Fred & all,
My goodness! I'd turn that question around: is there any proof (apart from an "indirect" proof, or "proof by contradiction") that one would *not* "consider as being explanatory in this sense?"
Speaking as a novice: yes, certainly. Isn't it a question of degree? Some proofs explain beautifully while others are clear as mud; most are between. Ideally a proof shouldn't depend upon natural language but most do. Striking sometimes how changing a few words of a sentence can make a concept obvious rather than nebulous. For example, I've proven some of the power laws for map objects. There should be a way to reduce the definition of a map object and the power laws to analogues in arithmetic. Still eludes me. My proofs have yet to help. So my understanding is incomplete and my power law proofs are poor. Best regards, ... Peter E. -- Telephone 1 360 450 2132. bcc: peasthope at shaw.ca Shop pages http://carnot.yi.org/ accessible as long as the old drives survive. Personal pages http://members.shaw.ca/peasthope/ . [For admin and other information see: http://www.mta.ca/~cat-dist/ ]