Earlier quoted context omitted.
I'll try to summarize my finitist position, which I seem stuck with despite years of trying to accept the mainstream / Cantorian view. One criticism is that the mainstream treatment of infinity is more invented, and less grounded in nature, relative to other areas of math. Another is that it is rife with equivocation, especially between the notion of infinity, and the notions of number and quantity. It's commonly deb…
> Infinity is neither a number nor a quantity. It's not a number, because you can't get there by counting. That's an oddly narrow implied definition of "number" which, as well as infinity, would exclude everything other than the natural numbers. Maybe it extends to the integers, if you use an unusually generous definition of "counting". But it certainly excludes non-integral rationals, and, a fortiori , all irrationa…
Re: Mathematicians Bridge Finite-Infinite Divide
#61Maybe "count" is too restrictive depending on how you think of counting. Substitute "reached" or "located" if you like. As another comment here says (paraphrasing) if a real can't be named, is it even a thing? I'd say any real that can be named can be "counted to" from another real that's arbitrarily close to it. If that's still too restrictive, then for any real that can be named, I can point to a segment of the number line and say "It's roughly, round about... there." Can't do that for infinity, again, because it's not a number.