Talk:Jules Richard
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Axel added "an investigation of the nature of axioms in geometry: are they necessarily true, are they arbitrary assumptions, are they definitions?"
Well this is part of the flawed work I am talking about. I think these questions had been answered several years prior to his writing, and he reached some incorrect conclusions.
"are they necessarily true" - yes, by definition all axioms are true, I mean that is simply what they *are*
"are they arbitrary assumptions" - we know this to be true as well.
"a variant of Cantor's diagonal argument."
No, I don't think this is correct. The diagnoal arguement was on the nature of infinite numbers, the Richard paradox was basically a restatement of the old Epimenides argument on self-negating recursion.
Richard used Cantor's diagonal argument. The failure of his argument is due to the change of language. A very well written article. Hippasos 16:40, 1 April 2007 (UTC)
