Concepts have occupied a central role in philosophy ever since the Socratic quest for definitions. But even if we abstract from merely terminological variations, concepts have been assigned a multitude of different and potentially conflicting roles. What we would nowadays call concepts have featured as:

• • universals or properties

• • components of propositions

• • meaning(s) of linguistic expressions

• • psychic or neurophysiological processes

• • ‘modes of presentation’, ways in which we think of objects.

In spite of this diversity, one can detect a pervasive contrast between two fundamentally opposed approaches.Footnote ¹ According to objectivist or logical conceptions, concepts exist independently of individual human minds, e.g. as self-subsistent abstract entities or as abstractions from linguistic practices. According to subjectivist or psychological conceptions, concepts are mental phenomena, entities or goings-on in the mind or in the head of individuals.

The most prominent contemporary version of subjectivism is the representational theory of mind or ‘RTM’ championed by Fodor and his followers. Its central claim is that concepts are mental particulars. Fodor portrays his enemies as part of a wide-ranging conspiracy, which includes Ryle, Wittgenstein, neo-Fregeans, conceptual or inferential role semanticists, and holists of various sorts. He labels this conspiracy ‘pragmatism’, because it links concepts to inferential rules and abilities rather than to inner goings-on. And he has pronounced pragmatism to be ‘the defining catastrophe of analytic philosophy of language and philosophy of mind in the second half of the twentieth century’.Footnote ²

Many aspects of the Manichean struggle between RTM and pragmatism have been discussed in recent literature.Footnote ³ My paper is devoted instead to a conflict which pits not just RTM against ‘pragmatism’, but subjectivism as such against any form of objectivism, including Platonist accounts deriving from Frege. And it concerns not the issue of concept-possession, which has tended to occupy centre-stage in recent debates, but concepts themselves: Can RTM, as a version of subjectivism, account for the shareability of concepts?

For RTM, ‘the mind is pre-eminently the locus of mental representation and mental causation’.Footnote ⁴ It is a ‘representational system’, and thinking is ‘representing things in the world’.Footnote ⁵ So-called propositional attitudes like belief and desire are mental states, and they ‘are constituted by relations to mental representations’. Furthermore, ‘mental processes consist of causal interactions among these interrelated states and entities’; they are ‘causal chains in which each link is sufficient for its successor’. ‘The constituents of mental processes are causal interactions among … ideas’.Footnote ⁶

As regards concepts, the central thesis of RTM is that they are ‘mental objects’. They constitute a kind of ‘mental representation’ and hence a ‘kind of mental particular’. As mental particulars, they are ‘objects in the mind’ or ‘in the head’ of individuals; they are ‘concrete’ rather than abstract; and they have causes and effects in the physical world.Footnote ⁷ As mental representations, they have ‘representational content’. They occur as part of propositional attitudes, and what they represent contributes to the content of these attitudes, to what we believe, desire, etc. They do so by determining the conditions under which the attitudes in which they occur are true (in the case of beliefs) or satisfied (in the case of desires).

At present it is often assumed that the conflict between Fregean objectivists and representationalists simply rests on two diverse conceptions of concepts, serving different yet compatible interests. On the one hand, logicians, formal semanticists and conceptual analysts require a notion of concepts that makes them independent of individual people (whether it be as Fregean modes of presentation, sets of real or possible objects, functions on such entities, or as abstractions from intersubjective linguistic practices). On the other hand, psychologists, philosophers of mind and members of the artificial intelligentsia need a notion of concepts which captures the mental or neural processes of individual speakers or thinkers.Footnote ⁸

As we shall see, this conciliatory picture of the situation is too sanguine.Footnote ⁹ On the one hand, any claim according to which concepts are phenomena in the minds of individuals faces an objectivist objection associated with Frege: concepts cannot be mental particulars since they can be shared between different individuals. On the other hand, some proponents of RTM, Fodor pre-eminent among them, not only regard their subjectivist approach as a superior research programme, but entirely dismiss the objectivist alternative. Thus Fodor lists the claim that concepts are mental particulars (i.e. mental causes and effects) as one of five ‘not-negotiable conditions on a theory of concepts’.Footnote ¹⁰ Furthermore, like several other proponents of RTM he holds that the Fregean objection is fallacious, since it ignores the difference between type- and token-representations or -signs.

