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Sunday, April 19, 2020

H. P. Grice Solves Zermelo's Antinomy

Zermelo read Cantor's essay and found an antinomy ("on the third page.").

Zermelo immediate wrote his uncle (translation mine):

Dear Uncle,

I'm reading Cantor's essay and have found an antinomy.
Should I write to HIM?
I fear he might overeact.
But the antinomy is so obvious:
Consider "the set of all sets that are not members of themselves."
This obviously leads to a contradiction since it must be a member of itself and not a member of itself.
Love,
    Your loving nephew

Grice had access to the Correspondence of Zermelo and re-wrote the antinomy.

Consider, Cantor asks us, "the set of all sets that are not members of themselves."

This obviously leads to a pragmatic contradiction, as G. E. Moore might agree, since this set must be a member of itself and not a member of itself.

Which remembers me of our friend J. L. Austin.

For _he_ thinks he can lead a class -- and he thinks Saturday morning is a good time,

"for a class," he says, "for all those who whose classes have no members."

Shall I take that as an insult,

Yours
      Grice.







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