The piece is just a bit of fun, a bit of a stunt — TonesInDeepFreeze
My opinion is supported by the fact that Kurt Gödel was a Platonist, and believed that there was a true fact of the matter for every mathematical proposition. — fishfry
People who understand that proof is relative, and who are already familiar with incompleteness, might appreciate that a brief spoken word bit doesn't have to provide all the qualifications. — TonesInDeepFreeze
That Godel was a platonist supports your opinion that Boolos's rhetorical lark is wrong and meaningless? — TonesInDeepFreeze
that's not who the article is aimed at — fishfry
"The whole of math" includes the ultimate truth or falsity of any given proposition, irrespective of its provability in any given axiomatic system. — fishfry
rhetorical fun — TonesInDeepFreeze
"The whole of math" includes the ultimate truth or falsity of any given proposition, irrespective of its provability in any given axiomatic system.
— fishfry
Yeah, I don't think that's what's mean by Boolos. — TonesInDeepFreeze
What?Cantor's proof is not a reductio ad absurdum. — TonesInDeepFreeze
The diagonal argument was not Cantor's first proof of the uncountability of the real numbers, which appeared in 1874. However, it demonstrates a general technique that has since been used in a wide range of proofs, including the first of Gödel's incompleteness theorems and Turing's answer to the Entscheidungsproblem.
Cantor's diagonal argument is a reductio ad absurdum proof. — ssu
So there is no enumeration of the naturals onto the reals. — TonesInDeepFreeze
This shows that every injection fails to be a surjection. — T H E
The link to incompleteness results should be obvious. — ssu
So I'm just saying, "Ward, don't you think you're being a little hard on the Beaver?" — TonesInDeepFreeze
You realize that you have just outed yourself as being of a certain age . . . :razz: — EricH
Aryamoy Mitra Quote from a 1960s USA TV show. You'll have to find the rest yourself . . . :nerd: — EricH
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