[FOM] Friedman on Urquhart on Corfield
John Baldwin
jbaldwin at uic.edu
Tue Oct 21 19:29:19 EDT 2003
Corfield wrote:
> one thought
>I had along these lines concerns probabilistic existence proofs of the
>Erdos variety.
>
>The existence of a mathematical object is established by proving that the
>probability of its existence is positive. The technique was first devised
>by Paul Erdös. In a few cases the proof can be translated to a counting
>argument, but this is not so in general.
Can you elaborate on the last sentence. What does it mean to say `this is
not a counting argument'.
> Rota calls for a "correspondence principle" to allow for this
> translation, or, failing this, a "new logic associated with probabilistic
> reasoning" (might Bayesianism be the key?). It would be good to prove his
> following jibe wrong: "philosophers of mathematics are too incompetent to
> deal with a problem which ought to be their bailiwick."
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