My first section introduces the Fregean argument and the RTM response. In the second section I show that this response misconstrues the Fregean argument, and that it ultimately rests either on an equivocation or on the untenable idea that one and the same entity can be both a shareable type and hence an abstract universal and a concrete mental particular. This absolves Frege of the charge of having committed a gross fallacy. But section 3 considers the further question of whether RTM might be protected from the Fregean argument by adopting unorthodox metaphysical theories about the contrasts between type and token and between universals and particulars. I deny this: the theories at issue are not just problematic in their own right, they also run counter to both the letter and the spirit of RTM. In the final section I argue that even by RTM's own lights concepts can be neither type- nor token-signs, instead they must be something signified by signs. In other words, concepts are not symbolic representations but something represented by symbols.

1. The Shareability of Concepts

Frege uses the term ‘idea’ [Vorstellung] to signify what RTM calls a mental particular. Frege's ideas include sensations, but they also include mental representations. Such an idea is capable of representing objects that are objective; yet the idea itself is subjective, i.e. ‘something that belongs to the mental life of an individual’ and is ‘quite as private to the individual as his pleasure or pain’. Concepts, by contrast, are objective: they ‘confront everyone in the same way’.Footnote ¹¹ Most importantly, concepts can be shared between different individuals, whereas ideas cannot.

For FregeFootnote ¹³ a concept is the ‘referent’ (Bedeutung) rather than the ‘sense’ of a ‘concept-word’ or predicate; and it is ‘senses’ rather than concepts that are components of propositions (Gedanken). His most explicit statement on shareability contrasts ideas not with concepts themselves, but with these senses. There is an ‘essential distinction’ between the ‘subjective’ idea associated with a sign and its ‘sense, which may be the common property of many people, and so is not a part or a mode of the individual mind’. Different people ‘are not prevented from grasping the same sense, but they cannot have the same idea’.Footnote ¹⁴

It is important to note that Frege's argument from the unshareability of ideas does not hinge on his tentative and highly problematic claim that the ideas of different individuals cannot be compared.Footnote ¹⁵ Even if we can establish that A and B both have mental images of the Eiffel Tower, these images will still be situated in different minds and hence be numerically distinct. Fregean ideas are unshareable by definition: an idea in the mind of A must be numerically distinct from one in the mind of B. But this does not settle the question of whether one can compare these ideas for their qualitative identity or difference, notably on the basis of how A and B describe their respective mental images.

What about the things that Frege regards as shareable? The sense of an expression is the ‘mode of presentation’ of its referent. Roughly speaking, the sense of a sentence is the thought expressed by it; the sense of a proper name is the features which determine what object, if any, is the referent of the name; the sense of a concept-word is the features which determine what objects, if any, fall under the concept-word.

Proponents of RTM often disregard Frege's distinction between senses or ‘modes of presentations’ on the one hand and concepts on the other. At least in the current context, however, this inaccuracy does not matter. Frege himself occasionally used ‘concept’ for the sense of concept-words.Footnote ¹⁶ Contemporary neo-Fregeans like Peacocke and Künne adopt this line, and for good reasons. Our preconception of concepts distinguishes, for instance, not just the concept of a cordate from that of a renate, but also the concept of an equiangular triangle from that of an equilateral triangle. In other words, we individuate concepts not just more finely than Fregean referents (extensions) but also than properties or intensions, and just as finely as Fregean senses (which are shared by predicates only if the latter are synonymous). Most importantly, Frege's point about the shareability of senses extends directly to concepts; and this extension is very much part of his frequent insistence on the objectivity of concepts. According to Frege, the shareability of senses/concepts can be guaranteed only by treating them as abstract entities, entities which are what Frege calls ‘non-actual’ (by contrast to material objects) yet ‘objective’ (by contrast to mental phenomena like ideas).

ShareabilityFootnote ¹⁷ is a feature of the ordinary concept of a concept in both everyday life and in disciplines like psychology and the history of ideas. One central use we make of ‘concept’ and terms that are equivalent in the relevant contexts (like ‘conception’, ‘idea’ or ‘notion’) is in claims about different individuals or even groups of individuals either sharing a concept, or failing to do so. For instance, different political and religious traditions may or may not share concepts like those of freedom of religion and of freedom of speech. Such claims are equally central to intellectual history, e.g. when it comes to comparing the Greek concept of eudaimonia with our concept of happiness.

