Every story and comment from the Hacker News API, in a layout borrowed from 2001.
A comment on Kurt Gödel’s Brilliant Madness. Parent comment
was for Russell's Principia Mathematica, which is much
stronger than a first-order theory of the natural numbers.
Also, Gödel's incompleteness result was not for the liar paradox.
Instead, it was for the proposition I'mUnprovable, which
[Gödel 1931] claimed to have constructed. However,
[Wittgenstein 1937-1944] showed that I'mUnprovable leads to
inconsistency in the foundations of mathematics. Fortunately,
I'mUnprovable cannot be constructed in foundations because
the attempted construction violates order on propositions.
Furthermore, Gödel did not have a proof of the second
incompleteness result at the time he wrote to von Neumann [von Plato 2018].
von Neumann never realized the deception by Gödel because it
was discovered after both had died.
There are no comments on this comment yet.
was for Russell's Principia Mathematica, which is much
stronger than a first-order theory of the natural numbers.
Also, Gödel's incompleteness result was not for the liar paradox.
Instead, it was for the proposition I'mUnprovable, which
[Gödel 1931] claimed to have constructed. However,
[Wittgenstein 1937-1944] showed that I'mUnprovable leads to
inconsistency in the foundations of mathematics. Fortunately,
I'mUnprovable cannot be constructed in foundations because
the attempted construction violates order on propositions.
Furthermore, Gödel did not have a proof of the second
incompleteness result at the time he wrote to von Neumann [von Plato 2018].
von Neumann never realized the deception by Gödel because it
was discovered after both had died.