the myth of reverse compositionality

PHILIP ROBBINS

THE MYTH OF REVERSE COMPOSITIONALITY

ABSTRACT. In the context of debates about what form a theory of meaningshould take, it is sometimes claimed that one cannot understand an intersec-tive modifier-head construction (e.g., ‘pet fish’) without understanding its lexicalparts. Neo-Russellians like Fodor and Lepore contend that non-denotationalisttheories of meaning, such as prototype theory and theory theory, cannot explainwhy this is so, because they cannot provide for the ‘reverse compositional’character of meaning. I argue that reverse compositionality is a red herring inthese debates. I begin by setting out some positive arguments for reverse composi-tionality and showing that they fail. Then I show that the principle of reversecompositionality has two big strikes against it. First, it is incompatible with alltheories of meaning on the market, including the denotationalism favored byneo-Russellians. Second, it explains nothing that is not already explained by itsvenerable predecessor, the principle of (forward) compositionality.

It’s a familiar fact about speakers of English that anyone who knowsthe meaning of ‘pet’ and the meaning of ‘fish’, and has the syntacticwherewithal to combine these words, knows (at least implicitly)the meaning of ‘pet fish’. More generally, given any modifier-headconstruction – for example, any intersective noun phrase – onecan understand any of its instances whose lexical parts one under-stands. This epistemological fact, a fact about speakers’ knowledgeof meaning, is usually explained by appeal to the principle ofcompositionality (PC). The principle governs the nature of the rulesknowledge of which underlies semantic competence (Larson andSegal, 1995). According to PC, the meaning of a modifer-headconstruction is derivable by these rules solely from the meaning ofits lexical parts plus its syntax. No further information, either aboutlanguage or about the world, is needed.1 Compositionality in thissense is old hat, its theoretical importance beyond dispute. There’s along-standing consensus in linguistics and philosophy, for example,that compositionality is needed to explain how natural languagescan be learned, given that languages are infinite and brains are not(Davidson, 1984).

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Lately it’s been argued that meaning in natural language is alsocompositional in a further sense, roughly converse to the tradi-tional one (Fodor, 1998b, 2002; Fodor and Lepore, 2001). FollowingFodor and Lepore, I’ll call this new property ‘reverse composi-tionality’. According to the principle of reverse compositionality(PRC), the meanings of a phrase’s lexical parts are derivable solelyfrom the meaning of the phrase plus its syntax, and nothing more.2

Proponents of PRC claim that this new principle is needed toaccount for why anyone who knows the meaning and syntax of ‘petfish’ also knows (at least implicitly) the meaning of ‘pet’ and themeaning of ‘fish’ – or, more generally, why anyone who understandsa modifier-head construction also understands the words it contains,solely in virtue of understanding that one phrase. Like composi-tionality of the traditional variety, reverse compositionality is putforth as a structural property of language itself, posited to explaina feature of our knowledge of language. In each case, the linguisticproperty is a type of derivability, and its epistemic manifestation isa type of dependence in understanding.

Compositionality principles have loomed large in recentdiscussions of the theory of meaning. In particular, contemporaryneo-Russellians – that is, advocates of a purely denotational (truth-conditional) approach to semantics – have pointed to them as knock-down evidence against rival views. Here is a representative passage:

Over the last few years, we have just about convinced ourselves that composi-tionality is the sovereign test for theories of lexical meaning. So hard is thistest to pass, we think, that it filters out practically all of the theories of lexicalmeaning that are current in either philosophy or cognitive science. (Fodor andLepore, 2001, p. 351)

The list of failures includes, inter alia, prototype theory, theorytheory, and use theory. In fact, it includes all views except for two:the classical view of lexical meanings as definitions (discredited onother grounds)3 and the denotation-based account favored by theauthors.

To see the test in action, consider how standard prototypesemantics treats ‘pet fish’. According to such a semantics, themeaning of an expression is its associated prototype, that is, a listof features characteristic of items to which the expression correctlyapplies. The prototype of ‘pet’ includes features such as furry, four-

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legged, and terrestrial, where the prototype of ‘fish’ includes scaly,finned, and aquatic. But the prototype associated with ‘pet fish’includes features – brightly colored, matchbook-sized, aquarium-dwelling – which cannot be traced back to the prototypes associatedwith ‘pet’ and ‘fish’. So the phrasal prototype cannot be derivedfrom the lexical prototypes plus syntax. Hence, prototype semanticswould seem to violate the principle of compositionality, leaving uswithout an explanation of the fact about understanding with whichwe began. The same line of reasoning applies, mutatis mutandis, toneighboring views on the list.

What about reverse compositionality? One might think that thetest of (forward) compositionality is stringent enough for Fodorand Lepore’s purposes. Not so, for there are non-classical, non-denotationalist theories of meaning that pass it. Fodor characterizesthe general form of such a theory as follows:

Epistemic properties, such as having some particular criteria of application, areessential to morphosyntactically primitive linguistic expressions (like ‘red’ and‘fish’) but not to their hosts (like ‘red triangle’ and ‘pet fish’) even in caseswhere the hosts are semantically compositional. (Fodor, 1998b, p. 52; italics inoriginal)

Here’s a specific example of the sort of theory Fodor has in mind,that is, a compositional theory of meaning which is neither classicalnor (strictly) denotational. Say we split the difference betweendenotation-based and prototype-based semantics, as follows: themeaning of a word is given by a pair consisting of its denotationand the associated prototype, and the meaning of a phrase by itsdenotation alone. (Being associated with a particular prototype isan ‘epistemic’ property of an expression, in Fodor’s sense.) Thishybrid theory complies with PC by (a) incorporating denotations atboth the lexical and the phrasal level and (b) dispensing with phrasalprototypes. This allows for the semantics to interpret a modifier-head construction even in cases where the associated prototypecannot be derived by compositional means, as with ‘pet fish’.Notice, however, that the theory fails the test of reverse composi-tionality, since it blocks the possibility of deriving lexical meaningssolely from phrasal meaning plus syntax. By bringing PRC intoplay, neo-Russellians seek to force hybrids like these out of therunning.