Appeals to established use outside of cognitive science would normally be given short shrift by supporters of RTM. Yet even Fodor accepts as another one of his ‘not-negotiable conditions on a theory of concepts’ that ‘concepts are public; they're the sorts of things that lots of people can, and do, share’.Footnote ¹⁸ At the same time, he thinks that he can easily account for shareability by introducing a distinction between type and token.

Peirce had introduced this well-known distinction for signs.Footnote ¹⁹ In recent philosophy of mind it has been liberally extended beyond its semiotic roots to cover the difference between kinds of mental states and events on the one hand, and individual instances of these kinds on the other. For example, there is the ‘type’ believing that-dogs-bark and its so-called ‘tokens’, i.e. individual instances such as Anne's believing that-dogs-bark. In my view, this extension is problematic.Footnote ²⁰ Even if justified, however, such qualms need not affect Fodor's version of RTM. His ‘language of thought hypothesis’ treats mental representations as symbols and consequently invites the semiotic distinction that Peirce himself introduced. Fodor maintains that both the meaning of public languages and the intentionality of thought can be explained by a ‘language of thought’.Footnote ²¹External sentences are meaningful because they are correlated with internal signs, sentence-like representations in the brain the tokening of which constitutes our thinking (believing, desiring, etc.). The ultimate carriers of intentional content are sentences in ‘Mentalese’, physical tokens of computational types. When we engage in conceptual thought, Mother Nature inscribes words of a computer programme into our brains. Concepts, according to Fodor, are nothing other than the token-words of the language of thought:

This explains the shareability of concepts by distinguishing between type and token.

Consider the scenario in which Anne and Sarah both believe that dogs bark and (improbably) utter ‘Dogs bark’ in close succession. In that case we are dealing with two tokens of a single type-sentence ‘Dogs bark’, and two tokens of a single type-word ‘bark’. Similarly, according to Fodor, in Anne's brain there occurs one neural token-sentence, and in Sarah's brain there occurs another neural token-sentence. Yet Anne and Sarah both believe the same thing, namely that dogs bark, since both tokens instantiate the same Mentalese type-sentence DOGS BARK. Finally, they share the concept DOG, because both have tokens of one and the same Mentalese type-word.

2. RTM vs. Frege

This position can account for shareability. It does so at a price, however. The type/token distinction cannot be used to invalidate Frege's argument, since it implies abandoning the claim that concepts themselves are particulars. After all, what can be shared between different individuals are representation-types; and these types, as Fodor duly acknowledges, are ‘abstracta’ rather than mental particulars. To be more precise, types are repeatable universals and hence abstract.Footnote ²⁴ Conversely, what can qualify as mental particulars are representation-tokens; and these tokens are confined to each individual rather than shareable. This leaves RTM in a perilous position.

On the one hand, the non-negotiable constraint on a theory of concepts, namely that concepts be shareable,

• ➢ is satisfied only by the abstract types

• ➢ which are neither particulars (mental, physical or otherwise) nor concrete.

On the other hand, the central claim of RTM, namely that concepts are concrete particulars,

• ➢ applies only to the tokens

• ➢ which are not shareable.

At issue between RTM and objectivism is not whether concepts allow of a type/token distinction.Footnote ²⁵ It is whether concepts, the things which can be shared between different subjects, could be mental particulars, that is, tokens rather than types. As far as the Fregean objection is concerned, proponents of RTM are perfectly entitled to postulate a language of thought involving the tokening of sign-types. Still, if they persistently kept apart types and tokens, they would be forced to abandon the central claim of RTM, namely that concepts are mental particulars that can enter into causal relations. Instead they would have to acknowledge that concepts themselves are not particulars. This would still allow them to insist that conceptual thinking consists in the tokening of shareable types and hence in the occurrence of particulars.Footnote ²⁶ They would remain free to explain what goes on in the head of thinkers by reference to mental particulars. But they would not remain free to maintain that concepts, the things which by common consent must be shareable between different thinkers, are those mental particulars.

