On Mon, 11 Nov 1996, W. Gary Martin wrote: >This really comes down to a conflict in views of mathematics. You seem to >be advancing a realist view of mathematics, that math exists independently >of human experience. Others take a more constructivist view, that math is >inherently a part of the human experience, meaning that social interaction >is a critical part of mathematics.
Math could be, and I believe is, both independent of and inherently a part of human experience. I'm not sure we want to get off into this very theoretical/philosophical debate when we have been primarily dealing with more directly mathematical issues recently. It goes to show you/us, however, that mathematics as we know it is definitely at least socially communicated.
I'm curious again, is the debate about constructivist versus realist philosophical perspectives as prevalent in the field(s) of science as it is in mathematics? Do most scientists believe their work deals primarily with a universe that is really "out there" or that it is merely a mental/social construct? Is mathematics no longer considered the mother of the sciences, but a illusional (delusional?) aunt? Science as I view it is both a socially constructed realm of human concepts and a system of valid/true representations of a reality that is really out there.
I know these are "faith" issues, and so it seems that to be consistent, the constructivist ought only to express his/her agnosticism about the nature of things, whereas the realist can press on with her/his beliefs, confident that the constructivist can't refute her/his perspective. To paraphrase Shakespeare: There are more than things in heaven and earth, Constuctivist, than conceived in your philosophy.