williams@kirk.DEC (John Williams 223-3402) (08/28/85)
There is one more class of mathematical philosophy you have left out, and that is that mathematics is a language. Like all language, it hopefully represents something in reality, but that is not a requirement. Like all language, it is intrinsically limited in accuracy in describing reality. In an idealistic sense, one could state that mathematics is perfect, but from a more practical sense, it is imperfect when it comes to application. One of the more striking features of mathematics is that there are a multitude of approaches, or techniques, that when performed, will yield the same result. In application, however, there exists an optimum method of analysis that will yield the least residual error. I'm surprised no one thought of this. John. Williams' first law of resolution: There wll never be an end to your problems. -------------------- Please note that this mail message is likely to be incomplete. The sender aborted the transmission. rhea::MAILER-DAEMON --------------------
franka@mmintl.UUCP (Frank Adams) (09/03/85)
In article <187@decwrl.UUCP> williams@kirk.DEC (John Williams 223-3402) writes: > > There is one more class of mathematical philosophy you have >left out, and that is that mathematics is a language. Like all >language, it hopefully represents something in reality, but that >is not a requirement. Like all language, it is intrinsically >limited in accuracy in describing reality. No, this is basically the formalist position. Or perhaps somewhere between the formalist and realist position, in the sense that it fails to decide between them. Saying mathematics is a language doesn't really tell us anything about the nature of the objects it deals with, which was the original question. > One of the more striking features of mathematics is that >there are a multitude of approaches, or techniques, that when >performed, will yield the same result. In application, however, >there exists an optimum method of analysis that will yield the >least residual error. What does this mean? Frank Adams ihpn4!philabs!pwa-b!mmintl!franka Multimate International 52 Oakland Ave North E. Hartford, CT 06108