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Metasemantics for Complex ExpressionsMichael Johnson

I. CMT for Natural Language

In virtue of what does a meaningful morpheme mean what it does, rather than having some other meaning, or no meaning at all? We can call attempts to answer this question metasemantics for morphemes. What is the correct metasemantics for morphemes? There’s a variety of views out there: descriptivist views, causal-historical views, views with stories about deference to experts, intentions, conventions, proper functions…

Here’s a somewhat less popular question: in virtue of what does a meaningful complex expression mean what it does, rather than something else, or nothing at all? What’s the correct metasemantics for complex expressions? In this paper I’m going to try to answer this question.

To get an understanding of what answers to this question look like and how different considerations bear on them, I will first present an attractive answer that I think is wrong. The answer is: A meaningful, complex (natural language) expression has the meaning that it does in virtue of its morphemes having the meanings they do and the way those morphemes are combined by the morphosyntactic rules of the language.

This view differs from a variety of claims that have been called “compositionality”. Compositionality is often taken to be the claim that the meaning of every complex expression is a function of the expression’s morphosyntax and the meanings of its morphemes. But A can be a function of B without B holding in virtue of A. The value of a sack of nickels is a function of its weight, but nickels aren’t worth what they are because of how much they weigh. So the view that the morphosyntax of an expression and the meanings of that expression’s morphemes metasemantically determine the meaning of that expression is a view that’s similar to compositionality, but stronger. Let’s call it compositionality as a metasemantic thesis for natural language, or just CMT (for NL).

The obvious problem for CMT and the standard version of compositionality is the existence of idioms and sentences that contain them. Consider the sentence “She let the cat out of the bag.” If you have never read or heard the expression “let the cat out of the bag”, but you are a native English speaker, and you know all the meanings of the morphemes in this sentence, and you have successfully parsed it, you will still not be able to work out its idiomatic meaning. Its idiomatic meaning does not metasemantically depend on its morphosyntax and the meanings of its morphemes.

The argument from idioms against the principle of compositionality is straightforward, but it can be difficult to see what we should take away from it. Surely it can’t be that easy to show that compositionality is false!

Here’s the standard argument for compositionality. First, we consider a novel sentence, something no one has ever read or said before, for example, “Pakistan abuts Nebraska.” Then, we notice that every English speaker who knows the meanings of the morphemes in this sentence, and who can successfully parse it, can understand it. Upon reflection, we see that most

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of the sentences we’ve heard or read in the past were novel, but we were always able to understand them, again, provided we could parse them and we knew the meanings of the morphemes in them. And it’s reasonable to suppose that most of the sentences we will hear or read in the future will also be like this. So for the vast majority of sentences, we can compute their meanings from their morphosyntax and the meanings of the morphemes in them. Hence the vast majority of English sentences are compositional.

This argument says nothing about those other sentences, the ones we couldn’t understand upon hearing them for the first time, even if we could parse them and even if we knew the meanings of their morphemes. Those things (sentences with unfamiliar idioms) are not compositional. This is fine for most purposes; if all you want to do with the principle of compositionality is argue against relevance theorists and verificationists, you can settle with the vast majority of the language being compositional. The verificationist (arguably) is committed to the vast majority of the language being non-compositional. A few cases here or there of non-compositional phenomena won’t help either the verificationist or her opponents.

But with regard to the metasemantics of complex expressions, the situation doesn’t look good for compositionality. We could say that the vast majority of sentences in English have the meanings they do in virtue of their morphosyntax and their morphemes having the meanings they do. But then we need a separate story to explain why the other complex expressions have the meanings they do. And more importantly, we need a story about why there are two stories instead of just one—why is the correct metasemantics for some expressions theory T1 (CMT, for example) and for other expressions (idioms) theory T2?

Of course, there are alternatives to compositionality as a metasemantic thesis. We could instead turn to what’s been called intention-based semantics (IBS), and say something like: expressions mean what they do in virtue of our intending that they have those meanings.

Here’s an extremely simplified IBS account: for simple expressions, we have specific intentions for each of them, embodied in what we might call the lexicon. For some tiny number of complex expressions (the idioms) we also have specific intentions regarding what they are to mean. But for everything else we have a more general intention that if expression E = [α β], then E means ⟦α⟧(⟦β ⟧)1.

On the intentions-based account, the metasemantic thesis is foremost about our intentions, and only accidentally about compositionality. Compositional processes do show up in a general intention about function application. But if we were to revise that intention or somehow gain specific intentions with regard to every complex expression, compositionality would disappear from IBS.

IBS has several virtues over CMT. First, it handles the cases CMT can’t handle (idioms), and it does so while telling one unified story for all complex expressions. Second, IBS can 1 This is not how any IBS theorist has ever stated her theory. Normally, the account begins with a story about how speakers mean things by uttering sentences, then proceeds to connect an abstract language to actual speaker practice via a story about the nature of conventions. But I have chosen to make no distinction between speaker meaning and semantic meaning, and I have omitted any mention of conventions. The intention here is simply to cut out all the working parts of the theory that I don’t intend to discuss, while foregrounding the parts relevant to the points I intend to make.

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capture the data that support the principle of compositionality in a way that nicely interfaces with the principal argument for compositionality. The reason we intend that most complex expressions be interpreted compositionally is because we can’t have specific intentions for all of them. And since we intend them to be interpreted compositionally, hearers can work out their meanings compositionally.

At the end of this paper, I’ll consider a view distinct from either CMT or IBS. But now I will set aside the metasemantic question for natural language, and turn to metasemantics for mental representations.

