FOM: Subjectivism and the computer?
Steve Stevenson
steve at cs.clemson.edu
Tue May 30 08:59:50 EDT 2000
If we agree that by "subjectivism" we mean the view that "mathematics
consists of constructions in the mind of the mathematician" (I'm using
Steve Simpson's words, FOM, 19 May), and constructivism is a
subjective viewpoint, what do we make of computer algebra? Surely, it
is constructive. A closed form Taylor series is just as representable,
for example. This would be, I think, Steve Wolfram's view (FOM, 1
Feb).
How is this different vis-à-vis non-subjective mathematics? Some
things are not finitely representable, surely. Steve continues
"And there are other coherent positions on the question ``What
is mathematics?''. These positions are philosophically
incompatible, but f.o.m. can sometimes find common ground
among them, at the level of formal systems."
What are those positions vis-à-vis computer algebra? Do we care?
best regards,
steve
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