Re: self-evident
Moorad Alexanian (alexanian@UNCWIL.EDU)
Tue, 07 Apr 1998 14:28:35 -0500 (EST)
At 10:07 AM 4/7/98 -0600, Garry DeWeese wrote:
>At 04:41 PM 4/5/1998 -0500, Moorad Alexanian wrote:
>>Mathematics is a human invention. Of course, the mystery is that this human
>>invention is indeed useful in describing the workings of nature. As a
>>logical game, the only requirement of the postulates is that they are not
>>contradictory and are in some sense complete.
>
>A minor point, perhaps, but I cannot let the assertion that "Mathematics is
>a human invention" go by without objection. (I had hoped that someone more
>qualified in the philosophy of mathematics than I am would respond; I
>suppose George Murphy is quite busy these days with Holy Week activities in
>his church.)
>Moorad, are you endorsing a constructivist account of mathematics? Would
>you really want to assert that when Pythagoras discovered his famous
>theorem, or when Wylie proved Fermat's Last Theorem, that they were
>*inventing* something, not *discovering* it? Unless I missed it recently,
>there still is no proof or disproof of Goldbach's Conjecture. On your
>view, it is neither true nor false. But I would maintain that it is either
>true or it is false; we may never know which, but its truth (or falsity) is
>not something we invent.
Dear Garry,
Mathematics deals with total abstractions and as such is almost
indistinguishable from logic. Within the context of a logical system, one
can pose problems and find solutions for them. What does that have to do
with the real world? Hence mathematics is a formal science and may be
distinguished from experimental science by the fact that it does not
describe actual, sensible matter.
>I think it is much more cogent for a Christian to hold that mathematical
>objects (numbers, relations, theorems, etc.) exist in the mind of God, and
>are necessarily and timelessly true, and that we merely discover them,
>thereby thinking God's thoughts after him. So the explanation of the
>"mystery" of why mathematics has real-world application is that the world
>was designed by God in conformity with the necessary, timeless mathematical
>truths which he knows.
>
>Best wishes,
>Garry DeWeese
That mathematics is a human invention does not preclude that God is indeed
the source of both the inventiveness of man and the "creations" which
emanate from the human mind. I agree that the mystery of why mathematics is
the language of science is no mystery to the Christian. Both have the very
same source.
Take care,
Moorad