Tuesday, November 21, 2006

Non-truth-functional Connectives

Lately I’ve been considering a linguistic phenomenon which leads me to believe that, in addition to the familiar concept of truth, there is a more general concept which we can call satisfaction, truth being but one kind of satisfaction. Consider for a moment (1)

(1) Wash your clothes and put your dishes in the sink.

Normally, philosophers and logicians think of “and” as being a truth functional connective that conjoins propositions or declarative sentences, the conjunction being true if both conjuncts are true, and false if either is false. Yet the above, which seems (to me, at least) to be an obvious case of conjunction, has no truth conditions at all, for the statements being conjoined are commands, or imperatives, the term I will use. Though “and” cannot be a truth function as it occurs in (1), we can think of it as something highly similar: A satisfaction function. We can say that a proposition (or declarative sentence) is satisfied if and only if it is true, and an imperative is satisfied if and only if it is obeyed. (Extending the analogy, we might say that a yes or no question is satisfied if and only if its answer is yes, and that a rule is satisfied if and only if it is followed correctly). (1), though not true, is satisfied if and only if both conjuncts are satisfied, which seems intuitively correct: It has been obeyed if and only if its intended recipient has both washed their clothes and put their dishes in the sink. The similarity between truth and obediance can be confirmed by the fact that an analogue of the liar paradox can be constructed for imperatives. Thus, (2)

(2) Do not obey this imperative.

seems to be obeyed if and only if it is not. That such a similar paradox can be generated for imperatives counts as strong evidence of the affinity of truth and obedience as two different kinds of satisfaction. Statements of mixed kind are also possible:

(3) If John calls, tell him I’m at the video store.

(3) is satisfied if the antecedent is true an the consequent is obeyed. As a whole, the conditional is neither true nor obeyed. It is, in my terminology, purely satisfied, where a statement S is purely satisfied if and only if it is satisfied without being satisfied in some more specific way, that is, if it is satisfied without being true, or obeyed, or correctly answered… . In this it differs from (1), which is obeyed as a whole: if either conjunct is disobeyed, the conjunction is disobeyed. If the antecedent of (3) is true and the consequent is disobeyed, then it is unsatisfied. If the antecedent is false, the conditional is satisfied[1], and the consequent is not so much disobeyed as void. Being disobeyed, then, is more like negative satisfaction than a mere lack of satisfaction.

[1] If we held it to be unsatisfied if the antecedent is false, then the conditional would be satisfied if and only if the antecedent is true and the consequent is obeyed, making it a mixed conjunction—and a conditional “If A , then B” which turns out to be equivalent to “A and B” is a very poor conditional in my eyes—properly speaking, it isn’t a conditional at all.


sean hermanson said...

Hi - not sure if you've looked at Austin, but his theory of Speech Acts might be relevant. Lycan's introduction to the philosophy of language also has a very useful discussion of Speech Act theory.

Perhaps imperatives like: "Wash your clothes and put your dishes in the sink" do contain propositional content after all (say, something along the lines of "it is true that you ought to do those things"). Crucially, this is compatible with saying that imperatives also have an "illocutionary force" - there is in addition a social act (an imperative) being performed that is distinct from the declarative content.

So, the connective "and" is truth functional here, as if it is true that you ought to wash your clothes and true that you ought to put your dishes in the sink, then of course it is true that you ought to wash your clothers and put your dishes in the sink.

In short, there is a long tradition in Speech Act theory which maintains that most utterances have both a performative aspect and propositional content.

Quirinius_Quine said...

Hi Sean,

Thanks for bringing up Austin, Lycan and Speech Act theory. I've read very little on the subject--just the first few chapters of Austin's "How to do Things With Words", and a little bit of the article on Speech Acts in the online Stanford Encyclopedia of Philosophy-- and I never thought to connect them to this before.

Anonymous said...

Isn't the case that imperatives have no truth-value?

Jason Zarri said...


Right, that's why I said that imperatives can be *satisfied*, not that they can be *true*.