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I don't think it is ever tenable to claim that mathematics is purely a human construction. The Formalist viewpoint is that mathematics is just the manipulatio
by swatow 12y ago
I don't think it is ever tenable to claim that mathematics is purely a human construction. The Formalist viewpoint is that mathematics is just the manipulation of symbols, according to certain rules. But Formalists accept that these rules regarding manipulation of symbols are themselves mathematical. That is, the Formalists are actually Platonists with regard to metamathematics. The Platonist says "1 + 1 = 2 is a meaningful, true statement" while the formalist says "that P is a correct proof that 1 + 1 = 2, is meaningful, true statement".
- evincarofautumn 12y agoA middle ground seems reasonable. The naturals probably correspond to a physical phenomenon—it seems to be possible to have, say, 1 proton—but I have deep doubts about the existence of the reals.