Truth as a Logical Connective

Truth without standard models: some conceptual problems reloaded

“…Moreover, it appears to be true according to FS since, by nec, T applies to every theorem of FS. However, FS proves the negation of RF L F S and its falsity 33 . ¬RF L F S is a highly counterintuitive principle but-worst of all-it is strictly false.…”

“…As a result, every theorem of FS is 32 Field in [8] also argues against non-standard models based on syntactic interference. 33 See Halbach and Horsten [16] for a proof. 34 Horsten, Leigh, Leitgeb and Welch [18] defend a similar position.…”

“…Although Leitgeb [21], Field [7] and [anonymized] [1] have criticized ω-inconsistent theories of truth, this issue continues to be controversial. In fact, for instance, Yatabe [32] [33], among others, has recently argued in favor of ω-inconsistent first-order theories of truth. In his papers, he focuses on the technical side of the matter and argues that rejecting ω-inconsistent theories of truth would involve to reject co-induction, which is a mathematical principle (dual to induction) useful to prove properties of infinite structures, e.g.…”