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The success of the neo-Russellian strategy seems to require, then,that both forms of compositionality – forward and reverse – consti-tute a bona fide constraint on theories of meaning. And it’s farfrom obvious that this is the case. Though PC is well entrenchedin linguistics and philosophy, the same cannot be said of PRC. Howmight one argue for this second principle, and how well do sucharguments stand up under scrutiny?

This is the question I propose to answer, negatively, in the firstpart of the paper (§1). Continuing in a negative vein, I’ll presenta pair of arguments against reverse compositionality, one of whichexplicitly invokes the neo-Russellian thesis as a premise (§§2–3).Then I’ll revisit the issue of hybrid theories in order to reassessthe challenge it poses to neo-Russellianism (§4). My overarchinggoal is to show that, as far as debates about the semantics of naturallanguage are concerned, reverse compositionality is a red herring.

1. THE CASE FOR REVERSE COMPOSITIONALITY

As noted above, advocacy of the principle of reverse composition-ality rests on an epistemological premise:

(EP) One cannot understand a modifier-head constructionwithout understanding the words it contains.

Assuming this claim to be correct, it seems natural enough toproceed, via inference to the best explanation, to:

(PRC) From the meaning of a modifier-head construction and itssyntax it is possible to derive the meanings of the wordsit contains.

Hence, if EP is true, then PRC is probably true as well.In the discussion to follow, I will focus on the justification for

EP. But before getting there, I need to say a few words about theplausibility of inferring PRC from EP. This is important, since Fodorand Lepore base much of their case for reverse compositionality onthe assumption that the inference is a good one (Fodor and Lepore,2001). Lest there be any confusion on this score, I want to emphasizethat the reason Fodor and Lepore endorse PRC is not that they seeit as a handy way to force out competitors to their favorite theory ofmeaning. Rather, they endorse the principle because they think it’s

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true. And they think PRC is true for two reasons: first, because EP istrue, and second, because PRC offers the most likely explanation ofthis fact. My view differs from theirs in that I see no reason to thinkthat either EP or PRC is true; but I agree with them that, if EP weretrue, it would make sense to endorse PRC on that basis.

1.1. The Route from EP to PRC

Suppose PRC were true. Then anyone who knew the meaning andsyntax of a phrase could derive the meanings of its lexical parts.So anyone who understood the complex would understand (at leastimplicitly) its parts. And that’s just what EP says. Thus, supposingEP were true, we could explain that fact by appeal to PRC. What’smore, it’s not clear what would count as a better explanation. Noticethat it won’t do to recruit the compositionality principle with whichwe began, namely:

(PC) The meaning of a modifer-head construction is derivablefrom the meaning of its lexical parts plus its syntax.

PC doesn’t explain EP, since even if PC were true, EP could be false.What PC would explain is a different epistemological claim:

(EP*) One cannot understand the words contained in a modifier-head construction plus its syntax without understandingthe construction itself.

EP* is plausibly true, but it is also consistent with the falsity of EP.So the fact that PC would explain EP* gives us no reason to thinkthat PC could explain EP. Indeed, it seems plain that EP cannot beexplained by appeal to compositionality, at least not in its familiarform.

What about a strengthened version of the compositionality prin-ciple? Perhaps something like this would do the trick:

(PC+) The meaning of a modifer-head construction is deriv-able from the meaning of its lexical parts plus its syntax,and there is no other way to derive the meaning of suchconstructions.

Alas, PC+ by itself won’t explain EP. But if we add to PC+ theepistemological assumption

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(DP) The only way to determine the meaning of a modifier-head construction is by deriving it from something else

then we arrive at EP. That yields an alternative account of why theepistemological premise might be true. But the alternative explana-tion seems inferior to the original, insofar as the original explanationis clearly simpler than the alternative. Whereas the explanation fromreverse compositionality relies on a single claim about derivability(PRC), the explanation from compositionality relies on two claims,one about derivability (PC+) and a second about the dependenceof knowability on derivability (DP). Since all of these claims arecontroversial, and roughly equally so, appealing to PRC seems likea better strategy for explaining EP.

Of course, other explanations of EP are possible, and it’s possiblethat among them is a better alternative to PRC than the explanationmooted above. But it’s unclear what such a better alternative wouldlook like. Until one comes along, inferring PRC from EP seemsreasonable.

In short, this much of the motivation behind reverse composition-ality – the structural aspect, as it were – seems sturdy enough. Thenext step for proponents of PRC is to motivate the epistemologicalpremise. If there is a good case to be made for EP, then the prospectsfor PRC will also be good. Conversely, without some justificationfor the premise, the principle will invite skepticism.

In the remainder of this section I’ll consider three ways in whichone might try to supply this justification. Though each strategy hassome initial plausibility, none of them comes to much in the end.The result is bad news for friends of reverse compositionality.

1.2. The Argument from Intuition

Consider a hypothetical speaker whom I’ll call Petra. Petra appliesthe phrase ‘pet fish’ correctly in standard cases, and she knowsthat ‘pet fish’ is an intersective noun phrase, but she is innocentof the meaning of ‘pet’ and ‘fish’. Petra has acquired the phrasein something like the way a foreigner might acquire some fragmentof English from a phrasebook. The principal difference is that she,unlike the foreigner, understands the syntax of the expression.

What should one say about the competence of such a speaker?Presumably this: though Petra has some grasp of the phrase, her

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understanding is defective. This intuitive verdict lends support toEP – or so an advocate of reverse compositionality might claim.

