cik@l.cc.purdue.edu (Herman Rubin) (08/16/89)
In article <2212@hub.UUCP>, silber@voodoo.ucsb.edu writes: > -Message-Text-Follows- > Joe Keane remarked that: > > >>The key is that mathematics is not based on any structure in our universe.You > >>can talk about mathematical objects completely independent of any physical > >>basis. > But mathematics IS based upon structure in our universe, the structure > which conceives/abstracts/computes it (as well as the external structures > whose observation by primordial 'mathematicians' provides the primal > experiential base of observations upon which the elaboration of mathematics > as a cultural phenomenon is based) (Mathematics as a phenomenological complex) > (??) (-: (-: (-: As a supposedly pretty good mathematician and statistician, who has also worked in the foundations of both of these fields, I see no way that the structure of the universe enters. Euclid was quite aware that Euclidean geometry was something which applied to a formal construct, and that this happened to approximate the properties of certain real-world objects. Different environments will put different means of proceding into minds, and mathematics might very well develop differently. But the mathematics will still be the same. The structure of the integers and the real numbers will not change one whit. Pi would have exactly the same value, etc. -- Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907 Phone: (317)494-6054 hrubin@l.cc.purdue.edu (Internet, bitnet, UUCP)