[FOM] Panel on "Inconsistency Robustness in Foundations of Mathematics" at IR'14 (http://ir14.org)
Charlie
silver_1 at mindspring.com
Mon Jun 9 15:20:37 EDT 2014
Dear Marcin,
There are lots of wild stories about Hippasus of Metapontum Since most of what we “know” about the Pre-Socrates (many were hostile to their views) comes from much later sources, there’s difficulty of determining the truth of his discovery. However, for fun, check out lots of notions of how he found irrationals. Was it algebraic, geometric,… ? Come up with your own analysis!
On Jun 8, 2014, at 3:54 PM, Marcin Mostowski <m.mostowski at uw.edu.pl> wrote:
> Dear all,
>
> I have two things related to the message by Carl Hewitt, one remark and a question.
>
> Remark:
>
> You write: "Was Wittgenstein after all correct that Gödel’s proof is erroneous because inconsistency results from allowing self-referential sentences constructed using fixed points for an untyped grammar of mathematical sentences?"
>
> You have two isomorphic reasonings. One about numbers and one rather logical. The first one was very well checked and we have very good reasons to accept it as a correct reasoning. The claim that the second one is incorrect seems to be a simple mistake. I do not see any use of discussing the issue.
>
> Question:
>
> You write: "Perhaps the first foundational crises was due to Hippasus “for having produced an element in the universe which denied the…doctrine that all phenomena in the universe can be reduced to whole numbers and their ratios.” Legend has it because he wouldn’t recant, Hippasus was literally thrown overboard to drown by his fellow Pythagoreans."
>
> Have you any good historical reference to the story? I agree that it was one of crucial points in our intellectual history.
>
> Marcin Mostowski
>
>
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