CUNY Graduate Center
The hallmark of a paradox is a set of mutually inconsistent propositions each of which enjoys some plausibility when viewed on its own. One solves the paradox by revealing which of the propositions must be rejected. This paper begins with such a paradox; it is a paradox about meaning that arises in connection with propositional-attitude ascriptions. Then my main concern will be to explore--but merely to explore, and not to establish--one possible solution to the paradox. This solution combines a denial of compositional semantics with a quite deflationary conception of propositions, and there will be some who charge it with being as paradoxical as the paradox that is supposed to lend it motivation. But what I am going to propose is at least a position in a puzzle's solution space, and when in the final bookkeeping we compare its pros and cons with those of its rivals, it may not seem so paradoxical. Anyway, a good title should reverberate with layers of meaning.
The puzzle I have in mind is about that-clause-containing sentences, such as any sentence of the form 'A believes that S', and it consists of the following set of propositions.
[P] (1) That-clauses refer to propositions.
(2) The reference of a that-clause is determined by its syntax and the references its words have in it.
(3) There is no tenable account of the compositional determination of that-clause reference consistent with (1) and (2).
Since, plainly, (1)-(3) cannot all be true, we have the beginnings of a paradox. It remains to show that each of (1)-(3) enjoys some plausibility. It will not be possible to make the full case for each of these propositions; that would take too many pages. But I think enough can be said to show that we have something of a paradox and to provide some motivation for the solution I shall later entertain.
Proposition (1): That-clauses refer to propositions. The full case for this has two parts: a certain positive case, and the case against rival accounts of that-clauses. The positive case can be briefly stated.
It begins with the case for supposing paradigmatic occurrences of that-clauses to function as referential singular terms.1 Certainly that-clauses typically behave syntactically like singular terms. Witness the way 'Dan's theory' might well be substitutable salva veritate for the that-clause in each of the following sentences:2
Ava believes that eating fish increases intelligence.
That eating fish increases intelligence is ridiculous.
That eating fish increases intelligence is also George's theory.
That these singular terms are also referential--and not, say, like 'the average accountant' in 'The average accountant has 2 1/3 children'--is strongly suggested by the way that hypothesis straightforwardly accounts for the way in which tokens of the following sorts of inference-types may be valid:
Ava believes that eating fish increases intelligence, and so does Dan.
So, there is something that they both believe (to wit, that eating fish increases intelligence).
Ava believes that eating fish increases intelligence.
That eating fish increases intelligence is ridiculous.
So, there is something ridiculous that Ava believes (to wit, that eating fish increases intelligence).
Ava believes everything that Dan says.
Dan says that eating fish increases intelligence.
So, Ava believes that eating fish increases intelligence.
Suppose, in this way, it is granted that that-clauses are referential singular terms. Then we may move to the question this assumption invites: to what does 'that eating fish increases intelligence' refer? But of course we know the answer to that question: what 'that eating fish increases intelligence' refers to is that eating fish increases intelligence. Yet what, we may now ask, is the nature of this thing, that eating fish increases intelligence, which is the referent of the that-clause singular term? Well, that eating fish increases intelligence is abstract in that it has no spatial location: it is not in Sicily or anywhere else. It is mind- and language-independent in that it exists in possible worlds in which there are neither thinkers nor speakers. It is also language-independent in that it cannot be said to belong to any language: that eating fish increases intelligence can be expressed by a sentence of any language, but it itself belongs to no language; it is neither English nor French nor Japanese. And it has a truth condition, and has its truth condition both essentially and absolutely. This is in contrast to the way in which the sequence of marks 'Eating fish increases intelligence' has its truth condition. First, it is a contingent fact that the sequence of marks is true among us iff eating fish increases intelligence; had our linguistic conventions been different, it might have had a different truth condition or none at all. Second, the sequence of marks has its truth condition only relative to some language or population of speakers: it does not have its truth condition absolutely, but only in English or among us. But it is a necessary truth that is relative to nothing that that eating fish increases intelligence is true iff eating fish increases intelligence; it has that truth condition absolutely and in every possible world. In sum, therefore, that eating fish increases intelligence is a proposition, in the philosophical sense of that term: an abstract, mind- and language-independent entity that has a truth condition and has it both essentially and absolutely. Needless to say, there is a further question, presently to be upon us, about the kind of proposition these that-clause referents are, but a positive motivation has been provided for the first member of our paradox set, the claim that that-clauses refer to propositions.
