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Quote: although Principia mathematica and Zermelo-Fraenkel set theory formalize all of mathematics, they contain simple, undecidable problems
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Topic:
limitations of formalism
Topic:
Godel's incompleteness theorem
Quotation Skeleton
The most comprehensive formal systems that have been … [Whitehead and Russell 1925] … and the Zermelo-Fraenkel axiom system of set theory … These two systems are so comprehensive that in … few axioms and rules of inference. One might … that can at all be formally expressed in … contrary there are in the two systems mentioned … the axioms. Google-1 Google-2
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Topic: limitations of formalism (92 items)
Topic: Godel's incompleteness theorem (19 items)