Does infinity actually exist, as something more than just a concept? If the universe is a closed, finite system (which is currently unknown) then it cannot. I believe mathematical concepts are not real and valid unless they can be expressed in a physical system. So, if we cannot have an infinite number of any 'thing,' then infinity is an invalid concept. There are no 'Platonic ideal forms.' Just because we can imagine something does not grant existence to that thing. I can imagine lots of things, like unicorns and flying pigs, but they aren't real.
So, if it turns out that we live in a finite universe, and infinity doesn't exist, then time is finite too. Time will eventually end and existence will cease, in a 'Big Crunch' or similar event. Would this provide a solution to the Halting Problem then? If there is an end of time, then no program or algorithm will run forever, so for all X, HALT(X, X) = TRUE.
I should probably file this under Ramblings...
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2 comments:
Apparently you're a materialist?
Yes, if by 'materialist' you mean one who holds that the only things that can be truly proven to exist are physical phenomena.
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