A complete case for the hypothesis that that-clauses refer to propositions must also respond to its rivals. These rivals are usefully divided into two kinds: those that deny that that-clauses are referential singular terms, and those that accept that but deny that propositions are the referents of that-clauses. The first kind contains Davidson's (1984b) paratactic treatment of that-clauses and the view I proposed (but now alas disown) in my 1987a according to which that-clauses do not have objectual reference and inferences such as those lately displayed are valid only when their quantifications ('There is something Ava believes') are read nonobjectually, in a way akin to substitutional quantification.3 Also belonging to this kind are various conceptions of the logical form of belief ascriptions according to which that-clauses disappear on analysis, the that-clause giving way to a complex existential generalization into that-clause position.4 The second kind of rival consists of sententialist positions of one stripe or another: that-clauses refer, but not to propositions; rather, they refer to linguistic entities of some kind or other--public language sentence types or tokens, Mentalese sentence types or tokens, or syntactical "logical forms," with or without the extensional semantic values of their constituent parts.5 I find none of these rivals plausible, but I cannot argue against them here and must leave the motivation for (1) of [P] in this incomplete state.6
Proposition (2): The reference of a that-clause is determined by its syntax and the references its words have in it. This, of course, is on the assumption that that-clauses have reference. But given that assumption, this proposition gets all the motivation that is enjoyed by the widely-held assumption that every natural language has a correct compositional truth theory, where such a theory for a language L is a finitely axiomatized theory of L whose theorems assign to each appropriate sentence of L the conditions under which an utterance of the sentence would be true. For it is clear that that-clauses are not semantically primitive, and therefore the only way to reconcile their having reference with the assumption that English has a compositional truth theory is to suppose, roughly speaking, that the reference of a that-clause is compositionally determined by its syntax and the references its component words have in it.
Proposition (3): There is no tenable account of the compositional determination of that-clause reference consistent with (1) and (2). Stated in its application to a particular example, the belief ascription
 Ralph believes that Fido is a dog,
the problem alluded to in (3) is that there seem not to be suitable references available for 'Fido' and 'dog' in 's that-clause. Let me explain.
Suppose (1) of [P] is true. Then we know that 's that-clause refers to something that may be called a proposition that Fido is a dog. Suppose next that (2) of [P] is also true. Then we know that the reference of 'that Fido is a dog' as it occurs in  is partly determined by the references that 'Fido' and 'dog' have in that that-clause. What might these references be? For all intents and purposes, there are but two possible answers consistent with the assumption that the that-clause refers to a proposition that is true iff Fido is a dog.
First, there is the Russellian proposal that 'Fido' and 'dog' in  refer to Fido and doghood respectively, the whole proposition being something which at a certain level of analysis might be represented as the ordered pair
a proposition that is true iff Fido instantiates doghood; i.e., iff Fido is a dog.
Second, there is the Fregean proposal, actually constructed in reaction to the Russellian proposal (though not under that description), that 'Fido' and 'dog' in  refer not to Fido and doghood but rather to modes of presentation of Fido and doghood. Then, at a certain level of analysis, the proposition referred to by a token of 'that Fido is a dog' could be represented as the ordered pair
where mf and md are modes of presentation of Fido and doghood respectively, this proposition being true just in case the thing of which mf is a mode of presentation has the property of which md is a mode of presentation. Here I understand the notion of a mode of presentation in an entirely theory-neutral way as whatever satisfies what I have elsewhere (e.g., in my 1992) called Frege's constraint. This constraint has two parts. First it says that a rational person x may both believe and disbelieve that a certain thing or property y is such and such only if there are distinct modes of presentation m and m' such that x believes y to be such and such under m and disbelieves it to be such and such under m'. Then it says that there are distinct modes of presentation m and m' such that rational person x believes y to be such and such under m and disbelieves y to be such and such under m' only if x fails to realize that m and m' are modes of presentation of one and the same thing. In other words, you cannot rationally believe and disbelieve something under one and the same mode of presentation, or under modes of presentation that you realize are modes of presentation of the same thing. The notion of a mode of presentation is functionally defined by Frege's constraint in that something is a mode of presentation if it plays the role defined by Frege's constraint, and nothing can be a mode of presentation unless it plays that role. It is because the notion of a mode of presentation is so neutrally defined that we can take the Russellian and Fregean positions exhaustively to divide the logical space.