Unfortunately, many advocates of RTM resist any such concession. Rather than granting that the Fregean argument necessitates a substantial modification of RTM, from a doctrine about concepts to one about the tokening of concepts in thought, these inveterate subjectivists dismiss the argument. Thus Margolis and Laurence describe it as ‘especially disappointing’:

Margolis and Laurence accuse Frege of a ‘type–token confusion’.Footnote ²⁸ This label is definitely misleading, since Frege never considered concepts in terms of a type/token distinction for mental representations, distinguishing instead between mental ideas and abstract senses. The real question is whether introducing the distinction permits subjectivists to insist, against Frege's objection, that concepts are mental representations and hence subjective particulars after all. The answer is No!

As Laurence and Margolis concede, tokens are unique to each individual. A token in A's head must be numerically distinct from a token in B's head. Consequently A and B cannot share the same token. But then, since concepts themselves are shareable, they cannot be identical with such tokens. By contrast to tokens, types of mental representations are shareable alright; and for this reason they are candidates for being concepts. Yet they are (abstract) universals rather than (concrete) particulars in the heads of individuals, which is just what objectivists have been claiming. Frege is not guilty of confusing type and token. Rather, Laurence and Margolis run together a claim that holds for the tokens postulated by RTM, namely that they are mental particulars, with a claim that holds for the types to which these tokens belong, namely that they are shareable.

Elsewhere, Laurence and Margolis write: ‘mental representations are subjective in that their tokens are uniquely possessed; they belong to one and only one subject. Their being subjective in this sense, however, doesn't preclude their being shareable in the relevant sense, since, …, two people can have the same representation by each having tokens of the same type’.Footnote ²⁹ This does not furnish the riposte to Frege which they seek, however. For it concedes that concepts are not subjective in the straightforward sense in which he denied them to be, namely of being uniquely possessed by individuals. That tokens of concepts can be unique to individuals does not mean that concepts themselves can be. Worse still, the passage does not rehabilitate subjectivism. The ‘mental representations’ of which it speaks cannot be mental particulars, since they have to be abstract universals capable of being tokened in different subjects.

Unlike Laurence and Margolis, Fodor explicitly stresses that sign-types are abstracta. This concession willy-nilly carries over to concepts, since for him people ‘have literally the same concept’ in that they have ‘tokens of literally the same concept’.Footnote ³⁰ Nevertheless Fodor tries to have his cake and eat it too. His argument is phrased mainly in terms of ‘MOPs’ or modes of presentation. But it is the conclusions Frege draws from the publicity of concepts that Fodor is explicitly addressing here.

According to Fodor, Frege's argument fails because MOPs/concepts ‘qua’ mental particulars can be tokens, while ‘qua’ abstract objects they can be types. But this rebuttal suffers from precisely the kind of vacillation Frege diagnosed in his psychologistic opponents. The qua-operator that Fodor relies on is notoriously slippery.Footnote ³² On one understanding it means in the capacity of, and ascribes two distinct roles to a single entity. For instance, qua environmentalist I welcome wind-farms whereas qua rambler I do not. On another understanding, ‘qua’ means in the sense of and functions as a tool of disambiguation. For instance, belief qua mental state or attitude –sometimes called a believing—differs from belief qua what is believed —the so-called (propositional) content.

Adopting this second understanding of ‘qua’, we must distinguish between two kinds of things signified by ‘MOP’ or ‘concept’—namely a mental particular on the one hand, an abstract entity on the other. This would mean, however, that Fodor's dismissal of the Fregean argument is based on equivocation. The Fregean claims that MOPs/concepts must be shareable and hence cannot be mental particulars; Fodor denies this by surreptitiously switching from one signification of ‘MOP’ or ‘concept’—a type, which is an abstract universal—to another—a token, which is a concrete particular.

On the first understanding of ‘qua’, Fodor postulates a single entity which can fulfil different roles. Even in Fodor's own theory, however, there is no single entity which in one capacity is an abstract type and in another capacity a token, a mental particular that is non-abstract. Rather, there are two: the type which is abstract yet non-mental, and the token which instantiates the type and which is mental yet non-abstract. This is no coincidence, moreover, since no single entity could have the dual capacities that Fodor requires. If x qua/in its capacity as (an) S is F and qua/in its capacity as T is G, then it must be possible for x to be both (an) S and (a) T. Thus one and the same person can be both an environmentalist and a rambler. But nothing can be both abstract and a particular in Fodor's sense, since such a particular has a spatio-temporal location and stands in causal relations.

