [26] 31 . In his work, Robinson shows how to build theories capable to express their own syntax properties using non-standard models.…”

“…See Kaye[19] for a proof 31. We are very grateful to an anonymous referee who pointed out this paper and its relevance in this subject.…”