II. CMT for the Language of Thought

I’m going to presuppose that there is a language of thought (LOT) in what follows. According to the LOT hypothesis, mental representations are very similar to NL representations, in that they have discrete parts arranged hierarchically (i.e. syntactically). Nothing in the view I ultimately want to endorse requires accepting the LOT hypothesis, and many of the arguments I’m about to give could be re-stated for other accounts of mental representations. I adopt the LOT hypothesis mainly for expository purposes.

In virtue of what does a complex LOT expression mean what it does rather than something else or nothing at all? This is one of the other question I aim to answer in this paper. Interestingly, the dialectic for LOT is almost completely the reverse of what we saw for natural languages in the previous section.

For example, an IBS account for complex LOT expressions is difficult to maintain. Such a view would say that complex LOT expressions have the meanings they do in virtue of our intending that they have those meanings. Such a theory invites an infinite regress. Suppose that for a LOT expression E to have a meaning, I had to have an intention, general or specific, that it have such-and-so meaning. I would have to either intend or have intentions that entailed intending2:

E MEANS X

Where ‘X’ is synonymous with E. But this representation itself contains a LOT expression—‘X’, which (we’re assuming), requires me to have yet another intention, namely:

‘X’ MEANS Y

And this representation contains a new LOT expression ‘Y’. I could stop by going in a circle, say by accepting that ‘Y’ MEANS X, but that would be viciously circular. I could keep going forever, but that would be like theory of vision that says what it is for me to see something is for a

2 Here I adopt Fodor’s convention of capitalizing English expressions to articulate LOT expressions.

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homunculus in my head to see it, and what it is for the homunculus to see it is for the homunculus in her head to see it…

So whereas for natural language, compositionality seemed like a bad metasemantic story for complex expressions, and some sort of story involving intentions seemed much more promising, for LOT, the intention-based story is a non-starter. This might, at first, seem to suggest that CMT for LOT was the correct metasemantic theory for LOT. Remember, this is the theory that says that complex LOT expressions mean what they do in virtue of their simple parts meaning what they do, and the way those parts are combined by the syntactic rules of LOT.

However, there’s yet another contrast between what’s true for LOT and what’s true for natural languages. The same considerations that decisively undermine IBS for LOT also decisively undermine the standard argument for compositionality. The standard argument claims that the understanding of novel, complex NL expressions, when possible, is made possible by our (a) representing the meanings of their morphemes and our (b) computing, from those representations, and in accord with the morphosyntactic structure of the larger expressions they compose, the meanings of those larger expressions. For example, the story makes commitments like: in my lexicon I have such representations as3:

‘brown’ MEANS λP. BROWN P‘cow’ MEANS COW

Further, when I want to understand a complex expression like ‘brown cow,’ what I do is parse it into [brown cow], then apply the intended compositional rule ⟦brown cow⟧ = ⟦brown⟧(⟦cow⟧), and arrive at the result:

‘brown cow’ MEANS BROWN COW

The argument for compositionality is that if the representations of complex NL expressions aren’t derivable from the morphosyntax of those expressions and the representations contained in the lexicon, then they aren’t derivable tout court; but, being derived on numerous occasions, they are derivable, and hence derivable compositionally.

If you don’t make the argument about deriving representations, it doesn’t work. Suppose you just said that morphemes have meanings, not that they’re represented by speakers; and that complex expressions have meanings, but that these aren’t represented by speakers. Now there’s no sense to be made of speakers computing the meanings of expressions from the meanings of their morphemes, because computing entails representing the inputs and deriving the outputs of a function. And there’s no reason to even suppose that the meaning function must be a function of the morphosyntax of an expression and the meanings of its morphemes. If speakers aren’t

3 To avoid messiness here, I am being sloppy. ‘‘brown’’ here and below alternately articulates a LOT name for an English expression and an English name for an English expression. As ‘‘BROWN’’ is a quote-name for a LOT expression, I have simply run out of articulatory devices.

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computing that function, there’s no barrier to it being as multi-parametered and intractable as you like.

To sum up: the standard argument for the compositionality of natural languages assumes, at a minimum, that for a speaker to understand a natural language expression, she must represent the meaning of that expression. Such a story cannot be accepted for LOT, for it clearly invites an infinite regress. Suppose that for me to understand a LOT expression E, I had to represent that it have such-and-so meaning. I would have to represent something like:

E MEANS X

Where ‘X’ is synonymous with E. But this representation itself contains a LOT expression—‘X’, which (if I’m to understand it), requires me to have yet another representation, namely:

‘X’ MEANS Y

And this representation contains a new LOT expression ‘Y’. Again, the only resolutions are (a) going on forever (b) accepting a vicious circularity and (c) denying that understanding LOT expressions requires representing their meanings, and thus denying that the standard argument for compositionality works for LOT. Fodor takes the third option:

[W]e should reject the following argument: ‘Mentalese must have a compositional semantics because mastering Mentalese requires grasping its compositional semantics.’ It isn't obvious that mastering Mentalese requires grasping anything… productivity doesn't literally entail semantic compositionality for either English or Mentalese. [Concepts, pp. 96-97]

In sum, in the last section I argued that although there’s an argument for the compositionality of NL, there’s also a good reason to think that compositionality is not the correct metasemantic theory for NL. Then I presented one viable alternative metasemantic theory: intention-based semantics. In this section, I argued that IBS is a non-starter for LOT. Since there aren’t any clear cases of LOT idioms, compositionality is viable as a metasemantic theory for LOT, but the standard arguments used to support compositionality are not available in the case of LOT. In the next section, I will endorse a third metasemantic account for LOT, called the direct theory.

