Re: Proof of Completeness of Algebraic Properties of Relational Lattice

> > Or more accurately/practically, how does one verify that a proof is correct?
>
> Absolute knowledge of truth is not part of the human condition.

So, are you saying we have no reference to judge by, whether a proof is correct?

> However, we have many things we can do to increase our confidence of a particular idea. A proof is a good first step. The more formal the proof, the better our confidence. (My proof here is not particularly formal.) Also good is publishing a proof so that it's in front of many eyes; the more people that see it, the more chances there are that flaws will be spotted. A single flaw is enough to invalidate a proof.

But what good is the definition of define, if it uses define to define it? Proofs that God exist are flaw-less (according to those providing the proof). The bible is published for many eyes and many can't find a flaw in it.

> Other good things to do: publication in a peer-reviewed journal. Also, use of a proof assistant, such as Coq, is an excellent, formal way of reinforcing proofs. But then we can ask, how do we verify the proof assistant is sound? This leads to infinite regress, which is part of why absolute knowledge of truth is impossible.

Are they really proofs or just self-consistent, self-supporting, self-confirming systems? Received on Sun May 21 2006 - 18:57:15 CDT