منابع مشابه
Syntactical Truth Predicates For Second Order Arithmetic
We introduce a notion of syntactical truth predicate (s.t.p.) for the second order arithmetic PA. An s.t.p. is a set T of closed formulas such that: i) T (t = u) iff the closed first order terms t and u are convertible, i.e. have the same value in the standard interpretation ii) T (A → B) iff (T (A) ⇒ T (B)) iii) T (∀xA) iff (T (A[x ← t]) for any closed first order term t) iv) T (∀XA) iff (T (A...
متن کاملComplexity and Hierarchy in Truth Predicates∗
Since seminal work of Tarski (e.g. Tarski, 1935), hierarchies have been much discussed in the literature on truth and paradox. Especially in recent years, this discussion has been decidedly negative. Tarski’s hierarchy of languages is sometimes described as the “orthodox” response to the Liar paradox (e.g. Kripke, 1975), but it is an orthodoxy many authors have gone to great lengths to avoid. F...
متن کاملRestricted truth predicates in first-order logic
It is well-known that there exist consistent first-order theories that become inconsistent when we add Tarski’s schema T. This is Tarski’s Theorem. To avoid the inconsistency result, one can restrict Tarski’s schema in different ways. In our paper we restrict Tarski’s schema T by only instantiating the schema with a proper subset of the set of all sentences. We prove several results concerning ...
متن کاملThe equational definability of truth predicates
By a ‘logic’ we mean here a substitution-invariant consequence relation on formulas over an algebraic signature. Propositional logics are obvious examples, but even first order logic can be re-formulated in this way. The notion of an ‘algebraizable’ logic was made precise in the 1980s, mainly by Blok and Pigozzi, who provided intrinsic characterizations of the logics that are indeed algebraizab...
متن کاملOn the "semantics" for Languages with Their Own Truth Predicates
In the 1920s, logical positivists were skeptical of the notion of truth. For one thing, the liar's paradox seemed to show that truth is inconsistent. Other sources of skepticism were, as Soames [26] notes, "the frequent use of truth in metaphysical discussions, the tendency to confuse truth with epistemological notions like certainty and confirmation, and the inability to see how acceptance of ...
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ژورنال
عنوان ژورنال: The Review of Symbolic Logic
سال: 2017
ISSN: 1755-0203,1755-0211
DOI: 10.1017/s1755020316000435