III. The Direct Theory

CMT and IBS are indirect metasemantic theories. In answer to the question: “in virtue of what does this complex expression mean what it does?” they reply: “in virtue of these other things which already and independently have meanings.” CMT appeals to the meanings of the simple parts; IBS appeals to the contents of our intentions. A direct metasemantic theory for complex

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expressions would assign such expressions contents directly, and not derivatively in terms of the contents of some other thing. Since I’ll only present one such theory here, I’ll call it the direct theory.

There are a number of causal metasemantic theories for simple mental representations. These theories invoke causal, informational, or nomic connections between mental representations and the things they represent to explain why the representations represent what they do. Such a theory might say, for instance, that R represents P in virtue of the fact that in appropriate circumstances, P causes the tokening of R.

The reasons for thinking causal, informational, or nomic relations are integral to a metasemantic account are myriad, but here are two. First, two people who are absolutely alike on the inside, might separately be looking at two different indiscernible tables. Though they are alike internally, they would be thinking of different tables, each the one she is confronted with. Intuitively, this difference has something to do with the fact that different tables are causing the experiences of each person. Second, we are capable of having radically false theories of things. But they are still theories of those things. Thus, our representations must be anchored to those things in a way that’s insensitive to what we think about them. Causation could provide such an anchor, as the causal powers of most objects are largely insensitive to what we think about them.

Even so, there are well-known problems with every causal metasemantic theory. For present purposes, I will adopt a simplified theory that says: R represents P in virtue of the fact that in appropriate circumstances, P causes R. Notably, I won’t say what circumstances count as “appropriate.”

My intention in avoiding saying what circumstances count as “appropriate” is to punt on the disjunction problem. The disjunction problem is the problem that lots of things besides, say, cows, cause me token COW. This includes things that I mistake for cows, like horses on a dark night; things that resemble cows, like cow-pictures; things that remind me of cows, like chickens; and even things that have nothing to do with cows, as when I infer COW OR DUCK from DUCK. The problem is, roughly, to say what makes cow-caused COW tokens “appropriate” for determining the meaning of COW and makes DUCK-caused COW tokens “inappropriate.” This is the problem for causal metasemantic theories of simple expressions, and the view I have articulated punts on it.

While the disjunction problem is interesting, and a solution is worth having, there can still be worthwhile arguments for causal metasemantic theories before we’ve solved it. We’ve already encountered two: the case of the tables, and the case of the radically false theory. Furthermore, with regard to metasemantic theories for complex LOT expressions, considerations for and against various theories are worth accumulating, because so few of them are out there and the standard argument for compositionality doesn’t work here. Finally, for at least some participants in the debate, it will be common ground that the disjunction problem is soluble. If you think a causal theory is true for simple LOT expressions and that CMT is true for complex LOT expressions, then you’re going to assume that the disjunction problem is soluble, and thus not object to a causal account of the metasemantics of complex LOT expressions on the ground that it doesn’t solve the disjunction problem.

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Thus, setting aside the disjunction problem for present purposes, I propose to defend the theory that for any LOT expression E, simple or complex, that represents P, E represents P in virtue of the fact that in appropriate circumstances, P causes E. For example, according to the direct theory, BROWN COW means brown cow, because it is brown cows that cause BROWN COW, in appropriate circumstances. BROWN COW, according to this theory, does not mean brown cow because it is composed of parts, BROWN and COW that mean, respectively, brown and cow, and which are put together in a certain syntactic arrangement.

The reason a brown cow causes you to token BROWN COW might be because a brown cow causes you to token BROWN and also causes you to token COW and whatever mental mechanism solves the binding problem outputs BROWN COW. In this case, the tokening of BROWN COW is mediated by the tokening of certain other representations, namely BROWN and COW. But even though a brown cow’s causing you to token BROWN COW is mediated by other representations, it doesn’t follow that the meaning of the former is metasemantically dependent on the meanings of the latter representations. Notice that causal theories for simple expressions accept that a cow’s causing you to token COW is mediated by many representations—edge detection algorithms in early vision, background beliefs about cows—while denying that the meaning of COW is determined by the meanings of the mediating representations. In Fodor (1990)’s idiom, such theories quantify over the mediating processes and representations.

At the sentential level, the direct theory says, for example, that SNOW IS WHITE means snow’s being white, because in appropriate circumstances, snow’s being white causes us to token SNOW IS WHITE. I will adopt some metaphysical details for the sake of exposition that are not an essential part of the direct theory. First, the meanings of sentences are states of affairs composed of objects, properties, and relations. Second, there are possible but not actual states of affairs. So, SNOW IS PURPLE means the non-actual state of affairs wherein snow is purple, and this state of affairs causes SNOW IS PURPLE in appropriate circumstances in the following sense: were the state of affairs wherein snow is purple to be actual, it would cause SNOW IS PURPLE in appropriate circumstances.

In the rest of this paper, I’ll present three arguments for the direct theory. Then I’ll consider several serious objections to the direct theory, not all of which I have satisfying answers to. Finally, I’ll turn back to our original question, regarding the metasemantics of complex expressions for natural language.

IV. Unarticulated Constituents

Compositionality in its standard sense says that the meaning of a complex expression is a function of—and a function only of—the meanings of its simple parts and the way that they are combined. Perry (1986) argued for the existence of what he called unarticulated constituents in language and thought. These are “parts” of a proposition expressed by a representation that are not expressed by any part of that expression. For example, consider (1)-(6):

1. ‘x and y happened simultaneously’ (no representation of frame of reference)

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2. ‘x has a mass of 5 kg’ (no representation of frame of reference)3. ‘It’s 5 o’clock’ (no representation of time zone)4. ‘What Jones said is true’ (no representation of language)5. ‘x weighs 5 pounds’ (no representation of the exerter of the force)6. ‘It’s raining’ (in Perry’s fictional Z-lander case; no representation of a location)

What seems right to say about these cases is that there exist at least some speakers who, when they think the thoughts they would express by (1)-(6), do not, even in thought, represent the missing parts (frames of reference, etc.). In essence, they think about n-ary relations with predicates that are less-than-n-ary.

