Re: Are mathematical proofs incomparable with proofs in other disciplines?

[Michael Barr <barr@math.mcgill.ca>]

On Wed, 7 Jul 2010, Vaughan Pratt wrote:

> My questions are
>
> 1.  Is mathematical proof so different from say legal proof that the two
> notions should be listed on a disambiguation page as being unrelated
> meanings of the same word, or should they be treated as essentially the
> same notion modulo provenance of evidence and strictness of sufficiency,
> both falling under the definition "sufficient evidence of the truth of a
> proposition."

Let me begin my answer with an aphorism.  I don't know who said it first,
but I heard it from Charles Wells.

In principle, there is no difference between principle and practice, but
in practice...

If mathematical proof were simply logical deductions, there would never be
mistaken proofs published.  On the other hand, if proofs weren't logical
deductions, we could never find errors in proofs, only in their
consequences.  Nonetheless, the biggest difference between mathematical
proof and, say, legal proof, is that the latter depends on real world
evidence.  Legal terms do not have definitions that can be understood
without reference to the real world.  we believe that, in principle, every
proof we publish is a surrogate for a formal logical deduction, but I once
tried that for a simple argument and gave up after I had filled a couple
pages with indecipherable chicken scratchings (cf. Russell & Whitehead).


>
> 2.  Gandalf61 evidently feels his sources, Krantz and Bornat, prove the
> notions are incomparable.  Are there suitable sources for the opposite
> assertion, that they are comparable?
>

I agree, however, that they are incomparable.

Michael



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