>>59
The problem with this is that you won't be able to form any theories/metatheories about why you have senses at all, or why physics (or just whatever makes your senses be this or that) behaves the way it does and so on.
Why should we form useless theories, which are completely unrelated to reality?
That inductive proposition talks about abstract systems, in the real-world, you will have a local limit imposed by physics.
Why do we need "abstract systems" or any other religion?
If for example you deduced by induction that reality corresponds to some specific mathematical structure.
I've a better idea! Lets find correspondency to some physicaly sensible structure, and throw the mathematics aways.
Why only that structure? Let's say its information limit is some constant k. Why not k-1 or k+1? Occam's Razor suggests that the simplest theory is that all possibilities are realizied, thus also the k+1 world. A belief in only world k is a stronger belief than a belief in all finite worlds 0,1,...,k,k+1,...
Does Occam's Razor suggests it's own validity. and how do define the "simples theory". For a religious man/woman the term "God" maybe simple (it's much "simpler" than your phyisical theories, Einstein).
It's a stronger belief just like the belief that the sun doesn't exist as long as you don't look at it(such as at night).
It exists in my memory (or machine's memoty, if we talk about AI).
Math itself tries to be as general as possible
You found the main problem with math. There is no such thing as "general" or "all" or "everything", without some kind of bounded universe, like cons-pair list, one passes to Lisp's `all` and "any" high-order function.
in that it can also be used by physics
Can you imagine a “physical process” whose outcome could depend on whether there’s a set larger than the set of integers but smaller than the set of real numbers? If so, what would it look like? -- Scott Aaronson
There is no reason why any finite natural number should be the limit, hence why you get a countable infinity of natural numbers.
There is no reason why physical world should be the limit, hence why you get a heaven with almighty God.
You could say that all this is abstract non-sense
Mathematicians themself call it nonsense:
http://en.wikipedia.org/wiki/Abstract_nonsense
There is good reason for that - it cant be justified by senses.
Consider this then: in the far future, you're very old and have developed some incurable brain tumor, the doctor offers you to get a digital brain replacement (be it gradual or instant, this is a thought experiment, so pick whatever suits you best), do you say yes or no? You have to bet on a theory because your future experiences depend on it, yet without having worked out all the possibilities you cannot make a choice, but you don't have the luxury of not making a choice - a default no also has costs.
How that is related to the question of existence? In both, "yes" and "no" cases, it wont contradict my point of view. Doctor just makes a replacement copy, like you copy audio CDs. No magic or paradoxes.