Gödel's Incompleteness Theorem
Informally, Gödel's incompleteness theorem states that all consistent axiomatic formulations of number theory include undecidable propositions.
http://mathworld.wolfram.com/Goedels...ssTheorem.html
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In order to understand what this theorem is saying it will be important to look at some definitions...
Proposition - a statement that is either true or false.
Consistency - The absence of the ability to prove that both a statement and it's negative are both true. (Think of this as non-contradiction.)
Axiom - A proposition that is not proven to be true but is taken for granted as being true.
So given any set of axioms which aren't contradictions then other propositions truth values can be derived from those axioms. The theorem states that there will be propositions in the subject of number theory that cannot be determined from any set of non-contradictory axioms given.
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I'm not so interested in talking about number theory here. What I want to speak on is the principle behind this. The principle is that in some subjects not everything about that subject can be proven to be true. Well technically this is true of all subjects because all subjects begin with axioms with aren't proven. But in some subjects not everything can be proven about that subject no matter what axioms one starts at.
I think God is one such subject. We begin by accepting a few axioms: God exists, God doesn't lie, God gave mankind the bible, and maybe a few others. But no matter which axioms we choose there will always be things that are true about God that we cannot know whether are true or not. I find this fascinating.
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