Truthmaking, grounding and Fitch’s paradox

Jago and Loss have recently used variations on Fitch's paradox to argue that every truth has a truthmaker, and that every fact is grounded. In this paper, I show that Fitch's paradox can also be adapted to prove the exact opposite conclusions: no truth has a truthmaker, and no fact is grounded. All of these arguments are as dialectically effective as each other, and so they are all in bad company.

Fitch's Paradox and Level-Bridging Principles

Fitch’s Paradox shows that if every truth is knowable, then every truth is known. Standard diagnoses identify the factivity/negative infallibility of the knowledge operator and Moorean contradictions as the root source of the result. This paper generalises Fitch’s result to show that such diagnoses are mistaken. In place of factivity/negative infallibility, the weaker assumption of any ‘level-bridging principle’ suffices. A consequence is that the result holds for some logics in which the “Moorean contradiction” commonly thought to underlie the result is in fact consistent. This generalised result improves on the current understanding of Fitch’s result and widens the range of modalities of philosophical interest to which the result might be fruitfully applied. Along the way, we also consider a semantic explanation for Fitch’s result which answers a challenge raised by Kvanvig.

When Protagoras Made Aristotle His Fitch

While defending the principle of non-contradiction in Metaphysics 4, Aristotle argues that the Measure Doctrine of Protagoras is equivalent to the claim that all contradictions are true; given all appearances are true (as the Protagorean maintains), anytime people disagree we get a true contradiction. This argument seems clearly invalid: nothing guarantees that actual disagreement occurs over every matter of fact. The argument in fact works perfectly, I propose, because the Protagorean view falls prey to a version of Fitch's “paradox” of knowability. The proposed reading shows how Aristotle treats the Protagorean view at issue as an epistemic theory of truth distinct from the mere claim that all appearances are true (which other opponents put forward on different grounds) and reveals Aristotle's underlying concern with the modal collapse of possibility into actuality. The revised Protagorean view Aristotle confronts in a subsequent chapter is furthermore best understood as an attempt to avoid this Fitch-style result.

THE AMBIGUITY OF KNOWABILITY

In this paper it is shown that the Verification Thesis (all truths are knowable) is only susceptible to Fitch’s Paradox if one conflates the de re and de dicto interpretation of knowability. A formalisation shows that if one treats knowability as a complex second-order predicate, then the paradox falls apart.