Treatise on Intuitionistic Type Theory

Contents.- List of Figures.- List of Tables.- Introduction.- Chapter I. Prolegomena. 1. A treefold correspondence.- 2. The acts of the mind.- 3. The principle of compositionality.- 4. Lingua characteristica.- Chapter II. Truth of Knowledge. 1. The meaning of meaning.- 2. A division of being.- 3. Mathematical entities.- 4. Judgement and assertion.- 5. Reasoning and demonstration.- 6. The proposition.- 7. The laws of logic.- 8. Variables and generality.- 9. Division of definitions.- Chapter III. The Notion of Set. 1. A History of set-like notions.- 2. Set-theoretical notation.- 3. Making universal concepts ito objects of thought.- 4. Canonical sets and elements.- 5. How to define a canonical set.- 6. More canonical sets.- Chapter IV. Reference and Computation. 1. Functions, algorithms, and programs.- 2. The concept of function.- 3. A formalization of computation.- 4. Noncanonical sets and elements.- 5. Nominal definitions.- 6. Functions as objects.- 7. Families of sets.- Chapter V. Assumption and Substitution. 1. The concept of function revisited.- 2. Hypothetical assertions.- 3. The calculus of substitutions.- 4. Sets and elements in hypothetical assertions.- 5. Closures and λ -calculas.- 6. The disjoint union of a family of sets.- 7. Elimination rukes.- 8. Propositions as sets.- Chapter VI. Intuitionism. 1. The intuitionistic interpretation of apagoge.- 2. the law of excluded middle.- 3. The philosophy of mathematics.- Bibliography.- Index of Proper Names.- Index of Subjects.-