But there are a couple of flies in the ointment. The first is this.While Petra’s case makes it plausible that full competence withphrases like ‘pet fish’ depends on knowing the meaning of the wordsthey contain, it does not show that phrasal understanding in theoperative (i.e., EP-relevant) sense – that is, knowledge of phrasalmeaning and syntax – so depends. For there are other possibilitiesto consider. It might be that the gap in Petra’s competence with‘pet fish’ is pragmatic, rather than semantic or syntactic. Perhapsshe knows full well what ‘pet fish’ means and what syntactic struc-ture it has, but she can only put the phrase to use correctly in alimited range of contexts. There’s not enough information given inthe story for us to tell. The second problem with the argument isthat the gap in Petra’s understanding might be purely lexical. Byhypothesis, there are common words of English whose meaning shedoesn’t know. Perhaps that gap in her understanding (a gap at thelevel of words) is being confused with a different gap (a gap atthe level of phrases). It’s important to bear in mind here that, if theepistemological premise is true, then understanding the phrase ‘petfish’ suffices all by itself for understanding ‘pet’ and ‘fish’. It doesnot say that a fully competent speaker of English who understands‘pet fish’ also understands ‘pet’ and ‘fish’. If it did, the claim wouldbe trivially true, since fully competent speakers of English ipso factounderstand the words ‘pet’ and ‘fish’. The real EP, by contrast, isdecidedly nontrivial.

In short, it’s pretty clear that Petra is missing something. It’smuch less clear what that something is. Unless the alternativediagnoses sketched above can be ruled out, her case lends littlecredence to EP.

1.3. The Argument from Concept Possession

A second strategy for motivating the epistemological premisebehind PRC appeals to the nexus between psychology andlinguistics. It is not uncommon for philosophers to go back andforth freely between talk of linguistic understanding, on the onehand, and talk of concept possession, on the other.4 On this wayof thinking about things, understanding a word or phrase is effec-

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tively equivalent to possessing the concept expressed thereby. Forexample, understanding ‘pet fish’ is equivalent to having the phrasalconcept PET FISH.5 And PET FISH is a complex concept: it has the(lexical) concepts PET and FISH as constituents. Since one cannotpossess a whole without possessing its parts, it follows that one can’tpossess PET FISH without possessing PET and FISH. According tothe equivalence assumption, then, one cannot understand ‘pet fish’without understanding ‘pet’ and ‘fish’.

The main problem with this line of reasoning is that under-standing a word or phrase is almost certainly not equivalent tohaving the concept it expresses.6 The latter is a necessary condi-tion for the former, but it is not sufficient. There are a coupleof reasons for this. First, it seems perfectly possible that mono-lingual speakers of a language which lacked a word translatableas ‘fish’ could have the concept FISH. Indeed, it seems possiblethat one could possess this concept without speaking any languageat all. Second, most accounts of lexical acquisition assume thatchildren learn words by tagging mental categories with verbal labels– a mapping process in which concepts typically precede words(Bloom, 2000). Standard lines of argument for the existence ofMentalese, an internal language of thought distinct from any naturallanguage, tend in the same direction (Fodor, 1981).

Here’s another route to the same conclusion. Anyone who under-stands the phrase ‘pet fish’ has the concept PET FISH, and (arguably)anyone who has the concept PET FISH has the concepts PET andFISH. But unless you know which concepts the words ‘pet’ and‘fish’ express – that is, unless you know that ‘pet’ expresses PET

and ‘fish’ expresses FISH, and (say) not the other way around – youdon’t understand these words. Hence, merely possessing a lexicalconcept does not suffice for understanding the word that expressesit; one has to solve the mapping problem as well.

1.4. The Argument from Learnability

A third pro-EP strategy is to show that giving up the premise wouldunduly constrain the sort of evidence required for language learning.In particular, Fodor has argued that if the premise were false, thenthe lexicon of a language could be learned only from a corpusthat contained atomic sentences, and not otherwise (Fodor, 1998b,

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2002). His reasoning is as follows. If the premise is false, under-standing a modifier-head construction ‘AdjN’ does not suffice forunderstanding ‘Adj’ and ‘N’. So exposure to sentences containingthat construction – that is, sentences of the form ‘This is an AdjN’– will not enable a child to learn these words. To acquire ‘Adj’ and‘N’, she needs to encounter sentences like ‘This is Adj’ and ‘Thisis an N’. But as Fodor observes, this seems implausible: one wouldexpect the lexicon to be learnable from a wholly non-atomic corpus.At the very least, the possibility should be left open. And this meansendorsing EP.

But this argument, like the previous two, fails to convince.To see why, consider a corpus containing sentences like thefollowing:

(1) Here are some pet fish.(2) This is a pet ferret.(3) How do you like my pet iguana?

Suppose that the child comes to understand each of these sentences.She knows that ‘pet fish’, ‘pet ferret’, and ‘pet iguana’ refer topet fish, pet ferrets, and pet iguanas, respectively. She also knowsthat each of these expressions is an intersective noun phrase, andhence that ‘pet’ refers to the intersection of pet fish, pet ferrets, petiguana, and the like. She also knows from experience that pet Ns,for all their diversity, have certain characteristics in common: theyare typically small animals kept in people’s homes, given names,fed with special food, offered for sale in special shops, and so on.Thus, with a sufficiently large supply of sentences like (1)–(3) – thatis, sentences containing the phrase ‘pet N’ – she can figure out, byinductive reasoning, what ‘pet’ means. Likewise, mutatis mutandis,with ‘fish’.

This story does not assume that understanding the phrase ‘petfish’ suffices for understanding the words ‘pet’ and ‘fish’, as perEP. All it assumes is that understanding a suitably large numberof modifier-head phrases containing ‘pet’ and ‘fish’ suffices forunderstanding these words. That’s a far cry from EP. And the prob-lems with Fodor’s argument don’t end there. There’s a further flaw,namely, his assumption that children cannot learn the meaning ofa word except by learning the meaning of sentences containingit. This too seems questionable. For example, it’s plausible that a

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child could learn the meanings of words for animals by seeing signsin the zoo, or appropriately labeled pictures of animals. There isalso the phenomenon of non-sentential assertion, and non-sententialspeech acts more generally, to consider (Stainton, 1995). All ofthis suggests that exposure to words in sentential form, atomic orotherwise, isn’t necessary for learning them.

Pace Fodor, then, the possibility of learning a word without beingexposed to it in the guise of atomic sentences does not require thatEP be true. Hence, Fodor’s argument for the premise – based asit is on an implausibly low estimate of the amount of informa-tion available in the linguistic training environment – does not gothrough.

