Do scientists from differing disciplines have the same goals in addressing the same facts? Linguists attempt to accommodate all the natural language intuitions in their theoretical frameworks. That may lead them to extralogical means. Logicians have often taken on one or another natural language intuition and attempt to augment the logic to accommodate that intuition. In both cases there’s a question of purview: why not accommodate all the intuitions through the logical system, or how much of logic should accommodate the intuitions?
This became the battle at a workshop on imperatives at NYU today. Craige Roberts incorporated pragmatics into her analysis of imperatives to include a wide variety of natural language intuitions, while Kit Fine and Peter Vranas developed new logics to deal with some, but not all, intuitions. They both seemed to ignore that traditional logics are not just inadequate for linguistic intuitions, but also inadequate to basic facts about reality. If we assume that development of logics is still in its infancy, the attempt to accommodate each outstanding challenge is a step towards a more inclusive, flexible and useful logic.
Think of Kratzer’s lumps of thought. She observed that a single event can be represented in multiple descriptions that in sentential logic would imply multiple events, or if not implied, then at least failed to imply that that the descriptions were of the same event: if Sally made a painting that was a portrait depicting her sister, sentential logic would imply three events (or at least not imply one event) “Sally made a painting and painted a portrait and painted a picture of her sister.” That these three descriptions are of one event is not a linguistic intuition, it’s a fact of what Sally did. To formulate a logic that can identify these conjuncts as three descriptions of one event would be progress for logic, not for linguistics.
So it seems to me, logic is justified in picking its challenges independent of the needs of linguistics. The real test would be between AI and neurolinguistics — how are imperatives represented in the brain, how can they best be represented in a robotic program? I didn’t see anything from the linguists giving a brain representation argument the way, say, Chomsky did with syntax. There doesn’t seem to be an experimental program to follow, as there was with generative syntax. The logicians, on the other hand, were always mindful of the algorithmic value of their logic, but that’s why they are logicians.
There was also an interesting exchange on whether the background conditions of an imperative are factual or relative to the speaker or addressee. So “if it’s raining, take an umbrella” can be evaluated on whether it’s actually raining or whether the speaker thinks it’s raining. Does it matter whether it’s actually raining for the force of the imperative to hold? Roberts, the linguist, wants it to be contextual information of the speaker; Vranas wants to take this as factual so that the entailments can be validated within his three-valued logic. At first they seem to be different views — why should it matter whether it’s actually raining, since the imperative is the speaker’s insistence. But if there are only beliefs, and no facts, both views are the same. The force of the imperative, shared by the speaker’s intention and the addressee’s understanding of it, will shift if she comes to believe that it’s not actually raining.
The two talked past each other for about an hour. The problem is a really tough one. The entailments of speakers’ assertions are trivial. Sally said “I’m lying” just in case she said it. So as an assertion, it’s true. But the content, indexed to a speaker, is a paradox. It’s worth remembering that three-valued logic began with an attempt to incorporate the epistemic into the logic. The result is a loss of a distinction between the factual and the epistemic. But there’s an underlying problem: no one knows what is factual; all we know are our beliefs. Deductions from our beliefs will always be trivial; deductions from facts will require extralogical overlays for the epistemic. I worked out the problem a few years back here. I’ve complained that trivalence flattens modality here.