1 the formalization of mathematics
| Abstract | It has been accepted since the early part of the Century that there is no problem formalizing mathematics in standard formal systems of axiomatic set theory. Most people feel that they know as much as they ever want to know about how one can reduce natural numbers, integers, rationals, reals, and complex numbers to sets, and prove all of their basic properties. Furthermore, that this can continue through more and more complicated material, and that there is never a real problem. | |||||||||
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Similar books and articlesConstantine Politis (1965). Limitations of Formalization. Philosophy of Science 32 (3/4):356-360.
José Ferreirós (2011). On Arbitrary Sets and ZFC. Bulletin of Symbolic Logic 17 (3):361-393.
Friedrich Waismann (1951/2003). Introduction to Mathematical Thinking: The Formation of Concepts in Modern Mathematics. Dover Publications.
Christopher Pincock (2009). Towards a Philosophy of Applied Mathematics. In Otávio Bueno & Øystein Linnebo (eds.), New Waves in Philosophy of Mathematics. Palgrave Macmillan.
Harvey Friedman (2000). Does Mathematics Need New Axioms? The Bulletin of Symbolic Logic 6 (4):401 - 446.
John Bigelow (1988). The Reality of Numbers: A Physicalist's Philosophy of Mathematics. Oxford University Press.
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