Re: Raatikainen's critique of Chaitin
From: KRamsay (kramsay_at_aol.com)
Date: 09/07/04
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Date: 07 Sep 2004 16:16:40 GMT
In article <fa69ae35.0409060859.22b28496@posting.google.com>,
erayo@bilkent.edu.tr (Eray Ozkural exa) writes:
|Your posts made me realize that my task is much more difficult than it
|seems. I want to erase Platonist tendencies from mathematics, e.g.
|decisively eliminate the idea of God and heaven.
There are theists who feel more comfortable about platonism as a
result of their religious beliefs, but in general these are quite
separate issues. I am told that Michael Dummett, one of the better
known philosophers arguing against realism, especially realism in
mathematics, is a theist. There are of course many mathematicians
who are atheists but realists about mathematics.
|If you can't
|understand that Chaitin's results elaborately show that there is
|randomness in the heart of mathematics and idealized reasoning in
|general, *then* it would be impossible for folks like you to
|appreciate that mathematical realism is bankrupt. Chaitin's work is
|not just a collection of footnotes, I think.
Your task is indeed enormously harder than it must have seemed
at first! It seems to be hard to believe how resistant philosophical
notions are to being "bankrupted". You really have to be ready to
approach them from their own point of view. Explaining again and
again how wrong it looks from your own just doesn't work. Issues
something akin to realism and non-realism have been banging around
for thousands of years now. I bet you're not the one to finish it
off.
One of the things non-realists have to remember about realism
is that simple appeals to epistemology just don't cut any ice
with realists. Nearly everything said about Omega pertains only
to the knowability of bits of Omega. To the realist, there just
isn't any reason why this should make a difference as to whether
there is a definite fact of the matter about what they are.
Keith Ramsay
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