Perry’s view was that the propositions expressed by such representations were partly determined by the meanings of the parts of the representation and the way they were combined and partly determined “directly” by informational connections between the thinker and the world she is representing. The direct view denies this hybrid solution and advances an entirely “direct” metasemantics. The reason a Z-lander’s tokening of IT’S RAINING means the state of affairs wherein it’s raining in Z-land, is that in appropriate circumstances, when that state of affairs obtains, it causes the Z-lander to token IT’S RAINING.

I am inclined to think that when the relevantly uninformed thinkers think the thoughts they’d express with (1)-(6), they think complete, truth-evaluable thoughts and thus that there is at least some “direct” determination of content. Denying this seems to threaten a rather serious skepticism. As hidden relativities are common and could be pervasive, if no content is ever determined directly, we might never have truth-evaluable thoughts. The existence/ possible existence of unarticulated constituents thus provides support for a theory containing at least some direct determination of content, such as Perry’s hybrid theory or the direct theory.

V. Metasemantic Uniformity

I endorse what I’ll call “the principle of metasemantic uniformity.” Here’s how Stalnaker puts the position:

If representation is essentially a causal relation, then no predicate, and no mental state, can represent in virtue of the intrinsic psychological properties of the person who is using the predicate, or who is in the mental state. [Inquiry, p. 21]

It’s possible to be a sort of “grab bag” theorist who thinks that what determines the meaning of this predicate is its causal-historical relation to such-and-so property; and what determines the meaning of this other predicate is what the experts think; and what determines the meaning of yet this other predicate is the intrinsic psychological properties of the person using the predicate; and so on. But this is only possible if the “grab bag” theorist is interpreted as not telling us in virtue of what these predicates mean what they do. The “grab bag” theorist is providing us with recipes that are extensionally adequate for determining what means what. But she’s not telling

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you what it is to represent. It’s just not possible that x means y in virtue of x bearing R1 to y, while z means w in virtue of bearing a wholly unrelated relation R2 to w, and so on. If such a disjunctive account were “true,” then there just wouldn’t be any meaning.

This is not to say that there’s nothing to “grab bag” theorizing. For example, suppose we accept some version of IBS, involving sub-personal intentions: the intentions that determine what predicates mean aren’t directly introspectible. These intentions might differ with regard to different classes of predicates: we might have intentions that names get their meanings one way; and qualitative predicates a different way; and expert jargon a different way; and so on. The in virtue of story might be easy (it’s IBS) while discovering the grab bag of intentions that speakers actually have might be the real hard philosophical problem requiring clever, carefully constructed thought experiments and insightful leaps. There’s nothing wrong with “grab bag” theorizing, but representation itself is not a grab bag. If expression4 E represents thing T in virtue of the fact that E bears R to T, then for any expression E*, if E* represents T*, it does so in virtue of the fact that it bears R to T*. This is the principle of metasemantic uniformity.

Causal metasemantic theories (for LOT) have trouble with the principle. Consider this apparent contradiction:

1. Metasemantic uniformity for simple expressions: If expression E represents thing T in virtue of the fact that E bears R to T, then for any expression E*, if E* represents T*, it does so in virtue of the fact that it bears R to T*.

2. Causal isolation: Disjunction never causes anything, not even our tokenings of OR.

3. FRED IS A CAT OR A DOG is true iff Fred is a dog or a cat.

Suppose that DOG has its content because of the causal relations it bears to the property of being a dog. Then by (1), OR must have its content be X, where X is what OR bears the appropriate causal relation to. Yet by (2), OR can’t bear any causal relation to disjunction, so either OR is meaningless or it means something other than disjunction. Finally, if OR doesn’t mean disjunction, then how can (3) be true? For if FRED represents Fred, IS A CAT represents the property of being a cat, IS A DOG represents the property of being a dog, OR represents nothing or something other than disjunction, and the whole represents what it does in virtue of its parts representing what they do, then how can FRED IS A CAT OR A DOG represent the disjunctive state of affairs: either Fred is a cat or Fred is a dog?

This paradox (like many paradoxes) is reached only by assuming compositionality. If we reject compositionality and hold that IS A CAT OR A DOG can represent the property of being a cat or a dog, regardless of what OR does or does not represent, the paradox is avoided. (The

4 I want to note that I have somewhat expanded the doctrine from Stalnaker’s less committal version involving just ‘predicates’ and ‘properties.’ I intend to slip much further down this slope in the sequel.

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property of being a cat or a dog, by the way, is causally efficacious5: things with this property cause me to token IS A CAT OR A DOG.)

If you’re a causal theorist, CMT and metasemantic uniformity are in contradiction, given some trivial assumptions. The direct theory removes this tension. Disjunctive mental expressions like IS A DOG OR A CAT mean the property of being a dog or a cat, because in appropriate circumstances, instantiations of that property cause tokening of that expression. This is so even though OR means nothing or something other than disjunction. A similar strategy can be extended to other causal isolates, such as numbers.

Thus far, I have ignored a pretty big implication of the principle of metasemantic uniformity. Here again is what Stalnaker says:

If representation is essentially a causal relation, then no predicate, and no mental state, can represent in virtue of the intrinsic psychological properties of the person who is using the predicate, or who is in the mental state.