We can see the problem with both proposals in three steps. Step one considers the Russellian proposal relative to the assumption that believing is a two-place relation. Believing, the relation expressed by 'believes' in a sentence of the form
A believes that S,
certainly appears to be a two-place relation (at least if we ignore, for simplicity, tense and temporal reference). If that-clauses are referential singular terms, then 'believes' in a sentence of the displayed form looks like a two-place relational predicate flanked by two singular terms specifying arguments for that relation. After all, it is hard to see how 'believes' can be more than a two-place predicate given that the sentence form seems complete as it stands and contains places for only two terms. In any case, the Russellian proposal conjoined with the two-place assumption is subject to the classic Fregean objection: (a) Lois Lane believes that Superman flies but does not believe that Clark Kent flies, but (b) that truth becomes impossible on the hypothesis in question. It has Lois both believing and failing to believe one and the same singular proposition--viz., <the guy with two names, the property of being a flier>.
It is true that clever philosophers like Nathan Salmon (1986) have bravely tried to meet the Fregean objection by arguing that the Lois sentence really is a contradiction. But in Schiffer 1987b I try to show why any such attempt must fail.7 We really do need an account of belief sentences which recognizes both the literal truth of the Lois sentence and the fact that the ancient astronomer appreciated Hesperus's self-identity long before he realized that Hesperus was Phosphorus. I shall assume that the extreme 'Fido'-Fido theory of belief--the theory that results from the marriage of the Russellian proposal and the assumption that believing is a two-place relation--cannot be made to work.
This brings us to step two and the Fregean counter-proposal. The leading idea here unfolds in the following way. A thing can be presented to us in different ways, or under different guises, and it is possible to believe it to be such and such under one such "mode of presentation" while disbelieving it to be such and such under a second mode of presentation and while suspending judgment altogether under a third mode of presentation. What we should now say is that terms in that-clauses refer not to the things and properties our beliefs are about, but rather to modes of presentation of them. Ralph's belief that Fido is a dog is perforce about Fido and doghood, but not directly: a belief about x must always be mediated by, or be under, some particular way of thinking about x, some guise or mode under which x is presented to the believer. Consequently, the proposition Ralph believes, while about Fido and doghood, does not contain them. It contains instead Ralph's ways of thinking about them, modes of presentation he has for them. These are what 'Fido' and 'dog' in  ('Ralph believes that Fido is a dog') refer to, and the logical form of an utterance of  may accordingly be represented as
B(Ralph, <mf, md>),
where mf is the referent of the occurrence of 'Fido' in , md is the referent of 'dog' in , and the entire mode-of-presentation-containing proposition is true just in case the thing of which mf is a mode of presentation--viz., Fido in the actual world--has the property of which md is a mode of presentation--viz., doghood in the actual world. In this way, there is no problem whatever with the examples that refute the Russellian. For example, notwithstanding the identity of Superman and Clark Kent, 'Lois believes that Superman flies' is true, while 'Lois believes that Clark Kent flies' is false. This is because the two that-clauses refer to different propositions, and this in turn is because the names in them have different references in those that-clauses: 'Superman' refers to one mode of presentation of the guy with two names, while 'Clark Kent' refers to a different mode of presentation of him.
The Fregean is right to reject the just-considered Russellian proposal. Unfortunately for the Fregean, however, his proposal cannot be right either: it is not plausible to take the words in a that-clause to refer to modes of presentation. Consider, for example, this utterance:
 Aristotle's mother doubtless believed that Aristotle was Greek.
