Jim Choate wrote: > Complete means that we can take any and all -legal- strings within that > formalism and assign them -one of only two- truth values; True v False.
Getting much closer. "Complete" means we can, within the formalism, _prove_ that all universally valid statements within the formalism are true. That's it. Little more to say. Except that at the time (1930)(in his doctoral thesis, later "The completeness of the axioms of the functional calculus of logic", in which he proved the completeness of FOL) Godel only proved that such proofs exist, and it was much later (1965?-ish) that a constructive procedure for proof generation was published... though he did also prove (for FOL, and the "usual suspect" logics, and some other logics) that that is the only way a logic _could_ be complete - and that, in those cases, the earlier disputed meanings of "complete" are identical/the differences are irrelevant; - and that his definition (above) is sufficient, eg (but not ie) that proof of negation is not required. -- Peter Fairbrother