As we’ve seen, solid support for the principle of reverse composi-tionality is hard to come by. That alone suggests that we shouldbe skeptical about the potential of PRC to serve as a constraint ontheories of meaning. In the next two sections I’ll go further in thedirection of skepticism, laying out two arguments against the prin-ciple. The first argument casts doubt on the principle by showinghow hard it is to find a semantics that complies with it (§2). Thesecond casts doubt on the explanatory value of PRC in a semanticswhich already complies with its forward counterpart (§3).

2. THE PRICE OF COMPLIANCE

We noted earlier, using the example of ‘pet fish’, that garden-variety prototype semantics is not compositional. The reason givenwas that the prototype associated with the phrase includes features(brightly colored, matchbook-sized, aquarium-dwelling) extrinsicto the prototypes associated with the words, thereby making itimpossible to derive the phrasal prototype from the lexical proto-types plus syntax. But there’s more. Since the prototype of ‘petfish’ excludes features contained in the prototypes of ‘pet’ (furry,four-legged) and ‘fish’ (outdoor-dwelling, meat-eating), the lexicalprototypes can’t be derived from the phrasal prototype. So proto-type theory isn’t reverse compositional either. The same applies,by parity of reasoning, to theory theory, use theory, and the othertheories on Fodor and Lepore’s hit list.

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What about denotational semantics? Well, just as prototypetheory says that the meaning of an expression is its prototype,denotationalism says that the meaning of an expression is its denota-tion (Fodor and Lepore, 2001). This goes for phrases as well aswords. For example, the meanings of ‘pet’, ‘fish’, and ‘pet fish’ arepets, fish, and pet fish, respectively. The latter may be modelledin a variety of different ways, depending on what sort of entityone chooses to identify denotations with. Standard options includesets (e.g., the set of actual and possible individual pets, or fish,or pet fish); functions (a mapping from possible worlds into setsof individuals); pluralities (the totality of actual and possible pets,or fish, or pet fish); and properties (pethood, fishhood, or pet-fish-hood).7

Denotationalists find it easy to meet the requirement that meaningis compositional. From the fact that ‘pet’ means pets and ‘fish’means fish, together with the fact that putting these words togetheryields an intersective NP, it follows that ‘pet fish’ means pet fish. SoPC is satisfied. The same holds for classical semantics, which iden-tifies the meaning of an expression with its analytic definition. Sinceanalytic definitions (viz. sets of necessary and sufficient conditionsfor membership), like denotations, compose, the classical theorysquares with PC.8

Reverse compositionality is a different story. To see why, supposewe fix the meaning and the logico-syntactic form of ‘pet fish’: ‘petfish’ means pet fish, and it’s an intersective modifier-head construc-tion. It does not follow that ‘pet’ means pets and ‘fish’ meansfish, since it’s consistent with these initial assumptions that ‘pet’means fish and ‘fish’ means pets. In fact it’s consistent with theseassumptions that ‘pet’ and ‘fish’ mean anything at all, providedthat the intersection of their meanings is pet fish. The possibilitiesare endless. For example, ‘pet’ and ‘fish’ could mean fish plusskyscrapers, and pets plus watermelons, respectively. Likewise, ifdenotational semantics is correct, then understanding of the phrasedoes not confer understanding of its parts, contra EP. Suppose youknow what ‘pet fish’ means. Suppose further that you know ‘petfish’ is an intersective modifier-head construction. Then you knowonly that pet fish is the intersection of the denotation of ‘pet’ andthe denotation of ‘fish’. For all you know, ‘pet’ denotes fish (or fish

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plus fire hydrants, or fish plus asteroids, or . . .) and ‘fish’ denotespets (or pets plus pomegranates, or pets plus skyscrapers, or . . .).Hence, as before, you may have no idea that ‘pet’ denotes petsand ‘fish’ denotes fish. So you may have no idea what these wordsmean. The same arguments apply, mutatis mutandis, to classicalsemantics.9

It appears, then, that no matter what meanings are – prototypes,theories, denotations, or definitions – they’re not reverse composi-tional. This should come as a surprise to Fodor and Lepore inparticular, since they take PRC to militate in favor of denotation-alism. The truth is, they’ve got it backwards: If meaning is reversecompositional, then meaning cannot be identified with denotation.In saying this, however, I do not mean to suggest that denotation-alism is false. For, as we’ve seen, PRC is not just inconsistentwith denotationalism; it’s inconsistent with every major theory ofmeaning in linguistics and philosophy today. One might concludefrom this that all of these theories are false. But in the absence ofindependent justification for the principle (see §1), it seems muchmore likely that meaning is not reverse compositional.

What this means is that a denotationalist who wants to hold ontothe principle of reverse compositionality has some work to do. Inparticular, she needs to poke a hole in the argument that denotation-alism violates PRC. But as we’re about to see, this is easier said thandone (§2.1). It turns out that there’s no way to make a denotation-based theory of meaning reverse compositional – or any other typeof meaning theory, for that matter – without substantially amendingthe standard version (§2.2).

2.1. Inconsistency Challenged

There are at least two ways in which a denotationalist might try toblock the conclusion that her theory runs afoul of PRC. The first isby objecting that the argument sketched above regarding ‘pet fish’overlooks some crucial information contained in the syntax of thephrase. In particular, she might reason as follows:

The NP ‘pet fish’ is an adjective-noun (AdjN) construction. Since ‘pet’ is of adifferent syntactic type than ‘fish’, the former cannot be assigned a semantic valueof the same type as the latter. So we can rule out the possibility that ‘pet’ denotesfish and ‘fish’ denotes pets. Likewise, we can rule out the possibility that ‘pet’

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denotes fish plus fire hydrants and ‘fish’ denotes pets plus pomegranates. And soon, for all possible deviant (viz. nonstandard) interpretations of ‘pet’ and ‘fish’consistent with the assumption that ‘pet fish’ is an intersective AdjN denoting petfish.