According to the Fregean proposal, the occurrence of 'Aristotle' in my utterance of  refers to some particular mode of presentation of Aristotle and the occurrence there of 'Greek' refers to some particular mode of presentation of the property of being Greek. But, in the first place, it is clear that these words carry no context-independent references to particular modes of presentation in the predicate 'believed that Aristotle was Greek', for the predicate can surely be correctly ascribed to people who think of Aristotle and the property of being Greek in radically different ways. For example, this would be so, I assume, when the predicate is applied to Aristotle's mother and when it is applied to your mother. And, in the second place, it is also clear that these words need carry no context-dependent reference. If there were a context-dependent reference, those references would be determined by my referential intentions, just as the reference of 'this book' would be determined when I say 'I bought this book'. Yet while my utterance of  is doubtless true, I am in no position to refer to any particular modes of presentation Aristotle's mother had for thinking about Aristotle or the property of being Greek. This evidently scotches the Fregean proposal. For if the words in a that-clause require neither a context-dependent nor a context-independent reference to modes of presentation, then they require no reference to modes of presentation, and the Fregean proposal is wrong (cf. Schiffer 1992, pp. 507-8).
Step three returns us to the Russellian proposal, the view that that-clauses refer to Russellian propositions. For that proposal can be combined with the idea that believing is a three-place relation to yield what I have elsewhere (1992) called the hidden-indexical theory of belief ascriptions. That theory, stated now in its application to the paradigmatic example, , has two parts. First, it holds that the relation expressed by 'believes' in  is a three-place relation, B(x, p, m), holding among a believer x, a Russellian proposition p, and a mode of presentation m under which x believes p. The idea is that x might believe p under one mode of presentation m, disbelieve p under a second mode of presentation m', and neither believe nor disbelieve p under a third mode of presentation m''. In this context, a mode of presentation of a proposition should be thought of as determined by modes of presentation of the objects and properties that compose the proposition. Second, the theory claims that the logical form of an utterance of  may be represented as
$m[F*m & B(Ralph, <Fido, doghood>, m)],
where F* is an implicitly referred to and contextually determined type of mode of presentation. For example, F* might be that property that a propositional mode of presentation has when and only when it requires thinking of Fido as being a dog of such-and-such appearance and requires thinking of doghood as a property shared by such-and-such similar-looking creatures. I call this the hidden-indexical theory because of the way the reference to the type of mode of presentation is implicit: although the sentence requires the speaker to be referring to a type of mode of presentation whenever the sentence is uttered, there is no word in  which refers to that type. In this respect, the reference to a type of mode of presentation required by a belief ascription is like the reference to a place required by an utterance of 'It's raining': one uttering this sentence must be referring to some place at which it is raining, but there is no word in the sentence to carry that reference. And I call the theory the hidden-indexical theory because of the way the reference to a type of mode of presentation is "contextually determined": different mode-of-presentation types may be referred to in different utterances of .
What recommends this theory is that it avoids the pitfall of the Fregean theory by not requiring reference to particular modes of presentation, while, at the same time, protecting the Russellian proposal from the Fregean objection. The hidden-indexical theory makes it easy to see how utterances of 'Lois believes that Superman flies' and 'Lois doesn't believe that Clark Kent flies' may both be true, notwithstanding that both that-clauses refer to the same singular proposition. Both utterances can be true because different types of modes of presentation can be referred to in them.
The hidden-indexical theory is an attractive theory. My own view is that it is the best account of the logical form of belief ascriptions available to a theorist intent on keeping (1) and (2) of [P], a fortiori the best theory available to one intent on seeing Russellian propositions as the referents of that-clauses. But I also think the theory has difficulties. In Schiffer 1992 I raise three problems for the hidden-indexical theory. One is a problem for any theory that appeals to modes of presentation; it worries that there might not be things capable of playing the mode-of-presentation role definitive of the notion of a mode of presentation. A second problem concerns the construal of the belief relation as a three-place relation holding among a believer, a proposition, and a mode of presentation of that proposition. For the reference to a mode of presentation in the sentence
Ralph believes that Fido is a dog in way w/under mode of presentation m
does not look like the specification of a third term in a three-place relation. The sentence looks more like it contains a two-place relation with an adverbial qualifier, where the term referring to a mode of presentation plays the same role as 'the most exciting way' in
Ralph kissed her in the most exciting way.
The third, and I think most serious, problem is one I call the meaning-intention problem. For it is doubtful, I have argued, that belief ascribers are in a position to mean what the hidden-indexical theory requires them to mean. According to the hidden-indexical theory, one uttering, say,
 Placido Domingo believes that Luciano Pavarotti will be arriving at Orly airport today at around 4 PM Paris time
must be referring to a type of mode of presentation, and his utterance must be such that it is true just in case Domingo believes the proposition about Pavarotti under a mode of presentation of that type. For this to be the case, there must be some type of mode of presentation F such that the one uttering  means that Placido Domingo believes the proposition that Luciano Pavarotti will be arriving at Orly airport today at around 4 PM Paris time under a mode of presentation of type F. But there are two problems with supposing that an ordinary person can have the meaning intentions such an act requires.
