Quote:
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Quote by: tman_ndsu08 Any statement is a belief unless you can prove it's true.
You can prove math statements true. |
Funny thing about that. If you knew what you were talking about you would know that there are mathematical proofs that say you cannot prove all "true" statements within a self consistent system based on the natural numbers.
http://en.wikipedia.org/wiki/G%F6del...teness_theorem Quote:
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Quote by: Gödel’s Theorem In any consistent formal system that is sufficiently strong to axiomatize the natural numbers – that is, sufficiently strong to define the operations that collectively define the natural numbers – one can construct a true statement that can neither be proved nor disproved within the system itself. |
So getting back to your 1 + 1 = 2 statement and your concept of "proof", it may not be as iron clad as you think.
Also if you try to take mathematics and make counting rigorous you discover what the mathematician/philosopher Bertrand Russell discovered and is known as Russell’s Paradox. This paradox is what lead to Gödel’s theorems.
And then there is Alan Turing. He is considered to be the founder of computer science. It is interesting to note that he was gay and was forced by the government of England to undergo treatment. During treatment he committed suicide. Anyway he approached the entire problem from computing. He was able to show that there is no solution to the Entscheidungsproblem, this is the challenge in symbolic logic to find a general algorithm which decides for given first-order statements whether they are universally valid or not.
So your idea of "proof" as some window to "truth" can be shown by the very "proof" that you seem to think is the key to the universe to be fundamentally flawed. And there are mathematical proofs to "prove" it.
Starboy