Concept calculus
| Abstract | PREFACE. We present a variety of basic theories involving fundamental concepts of naive thinking, of the sort that were common in "natural philosophy" before the dawn of physical science. The most extreme forms of infinity ever formulated are embodied in the branch of mathematics known as abstract set theory, which forms the accepted foundation for all of mathematics. Each of these theories embodies the most extreme forms of infinity ever formulated, in the following sense. ZFC, and even extensions of ZFC with the so called large cardinal axioms, are mutually interpretable with these theories. This is an extended abstract. Proofs of the claims will appear elsewhere. | |||||||||
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Similar books and articlesShaughan Lavine (1995). Finite Mathematics. Synthese 103 (3):389 - 420.
Ernest J. Welti (1987). The Philosophy of Strict Finitism. Theoria 2 (2):575-582.
Harvey M. Friedman (2011). Part III. Technical Perspectives on Infinity From Advanced Mathematics : 4. The Realm of the Infinite / W. Hugh Woodin ; 5. A Potential Subtlety Concerning the Distinction Between Determinism and Nondeterminism / W. Hugh Woodin ; 6. Concept Calculus : Much Better Than. [REVIEW] In Michał Heller & W. H. Woodin (eds.), Infinity: New Research Frontiers. Cambridge University Press.
Michał Heller & W. H. Woodin (eds.) (2011). Infinity: New Research Frontiers. Cambridge University Press.
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