He doesn’t say “no simple predicate” and he doesn’t say “no simple mental state” either. If you buy the motivation for the principle, then you shouldn’t limit yourself to just simple expressions. Anyone who believes in both a causal metasemantics for simple expressions and the uniformity principle must accept the direct theory.

For causal theorists, CMT is entirely incompatible, in several ways, with metasemantic uniformity. The direct theory on the other hand just is a combination of a causal theory of meaning with metasemantic uniformity. It is not the only theory that is uniform: verificationist and inferentialist accounts often are or can be stated in uniform ways. But there are strong independent reasons for rejecting verificationist and inferentialist accounts, and strong reasons for accepting a causal metasemantics for thought. Those who are swayed by such considerations have only the direct theory to turn to if we wish to respect the principle of metasemantic uniformity.

VI. Ontological Neutrality

If complex expressions derive their semantic features from the semantic features of their parts, then the parts must have semantic features, and have semantic features appropriate for deriving the features of the complex expressions they are parts of. As Dever [cite] puts it:

5 It might be thought that if disjunction is causally isolated, so must all disjunctive properties be (like the property of being a dog or a cat). But I don’t know of anyone who seriously entertains this. After all, were it true, there wouldn’t be a disjunction problem—we’d never have to worry that ‘cow’ meant cow or horse-on-a-dark-night, because the latter property would, being disjunctive and thus by supposition causally isolated, immediately be ruled out of contention as a referent in some causal theory.

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Without compositionality, semantic features of the linguistic practice can ‘float free’, not appearing anywhere in the lexicon but emerging non-compositionally as lexical items are combined. [p. 49]

Dever gives a “familiar example” of compositionality engendering ontological commitments: “Davidson’s compositional solution to adverbial modification leads to an ontology of events” (n. 58 p. 44). Compositionality, according to Dever, keeps semantic theorizing “honest” by “revealing the ontological commitments inchoately present in our linguistic practice” (p. 48). But is honesty the best policy in metasemantics?

I think not. You don’t have to look far to find compositional semanticists quantifying over individuals, times, events, states, processes, degrees, possible worlds, properties, propositions, information states… if we’re honest, we’re committed to lots of structure in the world. And yet, there’s no guarantee there is any of this.

Here are three brief examples. Esfeld et al. (2014) argues that the correct ontology for Bohmian mechanics involves no properties other than position—no mass, no charge, no spin. They are useful fictions in experimental contexts, but there is nothing they correspond to. Ladyman & Ross argue, on the other hand, that there are no objects. We cannot be sure that even the most basic assumptions in compositional semantics (that there are objects and properties) are satisfied by the world. Additionally, current dynamic semantic theories contain representations for discourse referents, for which there are no forthcoming realist interpretations. A close match between representation and content is something that no one who considers state of the art ontology or state of the art semantics would accept.

Understanding complex expressions (setting idioms aside) involves computing representations of their meanings from representations the meanings of their parts, and likely requires that these representations contain variables that (appear to) range over individuals, times, events, possible worlds, etc. But it’s an unjustifiable leap to require that the meanings—what these representations represent—have any of this structure. This would make it highly likely that everything anyone has ever said is false or meaningless.

The direct theory, by contrast, is ontologically neutral. Consider a simple example. There are infinitely many expressions of the form ‘has a mass of 5 kg’. Suppose it turns out that there are infinitely many primitive, unstructured mass properties. There’s a property of having a mass of 5 kg, but there’s not a part of that property that’s the “mass” part and a part that’s the “5” part and a part that’s the “kg” part. In fact, suppose there’s absolutely no referent for “mass” (nothing is mass), and no referent for “5”, and no referent for “kg”. But there are primitive, unstructured properties that objects tend to have when the scale says they weigh 5 kg. The direct theory can just treat these forms of words as infinitely many idioms. In appropriate circumstances, the property of weighing n kg causes us to token WEIGHS N KG. The same type of story can be told if more arcane metaphysical possibilities turn out to be correct.

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In a way, this is just the other side of the unarticulated constituents coin. Sometimes the structure of the world has more “places” than the predicates we use to describe it, and sometimes the structure of the world has fewer “places.” Ontology fails to recapitulate philology. The direct theory is built to handle this mismatch. Parts of the world, however structured, cause us, in appropriate circumstances, to think things, however structured. Which part of the world are our thoughts about? The parts that caused our thoughts. A metasemantic theory without such an ontological neutrality threatens to be swallowed by the mismatch in form between word and world.

VII. Some Problems

Before I spoke of causal isolates like logical operations and numbers. This wasn’t a problem for the direct theory, I argued, because it doesn’t preclude disjunctive states of affairs and states of affairs containing various numbers of things from having causal powers, and being the contents of expressions containing OR or SEVEN. But aren’t there states of affairs that are causal isolates, but intuitively the contents of certain expressions? Here are several candidates.

Candidate 1: Impossible states of affairs. Impossible states of affairs arguably lack causal powers. Yet intuitively, THIS IS A ROUND SQUARE has a content.

There are replies to this problem. I could aver, for instance, that there are facts regarding what would happen if various impossible states of affairs were to obtain6, and thus we can assign contents to mental representation caused appropriately in such circumstances. Alternatively, I could bite the bullet, and accept that ROUND & SQUARE has no meaning, or has a nonstandard meaning. Instead of making those replies, I will simply advertise the faults of the direct theory as faults. It is a fault of the theory that it can’t obviously deal with expressions like ROUND & SQUARE.

