On Nov 19, 11:47 am, Zuhair <zaljo...@gmail.com> wrote: > (4) Ultrafinistism: Those restrict human mathematical reasoning to > only feasible length descriptions, so it is more consistent than > finitism, but yet it is too restrictive that most mathematicians see > no clear justification for it to be true. > The mere justification of what is available around us, and the finite > nature of our abilities, is not a clear evidence of why should the > universe abide by such inabilities. That's besides the fact that > actual infinity through set construction is intelligible, so why > commit ourselves to such a restriction based on some inability that > the universe and reality around us might not necessarily copy and yet > at the same time this non copying can still be touched by some of our > descriptive apparatus though not in full as with ultra-finite matters. >
You should have a look at the first chapter of Edward Nelson's "Predicative Arithmetic", titled "The impredicativity of induction".