Blind Deduction and Syntax

Luo, Horsten and Roberts (2024) recently responded to a version of the so-called conservativeness argument against deflationism about truth that I presented in Fujimoto (2022). This article replies to them and raises two issues with their argument. However, despite these issues, their argument and the disagreements between them and me bring a new perspective to the fundamental question as to what the theory of syntax ought to be. In the final section, I explore this question and propose one possible argument that any adequate theory of self-applicable truth should derive the full schema of arithmetical induction for the language of theories of truth over arithmetic.