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

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.