I’m going to do something here that I very rarely did as a graduate student in philosophy: Present the beginnings of a positive theory. This, I think, was what I had seen my dissertation as leading up to, although it never got there and I’ve only recently thought of a completely choate way of expressing the idea.
Before I start presenting the positive, though, I have to indulge myself and do a little bit of teardown. The idea I want to tear down is one that equates the content of a sentence with its intension. The positive theory I’ll propose–and I’m only going to propose it in outline here; I think this may be a fairly major project to complete–is a replacement for this theory of content.
Before we start, I want to be clear on the terms involved. First, there’s “intension,” the technical term. Note that this is not a typo for “intention,” but rather an entirely different word. An intension is a function from possible worlds (however you define possible worlds) to something: When you’re talking about sentences; the something is generally taken to be truth values. So, for example, the intension of “Snow is white” is a function that expresses whether “Snow is white” is true or not in each possible world–that is, whether, in each possible world, snow is white.
Then, there’s “content,” which is really not a technical term, and that’s the problem. As a philosopher, you’re of course free to define any term of art any way you want, but once you get into words from ordinary language, you’d better be careful. I’m not actually going to attempt, for now, a fully fleshed-out definition of content, but I at least think there’s a statement we can certainly make about it that limits the possible definitions: The content of a sentence (the term for this is a proposition) is what you grasp when you understand the meaning of a sentence.
At first glance, the claim that the content of a sentence is its intension seems pretty reasonable. After all, what does it mean to understand the sentence “Snow is white?” Well, a decent first cut seems to be that, when presented with a particular fully-fleshed-out counterfactual situation (AKA a possible world), you could tell whether snow was white in that situation or not.
But there’s a problem with this picture of content. It’s not an unknown problem, but I don’t think it’s a problem that gets taken nearly seriously enough. The problem is this: Not all sentences with the same intension have the same content.
Consider, for example, the following two sentences:
- 1=1
- For any positive integers a, b, and c, and any integer n > 2, an + bn ≠ cn
Now, these two sentences clearly do not have the same content. What you grasp when you understand the sentence 1=1 is certainly not what you grasp when you understand the statement of Fermat’s Last Theorem. However, because both statements are mathematical truths, they’re both true in every possible world, so they share an intension. So content cannot be intension.
Another way of putting this is this: Not all stories with plot holes are different ways of telling the same story, despite the fact that they’re all true in exactly the same possible worlds (namely, none of them). With a little bit of suspension of disbelief or a brief lapse of logic, we can clearly understand these stories, and understand them as saying different things, despite the fact that there’s no way to create a fully fleshed-out countefactual situation that would make them true.
In fact, I’d venture to say that the notion of possible worlds, per se, is pretty useless in understanding content. Not useless in general, mind you–it may be very useful in doing modal logic, the logic of necessity and possibility–but not particularly relevent to content.
So, if possible worlds can’t be used to understand content, what can? The first step in figuring this out is to really understand the source of the problem with the “intension as content” theory.
It’s actually buried in the above discussion. “We can clearly understand [stories with plot holes]…despite the fact that there’s no way to create a fully fleshed-out countefactual situation that would make them true [emphasis new].” The problem is with requiring the domain of intensions to be true possible worlds: Ways the entire world could have been.
What I’d like to propose, instead of content based on possible worlds, is content based on a much broader category of counterfactual situations. Though it’s a metaphor, I’d like to use the term “pictures” to describe these counterfactual situations. A picture is a not necessarily true–not even necessarily possible–view of some portion of the world. (This doesn’t mean, necessarily, a geographic portion–we’ll talk about the details later.) A picture can be grasped as depicting things about the world, but it’s not necessarily the case that you could extend the picture past the frame in a way that would work out–think Escher’s various pictures (in the literal sense) of “impossible objects,” which appear to work fine in two dimensions but cannot be consistently fleshed out into three. A picture is, essentially, a story, not in the sense of a linguistic artifact but in the sense of an account, true or not, truly consistent or not.
Because a picture need not be completely fleshed out, not every sentence need have a truth value within a picture. For example, Fermat’s Last Theorem doesn’t, I’d say, have a truth value in the picture presented by the Sherlock Holmes stories, despite the fact that it’s a necessary truth. On the other hand, more sentences have a truth value in a picture than the bare minimum needed to describe it. For example, the sentence “Inspector Lestrade’s skin is not green” is clearly true in the picture presented by the Sherlock Holmes stories, despite the fact that it is never explicitly stated in those stories (and the illustrations, not being in full color, do not make it explicitly clear)–had his skin been green, for example, surely Watson would have commented upon it at (or, more tactfully, after) their first meeting.
The picture presented by a story includes the actual facts stated by the story, plus a penumbra of logical inferences and reasonable assumptions that surround the story. This does not include every logical consequence of the story (or there would be at most one picture presented by all stories with plot holes). Instead, it includes those that we immediately and automatically would accept.
If that sounds vague and subjective, that’s because, to a certain extent, it is. Not all people will agree that exactly the same sentences are true, false, or truth-valueless in exactly the same pictures; that is, not all people who understand a sentence will grasp exactly the same content from it. Even one person, with different interests at different times, may consider different inferences from a sentence to be a necessary part of any picture in which it’s true. But that is fine–using a sentence to communicate does not require that it have identical content for speaker and listener; it merely requires that the sentence has similar enough content that speaker and listener will draw most of the same practical inferences from it. That’s ample to get by; if I tell you, for example, “A lion is chasing you,” you don’t need to grasp exactly the same content I do to get a considerable amount of benefit from hearing the sentence–indeed, the same benefit that I intended to bestow upon you. Even communication that requires considerably more exactitude–scientific statements, for example–doesn’t require exact content sharing.
So, all of this more succinctly stated: The content of a sentence is not its intension (a function from possible worlds to truth values), but rather a partial function (since sentences can be truth value-less in some pictures) from pictures to truth values.
Obviously (since I think it would have been a fine dissertation topic), I think there’s an awful lot more to say about pictures and content, particularly about the relation of pictures to the content of names, natural kind terms and nouns in general, as well as the relation of pictures to the content of indexicals and demonstratives. But those are things for later posts.
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