> I admit that I don't understand WM's technical claims. However, when I see you and other mathematicians fail to comprehend, or at least fail to respond coherently to, very simple, clear and straightforward informal arguments, it doesn't inspire confidence in me that you are qualified to judge whether WM's technical claims are valid.
Wolfgang Mueckenheim's arguments aren't very simple, clear and straightforward. Also he doesn't argue in good faith: look at Jesse Hughes valiant efforts in the ZFC and God thread.
> Here is a simple, clear and straightforward informal argument, which I believe Mueckenheim would endorse, that I have never seen a Cantorian mathematician respond to in a coherent way: > > It is eminently reasonable to believe that the purpose of mathematics is to provide a rigorous and practically useful conceptual framework for reasoning quantitatively about real world phenomena. The objects that exist in a conceptual framework are concepts; the universe of mathematical objects is a collection of concepts. Concepts can be encoded in language. Languages are countable. The Cantorian claim that "uncountable" infinite collections exist is tantamount to the claim that mathematics should assert the existence of things that are not within the mathematical conceptual framework. That is a truly extraordinary and even bizarre claim that requires truly extraordinary evidence, and such evidence is lacking, and prominent and well respected mathematicians have pointed out that such evidence is lacking.
Is that a long winded way of saying 'I'm an ultrafinitist (like Esenin-Volpin, say)'? Is ultrafinitism logical? Yes, probably. Is it eminently reasonable? No.
[My apologies to Esenin-Volpin (for whom I have a high regard) for mentioning him in a thread about Wolfgang Mueckenheim.]
-- When a true genius appears in the world, you may know him by this sign, that the dunces are all in confederacy against him. Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting