The Laws of Thought and the Laws of Truth as Two Sides of One Coin

Abstract

Some think that logic concerns the "laws of truth"; others that logic concerns the "laws of thought." This paper presents a way to reconcile both views by building a bridge between truth-maker theory, à la Fine, and normative bilateralism, à la Restall and Ripley. The paper suggests a novel way of understanding consequence in truth-maker theory and shows that this allows us to identify a common structure shared by truth-maker theory and normative bilateralism. We can thus transfer ideas from normative bilateralism to truth-maker theory, such as non-transitive solutions to paradox, and vice versa, such as notions of factual equivalence and containment.

Why Must Incompatibility Be Symmetric?

“…Suppose for contradiction that s and t are coherent, s is incompatible with t, and t is compatible with s. If t and s are coherent, and the obtaining of t doesn't exclude the obtaining of s, then it seems clear that the fused state of affairs consisting in t along with s must also be coherent. 22 But if s is incompatible with t, that is, if s excludes t, then it seems that the fusion of s and t must be incoherent. After all, given the principle of Persistence stated above, if s is incompatible with t, then, since s t is a state that contains more information than s, then s t is incompatible with t, and, by the same reasoning with respect to t, s t is incompatible with s t. 23 So, given our supposition, the fusion of s and t both is and isn't coherent.…”

“…For discussion of this point, seeNickel (2013: 346-357),Hlobil (2016), and Brandom (2018) 25. For formal semantic frameworks in which negation is understood in terms of potentially non-monotonic relations of incompatibility, see, for instance, the phase space semantics proposed byPorello (2012) orKaplan (2021), or the truth-maker semantics proposed byHlobil (2023).…”

A truth-maker semantics for ST: refusing to climb the strict/tolerant hierarchy

“…I show elsewhere that one way to define TS is to reject Exclusivity while holding on to Exhaustivity(Hlobil, 2022). But this won't help with our current problem because we want to use the same space of models for both logics, just as we do in the strong Kleene semantics.…”