Truth-makers for Universal Statements

Studies in Logic, Vol. 13, No. 3 (2020): 19–31             PII: 1674-3202(2020)-03-0019-13
Difei Xu

Abstract. Fine (2016) provides some kinds of truth-maker semantics that explain how we understand our language, but these are controversial, especially in how we understand universal sentences. In his unpublished paper, Hale modifies Fine’s standard exact truth-maker semantics to explain how we understand law-like universal statements. In this paper, I suggest that if Hale insists that exact truth-maker semantics clauses for law-like universal statements differ from those for accidental universal statements, it would be better for Hale to formulate a lawlike generalization and an accidental generalization in different logical form, although the first entails the latter one. I also provide exact-truth-maker semantics for law-like generalization different from Hale’s. In the last part of this paper, locating universal statements in inexact truth-maker semantics, I compare the two formulations of the lawlike universal statements.