On Monday, April 1, 2013 8:09:26 AM UTC-7, Dan wrote:
> ... mathematics is 'the domain of thought'
That's a very good way of thinking about it. We can extend that idea to say that mathematics is implicit in our own self-awareness. That is, to say that we are self-aware is to say that we have a model of ourselves, and in particular we have a model of ourselves as thinking beings, and mathematics is part of that model.
> Falsifiability in mathematics is a category error .
No. Our model of ourselves includes an understanding of both our capabilities and our limitations. Falsifiability simply says that we must always take into consideration our limitations.