Papers by Matteo Zicchetti
Journal of Philosophical Logic
This paper focuses on the categoricity of arithmetic and determinacy of arithmetical truth. Sever... more This paper focuses on the categoricity of arithmetic and determinacy of arithmetical truth. Several ‘internal’ categoricity results have been discussed in the recent literature. Against the background of the philosophical position called internalism, we propose and investigate truth-theoretic versions of internal categoricity based on a primitive truth predicate. We argue for the compatibility of a primitive truth predicate with internalism and provide a novel argument for (and proof of) a truth-theoretic version of internal categoricity and internal determinacy with some positive properties.
Erkenntnis, 2022
The aim of this paper is twofold: first, I provide a cluster of theories of truth in classical lo... more The aim of this paper is twofold: first, I provide a cluster of theories of truth in classical logic that is (internally) consistent with global reflection principles: the theories of positive truth (and falsity). After that, I analyse the epistemic value of such theories. I do so employing the framework of cognitive projects introduced by Wright (Proc Aristot Soc 78:167–245, 2004), and employed—in the context of theories of truth—by Fischer et al. (Noûs 2019. 10.1111/nous.12292). In particular, I will argue that theories of positive truth are trustworthy, analogously to the theories of full disquotational truth. Moreover, I argue that, for a given cognitive project, if the acceptance of trustworthy theories is taken to be an epistemic norm of cognitive project, then one has good reasons to accept theories of positive truth over other rival theories of truth in classical logic. On the other hand, the latter theories are deemed epistemically unacceptable.
Proof-theoretic reflection principles have been discussed in proof theory ever since Gö del’s dis... more Proof-theoretic reflection principles have been discussed in proof theory ever since Gö del’s discovery of the incompleteness theorems. But these reflection principles have not received much attention in the philosoph ical community. The aim of the present chapter is to survey some of the principal meta-mathematical results on the iteration of proof-theoretic reflection principles, and also to investigate these results from a logico philosophical perspective; we will concentrate on the epistemological sig nificance of these technical results and on the epistemic notions involved in the proofs. In particular, we will focus on the notions of commitment to and acceptance of a theory. Special attention is given to the connec tion between proof-theoretic reflection and axiomatic truth theories. After distinguishing between different types of proof-theoretic reflec tion principles, we review some proof-theoretic results concerning exten sions of formal theories by (iterated) reflect...
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Papers by Matteo Zicchetti