But this objection doesn’t work, for a couple of reasons.To begin with, it’s not obvious that two words of different

syntactic type must also be of different semantic type. So justbecause ‘pet fish’ is interpreted as an AdjN doesn’t entail that ‘pet’and ‘fish’ belong to different semantic categories.10 Consider thewell-known analysis of intersective NPs such as ‘pet fish’ whichmaps ‘pet’ to the set of individuals kept as pets, ‘fish’ to the set offish, and ‘pet fish’ to the intersection of those sets (Partee, 1995).Here both constituents of the NP get assigned a semantic value ofthe same type, namely, a set of individuals. This isn’t the only wayto handle these constructions, but it’s a contender.

What’s more, even if ‘pet’ and ‘fish’ are assigned to differentsemantic categories, that leaves open an indefinite plurality ofdeviant interpretations. Say we interpret Adj as a function from thesemantic value of the N it modifies to the semantic value of AdjN(Montague, 1974). In the case of an intersective adjective like ‘pet’,for example, we assign a function which maps the value of ‘fish’(e.g., the set of fish) to its intersection with the set of individualskept as pets. On this view, ‘pet’ and ‘fish’ are semantically type-distinct: where the latter gets assigned a set, the former gets assigneda function from sets into sets. Still, the fact that ‘pet fish’ is an inter-sective NP referring to pet fish does not entail that ‘pet’ and ‘fish’are interpreted as above. For it’s consistent with these constraintsthat ‘pet’ is interpreted as a function from the value of the noun itmodifies to its intersection with the set of individuals kept as petsplus pomegranates. Similarly, it’s possible that the semantic valueof ‘fish’ is the set of fish plus fire hydrants. The possibilities are noless unbounded than before.

So much, then, for the first objection to the inconsistency argu-ment. The second objection is as follows. One might suppose thatfor the meaning of the lexical parts of a phrase to be derivable fromthe meaning and syntax of the whole, it suffices that the phrasalmeaning contains the lexical meanings as parts. This seems to bewhat Fodor and Lepore have in mind when they insist that

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the meaning of ‘dogs bark’ supervenes on the meanings of ‘dogs’ and ‘bark’because the meanings of ‘dogs’ and ‘bark’ are parts of the meaning of ‘dogsbark’; and the meanings of ‘dogs’ and ‘bark’ supervene on the meaning of ‘dogsbark’ for exactly the same reason . . . the meaning of ‘dogs’ and ‘bark’ mustbe contained in the meaning of ‘dogs bark’ because people who understand thesentence likewise understand the words. (Fodor and Lepore, 2001, p. 366)11

Now, there are a couple of points I want to make about thisproposal. The first is that it debars denotationalists from interpretingpredicates using sets, pluralities, or functions, and makes it naturalfor them to use properties instead. The second, more important pointis that the proposal doesn’t solve the problem, since a part-wholerelation between lexical and phrasal meanings cannot do the workrequired by PRC. I’ll expand on each of these points in turn.

What denotations could not be. To see why the mereological hypoth-esis rules out the identification of denotations with sets, pluralities,or functions, consider again the case of ‘pet fish’. According tothe hypothesis, the meaning of ‘pet’ and the meaning of ‘fish’ areparts of the meaning of ‘pet fish’. As we saw earlier, denotation-alists say that the meaning of a word is its denotation. They alsoendorse the idea that words and phrases of the same basic syntactictype are to be interpreted in a uniform manner.12 So they must saythat the meaning of ‘pet fish’ is its denotation, namely, pet fish.But if denotations are understood as sets of individuals, pluralities,or functions (from worlds into sets of individuals), then neitherthe denotation of ‘pet’ nor the denotation of ‘fish’ is part of thedenotation of ‘pet fish’.

Here’s why. It’s true that the set of pet fish is a subset of boththe set of pets and the set of fish. It’s also true that we can thinkof the subset relation as a parthood relation, with the subsets of aset as its parts. (Like the standard mereological relation of parthood,the subset relation is reflexive, transitive, and anti-symmetric.) Butthis is no help, as it yields the wrong result: namely, that the denota-tion of ‘pet fish’ is part of the denotation of ‘pet’ and part of thedenotation of ‘fish’, rather than the other way around. No matterhow you slice it, it seems, the mereological approach to the problemof reverse compositionality can’t be adopted without giving up theidentification of denotations with sets – at least on the assumption

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that words and phrases of the same syntactic type belong to the samesemantic type as well.13

This argument readily generalizes to versions of denotationalismthat identify denotations with set-like entities, such as pluralities andfunctions. Take the case of pluralities first. On the plurality view, thedenotations of ‘pet’, ‘fish’, and ‘pet fish’ are the plurality of pets, theplurality of fish, and the plurality of pet fish, respectively. Not allpets are pet fish, and not all fish are pet fish, so neither the pluralityof pets nor the plurality of fish is part of the plurality of pet fish.Hence, neither the denotation of ‘pet’ nor the denotation of ‘fish’is part of the denotation of ‘pet fish’. Rather, since every pet fish isa pet and a fish, the plurality of pet fish is part of the plurality ofpets and part of the plurality of fish. So, according to the plurality-theoretic view, the denotation of ‘pet fish’ is part of the denotationof ‘pet’ and part of the denotation of ‘fish’. Like the set-theoreticview, this gets things the wrong way around.

The same problem arises if we identify denotations with func-tions. This case is more complicated than the previous two, butthe underlying logic is much the same. On the function-theoreticapproach, the denotation of a predicative expression e is a func-tion from worlds into sets of individuals which maps each worldto the set of individuals in the extension of the predicate at thatworld. For example, the denotation of ‘pet’ is the function Funcpetwhich maps each world w to the unique set of individuals thatare pets at w; likewise, mutatis mutandis, with the denotation of‘fish’ (= Funcfish) and the denotation of ‘pet fish’ (= Funcpetfish).We can then characterize the parthood relation on such functions asfollows:

(Def. 1) Given predicates e and e∗, Funce is part of Funce∗ if andonly if for all worlds w, Funce(w) is part of Funce∗(w)

where

(Def. 2) Funce(w) is part of Funce∗(w) if and only if Funce(w)is a subset of Funce∗(w).

