• Korean Journal of Logic
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• v.14 no.3
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• pp.101-137
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• 2011

Based on his analysis of judgement forms in intuitionistic type theory, Martin-L$\ddot{o}$f claims that the usual logical laws and interesting mathematical judgements are synthetic, not analytic. He further claims that the logic of analytic judgements is decidable and complete, while the logic of synthetic judgements is undecidable and incomplete. The aim of this article is to clarify and examine his claims. In section 1, I explain and give some comments on the monomorphic version of intuitionistic type theory. In section 2, after clarifying Martin-L$\ddot{o}$f's distinction between analytic and synthetic judgements, I examine some possible objections to it and evaluate the thesis that the usual logical laws and interesting mathematical judgements are synthetic. In section 3, I clarify and examine the thesis that the logic of analytic judgements is decidable and complete, while the logic of synthetic judgements is undecidable and incomplete.