The Principle of Compositionality and Semantic Granularity

This is another post in my series on semantic granularity. The others so far, in chronological order, are:

Kripke's Puzzle and Semantic Granularity

Facts and Granularity

Granularity and Quine

Metaphysical Realism and Conceptual Relativity: An Application of Granularity

Granularity and Relativism about Truth

Granularity and the Paradox of Analysis

If meanings properly get carved up at different granularities, as I maintain, what are the implications for the 'the principle of compositionality'? I believe that granularity considerations can shed light on the status and application of this principle, and clear up much of the confusion surrounding it.

This confusion appears to be considerable. Witness Daniel Cohnitz ('Is Compositionality an A Priori Principle?'):

A superficial look at the literature on the principle of compositionality [...] could suggest that the discussion is as confused as a discussion can be.

I will now quote some classic and some typical formulations of the principle, and then indicate what we can say about it in light of granularity.

From the Tractatus:

I conceive the proposition—like Frege and Russell—as a function of the expressions contained in it. (3.318)

To understand a proposition means to know what is the case, if it is true.

(One can therefore understand it without knowing whether it is true or not.)

One understands it if one understands its constituent parts. (4.024)

It is essential to propositions, that they can communicate a new sense to us. (4.027)

Frege, in a letter to P.F. Jourdain, probably written in 1914:

The possibility of our understanding [my emphasis] propositions which we have never heard before rests evidently on this, that we construct the sense of a proposition out of the parts that correspond to the words.

Theo Janssen, 'Compositionality':

The principle of compositionality reads, in its best known formulation:

The meaning of a compound expression is a function of the meanings of its parts.

But this omits something. The way the parts are put together, not just their meaning, goes into determining the meaning of the whole. ('John loves Mary' means something different from 'Mary loves John'.)

This is the point made by 3.141 of the Tractatus:

The proposition is not a mixture of words (just as the musical theme is not a mixture of tones). 

The proposition is articulate.

The following instances do not omit this:

B.H. Partee, handout for Ling 310 The Structure of Meaning, Lecture 1, February 20, 2006 p.1:

The Principle of Compositionality: The meaning of an expression is a function of the meanings of its parts and of the way they are syntactically combined.

'Compositionality', The Stanford Encyclopedia of Philosophy:

[T]he meaning of a complex expression is fully determined by its structure and the meanings of its constituents.

We have now seen the principle of compositionality stated in various ways.

One idea I want to suggest is that, at a maximally fine granularity, the principle of compositionality can be thought of as guaranteed to hold – a blanket, a priori principle.

However, once we relax the granularity, compositionality can begin to fail in many cases.

This would give us an avenue by which to approach the confusion about whether the principle of compositionality is just a conceptual truth about how all languages – everything we would call a language – must work, or an ideal which is sometimes met and sometimes not, or just something which occurs sometimes (i.e. for some languages, or parts of languages) and not others, without necessarily being an ideal: from a fine-grained point of view, it can be construed as something which applies without exception, but from courser-grained points of view, we can make distinctions between cases where it holds and cases where it doesn't. (The stuff about being an ideal versus not being an ideal can then be considered using this as a basis.)

The proposal I just indicated – that at a maximally fine granularity, compositionality can be thought of as holding a priori and across the board – while it has a certain theoretical appeal, is problematic: it might seem straightforwardly false (in light of the existence of idioms, for example), but of course replies can be made to that (for example, that semantically, idiomatic phrases have less, or just different, parts or constituents than they would appear to have considered literalistically). I do not want to be dogmatic about this, and I suspect there is room for “having it both ways” by means of careful disambiguation.

Some of the points I want to make here can be made without any such strong principle (that is, without the proposal above – call it 'the blanket proposal'). I will therefore do that first, and then come back and reconsider the blanket proposal.

Compositionality Can Depend on Granularity

The proposal summed up in this heading is weaker than the blanket proposal (the proposal that granularity holds a priori across the board at maximally fine granularity but can fail in cases as the granularity is coarsened): all that is claimed is that some complex expressions are such that compositionality may be said to hold of them, given a certain granularity of individuation of their components' meanings, but also such that compositionality then fails to hold at a coarser granularity.

