Logic and Infinity: The Errors of Calculus

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.

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.

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