7.7. Soundness & completeness

7.7.0. Overview

While the positive use of derivations with generalizations is not too unlike what we had seen in previous chapters, their negative use involves some new ideas, and the change affects arguments for the adequacy of the system of derivations.

7.7.1. Aspects of adequacy
The system of derivations for generalizations may give no answer at all regarding validity, and as result, an argument for its completeness must be based on ideas a little different from those used in earlier chapters.

7.7.2. Soundness
New vocabulary may appear in the course of derivation, and the idea of a sound rule must be modified to accommodate this.

7.7.3. Thoroughness
The central new feature of derivations involving generalizations is that we need never run out of rules to apply, so we must make an effort to explore all options since we are never forced to do so.

7.7.4. Effectuality
To argue that any gap that cannot be closed has a counterexample lurking in it, we must take account of the possibility that a generalization will be exploited infinitely often in the course of a never-ending derivation.