Consider this bit of dialogue from season 2 of Flight of the Conchords:

Murray: Now, we've known each other for quite some time in the professional realm. I'd like to push things forward in the friendship realm.

Jemaine: What's the friendship realm?

Murray: Well, you've heard of a realm?

Bret: Mm.

Murray: Yep?

Jemaine: Yes.

Murray: Well this is like a friendship one.

What makes this sequence is the way Murray's compositional "explanation" of 'the friendship realm' fails drastically. Is this, then, a “counterexample to compositionality”? Not really; or at least, to say that would not be to tell the whole story.

I think we can take two views of this case, and many others like it: a compositional/fine-grained view and a non-compositional/course-grained view.

On the first conception, we think: Murray means something here, he has put together a meaningful proposition. 'Friendship' and 'realm' here are clearly functioning in a way that is continuous with and related to a great many other occurrences of these words. Therefore, whatever this proposition means, that 'friendship' and 'realm' contribute in the way they do, or that they appear here in the way they do, in a proposition with this meaning, is part of – or an aspect of – the meaning, or the use, of these words (given fineness of grain).

Taking this viewpoint does not commit us to saying that these fine-grained component meanings were fully present before the phrase 'friendship realm' was ever used: depending on the details of the case, we could say that some people attached those meanings to the component terms already and some attached others (but that the difference never showed up, or slightly, but not in such a way as to prevent mutual understanding), or that no one used the words with exactly those meanings before the phrase was used, but that they were spontaneously arrived at when the phrase was coined (and understood, if we change the case and suppose it was understood by Jemaine and Brett, as would be more likely in real life) – that is, the meanings of 'friendship' and 'realm' were spontaneously and slightly extended.

On the second conception, by contrast, we think: 'friendship' and 'realm' are familiar words, and they were both presumably around for a long time before 'friendship realm' was ever used. Putting these two meaningful words together, however, doesn't all by itself yield one and only one possible meaning. There is room for going different ways here. ('The friendship realm', for instance, might be used differently from how Murray uses it, to mean some mythical realm in which everyone is friends.) Of course, when 'friendship realm' does end up meaning some particular thing, this will not be unrelated to 'friendship' and 'realm' – they guide the meaning, without determining it. The gap between what they provide and the meaning of 'friendship realm' must be filled by semantic developments pertaining to 'friendship realm'. But we needn't say that these developments affect the meanings of 'friendship' and 'realm' taken by themselves – we can maintain that they haven't taken on new meanings.

(It may be that compositionality doesn't necessarily fail according to this second conception: perhaps the gap between what the pre-existing meanings of 'friendship' and 'realm' and a meaning for 'friendship realm' can be thought of as being filled by a structure or mode of composition, if we construe this as going beyond surface syntax.)

Now, what does this get us, i.e. what does it get us to see that there is all this room for manoeuvring here?

One thing it gets us is a way of explaining a large class of putative counterexamples to the principle of compositionality, without denying any natural point of view. In fact, we have before us two ways of accounting for the idea that this is a counterexample to compositionality. Rather than two equally good ways of accounting for exactly the same thing, I think they cover different sorts of cases, different instances of the idea that this is a counterexample to compositionality; compositionality can be said to fail here in two senses:

(1) While compositionality may be said to hold at a very fine granularity, it can be said not to hold at a coarser one. So, one thing that might be going on when we think we have a counterexample to compositionality is that we are operating at a granularity at which it is a counterexample – and if someone disagrees, we might be talking at crossed granularities.

(2) A dynamic, temporal sense. We make no bones about the fact that now we have some new complex expression, we can say that the meanings of its parts, plus its structure, determines the meaning of the whole. (Thus we are operating at the finer granularity.) But we insist that when it was introduced, its meaning wasn't so determined: rather, it induced spontaneous semantic development. So, we can call a use of language non-compositional in this sense if it involved such development – and we may relativize this to a thinker or speaker, a listener, etc. Something compositional for me might be non-compositional for you at first, but my saying it induces spontaneous semantic development on your side so that it becomes compositional after the fact. We might use 'dynamic compositionality' for this idea; when spontaneous semantic innovations occur involving complex expressions, we can say that those expression uses were dynamically non-compositional.

