Wolfgang Schwarz

Content, form, and hyperintensions

I'm off to the Blue Mountains for a week. In lieu of philosophical content, here is a rant on semantic contents and hyperintensions that I wrote last year.

When philosophers talk about meanings (or contents, or semantic values), they rarely explain what these things are meant to do -- what constraints an adequate theory of meaning would have to meet. Trying to figure out those constraints from what is implicitly used in discussions and arguments, one gets a laundry list of miscellaneous features with hardly any theoretical unity. Meanings are supposed to determine (together with syntactic structure) the truth-value of sentences; they are supposed to be known by competent speakers; they are supposed to be conventionally associated with symbols and sounds; they are supposed to track what a sentence is (intuitively) about, and also in which possible worlds it is (intuitively?) true; they are supposed to be part of a model of how our brain processes and generates words; they are supposed to be possible objects of beliefs and desires; they are supposed to play various roles in speech act theory; they are supposed to the referents of 'that' clauses; they are supposed be such that one can truly utter 'Fred said that P' if and sonly if Fred uttered a sentence whose meaning is the same as the meaning of 'P'. And so on and on.

Nothing could possibly do all of these things. So we have to choose. For some roles, classes of possible worlds work well as sentence meanings, for others we fare better with Russellian propositions, and for yet other we need completely different constructions. It is no objection to the classes of worlds account that these meanings don't track aboutness intuitions: that's not what they are meant to do.

It would be nice if we could find meanings that satisfy at least some of the roles. I would like to find meanings that are a) compositional, and b) can do the work of meanings in a general theory of linguistic communication and understanding (however such a theory will look in detail). But I'm afraid there are no such things either: these two roles are already incompatible.

The problem is that the meaning of a sentence sometimes depends not only on the meaning and arrangement of its parts, but also on things that I'd rather not classify as meanings (that is, as things that play the meaning role in a theory of communication and understanding). All such cases are controversial, but good candidates are direct and indirect speech reports, mixed and unmixed quotation, attitude ascriptions, and constructions with 'according to Roman law' or 'in maths terms'. For example, when Neil Armstrong stepped on the moon, he proclaimed to have made a giant leap for mankind; he did not proclaim to have made a huge leap for mankind. But if 'giant leap' means the same as 'huge leap', these two proclamation reports shouldn't differ in truth-value. Similarly, I just discovered that scallions are green onions, but I did not discover that green onions are green onions. Yet if 'scallions' and 'green onions' have the same meaning, these discovery reports shouldn't differ in truth-value.

Faced with such examples, we can either 1) give up compositionality, 2) deny the difference in truth-value, or 3) deny the sameness of constituent meanings. My preference is option (1), which I want to compare to option (3). I will ignore option (2).

In the scallion example, I want to say that 'scallion' does have the very same meaning as 'green onion', but that the truth-value of discovery reports is sensitive to extra-semantic properties of the embedded words, such as spelling and pronunciation. Since these extra-semantic properties are recursively specifiable, this doesn't affect the productivity, systematicity, or learnability of language. Still, we have a violation of compositionality in the sense that the truth-value (and meaning) of complex expressions is not in general determined by the meanings and arrangement of their parts.

The alternative -- option (3) -- is to deny that 'scallion' means the same as 'green onion'. Perhaps the meaning of 'green onion' somehow involves the property of greenness, which the meaning of 'scallion' does not. Since one can also discover that ophthalmologists are oculists and that tomatoes (pronounced one way) are tomatoes (pronounced the other way), this account needs very fine-grained meanings.

There's nothing wrong with very fine-grained meanings. In fact, if meanings are stipulated to be things that play the compositionality role, then I, too, want very fine-grained meanings. For sentences, I would suggest to use a tuple of a truth-condition, a set of indices, and the way the sentence is spelled and pronounced. I would prefer to not call that last part a component of meaning, but it doesn't make a difference to semantics. It's only a difference in labeling. Either way, the truth-conditions of complex expressions are partly a matter of how their constituents are pronounced.

There are other approaches to get fine-grained meanings. Take standard intensional semantics, and replace all intensions with hyperintensions, defined over the space of possible and impossible worlds. The class of impossible worlds has members where shallots are not green onions. We can therefore treat discovery and proclamation reports as applications of modal operators, operating on the hyperintension of the embedded sentence.

We not only need impossible worlds where shallots are not green onions, but also worlds where giant leaps are not huge leaps, and where tomatoes are not tomatoes. In general, for any two sentences S1 and S2, we need a world where S1 is false and S2 is true. Not a problem if we simply identify a world with an arbitrary set of sentences, and say that S is true at w iff S is a member of w. (For this purpose, sentences are individuated phonetically and orthographically.)

Let's see what this gives us. The resulting account satisfies compositionality, but in an unusual way: it entails that no two expressions ever have the same meaning; hence whenever sentences S1 and S2 are composed in the same way of parts with the same meaning, then S1 = S2, and so S1 has the same meaning as S2. If no two expressions have the same meaning, then the meaning of a complex expression is trivially a function of the meaning and arrangement of its parts. But this is not compositionality as we know it. The meaning of complex expressions is not derived by the rules of intensional semantics from the meaning of its constituents. For instance, the hyperintension of 'A & B' is not the intersection of the hyperintensions of 'A' and 'B'. (Nor could such an operator '&' even be added to the language, as Max Cresswell has pointed out.) 'A & B' is true at a world w iff w contains the sentence 'A & B'; some of these worlds also contain 'A', or 'B', or both, but there is no general connection between these properties. The same holds for discovery reports: 'I discovered that scallions are green onions' is true at all and only the worlds containing this very sentence, nevermind the hyperintension of the constituent sentence.

We set out to extend intensional semantics, but we've arrived at something completely different. On this account, the meaning of every sentence is entirely determined by its orthographic and phonetic properties. Once you know how a sentence is written and pronounced, you know its meaning: it is the class of sets of sentences one of whose members is written and pronounced just like that.

It should be obvious that these meanings can't play the role of meaning in a theory of communication and understanding. Knowing what sounds and scribbles constitute a sentence of, say, Narrinyeri, is not enough to understand Narrinyeri, or to communicate information in Narrinyeri.

We could add to our hyperintensions, which only contain orthographic and phonetic information about expressions, something that tells us what these expressions mean. For sentences, this could be an old-fashioned truth-condition, restricted to possible worlds. (For this purpose, possible worlds are not to be understood as sets of sentences in the object language.) We could then also do traditional intensional semantics on the truth-conditional component, occasionally drawing on the hyperintensional component for discovery reports and the like. We would be back at the kind of fine-grained meanings I mentioned above.

These meanings, pairs of a truth-condition together with orthographic and phonetic information (perhaps further enriched with a set of indices), are better suited to play the meaning role in a theory of communication and understanding. But I think they are too fine-grained. For example, I would like to hold a contingency constraint on meanings: anything could have meant anything. We could have used the words 'it is raining' to communicate that the sun is shining or that Cairo is the capital of Egypt. That is, 'it is raining' could have had exactly the same meaning (in our community) that 'Cairo is the capital of Egypt' actually has. But if meanings include spelling and pronunciation, this would be impossible. So I'd rather say meanings in the communication-theoretic sense are just truth-conditions, even though meanings in this sense aren't compositional.