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Quote: no complete set of effectively calculable invariants of conversion exist; for example, if Principia Mathematica is omega-consistent, its Enthscheidungsproblem is unsolvable
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Topic:
limitations of formalism
Topic:
Godel's incompleteness theorem
Quotation Skeleton
we shall prove (in Theorem XIX) that, under … [via recursion], no complete set of effectively calculable invariants of conversion exists … [p. 107] "Theorem XIX. There is no recursive function … B or not. … As a corollary of Theorem XIX, it follows … .omega.-consistent … in the sense of Godel [ref] and is … In particular, if the system of Principia Mathematica … Google-1 Google-2
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Topic: limitations of formalism (92 items)
Topic: Godel's incompleteness theorem (19 items)