Treatise on Intuitionistic Type TheorySpringer Science & Business Media, 2 giu 2011 - 198 pagine 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 Ample historical references are given throughout the book. |
Sommario
| 1 | |
Chapter II Truth and Knowledge | 13 |
Chapter III The Notion of Set | 52 |
Chapter IV Reference and Computation | 77 |
Chapter V Assumption and Substitution | 107 |
Chapter VI Intuitionism | 155 |
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| 186 | |
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abbreviated according algorithm application Aristotle ass(A ass(T becomes called canonical canonical assignment canonical set cause Chapter clear complete computation rule concept conclusion connection consider context corresponding defined definition demonstration determining distinction el(A el(B el(Bo el(C el(D el(N element equal evident exact example excluded middle existence explained expression fact false follows form of assertion formal four function give given important inference rule interpretation introduced intuitionistic type theory irrefutable Justification kind known language Let the premisses logic mathematics matter meaning mediate method mind natural noncanonical sets notation Note notion object philosophical possible predicate present principle programming proof prop proposition reason recognized referent relation sense side substitution taken things third treated true true A true truth universal valid variables write