The first is that the speaker will not be aware of meaning any such thing. In response to this it can be said that the belief ascriber means what the hidden-indexical theory requires her to mean thanks to her tacit meaning intentions, intentions she has but is unaware of having. The trouble with this response, though it is not decisive, is that it induces a rather radical error theory. Speakers will not have the first-person authority about what they consciously mean and intend which we seem to think they have. If you ask the speaker of  what she meant in uttering , she will tell you that what she meant, and all that she meant, was that Placido Domingo believes that Luciano Pavarotti will be arriving at Orly airport today at around 4 PM Paris time. But the hidden-indexical theory tells us she is in error: the only proposition she asserts in uttering  is not anything of which she is aware.
The second problem is that no one type of mode of presentation of the proposition about Pavarotti is sufficiently salient to enable the speaker to refer to it. Since a mode of presentation of a proposition is determined by modes of presentation of its constituents, the type of mode of presentation referred to in the utterance of  could be made up, so to speak, of types of modes of presentation of Pavarotti, the arrival relation, Orly airport, the number 4, today, Paris, etc. But there will be a huge number of potentially relevant such mode-of-presentation types, and it is extremely unlikely that any one of them will be sufficiently salient in the communicative context to enable the speaker to refer to it. The point can be appreciated in the following way. Pretend that I uttered  and that you are my audience. Certainly you would have understood my utterance perfectly well. But then what assertion did I make? What is the type of mode of presentation F such that I meant that Placido Domingo believes the proposition that Luciano Pavarotti will be arriving at Orly airport today at around 4 PM Paris time under a mode of presentation of type F? The question, I hazard, cannot be answered, and the reason it cannot is that I was not in a position to refer to a contextually determinate type of mode of presentation. None is sufficiently salient to enable you, my audience, to identify it as the one I meant, and this notwithstanding the fact that we understand all the concepts involved and everything has been raised for us to the level of conscious awareness.8
Anyway, that is a sketch of the prima facie case for (3) of [P]. Given (1) and (2), we shall have to find suitable referents for the words in a that-clause. Those referents will either be the objects and properties our beliefs are about (the Russellian idea) or modes of presentation of those things (the Fregean idea). But the case against the Fregean option seems decisive, and I find the case against the Russellian option formidable.
Thus [P] presents us with a paradox. It is clearly a set of mutually inconsistent propositions, and I hope I have said enough to make it plausible that there is a decent prima facie case for each of the three propositions when viewed on its own. The task now is to solve the paradox by saying which of (1)-(3) must go. On this matter, I suspect that most readers will be united in thinking that the least likely solution to the paradox is to reject (2) while keeping (1) and (3). Yet that is precisely the solution I wish to explore; it is a solution I feel is worth taking seriously. Naturally, I am motivated by two considerations. On the one hand, I am moved by the arguments for (1) and for (3) of [P], and I do not know any persuasive way of faulting them. On the other hand, I think there may be a way of making the rejection of (2) acceptable. In other words, I think one can support the idea that while that-clauses refer to propositions, the reference of a that-clause is not determined by its syntax and the references its component words have in the that-clause. At any rate, supporting this idea is what the rest of this paper will try to do.
The idea has its debts; two big debts, in fact. The first is that the proposed solution requires denying that natural languages have compositional truth theories. More than this, it also requires denying that natural languages have compositional meaning theories, finitely axiomatized theories whose theorems ascribe to each sentence of the language its meaning in the language. For it is part of the meaning of 'Snow is white' that an utterance of it is true iff snow is white, so if a compositional theory can assign meanings to sentences, then it should also be possible to have a compositional theory that assigns truth conditions to sentences that have them. So the proposed solution requires denying that natural languages have any kind of compositional semantics. Now, what motivates people to believe in compositional semantics is that they suppose languages to have features that defy explanation otherwise than on the assumption that languages have compositional semantics. My debt, then, is to say how those features can be explained without compositional semantics.
