I’ve always considered Grice’s theory of conversational implicature to be one of the most beautiful theories around. But nowhere is beauty so tightly yoked to truth as in the sciences, where beauty, in the form of simplicity, will decide the truth of two otherwise equally powerful theories. (It’s kind of remarkable when you think about it — truth and simplicity seem not only distinct, but unrelated, unlike say, truth and accuracy or consistency. A complex theory will cause more complexity in its relation to other theories, but if it’s still true, why should complexity ever matter? Is preference for simplicity just a bias?) Truth seems to be a necessary condition for the beauty of a theory in science, so if Grice’s theory isn’t true, its beauty all is lost. The application of conversational co-operation gets messy at and, impugning its truth. I’ve got an idea on how to clean up the mess and restore the symmetry of the structure.
Grice’s analysis of “and” goes like this:
Sometimes “and” is interpreted as simple logical conjunction
1. I brought cheese and bread and wine.
The order of conjuncts doesn’t change the meaning: I brought bread and cheese and wine; wine and cheese and bread; bread and wine and cheese; wine and bread and cheese; it’s all the same. This use of and is symmetric, exactly like the logical conjunction &: A&B<=>B&A
But sometimes and carries the sense of temporal order, “and then”
2. I took off my boots and climbed into bed.
(I think I got this example from Ed Bendix some years ago)
This conjunction is not symmetric: taking off your boots and then climbing into bed is not the same as climbing into bed and then taking off your boots, and the proof of the difference, you might say, comes out in the wash.
The difference in meaning, according to Grice, arises from the assumption that the speaker would not withhold relevant information or present it in a confusing form. If the order of events matters, the order of presentation will follow the order events, unless otherwise specifically indicated. So if I said
I climbed into bed and took off my boots
you’d be justified in surmising that I’d come home very late and very drunk.
The theory of conversational implicature avoids the undesirable circumstance that there might actually be two homonymic “and”s in English, one meaning “&” and the other meaning “and then.”
A problem for Grice was observed long ago by Bar-Lev and Palacas (1980, “Semantic command over pragmatic priority,” Lingua 51). They noted this wonderful minimal pair:
3. I stayed home. I got sick.
4. I stayed home and got sick.
If Grice is right, (3) should mean
3′. I stayed home and then got sick.
But it doesn’t. It means
3″. I got sick and therefore stayed home.
Now unless we are willing to say that the sentential boundary is a morpheme with meaning, we are compelled to drop Grice. Worse still, even though (3) means (3″), the sense of “and then” returns immediately we add “and” between the sentences. (4) means
4″. I stayed home and then I got sick.
even though that’s semantically unexpected. So it’s not about semantic bias, this violation of Grice’s principle. It’s a very real problem that Bar-Lev and Palacas pointed out.
So what’s with “and”?
Here’s my suggestion.
a. In order to use “and” you’ve got to be introducing something new. Think of Angelika Kratzer’s lumps of thought: you’d never say “I painted a portrait and my sister” if you’d only painted one portrait and it was of your sister. Information is structured in clumps of truths that the logical connectives don’t respect. Yes, a portrait was painted and a sister was painted, but if these two things were accomplished in the same act of painting a portrait of one’s sister, then they are in some sense the same fact, though two truths. Now notice the difference between :
“I painted a portrait. I painted my sister.”
Could be the same event. Not so easy to get the same-event interpretation from
“I painted a portrait and I painted my sister.”
The and implies a distinct, newly introduced fact not lumpable with the antecedent event.
b. Causal relations are internal to an event.
Put (a) and (b) together and you have an explanation for (3) and (4). I have a good deal more to say about this, but it’s really nice out, and I’ve been in all day.
More about and: a contextual, situational connective?
A few examples:
1. Pat washed her sweater and ruined it
2. Pat ruined her sweater and washed it.
3. Pat ruined her sweater. She washed it.
(1) means, I think, that by washing it Pat ruined it. The sentence allows and because washing doesn’t entail ruining; ruining is a consequence, not a cause.
(2) means that Pat ruined the sweater and then washed it presumably in an attempt to fix it, the outcome of which attempt the sentence doesn’t reveal. It can’t be read, as (3) can, to mean: Pat ruined her sweater by washing it.
