Alethic Reference

Abstract

I put forward precise and appealing notions of reference, self-reference, and wellfoundedness 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.

Reference and Truth

“…Luckily, this situation has been remedied. In my companion paper [27] I give a systematic and formal account of reference in the context of truth, designed specifically for the study of the reference patterns underlying paradoxical sentences. Moreover, since according to my account reference has a syntactic aspect, restricting disquotation to non-self-referential expressions could turn out to be simple enough for the formulation of axiomatic truth systems.…”

“…Unfortunately, the notions I put forward in [27] reveal that the self-reference diagnosis is not correct. As it turns out, there are semantic paradoxes that are free of self-reference.…”

“…In [27] I provide a systematic and rigorous account of reference in the context of truth -or "alethic reference", as I call it -and define self-reference and other reference patterns in terms of this notion. I hope the intuitive appeal of the definitions I put forward there helps dissipate the scepticism the corresponding notions are immersed in, at least with regard to the semantic paradoxes.…”

“…that the reference patterns that underlie paradoxical expressions can be given a more fine-grained characterization. In short, I deploy the reference notions introduced in [27] to formulate different restricting criteria for admissible instances of T-schema in terms of their underlying reference patterns and show that this strategy is successful, as it results in classically consistent, sound, and fairly attractive theories of truth. Section 2 provides a technical introduction to formal theories of truth, followed by an overview of the state of the issue regarding different restrictive criteria for the truth predicate that have been proposed in the literature.…”

“…Section 2 provides a technical introduction to formal theories of truth, followed by an overview of the state of the issue regarding different restrictive criteria for the truth predicate that have been proposed in the literature. I also give a compact presentation of the approach to reference in the context of truth introduced in [27]. Section 3 employs these notions to construct semantic truth theories.…”