Abstract
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. https://doi.org/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.
Highlights
Notation and ConventionsI present the notation and conventions adopted in the paper.2 Here, we focus on PA and on theories of truth extending PA
The aim of this paper is twofold: first, I provide a cluster of theories of truth in classical logic that is consistent with global reflection principles: the theories of positive truth
A theory of truth and falsity over PA is formulated in a language LTF expanding the arithmetical vocabulary with additional unary truth and falsity predicates T and F
Summary
In their recent paper Fischer et al (2019), Fischer, Horsten and Nicolai provided a novel epistemological investigation of axiomatic theories of truth They investigate the epistemic value of theories of full disquotational truth in the context of our epistemic practices; they show that theories of full disquotational truth are to be prefered as theories to be employed in our cognitive projects, in contrast to—what they call— theories of scientific truth in classical logic. 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).
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