It might seem that I have been uncharitable to the inveterate subjectivists. Although they often express themselves in an awkward fashion, all they mean is this: there are token concepts, which are unshareable; but they are tokens of types of concepts that are shareable, just as different tokens of the Union Jack share one and the same design. This response would be adequate if the aim were to accommodate Frege's point by distinguishing between shareable concepts and their physical tokens. In fact, however, inveterate subjectivists reject Frege's argument as fallacious. Thus Fodor's uncharitable diagnosis of the Fregean argument runs as follows: the Fregean reasons from ‘types are abstract’ to ‘tokens are not particulars’, which is just as fallacious as reasoning from ‘properties are universal’ to ‘instances of properties are not particulars’. But the Fregean is not guilty of any such howler. His argument simply relies on the difference between two kinds of entity: the type or property, which is abstract or universal, and the token or instance of the property, which is not. Acknowledging the difference between abstract types and their physical tokens is perfectly compatible both with the mandatory recognition that the two kinds of entity are connected and with the plausible (though by no means truistic) claim that a type owes its existence to the existence of tokens that share a certain role or function (mutatis mutandis for universals and particulars).

The insistence that concepts are both shareable and particular faces an intolerable dilemma. Either it commits a fallacy of equivocation by reasoning roughly as follows:

1. P₁ Concepts (in the sense of types) are shareable.

2. P₂ Concepts (in the sense of tokens) are particulars.

3. C₁ Concepts are shareable particulars.Footnote ³³

Or it conjures up a chimerical amalgamation, some we-know-not-what which combines the useful property of being a universal and hence shareable or repeatable with the agreeable property of being a particular and hence in line with RTM doctrine.

3. Metaphysical Escape Routes

I do not see how the rebuttals of the Fregean argument that one finds in Fodor, Laurence and Margolis can be absolved from the charge of either committing an equivocation or invoking a category mongrel. But perhaps the Fregean argument can be blocked after all by modifying these rebuttals. There are various options here, and some of them raise issues that are hotly debated in contemporary metaphysics and which I cannot fully address in this context. Nevertheless I shall make out a case that these options are unviable because they are unattractive and incompatible with RTM.

Inveterate subjectivists could respond to the Fregean argument by avoiding the concession that the physical tokens of the language of thought are not shareable. At first sight this may seem attractive. The tokens of a public language can be shared, at least if they are inscriptions. For instance, two different demonstrators can hold up a single placard together.

The trouble is that this possibility does not extend to the tokens postulated by RTM, which are supposed to be phenomena in the mind or brain of an individual. What can be shared between different subjects of thought is not such a token but only a type—no matter whether a type is identified in typographic terms, as in public languages, or in the computational-syntactic terms that individuate the types of Fodor's postulated language of thought. With a bit of help from science-fiction one can conceive of a scenario in which two Siamese twins share neural firings. But this is out of the question for the standard cases in which, by common consent, concepts are shared nonetheless. When Anne and Sarah both think that dogs bark, what they have in common (granting the language of thought hypothesis) is the occurrence of tokens of the same type; they share the type DOG, and the property of having tokens of that type, but they do not share the tokens. Finally, returning to the analogy Fodor mistakenly invokes against Frege, what two spines share is the universal of being a vertebra, they do not share a specific instance of being a vertebra or being a specific instance of the property of being a vertebra.

But couldn't an inveterate subjectivist question the notion of shareability and sharing which I invoked against Fodor, Lawrence and Margolis? One might define shareability as follows: a representation-token x is shareable iff x belongs to a representation-type which can be instantiated by many different tokens. On that understanding, the tokens themselves are the entities which can fulfil the dual requirements of being both particulars and shareable. But this gambit relies on an ignoratio elenchi. The Fregean pointed out that in the literal and straightforward sense concepts (representation-types) can and mental particulars (representation-tokens) cannot be shared, in that the former can and the latter cannot be possessed by two different individuals. This would suffice to show that concepts are not mental particulars, even if one could fashion a different notion of sharing which applies to both types and tokens. In fact, however, the notion of sharing and shareability now invoked by the inveterate subjectivist applies exclusively to the tokens. For the concept type is obviously not shareable in the sense of being a token of a type that can be variously instantiated.

