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 Originally Posted by wufwugy
Related question: is there a way to know if something is true based exclusively on the math? Or is it that math can operate within its own systems, so even a mathematical model that explains every known thing perfectly may still be false?
I'll wait for MMMs answer as far as the physics goes, but as an interesting tangent:
http://en.wikipedia.org/wiki/G%C3%B6...eness_theorems
http://en.wikipedia.org/wiki/Entscheidungsproblem
One of the themes of early 20th century mathematics was the attempt to prove that our systems of mathematics were internally consistent - that is to say, if we had a set of axioms and a system such as the natural numbers, that we could, in theory at least, prove that every true statement in that system was true, or that we could, in theory at least, construct a hypothetical "maths machine" that could take a statement and decide it's truth or falseness. In many ways, this parrallels newtonian physics - the idea that even if only in theory, we could predict/understand all the physical phenomena in the universe.
Both physics and maths turned out to be more subtle than was believed, physics with the discovery of relativity and quantum theories, and mathematics with Godel/Turing and the work done on computability/decidability and the discovery that, to state Godels theorem in the plainest way, if a mathematical system is internally consistent then it must not be complete (there must be things we can't state or prove within it), and that quite aside from that a system can't be used to prove it's own consistency.
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