Most work on the semantic paradoxes within classical logic has centered around what this essay calls “linguistic” accounts of the paradoxes: they attribute to sentences or utterances of sentences some property that is supposed to explain their paradoxical or nonparadoxical status. “No proposition” views are paradigm examples of linguistic theories, although practically all accounts of the paradoxes subscribe to some kind of linguistic theory. This essay shows that linguistic accounts of the paradoxes endorsing classical logic are subject to a particularly (...) acute form of the revenge paradox: that there is no exhaustive classification of sentences into “good” and “bad” such that the T-schema holds when restricted to the “good” sentences unless it is also possible to prove some “bad” sentences. The foundations for an alternative classical nonlinguistic approach is outlined that is not subject to the same kinds of problems. Although revenge paradoxes of different strengths can be formulated, they are found to be indeterminate at higher orders and not inconsistent. (shrink)

In this paper, we do two things. First, we provide some support for adopting a version of the meaningless strategy with respect to the liar paradox, and, second, we extend that strategy, by providing, albeit tentatively, a solution to that paradox—one that is semantic, rather than logical.

A formal theory of truth, alternative to tarski's 'orthodox' theory, based on truth-value gaps, is presented. the theory is proposed as a fairly plausible model for natural language and as one which allows rigorous definitions to be given for various intuitive concepts, such as those of 'grounded' and 'paradoxical' sentences.

I apply the notions of alethic reference introduced in previous work in the construction of several classical semantic truth theories. Furthermore, I provide proof-theoretic versions of those notions and use them to formulate axiomatic disquotational truth systems over classical logic. Some of these systems are shown to be sound, proof-theoretically strong, and compare well to the most renowned systems in the literature.

I put forward precise and appealing notions of reference, self-reference, and well-foundedness for sentences of the language of first-order Peano arithmetic extended with a truth predicate. These notions are intended to play a central role in the study of the reference patterns that underlie expressions leading to semantic paradox and, thus, in the construction of philosophically well-motivated semantic theories of truth.

What Numbers Could Not Be’) that an adequate account of the numbers and our arithmetic practice must satisfy not only the conditions usually recognized to be necessary: (a) identify some w-sequence as the numbers, and (b) correctly characterize the cardinality relation that relates a set to a member of that sequence as its cardinal number—it must also satisfy a third condition: the ‘<’ of the sequence must be recursive. This paper argues that adding this further condition was a mistake—any w-sequence (...) would do, no matter how undecidable its ‘<’ relation. (shrink)

Dummett's account of the semantic paradoxes in terms of his theory of indefinitely extensible concepts is compared with Bürge's account in terms of indexicality. Dummett's appeal to intuitionistic logic does not block the paradoxes but Bürge's attempt to avoid the Strengthened Liar is unconvincing. It is argued that in order to avoid the Strengthened Liar and other semantic paradoxes involving nonindexical expressions (constants), one must postulate that when we reflect on the paradoxes there are slight shifts in the meaning (not (...) just reference) we ascribe to metalinguistic expressions (in particular 'say', and derivatively 'true' and 'false'). Consideration of metaphor and gradual linguistic change suggests that such semantic shifts are consistent with language-learning and communication. On this account there is no threat to classical logic, bivalence or the fundamental principles governing 'true' and 'false'. (shrink)