Getting back to ‘pet fish’: since we have, for all worlds w,

(4) Funcpet(w) = {x: x is a pet at w}(5) Funcfish(w) = {x: x is a fish at w}(6) Funcpetfish(w) = {x: x is a pet fish at w}

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it follows from our second definition (Def. 2) that

(7) Funcpetfish(w) is part of Funcpet(w) [from (4) and (6)]

and

(8) Funcpetfish(w) is part of Funcfish(w) [from (5) and (6)].

And it follows from our first definition (Def. 1) that (7) and (8)entail, respectively,

(9) Funcpetfish is part of Funcpet

and

(10) Funcpetfish is part of Funcfish.

If denotations were functions, then, the denotation of ‘pet fish’would be part of the denotation of ‘pet’ and part of the denotation of‘fish’, not conversely. And in that case, the mereological hypothesiswould be false.

Hence, denotationalists who wish to endorse the hypothesis andcomply with the uniformity assumption need a way of modelingdenotations in terms of something other than sets, pluralities, orfunctions. The most familiar alternative is properties. On thisapproach, the meanings of ‘pet’, ‘fish’, and ‘pet fish’ are the prop-erty of being a pet, the property of being a fish, and the property ofbeing a pet fish, respectively. By adapting the analysis of the part-whole (‘classical constituency’) relation on expression types givenin Fodor and McLaughlin (1990), we have the following:

(PartProp) For all properties F and G, F is a part of G iffnecessarily, G is tokened only if F is tokened.

It follows from this that the property of being a pet fish has theproperty of being a pet and the property of being a fish as parts.Hence, if denotations are identified with properties, denotationalismis consistent with the assumption that the meaning of a modifier-head construction (e.g., ‘pet fish’) has the meaning of the words itcontains (‘pet’, ‘fish’) as parts. Given that the same can’t be saidabout any of the other standard candidates for denotations (sets,functions, pluralities), denotationalists who adopt the mereologicalhypothesis are well advised to try the property-theoretic route – or,failing that, some non-standard alternative to the options canvassedabove – instead. This isn’t necessarily a problem for their view.14

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But it is noteworthy – especially in light of the tendency on the partof some neo-Russellians, including Fodor, to identify denotationswith sets (Fodor, 1998b).

Mereological impotence. Now, here is a problem. Suppose that themeanings of ‘pet’ and ‘fish’ are parts of the meaning of ‘pet fish’,as per property-theoretic denotationalism. It follows that the formermeanings are derivable from the latter (plus syntax) in some sense,but not in the sense required to explain why anyone who understands‘pet fish’ also understands ‘pet’ and ‘fish’ (as per EP). The explana-torily relevant relation is this: the fact that ‘pet’ means pets and ‘fish’means fish is derivable from the fact that ‘pet fish’ is an intersectiveNP meaning pet fish. Mereological containment falls short of this,since it’s possible that ‘pet fish’ is an intersective NP meaning petfish, the meanings of ‘pet’ and ‘fish’ are parts of the meaning of ‘petfish’, and ‘pet’ and ‘fish’ have deviant interpretations. For example,‘pet’ might mean the property of being a fish and ‘fish’ might meanthe property of being a pet. The fact that ‘pet fish’ is an intersectiveNP which means the property of being a pet fish, together with thefact that the meaning of ‘pet fish’ contains the meanings of ‘pet’and ‘fish’ as parts, does not rule out this assignment of properties to‘pet’ and ‘fish’, or any number of other bizarre assignments. Hence,even if the mereological hypothesis were true, it wouldn’t followthat denotationalism is reverse compositional.

2.2. What Reverse Compositionality Requires

So what does it take to make a denotational theory of meaningreverse compositional? We’ve seen that the mereological approachsuggested by Fodor and Lepore doesn’t work. Nevertheless, the gistof the approach – that phrasal meanings have constituent structure– seems promising. The trick is to find the right kind of structure.As far as reverse compositionality goes, it’s not enough for a phraseto encode the meaning of its lexical parts. Compliance with PRCalso requires that a phrase encode the derivational history of thosemeanings: that is, it must specify what each syntactic constituentof the phrase contributed to determining the meaning of thewhole.

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Here’s one way to represent the necessary information. Thereare three levels: one syntactic, another semantic, and a third at theinterface between the first two. At the first level, we have a phrasemarker:

(Syn) [NP [Adj pet] [N fish]]

At the second level, we have a denotation:

(Sem) {x: x is kept as a pet} ∩ {x: x is a fish}

And at the interface we have a semantic annotation for eachconstituent of the phrase:

(Int1) [Adj pet]: {x: x is kept as a pet}(Int2) [N fish]: {x: x is a fish}

The three types of information can be combined into a singlerepresentation, an annotated phrase marker:15

(APM-D) [NP [Adj pet]: {x: x is kept as a pet} [N fish]: {x: x isa fish}]: {x: x is kept as a pet} ∩ {x: x is a fish}

Since the annotated phrase marker (APM) for ‘pet fish’ encodesboth the meaning and derivational history of its constituents, reversecompositionality is satisfied. Thus, if knowing the meaning andsyntax of a phrase consists in knowing the associated APM, then onecannot know the meaning and syntax of ‘pet fish’ without knowingthe meaning of ‘pet’ and ‘fish’. And that is just what we wereafter.

Having shown how to make denotational semantics reversecompositional, it is natural to wonder whether a similar strategymight be applied to rival theories, such as prototype semantics.The answer is yes. The solution is identical to what we did before,modulo the substitution of prototypes for denotations. The phrase‘pet fish’ can be represented as follows:

(APM-P) [NP [Adj pet]: Prototype(‘pet’)[N fish]: Prototype (‘fish’)]: Prototype(‘pet fish’)

As before, if the meaning and syntax of ‘pet fish’ are encodedin this form, then anyone who understands the phrase ipso factounderstands the words it contains. Given the nature of APMs,it’s to be expected that prototype semantics can be adapted tocomply with PRC just as easily as denotationalism can. In fact, all

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standard theories of meaning – denotation-based, prototype-based,definition-based, theory-based, what have you – are equivalent inthis respect. The general form of the solution is as follows:

(APM-G) [NP [Adj pet]: Val(‘pet’) [N fish]: Val(‘fish’)]:Val (‘pet fish’)

where ‘Val(‘e’)’ denotes the meaning (i.e., semantic value) of theexpression ‘e’. In short, no standard theory is reverse compositionalas it stands, but every one can be made reverse compositional bymeans of the same technical device.

