A Study of the Relations between Grammar and Logical Form*
Modus ponens is the principle that P and if P, then Q imply Q. I want to argue that modus ponens is not a principle of logic.
I agree that P and i/P, then Q do imply Q. This is so, at any rate, ifP and Q are indicative statements, with certain exceptions that I will mention. Nevertheless, I do not agree that P and i/P, then Q logically imply Q.
I want to say that an implication is a logical implication if it holds solely by virtue of logical form. When I say that P and i/P, then Q do not logically imply Q, it is because of my view about the logical form of the conditional i/P, then Q.
Compare if P, then Q with that P implies Q. P and that P implies that Q imply Q. But I do not want to say that this is a logical implication, since I hold that it depends not only on logical form but also on the meaning of the word implies. If, for example, the word suggests replaces the word implies, the implication does not always hold. P and that P suggests that Q can both be true even though Q is not true. Therefore, even though P and that P implies that Q always imply Q, I want to say that the implication does not hold solely by virtue of logical form and is, consequently, not a logical implication.
In saying this, I am assuming that the word implies is not a logical particle. For consider this. P and Q logically implies Q. This implication depends only on logical form. But it obviously depends on the meaning of the word and. If, for example, the word or were to replace the word and, the corresponding implication would not always hold. P or Q can be true even though Q is not true. But I do not take this to show that the implication from P and Q to Q is not a logical implication. For I assume that and is a logical particle. If I say that an implication holds solely by virtue of logical form, I mean that it does not depend on the meanings of any terms other than logical particles.
I want to say that the difference between logical particles and nonlogical terms is this: logical particles are members of small closed classes whereas