[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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