Candidate 2: Abstract states of affairs. The state of affairs wherein 2 + 2 = 4 is not known for its effects. This case is very similar to the previous case, but the implausibility of biting the bullet and claiming that 2 + 2 = 4 has no meaning, or a nonstandard meaning, is much greater. This is a fault of the theory.

Candidate 3: Future states of affairs. The future is only relatively causally isolated. Events therein can have effects, they just can’t have past effects, unless there’s time travel. It’s problematic to say that representations ostensibly about future events are instead meaningless or about present or past events.

This case has some notable differences from the previous cases. After all, time travel is possible. So if it turned out that the only appropriately caused tokens of HILARY CLINTON WILL WIN THE U.S. PRESIDENCY IN 2016 are tokens caused by the effects of Clinton’s winning rippling backward in time through a wormhole, then there wouldn’t be any problem for the direct theory. So a lot depends on one’s theory of appropriateness. But consideration of the case does make the direct theory look rather ridiculous. 6 Just as Fodor (1990) allows that there are facts regarding what would happen if various physically impossible states of affairs were to obtain. See pp. 94-95.

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Again, there are responses. The theory as-stated looks ridiculous. A lot of “causal” theories are stated instead in terms of information as opposed to causation. On the surface, it’s less ridiculous to think that tokens of HILARY CLINTON WILL WIN THE U.S. PRESIDENCY IN 2016 carry information about Clinton winning, in appropriate circumstances. A lot is still riding on ‘appropriate,’ but that’s true of any causal metasemantic theory. Nevertheless, it would take a lot of maneuvering to build a version of the direct theory that works for future states of affairs, and it’s not clear that it’s possible to do so.

Candidate 3: Inconceivable states of affairs. Recall how it is that not having a story about appropriateness is punting on the disjunction problem. All sorts of things cause us to token various representations. If I’m stuck on a desert island with a large supply of fresh water and spam, my desire for SPAM TO BE DELICIOUS is presumably not caused by the state of affairs wherein spam is delicious. So we have to distinguish tokens of SPAM IS DELICIOUS caused in appropriate circumstances from those caused in inappropriate ones. The cause(s) in the appropriate circumstances, and only those, determine the content of all the tokens. Causal pathways to desires or wonderings are typically not the appropriate ones.

Now consider the irrational homophobe. George is simply incapable of coming to believe that his son Fred is gay. Fred is in fact gay. Fred says as much to George in so many words. He introduces George to his (male) partner. George attends his wedding to his partner. Still, George will never, and would never, under any circumstance, token FRED IS GAY in his belief box. This does not mean he never tokens FRED IS GAY. His persistent homophobia causes him to wonder whether various people he knows are gay, dozens of times a day. Thus George frequently wonders IS FRED GAY? He just never resolves his wonder in the affirmative.

This case is just the inverse of the impossible states of affairs case. For A to cause B, both A and B must cooperate. If A has no causal powers, or not-B is immutable, then A cannot cause B.

I think this case is more easily resolved. Take the simple expressions version with GAY. George doesn’t token GAY in response to gay people; he tokens GAY in response to gay-people-who-aren’t-Fred. So a standard causal theory (plus CMT) will say that FRED IS GAY, for George, means something like the state of affairs wherein Fred is gay-and-not-Fred—the empty or impossible state of affairs. That’s what the direct theory says too, when you recognize that FRED IS GAY can never be appropriately tokened in George.

In sum, the direct theory has various faults that don’t accrue to, for example, CMT. These are reasons for rejecting the theory that must be weighed against the reasons I provided for accepting it. [here’s where a theory of appropriate circumstances matters. Other than the disjunction problem, there’s an ‘emptiness’ problem that faces causal theories. It’s more hidden (irrealis markers, future tense markers) in the simple case, but it’s there.]

VIII. Inferential Coherence

Consider the following view: the meaning of ‘&’ is and and the meaning of complex sentences is determined by their syntax and the meanings of their simple parts. Such a view seems to

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recommend certain inferences, for instance, from P and Q to infer (P & Q). This is because (P & Q), on this view, means P and Q, and is thus true if P and Q are both true.

Of course, depending on the details, such a view might not actually recommend any inferences. If the metasemantic story says that ‘&’ means and in virtue of the fact that we accept the inference from P and Q to (P & Q) and the standard &-elimination rules, then the recommendation to accept the rule is rather empty: there only is a recommendation to accept the rule after we accept the rule.

On the direct theory, there’s no semantic reason to pay attention to a complex expression’s parts or the way they’re syntactically combined, because these don’t play a role in determining its meaning. So instead of ‘(P & Q)’ it might be clearer just to write ‘X’. It’s reasonable to ask what recommends the inference from P and Q to X. Unlike the compositional story, nothing about the form of X and the meanings of its parts guarantees that it’s true when P and Q are both true. What determines the meaning of X is what causes X, in appropriate circumstances. If this happens to be the state of affairs wherein P and Q are both true, then the inference is a valid one. One way in which the state of affairs wherein P and Q are both true could be the cause of X is when the state of affairs wherein P is true causes P (in appropriate circumstances) and the state of affairs wherein Q is true causes Q (in appropriate circumstances) and we abide by the inference rule from P and Q to infer (P & Q) = X. In this sense, the rule is recommended after we accept it.

