Timeline for Should Wittgenstein be given partial credit for Gödel’s incompleteness theorem?
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| Aug 22, 2011 at 0:10 | comment | added | anon | I think I should point out a technicality that many might not get by reading a lot of popular references on the incompleteness theorems: Gödel sentences don't explicitly refer to themselves. In arithmetic or number theory, for example, there is no symbol or symbolic way of saying "this formula." However, the proofs of the incompleteness theorems explicitly construct a Gödel sentence, and show that it will always be logically equivalent (in effect) to our informal interpretation of "this statement is not provable within the theory." | |
| Aug 17, 2011 at 6:52 | comment | added | Michael Dorfman | The short answer is that the history of Logical Positivism is also the history of its unravelling. Russell's "barber paradox" pointed to problems with set theory, so he invented the theory of types to try to address that. Wittgenstein found problems in the theory of types (in the Tractatus, and afterwards); Gödel later developed his own attack along these lines, etc. | |
| Aug 15, 2011 at 16:30 | vote | accept | Andrew Stout | ||
| Aug 14, 2011 at 16:07 | history | edited | Cody Gray | CC BY-SA 3.0 |
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| Aug 14, 2011 at 14:00 | comment | added | Mitch | I thought Russell's type theory was intended to avoid paradoxes in set creation. Was W's argument against type theory inTLP or was it later? (the time line of the 'changes' is confusing to me? | |
| Aug 14, 2011 at 13:36 | history | answered | Michael Dorfman | CC BY-SA 3.0 |