Notes, Quotes, Homework for Methods of Logic, 1.6

Nice quotations/passages:

"'Validty' is not to be thought of as a term of praise. When a schema is valid, any statement whose form that schemata depicts is bound to be, in some sense, trivial. It will be trivial in the sense that it conveys no real information regarding the subject matter whereof its component clauses speak" (42).

"Valid schemata are important not as an end, but as a means" (42).

Important note:

Substitution of schemata for letters preserves validity!
Substitution of schemata for letters preserves inconsistency!
Substitution of schemata for letters DOES NOT preserve consistency!

Bit of homework:

3. Yes. Conjunction is a schema that is merely consistent, not valid. The schema 'pq' then, is consistent. But if you conjunct two distinct valid schemata, the result is a valid schema; if you conjunct two distinct inconsistent schemata, the result is an inconsistent schema.
For example:
(pV-p)(qV-q) is valid, but is simply a substitution of schemata into some consistent schema.
(p↔-p)(q↔-q) is inconsistent, but is simply a substitution of schemata into some consistent schema.