Patrick Suppes gives a working definition of sentential interpretation, based on a sentence maintaining its form. By working definition, I mean an incomplete definition that is needed for someone to understand something else. Here is his precise working definition:
A sentence P is a sentential interpretation of a sentence Q if and only if P can be obtained from Q by replacing the component sentences of Q by other (not necessarily distinct) sentences.
He then goes on to state a sufficient but not necessary condition for one sentence to be a logical consequence of another as follows:
(I) Q logically follows from P if every sentential interpretation of the implication P → Q is true.
Now, I understand what is meant by the working definition of sentential interpretation, but I do not understand the second part of (I) - how every sentential interpretation of a sentence, such as P → Q, can always be true. May someone please help provide me with examples of sentences P and Q such that every sentential interpretation of the sentence P → Q is true? Would it have to be the case that either (1) every interpretation of P can be true or false, while every interpretation of Q is true (because Q is a tautology); or (2) every interpretation of P is false (because P is a contradiction), while every interpretation of Q can either be true of false?