Proof-Theoretic Justification for Deduction and the Fundamental Assumption

Proof-theoretic semantics is a semantic framework that explains the meaning of sentences through the notion of proof. In proof-theoretic semantics, the validity of an argument is defined in such a way that, if the premises can be correctly asserted, then the conclusion can also be correctly asserted. This paper examines Dummett's definition of validity and elucidates its meaning by exploring the relationship between validity and the fundamental assumption. In addition, I clarify the relationship between the fundamental assumption and the thesis that self-justifying introduction rules fix the meaning of logical constants. In particular, by refuting Kürbis's criticism, I reaffirm the necessity of the fundamental assumption for the proof-theoretic definition of validity in formal language. On this basis, I claim that the fundamental assumption is a fundamental assumption.