The mind.
An unusually sequenced set of events forced me to realize that I have no integrity. So if an alien child that poses to be God comes down tomorrow and asks me, "what holds you together?", I 'll have no answer.
The mind is a funny thing. It makes you judge yourself- but when you realize that you are actually judging your thoughts, a sudden bolt of lightening in your head tells you that the mind, in fact, is judging itself.
How can the mind judge itself? On what presumptions will it base it's judgements? When a system has to declare it's own liability, how does one know whether it's definition of liability is flawed or not? When you create a system and you ask it a question about itself, you can easily manipulate it into proving that logic is incomplete.
For example, (the following is taken from this site):
" The proof of Godel's Incompleteness Theorem is so simple, and so sneaky, that it is almost embarassing to relate. His basic procedure is as follows:
1. Someone introduces Godel to a UTM, a machine that is supposed to be a Universal Truth Machine, capable of correctly answering any question at all.
2. Godel asks for the program and the circuit design of the UTM. The program may be complicated, but it can only be finitely long. Call the program P(UTM) for Program of the Universal Truth Machine.
3. Smiling a little, Godel writes out the following sentence: "The machine constructed on the basis of the program P(UTM) will never say that this sentence is true." Call this sentence G for Godel. Note that G is equivalent to: "UTM will never say G is true."
4. Now Godel laughs his high laugh and asks UTM whether G is true or not.
5. If UTM says G is true, then "UTM will never say G is true" is false. If "UTM will never say G is true" is false, then G is false (since G = "UTM will never say G is true"). So if UTM says G is true, then G is in fact false, and UTM has made a false statement. So UTM will never say that G is true, since UTM makes only true statements.
6. We have established that UTM will never say G is true. So "UTM will never say G is true" is in fact a true statement. So G is true (since G = "UTM will never say G is true").
7. "I know a truth that UTM can never utter," Godel says. "I know that G is true. UTM is not truly universal."
Think about it - it grows on you ...
With his great mathematical and logical genius, Godel was able to find a way (for any given P(UTM)) actually to write down a complicated polynomial equation that has a solution if and only if G is true. So G is not at all some vague or non-mathematical sentence. G is a specific mathematical problem that we know the answer to, even though UTM does not! So UTM does not, and cannot, embody a best and final theory of mathematics ...
Although this theorem can be stated and proved in a rigorously mathematical way, what it seems to say is that rational thought can never penetrate to the final ultimate truth ... But, paradoxically, to understand Godel's proof is to find a sort of liberation. For many logic students, the final breakthrough to full understanding of the Incompleteness Theorem is practically a conversion experience. This is partly a by-product of the potent mystique Godel's name carries. But, more profoundly, to understand the essentially labyrinthine nature of the castle is, somehow, to be free of it." (William Denton, http://www.miskatonic.org/godel.html)