The other big debt is that the proposed solution implies a conception of noncompositionally-determined propositions, and I shall need to say why this is not problematic. To the extent that the conception really is problematic, that is further reason for not locating [P]'s middle proposition as the odd man out. Let me explain this a little.
There is something quite attractive about kicking (2) out while retaining (1) and (3). It allows us to take a belief report such as 'Ralph believes that Fido is a dog' at face value: as involving a two-place verb linking two arguments. And it allows us to say that the two that-clauses in
Lois believes that Superman flies but doesn't believe that Clark Kent flies
refer to distinct propositions without having to find two different things to be the semantic values of 'Superman' and 'Clark Kent' in those that-clauses. But one taking this line is committed to a novel conception of the propositions referred to by that-clauses. Standard conceptions of those propositions see them as compositionally determined in the sense that there are finitely statable rules that construct all the propositions there are from things that are not propositions. These things, these propositional "building blocks," will be the referents words have when they occur in that-clauses, on the assumption that the reference of a that-clause is itself compositionally determined by its syntax and the references its words have in it. It is clear that if (1) and (2) of [P] are true, then the propositions we believe are compositionally determined in this sense. It should also be clear that one who accepts (1) while rejecting (2) will be constrained to deny that the propositions to which that-clauses refer are thus compositionally determined; for the idea that the reference of a that-clause was both to a proposition and not compositionally determined in the way (2) requires could be sustained only if the propositions referred to by that-clauses were themselves undetermined by any finitely definable function from things that could be the references of words in that-clauses. Also, the most popular views of propositions nowadays construe them as structured entities made up out of the references of words in that-clauses. Combining the structured idea with the idea that propositions are compositionally determined, the standard conceptions see the infinitely many propositions to which our that-clauses refer as built up out of propositional building blocks by finitely many finitely specifiable combining operations. It is obvious that the propositions to which that-clauses refer must be unstructured for the theorist who rejects (2) while retaining (1).
As I said, this conception of propositions as noncompositionally-determined entities is apt to seem problematic, and this for at least two reasons over and above the fact that it also commits one to denying that natural languages have compositional semantics. First there is a general challenge, about whose favorable resolution one might be skeptical. If the propositions to which that-clauses refer really are unstructured and noncompositionally determined, then this conception of propositions as, so to say, structureless blobs would seem to require some stronger motivation than its ability to occupy a position in the logical space of possible solutions to our paradox. That is, one would expect something positive to recommend the view other than its being a way of hanging onto (1) in the face of (3). But what might this be? Then there are more specific challenges that test the intelligibility of the idea of noncompositionally-determined propositions. These will be considered later. Let us begin with the need to reject compositional semantics.
I want to entertain the solution to [P] that locates (2) as the odd man out. This solution implies that natural languages do not have compositional truth theories, which is contrary to what the reigning orthodoxy holds. So we shall need to assess the reasons for supposing that natural languages must have such theories.
One argument for compositional truth theories is via an argument for compositional meaning theories. The idea is that natural languages must have compositional meaning theories, and a language cannot have a compositional meaning theory without also having a compositional truth theory. The intuitive basis for the second step is that a sentence's meaning determines its truth condition: if a sentence means that snow is white, then it is true iff snow is white. So if it is reasonable to suppose that a finite theory can match each sentence with its meaning, then it is also reasonable to suppose that a finite theory can match each sentence with its truth condition. I believe that this intuitive basis can be fleshed out into a sound argument, so I shall concede that if a language has a correct compositional meaning theory, then it also has a correct compositional truth theory. But why should we suppose that every natural language must have a correct compositional meaning theory? Because, the familiar answer goes, without the assumption that languages have such meaning theories, we shall not be able to account for the following features of natural languages.
Natural languages are productive: each of the infinitely many sentences of a natural language has a meaning. Surely, this infinity of meaning facts must emanate from a finite basis, some nonendless state of affairs. Since the infinitely many sentences of a language are composed from finitely many words in accordance with finitely many syntactical devices, it is reasonable to think that a sentence has its meaning because its component words have their meanings and because the sentence's syntax is correlated with a rule that composes sentence-size meanings from word-size meanings. In short, it is reasonable to suppose that what accounts for the productivity of natural languages is that they have compositional meaning theories.
