Truth and Finite Conjunction.

This article critically examines Kentaro Fujimoto's new conservativeness argument against deflationism about truth, which relies on formalizing finite conjunctions within first-order arithmetic. Deflationism holds that truth is an insubstantial, quasi-logical notion, often explicated via proof-theoretic conservativeness—meaning adding truth axioms does not yield new theorems about truth-free subject matter. Fujimoto's argument claims that adding the principle of conjunctive correctness (that a finite conjunction is true if and only if each conjunct is true) leads to non-conservativeness, thus challenging deflationism. However, the authors argue that this conclusion depends heavily on the specific first-order formalization of finiteness; when finiteness and finite conjunctions are instead formalized naturally in set theory or second-order logic, the resulting truth theories remain conservative over the base theory. They further analyze Fujimoto's informal "blind deduction" arguments, showing that for the first two, finiteness assumptions are not essential, and for the third, a second-order treatment preserves conservativeness. The article concludes that the non-conservativeness result is sensitive to the formal framework chosen and that deflationism about truth is not decisively refuted by Fujimoto's argument when broader formalizations of finiteness are allowed.