[FoM] What is a proof?

[John T. Baldwin]

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.


John