Post by Matthew JohnsonBegin quote----------------------
The history of mathematics has known many occasions where a discovery made by a
scientist remains unknown until somebody else makes it again later, with
astonishing preciseness. In the letter that Galois wrote the day before his
fatal duel, he reached some conclusions of extreme importance in the study of
integrals of algebraic functions. More than twenty years later, Riemann,
undoubtedly unaware of Galois' letter, re-discovered and proved the same
propositions. Another example: after Lobachevski and Bolyai built the
foundations of non-Euclidean geometry independent of each other, it appeared
that two other mathematicians, Gauss and Schweikart, had both reached the same
conclusions ten years earlier, also working independently. There is a strange
feeling in reading exactly the same ideas, as coming from one mind, in the work
of four scientists who studied the subject alone
End quote-------------------
That "one mind" is the mind of God.
I am not sure this really is about God. The ideas of mathematics could
be implicit in the subject matter. That is, given the same germ of a
thought in Gauss and Schweikart and Lobachevski and Bolyai, their
further expositions must be almost identical because they are all
describing the same object.
This seems to me to be an aspect of the Platonic problem in
mathematics. That is, do the entities of mathematics exist is some
sense before any mathematician looks at them and is, therefore, what
the mathematician is doing a discovery of something that exists
independently (at least of human mathematics) or is the mathematician
inventing something new that never existed before?
You can summarize what I just said as "what, exactly, does 'exist'
mean?"
You will get no satisfactory answer to that question. The ontological
proof of the existence of God played fast and loose with this problem.
Thomas of Aquino did not accept the ontological proof and concocted an
alternative by skillfully redefining "exist" (in Latin, of course, so
he was redefining "esse" or something like that). I fear that Thomas'
solution was even less popular than the ontological solution.
I am not going to make any contributions to this philosophical
dilemma. In my opinion all attempts to prove the existence of God will
fail and, moreover, they are all unnecessary because existence of God
is an empirical fact and, therefore, independent of logical thinking,
no matter how convoluted.