(Original post by **icy**)

hey all

i've got a tok essay to do, and i need some ideas...

can we know something that has not been proven true?

From Gödel Escher Bash, an Eternal Golden Braid , by Hofstadter:

Tortoise: So what you are saying is that if two things are equal to the same they are equal to each other?

Achilles: Yes, I just wrote it down in my notebook:

A Things which are equal to the same are equal to each other

Tortoise: And we both agree that the two sides of a specific triangle may be equal to teh same.

Achilles: I have called that statement B, so we have:

A: Things which are equal to the same are equal to each other

B: The two sides of this triangle are equal to the same

Achilles: And so we may deduce:

A: Things which are equal to the same are equal to each other

B: The two sides of this triangle are equal to the same

Z: The two sides of this triangle are equal to each other

Tortoise: But might I not agree to statement A and B but still not to statement Z ?

Achilles: That would be remarkably foolish, but it is of course possible. Therefore I will addd a third statement which I should ask you to accept.

Tortois: Go ahead my dear Achilles.

Achilles:

A: Things which are equal to the same are equal to each other

B: The two sides of this triangle are equal to the same

C: If both statement A and B is correct, then statement Z is correct.

Z: The two sides of this triangle are equal to each other

Tortoise: But might I not accept A, B and C , but STILL not accept Z ?

Achilles: I suppose you could do so, even though it may be exceptionally foolish of you , but yet.....

My ( Jonatan's )conclusion: It is not possible to prove anything , regardless of the number of accepted postulates and axioms. Thus Mathematics is not absolutely proven. The proofs in mathematics seem obvious, but yet they are, just as any other proofs, only arguments which you may accept or not.