Re: Opinions on mathematics.
- From: Bob Kolker <nowhere@xxxxxxxxxxx>
- Date: Sun, 10 Dec 2006 20:52:37 -0500
Michael Press wrote:
Folks have talked about the how mathematics is practiced and the nature of mathematical objects. It is difficult to address these matters without saying 'mathematical objects' and expecting to be understood. It looks like we are stuck with the notion of mathematical objects.
From time to time someone tells me that mathematics is not science. I disagree with this assertion. The reason is that a mathematical object is a structure that we construct in our mind with the aid of writings and diagrams. When doing mathematics we are mapping our minds, and changing our minds. This is my outlook in a nutshell. Mathematics is a science. Our minds are real.
Your brain is real. It can be objectively observed. Have you ever emprically observed a mind in anyone's body but your own.
Futhermore, mathematics when done abstractly and formally has no empircal content whatsoever. The only constrain on a mathematical system is that it be internally consistent (i.e. free of contradictions or possesss one wellformed formula not provable from the axioms). Science requires correct correspondence with the external world. There is the difference.
Write us when a mind is objectively observed in a body other than the observer. Or write us when a mind is seen in an autopsy.
Bob Kolker
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