
Logic and Infinity: The Errors of Calculus - misesed
http://steve-patterson.com/logic-and-infinity/
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dmfdmf
I noticed how the only two comments by d_e_solomon and thyrus a) assume the
author doesn't understand infinity and b)assume someone else has already
proved him wrong -- neither position without proof, just a feeling.

d_e_solomon just reasserts the philosophic context that mathematics assumes
today and misses the point that the author of this essay is challenging that
assumption. But we can't have an infinite regression of mathematical
assumptions and views on logic and infinity are epistemological and
metaphysical questions answered in philosophy.

The conflict here is a conflict in "worldview" that _precedes_ mathematics not
a difference in definition or meaning or a misunderstanding. If you believe
that infinities can _exist_ or be completed then you are on the side of
Cantor, Hilbert, et. al. As Hilbert wrote "No one shall drive us from the
paradise which Cantor has created for us". Hopefully Steve Patterson succeeds
in his aim to destroy Cantor's paradise and drive irrational metaphysics out
of calculus and mathematics.

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d_e_solomon
Kudos to the author on spending some time on this one. Not too many people
spend much time considering this one.

Unfortunately, philosophy applied to maths usually goes sideways and this
feels like such a case.

Mathematicians use delta-epsilon definition of a limit as a starting point to
apply rigor to thinking about infinities. Learning and understanding that
approach I suspect would go a long way to clearing up the author's quandaries.

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thyrsus
Surely, this has been discussed before. I'd like to see the rebuttal to the
"categorical error" argument.

