Treatise on Intuitionistic Type Theory (Logic, Epistemology, and the Unity of Science, 22) (English and German Edition)

Intuitionistic type theory can be described, somewhat boldly, as a fulfillment of the dream of a universal language for science.¡ In particular, intuitionistic type theory is a foundation for mathematics and a programming language.¡ This book expounds several aspects of intuitionistic type theory, such as the notion of set, reference vs. computation, assumption, and substitution.¡ Moreover, the book includes philosophically relevant sections on the principle of compositionality, lingua characteristica, epistemology, propositional logic, intuitionism, and the law of excluded middle. Ample historical references are given throughout the book Intuitionistic type theory can be described, somewhat boldly, as a partial fulfillment of the dream of a universal language for science. This book expounds several aspects of intuitionistic type theory, such as the notion of set, reference vs. computation, assumption, and substitution. Moreover, the book includes philosophically relevant sections on the principle of compositionality, lingua characteristica, epistemology, propositional logic, intuitionism, and the law of excluded middle. Ample historical references are given throughout the book. Front Matter....Pages i-xiii Prolegomena....Pages 1-11 Truth and Knowledge....Pages 13-51 The Notion of Set....Pages 53-76 Reference and Computation....Pages 77-106 Assumption and Substitution....Pages 107-154 Intuitionism....Pages 155-173 Back Matter....Pages 175-196