CONVERSATIONAL IMPLICATURE (ADVANCED LEVEL MATERIAL)
The above example raises the question: can’t “only if’ statements always be regarded as disguised biconditionals? If a mother promises her son, for instance, that he will be allowed to watch television only if he finishes his homework, and then refuses to let him watch after he has finished on the grounds that she had said “only if,” he would be rightly indignant.
This is an example of what has been called, following the pioneering work of H.P. Grice, “conversational implicature.” In the context of a conversation, our statements commit us to more than what those statements imply in a narrow logical sense, i.e., if they are literally interpreted. This is illustrated by the following fictional dialogue between Mr. Bamard and a certain Ms. C. who storms into his office with her clothes on fire:She: Is there a fire extinguisher near here?
He: Yes, there is.
She: Well, could you tell me where it is?
He: Yes, I most certainly could!
l‰∙DO it!!
He: There’s a fire extinguisher on the eighth floor, next to the staircase.
Suppose Ms. C. now discovers (i) that the extinguisher on the eighth floor is out of order, (ii) that there is one much closer, near the staircase on the same floor, and (iii) that Mr. B. knew both these facts very well, having participated in a fire drill that very morning. We can safely infer that Ms. C. (if she has not been burnt to a crisp in the meantime) will be more than “rightly indignant” at Mr. B. Yet he has not answered any of her questions untruthfully—just in such a way as to undermine the normal pragmatic assumptions implicit in such an exchange: for instance, that the fire extinguisher she is interested in is the nearest one, that it is in working order, and so forth. Such assumptions are said to be conversational implicatures of Mr. B.’s statement (and indeed of Ms.
C.’s questions, which Mr. B. has infuriatingly answered without taking them into account).For our purposes here, we shall certainly have to be alive to conversational implicatures in evaluating natural arguments. This means that if they are relevant to the soundness of an inference, we will have to treat them as implicit premises that need to be made explicit. As is the case with all implicit premises, however, we only need to make them explicit if they are relevant to the soundness of an inference. Otherwise, if we are symbolizing a statement taken out of context, we will, wherever possible, symbolize the statement literally, without guessing at what the speaker intended to say. For instance, the statement
(4) I can MAKE it to my appointment if I RUSH.
will be interpreted as a simple conditional,
x even though the speaker probably intended it to be understood as a biconditional,
Likewise “only if’ statements will be interpreted as simple conditionals unless, as in example (3) above, that proves impossible. Statements like (3), i.e., ones having the form “p, but only if have to be interpreted as biconditionals
8.2.3