>>31
If you do meaningless things and be an autist, evolution will clean you and genes from population.
We were talking about different things. Meaning that I was talking about is about the descriptive equivalence between things. Meaning that you're now talking about is about what is evolutionarily good/leads to survival.
Why should I? What would be the meaning of those actions?
If you're really going to talk about usefulness here, math is quite useful in engineering and physics and more general computation (such as what you do on a computer).
The factorial of 9999999999999999999999 is constant. There are no computation. The program can be expanded.
I'd figure an ultrafinitist like you would ignore such large numbers. Yes, it's a constant, but reaching the exact value of that constant (that is, evaluating 9999999999999999999999!) requires a process (which can be a computation), the fact that the factorial equals to some constant is clear, but what the constant is cannot be reached except by computation (mathematical proof, that is, following a finite number of steps by applying some rules to find the literal value is also a computation, despite that the equality between 9999999999999999999999! and its literal value cannot be disputed).
http://www.infinite-beyond.com/scripts/kaplan_theartoftheinfinitethepleasuresofmath.pdf
Now that I know what the context is, it seems it talks about some axiomatic system's ontological existence. That is indeed a valid question. Personally, I assign a higher than 50% probability for the existence (truth) of arithmetic (thus all finite computational systems). I'm undecided by iterative set theories for now, but my belief in arithmetic seems to imply that infinity at least up to Aleph Null (ℵ
0) exists. Wether 2
ℵ0 or higher infinities exists depends on wether various set theories make sense, hence I'm undecided about the existence/truth of real numbers, the continuum or higher infinities, however as far as I've read about set theories, a belief in the lowest countable infinity can lead one to think certain set theories are sound and thus higher infinities must also exist, but at the same time, even for some particular set theory, you'll reach such a high infinity where you cannot even prove its existence in that particular set theory. A better way to talk about this would be
http://en.wikipedia.org/wiki/Ordinal_analysis (a particular infinite axiomatic system is true if specific ordinals exist, that is, if you can perform transfinite induction up to that ordinal to show that the axiomatic system is a theorem of some particular set theory).