That Sarah and Anne share a token in the artificial sense introduced by the inveterate subjectivist simply means that they have different tokens of the same type. Once more, what is the same between them concerns an abstract universal rather than a mental particular; therefore only the former, not the latter, is a candidate for being the concept which, ex hypothesis, they both possess. Consider the following analogy. It is perfectly legitimate to maintain that at this very moment two spatially remote individuals Anne and Sarah ride the same bicycle. But what one means is that their numerically distinct bicycles are of the same type. Glossing this fact by saying that they ‘ride the same individual bicycle’ and fending off inevitable protests by stipulating this to mean that their different bikes belong to the same type is at best a confusing verbal manoeuvre.

Neither equivocation, nor the idea of a type/token mongrel, nor the insistence that mental tokens can be shared is viable. One might accept this verdict, while trying to preserve the naturalistic-cum-physicalist aspirations that underlie RTM's resistance to the Fregean argument. Why not grant that shareable concepts would have to be types rather than tokens, while insisting that types no less than tokens can have spatio-temporal location and stand in causal relations? A precedent might be provided by Armstrong's suggestion that universals are ‘wholly present’ in each particular that instantiates them and hence located in space and time.Footnote ³⁴ If we apply this idea to our present topic, the following suggestion emerges: Rather than sharing a token, Anne and Sarah share a type which is nonetheless wholly located in their respective minds or brains.

There are strong arguments against the idea that a universal U can be wholly present in two distinct and spatio-temporally separate particulars x ₁ and x ₂. In that case U would have to be located where x ₁ is and located where x ₂ is. But since having the same spatio-temporal location is a transitive relation, this implies that x ₁ and x ₂ have the same spatio-temporal location.Footnote ³⁵ Furthermore, if the universal of being red were wholly present in a particular tomato, it could be destroyed by painting that tomato green. Unlike the previous consequence, this is not a contradiction; yet it is still absurd.Footnote ³⁶

Both of these unpalatable consequences carry over directly to the suggestion that a type is wholly present in each of its tokens. Furthermore, invoking this variant of Armstrong's position is incompatible with the trajectory of RTM. Admittedly, it preserves the naturalistic assumption that concepts should be part of the causal order. But for RTM this assumption is intimately tied to the idea that concepts are mental particulars rather than universals that somehow manage to be concrete (and for good reasons, in light of the previous paragraph). Thus Fodor alleges that the failure to admit ‘concrete particulars’ in the mind is the original sin which prevents ‘pragmatists’ from doing justice to mental causation.Footnote ³⁷

We are now in a position to sharpen the Fregean objection to subjectivism. The constraint on concepts that RTM accepts fuels an argument the conclusion of which is the very opposite of what RTM claims:

1. P₃ Concepts must satisfy the non-negotiable constraints on concepts (the constraints that have to be respected by a theory of concepts), including that they be shareable.

2. P₄ Mental particulars cannot satisfy one of these constraints, since they are not shareable.

3. C₂ Concepts are not mental particulars.

Put differently, Fodor's contested ‘constraint’ that concepts be mental particulars is incompatible with the constraint which he shares with his objectivist opponents, namely that concepts be shareable. As we have seen, even the appeal to unorthodox metaphysical views does not provide grounds for condemning the Fregean argument as invalid. But the argument might still be unsound. Perhaps Fodor was precipitate in embracing shareability as a non-negotiable constraint. As we have seen, he accepts that different individuals like Anne and Sarah ‘share a concept’ in that they ‘have literally the same concepts’, which means that they have ‘tokens of literally the same concept’. This gives the game away, since it explicitly contrasts the concept itself with the particulars that are its tokens.

One might hold instead that Anne and Sarah can entertain the same thought not because they share a single concept DOG (which could not be a particular), but because they merely have distinct (particular) concepts which stand in a certain similarity relation, e.g. in that they play similar roles in their respective mental lives. Here one might take a leaf out of the book of metaphysicians who want to avoid universals by relying on particularized properties or ‘tropes’. Rather than Anne and Sarah instantiating a universal which is strictly identical in the two cases—believing that dogs bark—Anne's and Sarah's respective believings that dogs bark merely stand in a certain similarity relation.

In the current debate about universals the crucial question at this juncture is whether this similarity relation presupposes a universal property after all. Fortunately, we do not have to decide this complex issue here. For as we shall see in the next section, Fodor himself explicitly rejects the suggestion that different individuals only have similar rather than numerically identical concepts, and on the basis of considerations that are central to RTM.Footnote ³⁸ He thereby commits himself to the idea that concepts are objects that can be shared by different individuals, an idea which is incompatible with insisting that they are particulars unique to each individual.

