Truth and Finite Conjunction

This note is a critical response to Kentaro Fujimoto’s new conservativeness argument about truth, which centres on the notion of finite conjunction. We argue that Fujimoto’s arguments turn on a specific way of formalizing the notions of finite collection and finite conjunction in first-order logic. In particular, by instead formalizing these concepts in a natural way in set theory or in second-order logic, Fujimoto’s new conservativeness argument can be resisted.