God and Stone

Logical theory is an interesting field in Mathematics. I would like to say this is more related to philosophy of science than mathematics. The two words often debate in this field is the consistency and completeness.

Let us consider the theory about God. A theory basically consists of propositions.
Let us take the propositions relating God and stone.

1. God can crate stone of any size
2. God can lift stone of any size
3. God can destroy stone of any size
   

Now let us try to answer the following questions.

• Can God create stone of any size, say infinitely big and heavy?

The answer is yes, he can. Here comes the tricky question.

• Can God create a stone, he can't lift?

If you say No, then he cant create every stone(I mean the one he can't lift)
If you say Yes, then he cant lift every stone in the world(violation of proposition no:2)

One can ask similar question for proposition no:3 also.

If you can answer the question(doesn't matter either yes or no), the consistency of the theory is destroyed. If you can't answer the question , then the theory appears to be incomplete.

This is true for every theory in the scientific world. No theory in this world is complete and consistent. This was proved by a Austrian logician Kurt Gödel in 1931.

These theories are hard to understand.
Till this point, what ever I described is just to demonstrate the incompleteness theorem.
Today morning I got a funny idea, that I can use the incompleteness theorem to prove the existence of complete theorem.

If a formal theory exists to prove that no formal theory is consistent and complete, that theory it self is inconsistent or incomplete(again self referential :)). So it is possible to make valid arguments for the existence of complete and consistent theory from the incompleteness theory itself. I am just laughing about my arguments. Sometimes I feel this is great argument and sometimes I feel there is a flaw in it.

Anyway I don't mind what ever is the outcome. It's just a fun to think about all these stuffs