Neither sense conflicts with the claim that, at fine-grain and timelessly, 'friendship realm' and similar cases are perfectly compositional.

These considerations may also shed some light on the issue of whether, or in what circumstances, compositionality is to be regarded as an ideal to be striven towards, if not attained. In some cases, we may have as an ideal that no spontaneous semantic innovation – no guesswork, we might say, from an interpreter's perspective – be required for a certain language-game (use of language), for example in parts of science, certain personal encounters, or in parts of legislature. That is, dynamic compositionality may be desired. But it is just as clear that sometimes we want dynamic non-compositionality.

Or we might want a language, or a part of language, to be so simple that there is no room for granularity shifting: each expression has a couple of clear rules attached to it, and if you change any of them, it's just not natural to say that the meanings stayed the same. We might be able to ensure this by laying it down that compositionality must not fail. (If we're aware of granularity considerations, we might say 'must not fail at any reasonable granularity', but we need not be aware of them to pull off the trick.)

So, the above considerations get us a few things. What remains?

We have seen that many cases where compositionality seems to fail – such as Murray's use of 'friendship realm' – may be explained away by saying: if you individuate the components' meanings at a finer granularity, this is no longer a counterexample. But the question remains: can that be done in every case? That is, does the blanket proposal hold?

By getting clearer about the blanket proposal, we will get clearer about the nature or meaning of the principle of compositionality. In this connection, we should consider idioms, metaphors and similes, sarcasm and the like, and semantic “outgrowths” like 'Wednesday is fat' and 'The letter a is yellow'.

Such linguistic phenomena also suggest that there may be more to say about the notion of compositionality as an ideal.

The Blanket Proposal

A proponent of the blanket proposal might say that, when compositionality fails, we have decided to bundle together as having one meaning expressions, or possible occurrences of expressions, which on a more fine-grained conception would be regarded as having (perhaps only slightly) different meanings. But is this really plausible in every case?

Here are some difficult types of cases:

Idioms: Consider phrases like 'spitting image', 'dead ringer', 'nest egg', 'piece of cake', 'funny farm', 'loose cannon', 'no dice', 'from scratch', 'kick the bucket'.

Propositions like 'He is a loose cannon'

'Pull strings' a bit more flexible. Frozen metaphor.

Sarcasm and the like: A sarcastic utterance of 'That's just great' may seem to be a kind of counterexample to compositionality: what is meant is that something is terrible, but this depends not just on the meanings of the components and how they are put together, but also on the context: it might be meant non-sarcastically.

But we can invoke an intensional (internal semantic) analogue of Kripke's distinction between speaker's reference and semantic reference here, and insist that what this expression means, even in the sarcastic use, is that the thing in question is very good, even though what the speaker means by it is something else.

From the point of view of expression-meaning, then, sarcasm and the like do not threaten compositionality in the least. But there is nothing stopping us talking about compositionality in connection with speaker-meaning, and saying that it fails in this case ('That's just great').

Or, we may say that what the speaker means by the whole is determined by what the speaker means by the parts, together with their mode of composition, by maintaining that by 'great' the speaker means 'terrible'.

But other cases seem different. Suppose someone takes something to be very obvious, but, by way of parody of some other group who may doubt it, might sarcastically say, 'Of course, empirical studies may prove me wrong' (let's suppose they're quite nerdy). Here, the meaning is something like 'Come on, we know this!', but the sarcasm cannot be located, so to speak, in any particular phrase. The whole construction is bound up with the sarcasm – what is literally meant cannot aptly be stated using the same syntactic form, only negated (e.g. 'Of course, it's not the case that empirical studies may prove me wrong', or some other placement of negation).

For now I remain agnostic.

A Final Observation about Wholes and Parts and Granularity

Observation: Two propositions - or more generally, complex expressions - can be identical in meaning at one granularity, while none of their parts have the same meaning at any reasonable granularity. Or less extremely, while few of their parts, or none of their "key words", have the same meaning at any reasonable granularity. Or again, while their overall structure and arrangement of parts is quite different.

For example: 'Get out!' and 'Leave at once!'.