4. Representations or Things Represented?

Even if Fodor owned up to the consequence that shareable concepts are not particulars, his position would still suffer from incoherence.

Nothing in Fodor's writings indicates that he distinguishes constituents from parts. In that case, however, it is difficult to see how he can avoid inconsistency. On the one hand, concepts are supposed to be constituents/parts of mental states and processes, which in turn are declared to be relations to mental representations. On the other hand, concepts are supposed to be constituents/parts of the mental representations themselves.

It is doubtful that there is any case of a thing being both part of a relation and part of one of the relata of that same relation. Superficial appearances notwithstanding, Fodor cannot restore consistency here by adopting a set-theoretic account of relations, even if, for the sake of argument, we assume the latter to be correct and to be compatible with his overall position. The set-theoretic account identifies a relation with a set of ordered n-tuples; but although the relata are elements of those n-tuples, the parts or components of the relation itself are the n-tuples rather than the relata. In any event, it is hard to make sense of the above quote in the context of RTM. For it commits Fodor to the untenable idea that when Anne believes that dogs bark the concept DOG is both a part of what she has in her belief-box—i.e. of the Mentalese token-sentence DOGS BARK—and of the relation ‘x has … in x's belief-box’.

The former is Fodor's considered position: ‘concepts are the constituents of thoughts’.Footnote ⁴⁰, rather than of states or processes of thinking thoughts. But that position revolves around a more insidious oscillation between subjective and objective categories, in particular the realm of signs and the realm of what signs signify. Fodor continues:

According to Fodor, Anne and Sarah do not stand directly in a relation of believing to the proposition that dogs bark. Rather, they stand in a relation to tokens of the thought or Mentalese type-sentence DOGS BARK; and that thought expresses the proposition, it ‘means that’ Dogs bark.Footnote ⁴² By the same lights, the concept DOG is a Mentalese type-word which has the property being human as its meaning.

At the same time, Fodor also suggests that ‘word meanings just are concepts’.Footnote ⁴³ Perhaps the tension is merely apparent, in that concepts are supposed to be both the meanings of the words of public languages and words of a mental language that mean properties. Yet Fodor nowhere indicates that this is what he has in mind. Worse still, one passage strongly suggests something more sinister. Fodor insists that we must recognize ‘mental representations that express concepts’, i.e. that concepts are meanings of mental rather than public symbols.Footnote ⁴⁴ Accordingly he is committed to the inconsistent idea that concepts are both mental words and the meanings of those very same words.Footnote ⁴⁵

This immediate inconsistency could be avoided by abandoning the second claim, according to which concepts are meanings. But a viable overall position emerges only by dropping the first claim and treating concepts as components of the contents of propositional attitudes, parts of what we think (believe, desire, etc.) rather than parts of representations that express or mean what we think.Footnote ⁴⁶ For it is central to Fodor's case for the shareability of concepts that they should be components of the contents of propositional attitudes. His theory of concepts is supposed to explain the possibility of psychological explanations which are both intentional and ‘nomic’; that is to say, they invoke general law-like connections between propositional attitudes. Such explanations require ‘covering generalizations’ about people who believe or intend that such-and-such, etc. As a result, RTM can underwrite psychological explanations of the required general kind only to the extent to which ‘mental contents are supposed to be shared. If everybody else's concept WATER is different from mine, then it is literally true that only I have ever wanted a drink of water, and that the intentional generalization “Thirsty people seek water” applies only to me’.Footnote ⁴⁷

Intentional explanation presupposes ‘a robust notion of content identity’, which is tied to a robust notion of concept identity: belief contents and their component concepts are literally shared, rather than merely similar. This means that Fodor is absolutely right to accept shareability as a non-negotiable constraint. The only way RTM could resist the Fregean argument is by demonstrating it to be invalid, and that path has been blocked in the last section. It also means that Fodor is committed to the idea that concepts are components of propositional contents. For he insists that concepts are shared because people can literally believe the same. But what people believe is the propositional content of their beliefs.

It is not just that Fodor's specific argument for shareability requires that concepts be parts of what we think rather than of representations, of mental sentences which express what we think. The alternative assumption simply cannot account for shareability. Peacocke points out that ‘It is possible for one and the same concept to receive different mental representations in different individuals’.Footnote ⁴⁸ And according to Rey, even mental representation types need no more be shared between individuals that entertain the same thought than the type words need to be shared in sentences of public languages that express the same proposition.

