Sentence examples similar to theoretic validity from inspiring English sources

We accept also, of course, that (ii) for every calculus $C$ sound with respect to model-theoretic validity there is a model-theoretically valid formula that is not derivable in $C$.

For model-theoretic validity to be theoretically adequate, it might be held, it is enough if we have other reasons to think that it is extensionally adequate, i.e. that it coincides in extension with our preferred pretheoretic notion of logical truth.

But model-theoretic validity (or derivability) might be theoretically adequate in some way even if some possible meaning-assignments are not modeled straightforwardly by (actual) set-theoretic structures.

From all this it doesn't follow that (iii) there is a model-theoretically valid formula $F$ such that for every calculus $C$ sound for model-theoretic validity $F$ is not derivable in C. From (iii) and (i) it follows of course that there are model-theoretically valid formulae that are not obtainable by a priori or analytic reasoning.

For Prawitz's definition of proof-theoretic validity see Schroeder-Heister (2006).

A common reaction is to think that model-theoretic validity must be unsound with respect to logical truth.

Perhaps it could be argued that the situation with model-theoretic validity, or derivability, or both, is the same.

The first implication is the soundness of derivability; the second is the completeness of model-theoretic validity.

The second idea makes Martin-Löf's approach strongly differ from all other definitions of proof-theoretic validity.

Using another terminology, we can conclude that model-theoretic validity is complete with respect to logical truth.

We may call this result the incompleteness of second-order calculi with respect to model-theoretic validity.