Quoted from Jean-Pierre Marquis email: "yes, of course, Salmon is certainly one of the important contributors to the field [scientific explanation]. In mathematics, Paolo Mancosu has been pushing the issue for the past 10 years or so, following the paths of Steiner, Resnik and a few others." In science, the issue of explanation has been discussed for at least a century. Since mathematics is a formal system and not a physical system, we have to be more careful about what *explanation* means. This makes it a "worldview" problems? As a constructionist/computationalist I would say no constructive, computational proof then there is no explanation. Platonist have their own. Is their explanation useful to me? Don't know because if I can figure a constructive technique out from the plationic technique, I'm good. steve stevenson clemson On 4/23/11 17:52, Dusko Pavlovic wrote:
a friend told me that there was a conference where music critics and professors discussed the visual content of music. on the other side, there are learned essays about the deep links between music and architecture. (hegel in particular wrote about that.)
the question whether a mathematical proof explains the theorem might be of a similar kind. while most proofs of the pythagoras theorem do explain why it is true, wyles' proof of the great fermat theorem (just a slightly different statement) does not seem to be explaining it to too many people.
-- Steve Stevenson Clemson University [For admin and other information see: http://www.mta.ca/~cat-dist/ ]