Laurence and Margolis try to rebut this argument on two grounds. First, they deny that different types of mental representations can express the same concept, since they ‘will have substantially different inferential roles’. Secondly, even if different types of internal representations could express the same concept this would raise ‘no difficulties for the view that concepts are mental representations’:

This response betokens a misunderstanding of the type/token distinction. Persian and Siamese cats both instantiate the kind cat or the property of being a cat. But there is no symbol or representation type of which both ‘city’ and ‘ville’ are tokens. Of course, they have something in common. Yet it has nothing to do with either the typographic level at which type-words in public languages are individuated or the syntactic computational level at which type-words in Mentalese are supposed to be individuated. It lies rather at the semantic level: both mean the same, they represent the same kind of thing.Footnote ⁵¹

One might protest that neither Rey's passage nor the response by Laurence and Margolis really engage with RTM, at least in the version Fodor advocates. According to the language of thought hypothesis, anyone who thinks that cities are crowded must ipso facto have a Mentalese sentence of the type CITIES ARE CROWDED in her belief-box, irrespective of what images or words from natural languages may cross her mind.

Far from defusing the more general objection, however, this protest merely suggests that the language of thought hypothesis with its type/token distinction taken from semiotics is inapposite in the case of thought. Even if computationally individuated patterns of neural firing can be symbolic representationsFootnote ⁵² they will not have to be shared by people entertaining the same thought. Fodor's representation types are individuated not typographically, but through their syntax, through how they are cognitively processed. Yet A and B may have one and the same belief, and this belief may involve one and the same concept, without there being anything that is processed in the same way in both. If you associate the term ‘grandmother’ with an image of your grandmother and I associate it with the first line of Brahms’ Lullaby, this is no bar to our expressing the same concept by it. Similarly, if, for the sake of exemplification, we accept the popular idea that neural networks present cities pictorially and digital computers present them symbolically, it is clear that the representations cannot be processed in the same way; yet this is no bar to them expressing the same concept. Note, finally, that believing cities are crowded can lead to different conclusions and actions in A and B. A may conclude that cities are desirable places and seek to live in them, while B may draw the opposite conclusions. There is no reason why one and the same concept should not play slightly different roles in the thinking of different individuals.

Laurence and Margolis are right to insist that one and the same concept cannot play different inferential roles in the cognition of different individuals. But, their second response to Rey notwithstanding, this kind of equivalence is ensured in the case of ‘city’ and ‘ville’. That x is densely populated, for instance, follows equally from the fact that x satisfies ‘city’ and that x satisfies ‘ville’. The problem for RTM is that the roles that need to be shared between representations to ensure sameness of concepts are, trivially, those which are constitutive of conceptual content. This not only contradicts Fodor's adamant rejection of any kind of analytic/synthetic distinction, it also makes the sharing of concepts once more dependent on the semantic level of meaning or content.

On a coherent account that preserves the connection between concepts and shared thoughts (in the sense of thinking the same content), a concept is neither a token- nor a type- sign. Rather, it is what is signified or expressed by such signs. It is central to RTM that ‘concepts are symbols’.Footnote ⁵³ Yet concepts cannot themselves be symbols (whether mental or public), since they are among the kinds of things which symbols represent.Footnote ⁵⁴ In a Teutonic vein, you might speak of ‘Frege's Revenge’.Footnote ⁵⁵ In an American vein, you might exclaim: ‘Any way you cut up the pie, concepts ain't in the head!’.

A version of RTM which takes these lessons on board will still be a representationalist model of the mind in general and of conceptual thinking in particular. Yet it will no longer constitute a genuinely subjectivist position about concepts. RTM's case against objectivism has evaporated, and its case against concept pragmatism has to be re-jigged as follows: we entertain conceptual thoughts not by exercising an ability, but through the occurrence of neural tokenings of symbolic types; and we share a conceptual thought if those types have the same meaning or content. This case ought to be resisted, in my view. In that context one should also try to provide an account of the shareability of concepts which avoids both subjectivism and the Platonism of Frege's own brand of objectivism. The purpose of this paper was more modest, namely to rehabilitate the Fregean argument against the idea that concepts are mental particulars.Footnote ⁵⁶