I don’t think this recommendation is as empty as the one you get when you take the meaning of ‘&’ to be determined by the inferences we accept. Consider a slightly different case: why accept the inference from UNMARRIED & MAN to BACHELOR? Because someone’s a bachelor if they’re an unmarried man. On the direct theory, BACHELOR means bachelor because there is some mechanism that causally mediates the relation between tokens of bachelorhood and tokens of BACHELOR. It’s not required that you accept any particular inferences for there to be such a mechanism. It could be that you determine when to token BACHELOR in response to seeing someone whom your Google goggles identifies as ‘bachelor.’ That is, it could be that the inference from UNMARRIED & MAN to BACHELOR is recommended even when you don’t accept it. The same is true regarding the inference from P and Q to X. So long as X is caused by a state of affairs entailed by the truth of P and Q, the inference is recommended. Sometimes this causal relation will be mediated by your accepting this very inference, but nothing about the theory requires this.

Nevertheless, there’s still a worry. As a matter of fact, we accept the inference from P and Q to (P & Q), for any P and Q. Since (P & Q) is true when P is true and Q is true, this inference is to be recommended. But nothing about the theory requires (P & Q) to be related in meaning in any way to P and Q. The theory allows isolated counterexamples—say, cases where P means that snow is white, Q means that grass is green, and (P & Q) means tigers are blue—but it also allows massive inferential incoherence, with different instances of (P & Q) being unrelated to P and Q in wildly unsystematic ways. As a matter of fact, the only thing that binds the causes of (P & Q) to the causes of P and the causes of Q is our acceptance of the rule to infer from P and Q to (P & Q), for any P and Q.

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It’s fine to say that the theory recommends the rule in a way that’s conceptually prior to our accepting it. But that doesn’t really remove the puzzle of why we do things in this way when we really don’t have to (according to the theory). I denied compositionality, but then it didn’t turn out that things really changed. The meanings of complex expressions still look like they’re determined by what their parts mean and the way those parts are arranged. It’s good that the direct theory says that, because otherwise it’d be assigning the wrong meanings to those expressions. But isn’t it, from a theoretical perspective, really strange that the theory says that?

Consider two facts. First: the causal powers of computing devices are independent of the contents of their representations. Presumably, something like the intention-based metasemantic account is correct for artificial computing languages: it’s how we interpret or intend to interpret certain symbols that determines, say, which function the computer is computing. If we all stopped interpreting these symbols, a computer’s causal powers would remain unchanged. It would no longer be able to compute functions (because computation requires representation), but as far as its causal interactions with the environment are concerned, nothing would change.

Second: solving problems requires a high degree of inferential coherence. It is easy to write down algorithms for manipulating numbers represented by Arabic numerals or in binary. But if our representational format is given by a map from the numbers to arbitrary strings of Roman letters, writing down an algorithm for addition amounts to writing down a look-up table (which expands exponentially with the number of numbers we want to be able to add).

Now consider a mind “uninterpreted.” It has been designed to solve problems— to get from its perceptions to actions that increase its odds of survival. Problem solving (for finite machines) requires systematicity and inferential coherence. Minds without these features will have ceased to be. So we can expect that our “uninterpreted” mind will have hierarchically structured representations and abide by inference rules that are easy to state formally. The direct theory says that once you accept inferences, you create causal patterns between symbols that imbue those symbols with related meanings. Thus it’s not really “anything goes” on the direct theory: the structure of the problems we need to solve imposes certain formal structures on our thought processes, which in turn determine the contents of our thoughts.

IX. Coda: Compositionality and Natural Language

I want to end by arguing that a commonly held belief is unfounded. The belief is that compositionality must be true for natural language, and that theories that posit non-compositional accounts of some phenomena—say, theories of attitude ascriptions or non-cognitivist meta-ethical theories—must be false.

As we saw, intention-based metasemantic accounts are far more plausible for NL than accounts that say that complex NL expressions have the meanings they do in virtue of the meanings of their morphemes and the way they are combined (i.e. CMT for NL). Nevertheless, before I suggested that IBS nevertheless forces a kind of compositionality: since we cannot have specific intentions toward every complex expression of the language(s) we speak, we must have some sort of general intention about how they are to be interpreted.

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Again, suppose that general intention is: if expression E = [α β], then E means ⟦α⟧(⟦β ⟧). And suppose it thus follows that it thus follows that we intend that ‘brown cow’ MEANS ⟦brown cow⟧ = ⟦brown⟧(⟦cow ⟧) = λP. BROWN P (COW) = BROWN COW. That is, we intend that ‘brown cow’ MEANS BROWN COW, and this intention determines that this so. Thus, it follows that the meaning of ‘brown cow’ depends on the meanings of ‘brown’ and ‘cow’ only if the meaning of BROWN COW depends on the meanings of BROWN and COW assigned to ‘brown’ and ‘cow’, respectively. But this is false if the direct theory is true for LOT. For example, it’s easy to tell a compositional-looking theory whereby speakers intend that ‘e1 and e2 are simultaneous’ MEANS E1 AND E2 ARE SIMULTANEOUS. But on the direct theory, the meaning of the latter (LOT) representation will be determined directly and include unarticulated content—and thus, even accepting IBS, so will the former (English) representation.

This in itself may not bother anyone, simply because the argument turns on the possibility that the direct theory is true, and maybe only I believe that. But the case can be made stronger. NL looks like it must be compositional when you accept the intention-based account for NL and some compositional account for LOT. I just argued that abandoning a compositional account for LOT undermines any sort of requirement that theories of NL phenomena must be compositional. But the same goes if you abandon the intention-based account.

Direct theories are possible for NL too. It’s beyond the scope of this paper to argue for any such theory, but I will present a cartoon version to illustrate the point:

Ideal Speaker Theory (IST): English sentence S is true if a cognitively ideal English speaker would accept S, and is false if she would reject S.

