Epistemic Operators
FRED I. DRETSKE · Cambridge University Press eBooks · 2000
Suppose Q is a necessary consequence of P . Given only this much, it is, of course, quite trivial that if it is true that P , then it must also be true that Q. If it is a fact that P , then it must also be a fact that Q. If it is necessary that P , then it is necessary that Q; and if it is possible that P , then it must also be possible that Q. I have just mentioned four prefixes: “it is true that,” “it is a fact that,” “it is necessary that,” and “it is possible that.” In this essay I shall refer to such affixes as sentential operators or simply operators ; when affixed to a sentence or statement, they operate on it to generate another sentence or statement. The distinctive thing about the four operators I have just mentioned is that, if Q is a necessary consequence of P , then the statement we get by operating on Q with one of these four operators is a necessary consequence of the statement we get by operating on P with the same operator. This may be put more succinctly if we let “O” stand for the operator in question and “O( P )” for the statement we get by affixing the operator “O” to the statement “ P .” We can now say that the preceding four operators share the following property: if P entails Q, then O( P ) entails O(Q).