Bhaskar and dialectics

wpc at cs.strath.ac.uk wpc at cs.strath.ac.uk
Fri Feb 24 08:37:01 MST 1995


 Ralph Dumain wrote

Are there real contradictions in mathematics, which left behind
popular expositions of dialectical vs. formal logic a century ago?
Well, some real mathematicians do find contradictions in
mathematics, but not where you think they would, eg. the paradox
of motion.  Have you ever heard of "adjoint functors"?  I will
upload a bibliography on this topic too.  I came across a
pertinent article just last night.

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There has been a recognition that mathematical systems
of any utility will contain inconsistencies - contraditions
if you will - since the work of Goedel and Turing in the
30s showed that there can be no general decision procedure
for the validity of theorems. More recently, Chaitin has
shown that even relatively simple things like Diophantine
equations can give 'random' results.

The work of Turing in particular was a devastating critique
of the pretensions of idealism in mathematics.


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