Actual Infinity in Reality?

[SteveII]

Ok... .so how would you answer?  Would you agree, that if there is a logical contradiction, that this would disprove the math?   Perhaps a problem in the assumptions or in the way things are being explained, that it is not an actual infinite but something else. 

This guy has a number of articles about Infinity and what he sees as philosophical problems underpinning this relatively recent theory.  The following observation is interesting. 

Mathematicians are an interesting bunch. They are very, very rigorous when it comes to analyzing implications – what follows from what. They do not seem nearly as rigorous when it comes to analyzing presuppositions – what precedes from what. In fact, they do not even seem to be aware of their own presuppositions. I’ve been told countless times, “It’s absolutely certain that Cantor proved the existence of different sizes of infinite sets! Mathematicians have double-checked his work for a century!”

But they don’t seem to be aware of one problem: what if the presuppositions of Cantor’s proof are wrong? What if – specifically – the concepts that he presupposed were imprecise.

Awesome article. Explains with much more clarity some of my modest points (by comparison) I was trying to make between mathematics and the real world. But holy cow, he lays mathematicians out over the concept of infinity. I liked this summary near the end:

Impolite Implications

To be frank, if I were a mathematician, I would be embarrassed by the conceptual holes in Cantor’s argument. It’s worse than the Copenhagen Interpretation of quantum physics. It’s worse than blind faith in deities. At least blind faith does not demand accepting logical contradictions into your worldview.

Cantor’s argument isn’t ridiculous in isolation; the entire modern mathematics profession is also damned by association. Modern math, by not weeding out the illogical presuppositions of Cantor, has turned itself into modern Numerology.

Pure mathematicians, to use a phrase by Marcelo Gleiser, have relegated themselves to being “monks of a secret order”. They think they have special access to the magical and mysterious world of numbers, and the great infinity of infinities.

Many contemporaries of Cantor mocked and despised his work. Mathematician Henri Poincaré is famously quoted as saying, “Later generations will regard [set theory] as a disease from which one has recovered.”

Mathematician Leopold Kronecker wrote, “I don’t know what predominates in Cantor’s theory — philosophy or theology – but I am sure that there is no mathematics there.”

The philosopher Wittgenstein at one point said, “Mathematics is ridden through and through with the pernicious idioms of set theory” which he called “utter nonsense” and “laughable.”

This is the type of article I have asked from Grandizer and Polymath for 40 pages. Where are the philosophy articles that defend an actual infinite in the real world?