“Cognitively ideal” agents are just agents who are informed of all the relevant non-semantic facts, like that this liquid on Twin Earth is not water, or that this animal I’m seeing on this dark night is not a cow, though it looks like one. You could worry about a number of aspects of IST—for example, can one characterize English speakers prior to establishing the truth-conditions of English sentences?—but I’m not defending it. It’s a cartoon view, to make a point.

IST assigns truth-conditions to sentences in a way that’s not sensitive to the meanings of the morphemes in those sentences. As far as IST is concerned, the things we’ve been calling ‘morphemes’ might not have any meanings. For example, cognitively ideal English speakers might accept “X weighs 5 pounds” when and only when X weighs 5 pounds on Earth. Or they might accept “Lois Lane believes Superman can fly” when and only when Lois Lane tokens such-and-such representation in her belief-box. If we reject IBS for NL, there’s no basis for requiring theories to provide us with a compositional semantics.

Where does the novelty argument fit in here? Isn’t the IST silent on the question of how we understand novel complex expressions we haven’t heard before? Yes. You can have separate theories of meaning determination and understanding. You don’t need to say that there is some representation we token when we understand an expression that determines the meaning of that expression. You could say that understanding an expression S is conforming to a convention to

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accept E (when you are cognitively ideal) in such-and-so conditions. The meaning of S is the conditions in which you accept S; you understand S when your S-meaning is the conventional one. Does this require compositional processes at some point? No. Think about the unarticulated consituents case once more. It’s completely possible for you and everyone else to conform to a convention to accept S in conditions C(U) where no part of S articulates U.

A lot of philosophers feel obligated to only offer compositional accounts of phenomena (like attitude ascriptions). But the motivation for such a constraint is extremely contentious. IBS is not a consensus view and there are alternatives. Even if you established IBS, the compositionality of LOT is not wholly uncontroversial. And if someone isn’t already committed to both IBS and the compositionality of LOT, I don’t see how it could be incumbent on them to provide compositional accounts.

X. Conclusion

To conclude, I want to start by stating what I have not done. Despite calling my view “the direct theory,” I have not offered a theory, but rather something like a theory schema. A necessary condition on any theory is that it not tell you that something is true in circumstances C and then fail to characterize C; this is not remedied by adding “appropriate circumstances C.” An explanation of what circumstances are appropriate, in the context of causal metasemantic theories, is a solution to the disjunction problem; I have left that problem aside here.

Secondly, I have not resolved certain patent and systemic problems for the direct theory. The direct theory says that the meaning of LOT expressions is whatever would cause them in appropriate circumstances. Thus if there are statements about the future that can’t be caused by future events, or statements about mathematical facts that can’t be caused by mathematical facts, then those statements are counterexamples to the direct theory. The direct theory most likely needs to be amended. There are extant causal theories more sophisticated than the crude theory presented here, but I have not attempted to survey them here.

What I have done is first, foregrounded a question that rarely reaches the surface in discussions of metasemantics, namely, what is the correct metasemantic theory for complex expressions? Presumably there is some fact in virtue of which a complex expression has the meaning it does, rather than some other meaning, or no meaning at all. We are often told that the meaning of a complex expression is a function of, is a computable function of, or supervenes on the meanings of its parts and the way those parts are syntactically combined. But we are not told complex expressions have their meanings in virtue of the meanings of their parts and the way those parts are syntactically combined. I have argued that this thesis (CMT) is nor so easy to defend as might first be supposed.

In defense of an alternative to CMT, the direct theory, I made three arguments. One of those arguments had to do with the principle of metasemantic uniformity. According to this principle, a metasemantic theory cannot be a “grab bag” where terms of class C1 have their meanings determined by what they bear relation R1 to, and terms of class C2 have their meanings determined by what they bear relation R2 to, and so on, with no commonality among the R’s. The

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direct theory by design satisfies this principle: it simply says that all expressions, simple or complex, have their meanings determined by what causes them in appropriate circumstances. CMT, I argued, falls afoul of the principle twice over: first in separating the meanings of simple expressions from complex expressions, and then again in requiring different simple expressions to have their meanings determined in different ways.

The other two arguments had to do with the gap between how the world is and how we represent it. There are incontrovertibly unarticulated constituents in mental representations. Hidden relativities abound, and we have spent millennia thinking about phenomena that were relative to things we could not possibly have known about, much less represented. On the direct theory, we nevertheless succeeded in having a truth-evaluable thoughts. The direct theory says the causal relations between states of affairs and thoughts directly determine the contents of those thoughts, and does not require content to be provided by the simple representations those thoughts comprise.

Additionally, I argued that the gap can go the other way: the world may possess less structure than we represent it as having, perhaps far less. CMT is ontologically committing. If the meaning of the whole is determined by the meanings of its parts, those parts must have meanings. Linguists have done a very thorough job in uncovering the hidden representations required for linguistic processing: representations of events, worlds, times, degrees, and so on. But what the physicist has in her ontology may look nothing like the human-centric representations we use to conceptualize and reason about the world. There is a genuine threat for CMT that none of our thoughts are contentful. Not so for the direct theory. On the latter, states of affairs, no matter their structure, can be the contents of our thoughts, no matter their structure, so long as those are the states of affairs our thoughts track.

Finally, I argued that the common claim that natural language has to be at least quasi-compositional is founded on two contentious assumptions: first, that something like an intention-based metasemantic theory is true for NL, and second, that LOT must be compositional. But there are competitors to both IBS and compositional semantic accounts of LOT. Thus I argued that compositionality in philosophical analyses is not a requirement for anyone who does not already accept the metasemantic theories that make it a requirement.