On Thursday, January 31, 2013 3:48:12 PM UTC-8, Frederick Williams wrote: > david petry wrote:
> > 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)'?
Definitely not. It could be described as an attempt to flesh out an argument made by Poincare and many others.