Given the non-trivial character of this revision, and the addedcomplexity of the resulting theory, it seems natural to questionthe claim that compliance with PRC is desirable. Indeed, it seemsnatural to suspect that it’s not, and that the principle is probablyfalse.

3. THE PROBLEM OF SUPERFLUITY

We’ve seen that every standard theory of meaning, including denota-tionalism, fails the test of reverse compositionality. We’ve also seenthat bringing a theory of meaning into compliance with PRC meansrevising the theory in a fundamental respect. Especially in the wakeof an unsuccessful search for evidence of the principle’s truth, theseresults raised suspicion of its falsity. In this section I want to addto that suspicion by sketching an auxiliary line of argument againstPRC.

The second argument goes like this. Say we’re working with acompositional meaning theory, that is, a theory that complies withPC. It follows, then, that the meaning of ‘pet fish’ is derivablefrom the meaning of ‘pet’ and ‘fish’ plus syntax. This gives us theresources to explain why knowing the meaning of ‘pet’ and ‘fish’,together with knowing how to combine these expressions, sufficesfor knowing the meaning of ‘pet fish’. Notice, now, that anyone whocomes by her understanding of ‘pet fish’ in a compositional fashion– that is, anyone who gets to the whole by assembling it from theparts – will ipso facto understand ‘pet’ and ‘fish’. And it seemslikely that the vast majority of speakers will have followed preciselythis recipe when learning the phrase. Hence, just by assuming PC,

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we’re already in a position to explain a weakened form of theepistemological premise (EP):

(EP−) Typically, speakers who understand a modifier-headconstruction understand the words it contains.

The principle EP− does not say that every speaker fits this pattern.It merely says that most speakers do. Thus, unlike its predecessor(EP), EP− leaves open the possibility of speakers whose grasp ofthe meaning and syntax of ‘pet fish’ is intact despite their ignoranceof the meaning of ‘pet’ and ‘fish’. (Recall the case of Petra discussedabove, in §1.2.) This, together with the general lack of motivationfor EP, seems a point in its favor. Despite what the proponents ofPRC seem to think, there is no reason to suppose that any morerobust generalization is available.

The upshot of this reasoning is that PRC is explanatorily super-fluous, in the following sense: it doesn’t explain anything that’s both(a) plausibly true and (b) not already explained by PC. Composi-tional meaning theories are already able to account for the factthat phrasal understanding suffices for lexical understanding in mostcases, as per EP−. Without a warrant for strengthening EP− toEP, the further assumption that meaning is reverse compositionalis unnecessary, and does no useful explanatory work. So it shouldprobably be abandoned as a constraint on theory construction in thearea.

4. CODA: NEO-RUSSELLIANISM REDUX

Having presented my case against the principle of reverse composi-tionality, I want to close by returning to the metatheoretical contextin which the principle was introduced. Toward the outset of thepaper I noted Fodor’s observation that there are compositionaltheories of meaning that don’t fit the denotational (or the classical)mold (Fodor, 1998b). An example was then given in the form of atheory that assigned a denotation to each modifier-head construc-tion, and a pair consisting of a denotation and prototype to eachword contained therein. Reverse compositionality was originallybrought onto the scene in order to satisfy Fodor’s desire to discreditsuch hybrids. This was deemed necessary and important because

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these rivals to neo-Russellianism – unlike ‘pure’ prototype theory,‘pure’ theory theory, and the like – were impervious to attack oncompositionality grounds.

Since the principle of reverse compositionality probably isn’ttrue, the problem of hybrid theories cannot be solved in the mannerFodor suggests. But the seriousness of the problem should notbe overestimated. It can be solved by other means – namely,by giving independent reasons to think that hybrid theories areunworkable.

Reasons of this sort abound. To start with, on the hybrid theorysketched above, prototypes are implicated in the interpretation ofwords only, not phrases. As a result, lexical and phrasal expressionsof the same syntactic type (e.g., ‘fish’ and ‘pet fish’) get assigned todifferent semantic types – thereby violating the uniformity assump-tion in a very stark way. But this is a bad idea (Robbins, 2001). Afterall, phrases like ‘pet fish’ exhibit prototype effects just as words like‘fish’ do. It’s hard to see why lexical prototypes should play a rolein the semantics of natural language if phrasal prototypes do not.Without some justification for treating the two kinds of prototypesdifferently, the theory looks suspiciously ad hoc.

Further, though the hybrid theory avoids the charge of violatingcompositionality, it inherits all the other objections that plaguestandard prototype semantics. And there is no shortage of those.Three of the more serious objections are as follows.16 First, thereis the fact that lexical prototypes tend to vary across individuals,and even within individuals over time. This is troublesome becauseword meaning is generally supposed to be inter- and intrapersonallystable. Second, there is the fact that lexical prototypes are unavail-able in some cases, e.g., abstract or highly theoretical words like‘quark’ and ‘grammar’. It’s not clear what the theory should sayabout such cases. Third, there is the absence of determinate identityconditions for lexical prototypes, arising from the fact that thereseems to be no principled, systematic distinction between lexicalknowledge of the sort allegedly encoded by prototypes, on the onehand, and commonsense or world knowledge, on the other. Thesepoints militate strongly against any prototype-theoretic approach tothe lexicon, hybrid or otherwise.17

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Hence, neo-Russellians don’t need the principle of reversecompositionality to solve the problem it was introduced to solve;they can get the job done by more familiar, less controversial means.So even if the principle were consistent with neo-Russellianism, itwouldn’t be necessary or important in the way Fodor suggests itis.18

