[FOM] Choice of new axioms 1
Eray Ozkural
examachine at gmail.com
Mon Feb 13 19:25:08 EST 2006
I agree with Bauer in that the independence results hint at a
fundamental relativism in mathematics rather than an
absolute truth. In fact, I find that I do not understand how
the independence of the continuum hypothesis would entail
the existence of absolute mathematical truth.
At least, I think the very act of looking for new axioms that
will supposedly be adopted in textbooks, presupposes the
correctness of a realist philosophy of mathematics, much like
Goedel's. In my opinion, the current variety of formal systems
suffice to show us that mathematicians in the new century may
need to think more flexibly as Bauer suggests. Also, it seems
to me that presupposing a particular philosophy is not healthy,
since all popularized philosophical interpretations are essentially
up in the air.
Regards,
--
Eray Ozkural (exa), PhD candidate. Comp. Sci. Dept., Bilkent University, Ankara
http://www.cs.bilkent.edu.tr/~erayo Malfunct: http://www.malfunct.com
ai-philosophy: http://groups.yahoo.com/group/ai-philosophy
Pardus: www.uludag.org.tr KDE Project: http://www.kde.org
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