Full Idea
In first-order logic a set of sentences is 'consistent' iff there is an interpretation (or structure) in which the set of sentences is true. ..For Frege, though, a set of sentences is consistent if it is not possible to deduce a contradiction from it.
Gist of Idea
Sentences are consistent if they can all be true; for Frege it is that no contradiction can be deduced
Source
Charles Chihara (A Structural Account of Mathematics [2004], 02.1)
Book Reference
Chihara,Charles: 'A Structural Account of Mathematics' [OUP 2004], p.33
A Reaction
The first approach seems positive, the second negative. Frege seems to have a higher standard, which is appealing, but the first one seems intuitively right. There is a possible world where this could work.