Gödel's incompleteness theorems are two theorems of mathematical logic that establish inherent limitations of all but the most trivial axiomatic systems capable of doing arithmetic.
Essentially, any system of axioms will have an inconsistency of essentially the form you described. But this only says that all models will be incomplete. Eliezer is questioning -- or perhaps reminding his readers -- the relationship between models of reality and reality itself.
In other words, the only thing you "know" is that you cannot model consistently a system where truth is non-existent. You don't know that, therefore, truth exists.
And more precisely, you are only pointing out a flaw in logical truth, and logic is merely one model.
http://en.m.wikipedia.org/wiki/Gödels_incompleteness_theorem...
Gödel's incompleteness theorems are two theorems of mathematical logic that establish inherent limitations of all but the most trivial axiomatic systems capable of doing arithmetic.
Essentially, any system of axioms will have an inconsistency of essentially the form you described. But this only says that all models will be incomplete. Eliezer is questioning -- or perhaps reminding his readers -- the relationship between models of reality and reality itself.
In other words, the only thing you "know" is that you cannot model consistently a system where truth is non-existent. You don't know that, therefore, truth exists.
And more precisely, you are only pointing out a flaw in logical truth, and logic is merely one model.