[FoM] What is a proof?

John T. Baldwin jbaldwin at uic.edu
Tue Oct 28 20:49:24 EST 2003

William Tait wrote:

> On Oct 28, 2003, at 11:42 AM, John T. Baldwin wrote:

Baldwin wrote:

>> Standard Definition. 1. A proof is a sequence of propositions each of 
>> which is either an axiom or follows from those earlier in the list by 
>> a rule of inference.
Tait wrote:

> John,
> You first raised an interesting question about the explanatory content 
> of proofs---and THEN  gave a definition of proof which for-ordained a 
> negative answer. Your definition is `standard' only in logic textbooks 
> which are interested, not in proofs, but in provability.   I had 
> intended to be improving your question.

Dear Bill,

Thank you; that is an excellent disctinction that is right on the mark. 
 Looking again at your note
I see that explicitly finding a witness does indeed speak to my 
question.  It seems to be more
a partial answer than improving the question.


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