martillo@ihuxt.UUCP (Yehoyaqim Martillo) (05/02/84)
Modern physicists and consequently all of modern scientists make a great leap of faith when they assume the universe can be described mathematically. I as a physicist do not find this leap of faith difficult because I believe in a God who ordered the universe. But if I did not, I would have great difficulties because Goedel demonstrated that all mathematical systems are incomplete, inconsistent, or insufficient. Cohen went further and demonstrated that some statements are independent. Since the universe clearly works, I would have to be dubious of mathematical description of the universe if I did not believe in God. Why should I require scientific proof of God's existence, when I cannot be sure science works because my mathematical system is incomplete? Perhaps, the incompleteness of math shows that the universe has enough space that God and science can coexist.
ka@hou3c.UUCP (Kenneth Almquist) (05/07/84)
As I understand it, Goedel proved that given a reasonably powerful language and a finite set of postulates, it is possible to express statements in the language that can be neither proved nor disproved using the postulates. What limitations this places on physics is not clear. Mathematics, or at least the less abstract branches of mathematics, have been able to proceed in spite of this limitation. Although Godel proved that statements that are independent of a set of axioms must exist, he did not prove that any such statements would be of interest to applied mathematitions. My own belief is that physicists will never achieve a complete description of the universe; they will always be able to refine further even if they are not limited by their math- ematical tools. The belief that mathematics is an effective tool for understanding the universe is not based upon a leap of faith; physicists use mathematics because it appears to work. Kenneth Almquist