Editing Talk:1724: Proofs
Please sign your posts with ~~~~ |
Warning: You are not logged in. Your IP address will be publicly visible if you make any edits. If you log in or create an account, your edits will be attributed to your username, along with other benefits.
The edit can be undone.
Please check the comparison below to verify that this is what you want to do, and then save the changes below to finish undoing the edit.
Latest revision | Your text | ||
Line 29: | Line 29: | ||
It seems pretty obvious to me that by "weird, dark magic proofs", the student is talking about proofs that drag in far-flung reaches of mathematics so distant that they no longer appear to be mathematics, especially ones that involve meta-reasoning. Gödel's proof of the incompleteness of Peano arithmetic is the archetypical example, but others include Lob's theorem and any proof by contradiction involving the halting problem. Ms Lenhart's proof starts out by setting up a proof-by-contradiction, already a warning sign, and she then escalates it at the end by implying that this proof will somehow involve the actual physics of where the solution can and cannot be written. [[Special:Contributions/108.162.241.123|108.162.241.123]] 17:27, 24 August 2016 (UTC) | It seems pretty obvious to me that by "weird, dark magic proofs", the student is talking about proofs that drag in far-flung reaches of mathematics so distant that they no longer appear to be mathematics, especially ones that involve meta-reasoning. Gödel's proof of the incompleteness of Peano arithmetic is the archetypical example, but others include Lob's theorem and any proof by contradiction involving the halting problem. Ms Lenhart's proof starts out by setting up a proof-by-contradiction, already a warning sign, and she then escalates it at the end by implying that this proof will somehow involve the actual physics of where the solution can and cannot be written. [[Special:Contributions/108.162.241.123|108.162.241.123]] 17:27, 24 August 2016 (UTC) | ||
− | + | ||
:: The fact that the proof mentions the actual blackboard on which it is written is of course problematic in numerous ways, as is predicating on whether something "will eventually" happen. This is well outside the scope of the [https://en.wikipedia.org/wiki/Zermelo–Fraenkel_set_theory usual mathematical foundations]. Since careless use of meta-recursion is a [https://en.wikipedia.org/wiki/Curry's_paradox trap], such a proof would have to very very carefully consider foundational issues and cannot handwave over them. [[User:Zmatt|Zmatt]] ([[User talk:Zmatt|talk]]) 19:13, 24 August 2016 (UTC) | :: The fact that the proof mentions the actual blackboard on which it is written is of course problematic in numerous ways, as is predicating on whether something "will eventually" happen. This is well outside the scope of the [https://en.wikipedia.org/wiki/Zermelo–Fraenkel_set_theory usual mathematical foundations]. Since careless use of meta-recursion is a [https://en.wikipedia.org/wiki/Curry's_paradox trap], such a proof would have to very very carefully consider foundational issues and cannot handwave over them. [[User:Zmatt|Zmatt]] ([[User talk:Zmatt|talk]]) 19:13, 24 August 2016 (UTC) |