Halbach has argued that Tarski biconditionals are not ontologically conservative over classical logic, but his argument is undermined by the fact that he cannot include a theory of arithmetic, which functions as a theory of syntax. This article is an improvement on Halbach’s argument. By adding the Tarski biconditionals to inclusive negative free logic and the universal closure of minimal arithmetic, which is by itself an ontologically neutral combination, one can prove that at least one thing exists. The result can then be strengthened to the conclusion that infinitely many things exist. Those things are not just all Gödel codes of sentences but rather all natural numbers. Against this background inclusive negative free logic collapses into non-inclusive free logic, which collapses into classical logic. The consequences for ontological deflationism with respect to truth are discussed.
- disquotational theory of truth
- Tarski biconditionals
- ontological deflationism
- inclusive negative free logic
- universal closure of arithmetic