NOTES

1 Contrast the case of compounds (‘topless bar’, ‘computer game’) and full-blown idioms (‘red herring’, ‘hot dog’), which are generally assumed to lack acompositional semantics (Partee, 1995).2 This is a strong claim. It says that the meaning of a word is derivable fromthe meaning and syntax of any single modifier-head construction containing thatword. As such, it should not be confused with weaker principles of the same type,such as the claim that the meaning of a word is derivable from the meaning andsyntax of the totality of modifier-head constructions containing it.3 Chief among them, the fact that most words don’t seem to be definable, at leastnot in the classical (i.e., necessary-and-sufficient-conditions-specifying) sense.See Laurence and Margolis (1999) for a survey of problems facing the classicalview.4 See e.g. Fodor (1998b), 61n.1, and Fodor and Lepore (2001), 351n.1.5 Notational conventions as follows: Small capital letters indicate concepts,quote marks indicate expressions of natural language.6 One might also take issue with the assumption that phrasal concepts arecomplex in the sense of having lexical concepts as constituents – what is, in effect,the conceptual analogue of reverse compositionality. Since this objection wouldtake us too far afield, I won’t pursue it here.7 To see how these differences can make a difference, see below, §2.1.8 For example, the intersection of the definition of ‘pet’ (animal, kept for amuse-ment or companionship) with the definition of ‘fish’ (animal, aquatic, vertebrate,cold-blooded, finned, having gills) yields – by pooling of features – the definitionof ‘pet fish’ (animal, aquatic, vertebrate, cold-blooded, finned, having gills, keptfor amusement or companionship).9 Note that the definitions of ‘pet’ and ‘fish’ are not derivable from the definitionof ‘pet fish’, since neither the syntax nor the semantics of the phrase carries infor-mation about which features in its definition belong to ‘pet’ and which belong to‘fish’.10 Note also that ‘pet fish’ is plausibly regarded as an NP in which both head andmodifier are nouns (Hampton, 1991; Levi, 1978). This classification is supportedby the fact that adjectives, unlike nouns, tend to be gradable (Larson and Segal,1995). Gradable expressions admit of degree modifiers (e.g., ‘very’, ‘so’, ‘too’)and come in comparative and superlative forms. By this criterion the occurrence

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of ‘pet’ in ‘pet fish’ is not adjectival, as witnessed by the unacceptability ofsentences like “*Madonna has a very pet fish” and “*Tom’s pet fish is morepet than Ray’s”. Such evidence suggests that the lexical parts of ‘pet fish’ areof the same syntactic type – in which case the objection cannot get off theground.11 Italics in original. The talk of supervenience in this passage is presumablyequivalent to talk of derivability by semantic rules.12 Fodor and Lepore put the point as follows: “If the meanings of the primitivesare stereotypes (or uses, or prototypes, or inferential roles, or whatever), then themeanings of the complexes are also stereotypes (or uses, or prototypes, or infer-ential roles, etc.)” (Fodor and Lepore, 2001, p. 365; italics in original). For furtherendorsements, see Fodor (1998a, 1998b, 2000, 2001). It’s important to be clearabout the strength of this assumption. On the basis of distributional evidence, it’ssafe to say that common nouns and noun phrases (e.g., ‘cat’, ‘black cat’), propernouns (‘Morris’, ‘Felix’), and quantified noun phrases (‘some cats’, ‘the favoritecat’) comprise distinct syntactic categories. Hence, the uniformity assumptionshould not be taken to imply the semantic co-classification of expressions acrossthese syntactic types – a good thing, since otherwise the assumption would haveto be rejected out of hand.13 Focussing on the semantics of sentential phrases (e.g., ‘dogs bark’), PaulHorwich argues for the same conclusion as follows (Horwich, 2001, pp. 380–381). If lexical meanings are parts of phrasal meanings, then phrasal meaningsare probably sets (in particular, ordered sets of lexical meanings); but lexicalmeanings are probably not sets of any sort; hence, phrasal meanings and lexicalmeanings are probably different kinds of entity, i.e., not uniformly constituted.But there are weaknesses in this argument. For one thing, it’s unclear whyHorwich thinks word meanings can’t be sets. Many denotationalists, who arewont to speak of the intersection of denotations, would disagree: on their view,the meaning of a word like ‘fish’ is the set of actual and possible fish (Fodor,1998b). Intersection is, after all, a set-theoretic operation.14 Though it has been argued that property-based approaches to the semanticsof predication are suspect on ontological, methodological, and empirical grounds.For discussion, see Larson and Segal (1995, pp. 140ff).15 Structures of this sort, which combine semantic and syntactic information,have played a key role in recent accounts of the semantics of attitude reports.Examples include interpreted logical forms (ILFs) and Russellian annotatedmatrices (RAMs); for discussion, see Larson and Ludlow (1993) and Richard(1990), respectively.16 See Laurence and Margolis (1999) for a more complete catalogue.17 Similar remarks apply to theory theory, use theory, and other (non-classical)alternatives to denotationalism.18 Many thanks to Murat Aydede, José Bermúdez, Jonathan Cohen, Brett Hyde,John Kulvicki, Heidi Maibom, Eric Margolis, Jesse Prinz, Rob Stainton, andDan Weiskopf for advice and criticism. Earlier versions of this material werepresented at meetings of the Central States Philosophical Association (October

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2002), the American Philosophical Association Pacific Division (March 2003),and the Society for Philosophy and Psychology (June 2003), and in a colloquiumat the University of Missouri at St. Louis (November 2002). I’m grateful to theaudiences for their feedback, and to my commentators – Doug Patterson (CSPA),Kent Johnson (APA), and Terry Parsons (SPP) – for helping to advance the cause.My biggest single debt is to the anonymous referee for this journal who suppliedme with a raft of objections and suggestions, leading me to revise and expand thematerial in a variety of substantial ways – all of them, I think, to the good.

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Philosophy-Neuroscience-Psychology ProgramWashington University in St. LouisCampus Box 1073One Brookings DriveSt. Louis, MO 63130-4899USAE-mail: [email protected]

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the myth of reverse compositionality

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