[dwohnitmok]

Godel's completeness theorem is not in opposition to his incompleteness theorems.

Godel's incompleteness theorems and completeness theorem can hold at the same time. They talk about two separate notions of completeness (the former about incompleteness in the sense of logical independence and the latter in the sense of the correspondence between semantics and syntax). Indeed Godel's incompleteness theorem is usually presented in the context of first-order Peano arithmetic.

This is again why I don't like talking about "truth." It is not completely inaccurate to say Godel's completeness theorem says "a statement is true if and only if it's provable." It is also not completely inaccurate to say Godel's incompleteness theorems say "some true statements are not provable." But the vagaries and philosophical baggage behind the two statements mean you have to tread _very_ carefully and without _extremely_ careful qualifications you can start making philosophical statements that are extrapolations of those theorems rather than the theorems themselves. That's why I strongly believe that it's much much much more productive to talk about incompleteness and consistency rather than truth.

[jfarmer]

You're right! I confused the deductive system/language w/ the theory. Oops.

Something like Presburger Arithmetic would've been a proper example.