Now, (3) can be read also as: she ruined her sweater then washed it. That’s not surprising. What’s surprising is that (3) has the grammatical-consequent-as-semantic-antecedent reading as well, while (2) doesn’t. So the explanation above has to be modified a bit:
a’) consequences are external to an event — they are new facts justifying and
a”) causes are internal to an event — they lump with their consequence and don’t justify and
Bar-Lev and Palacas use another example that goes something like this:
Napoleon took thousands of prisoners and defeated the army. (=and then)
Napoleon defeated the army and took thousands of prisoners (=and then)
Napoleon took thousands of prisoners. He defeated the army. (=backwards cause)
So even when the real-world knowledge bias leans in favor of backward cause, and prevents it.
Here’s another strong example against real-world experiential bias. In answer to the question, “What did you do today?”:
I went to the store and I went out. (two unrelated round-trip forays outside, the latter possibly to a bar or club)
I went out and I went to the store. (two related events: one followed by a consequence: and=and then)
I went out. I went to the store. (One round-trip foray, the consequent explaining the antecedent)
I went to the store. I went out. (Two events: the consequent can’t explain the antecedent, so they are interpreted as two distinct events)
Given a context in which going out explains going to the store, this last sentence pair should reduce to one event, if this analysis of and is right. I think it does: if the question is, “Did you or did you not go out today?” the answer: “I went to the store. I went out,” indicates one event, the antecedent indicating the specific event and the consequent clause explaining how the antecedent is an answer to the question.
This last example also shows that it’s not just cause that is internal to an event, but anything that explains the antecedently described event. Explanation seems the informationally relevant function from utterance to acceptability. Explanations are internal to a fact. The next step in this investigation would be to figure out what kinds of information qualify as explanations / internal to the fact, and what kinds as additional, new information external to the fact.
And or &: ideas for a contextual logic
On one view of this analysis, it looks like Grice was partly right about and. There’s just one and. But he was wrong to equate English and with logical conjunction &. The one and in English carries a conventional implicature just as but does, but where the conventional implicature of but requires the denial of some association of the antecedent clause, the conventional implicature of and requires that the consequent add some information external to the antecedent clause. and always means something like and also, carrying the conventional implicature that what follows and is additional information external to what preceded and.
There’s an alternative to explore for fun. Suppose Grice was completely right that and means the logical connective &. It’s just that the logical connective & is not the familiar one. It’s truth values are dependent on the relationship of consequent with antecedent. I mean, why couldn’t we have a causal relations-based logic? It would be very different from familiar freshman logic, but it might be a lot of fun and useful too. This connective (I’ll use “+” to avoid confusion with traditional conjunction “&”) would not be symmetric:
a+b ≠ b+a
and there could be two ways of dealing with the truth tables:
if a and b are true and a causes b then a+b =t
if a and b are true and b causes a then a+b=f
if a and b are true, and a and b denote distinct facts that are causally unrelated, then a+b=t,
The last two clauses cover the “I painted a painting and painted a portrait” — two conjuncts denoting the same fact. That sentence will be false if denoting one fact/event, true if denoting two causally unrelated distinct facts/events (assuming that there is no causal relation in this sentence in either direction).
(Now, I’ve forgot the second way I was going to do this. Well, it’ll come to me.)
Ah, yes. [Two years later.] How about defining what is included in an event or using the connective to do that work?
a+b entails that b is not included in a
where “included” means either ‘denoting the same event’ or ‘causing’.
It may seem odd to contextualize truth values so that they depend on denotations and situational relations, but truth values are themselves semantic and denotational. We’re just shoving the contextualization deeper in the muddy murk. Why not have logical connectives that reflect the language or reflect thought?
One application would be to lumps of thought. The whole notion of lumps is model-dependent / context-dependent. Here’s a context-dependent (model-dependent) connective that reflects the lumping of reality.
I can think of some obvious objections to a context-dependent logic. It’s not really truth-functional in its syntax. The falsehood, for example, of a+b, does not entail either the falsehood of a or the falsehood of b. a+b could be false simply because b is included in a. But something like this is true of other familiar logical connectives. For example, the falsehood of avb does not entail the falsehood of a or the falsehood of b. It might be that b is true and a false, or a true and b false. The difference between + and v is that the truth value of v depends on the truth values of the statements it joins, while the value of + depends also on event/fact inclusion.
How are the connectives syntactically interdefined? How can deductions be proved syntactically? What would the laws of deduction look like?