Alain Badiou. The Event of Truth. 2002 4/7

[Zadokor]

There are two incompleteness theorems. The second has to do with not being able to prove consistency from within or something...

[mahyarmohaghegh]

actually they are three

but it can become a subset of a single theory as incompleteness, if only two conditions were not met Godel wouldve tried to incorporate it within a more inclusive condition, the problem is that as badiuo points out actually that the exception becomes the signifier of the theory itself. like for example if something is not consistent it is then both complete and coherent. so by knowing the exception we can find the theory itself.

ps. im not trieing to be condescending.

[Krelianx]

I am wondering about his comments about Godel's incompleteness theorem. He mentions that a theory can never be proved to be non-contradictory within the system. But is this actually what Godel's theorem shows? I thought the first-order logic was provable as being CONSISTENT. The incompleteness theorems tells us only that within a theory one may construct a non-provable truth within the theory. But is this truth 'non-contradiction' as such in the mathematical? I'm sure i'm not getting this right.