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.
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