Natural languages are systematic: the meaning of a sentence is obviously determined by features of its words and syntax, and those features play the same meaning-determining roles in every sentence in which a word or structure having them occurs. Thus it is that the fact that 'John loves Mary' means that John loves Mary is not unrelated to the fact that 'Mary loves John' means that Mary loves John (cf. Fodor 1987). A language will be systematic if it has a compositional meaning theory, and it may seem hard to see how it could be systematic otherwise.
Natural languages are mastered by finite creatures: a normal speaker of a natural language has the ability to understand indefinitely many novel sentences of the language, sentences she has never before encountered. One popular explanation of this remarkable ability is that although the sentence is novel, its words and syntax are not: the person understands the novel sentence because she in some sense knows the meanings of its component words and the semantic import of its syntax. This in turn naturally suggests the Chomskian idea that language comprehension implicates an internally represented compositional meaning theory of the comprehended language.
So that is how one might motivate the claim that natural languages have compositional truth theories via the claim that they have compositional meaning theories. One could also motivate the claim directly by appealing to productivity and systematicity features of sentences which pertain to their truth conditions. A language needs a compositional truth theory, it might be claimed, simply to account for how it is that infinitely many of its sentences have truth conditions and for how the truth condition of a sentence depends in systematic ways on features of the sentence's words and syntax. It might even be possible to use considerations pertaining to language understanding directly to motivate the need for a compositional truth theory. For understanding an utterance in the indicative mood does seem to require knowing its truth condition.
Nevertheless, my strategy will be to challenge the reasons for supposing natural languages to have compositional meaning theories. For the concern about meaning is the more foundational concern (sentences have the truth conditions they have because they have the meanings they have), and, in any case, what will be said in response to the claim that a compositional meaning theory is needed to account for a sentence's meaning productivity and systematicity will translate into a response to the claim that a compositional truth theory is needed to account for a sentence's truth-conditional productivity and systematicity. More specifically, my strategy will be to assume that we think in a language of thought and to address, in the first instance, the question of whether a compositional meaning theory for Mentalese, one's neural lingua mentis, is needed to account for any of its features. The answer will turn on a question about the nature of propositions, and will imply an answer to the question about the need for natural languages, our public languages of communication, to have any kind of compositional semantics. One might be apprehensive about argumentation relative to the assumption that we think in a language of thought, but although I shall strive to state that assumption in a way I think makes it plausible, I shall not here explicitly seek to justify it. That would take too long, and, besides, I strongly suspect that the assumption is concessive on my part, in that the case against compositional semantics plays better without it. Anyway, the first thing I need to do is elaborate and explain the assumption that we think in a language of thought; that is to say, that we use some "language" as an internal system of mental representation.
A language, David Lewis has taught us,9 is usefully regarded as a function from finite sequences of things (e.g., types of marks or sounds or neural states) to propositions. If L(s) = p, then we may say that s is a sentence of L and p its meaning in L. Among other advantages, this conception of language nicely accounts for the fact that a language is an abstract object that, like Esperanto, may or may not be used by anyone, and it nicely accounts for the fact that, while it is a contingent truth that 'La neige est blanche' means that snow is white among the French, it is a necessary truth that it means that in French. Of course, the idea that a language can be represented as a function from its sentences to the propositions those sentences mean is a considerable simplification, especially as it concerns natural languages, for it ignores indexicals, ambiguity, and nonindicative moods. But let us make these simplifications, for they will not affect present concerns.
If a language is an abstract object that may or may not be used by someone, then the question of moment becomes: What is it for a person x to use a language L? Otherwise put, there is some relation R--call it the language relation10--such that a person x uses a language L just in case x bears R to L, and the problem--call it the language-relation problem--is to say what R is. On second thought, however, that is not a very good way of putting the question of moment, for one can use a language in more than one way: one may use a language as a public language of communication, or one may use a language by thinking in it, that is to say, by using it as one's language of thought, and no doubt there are other ways of using a language. So there are at least two language relations--the public-language relation and the language-of-thought relation--and therefore two language-relation problems. Our immediate concern, I have already implied, is the language-of-thought-relation problem. What relation must obtain between a person x and a language L in order for x to think in L, to have L as her lingua mentis?
Here is a first thought to get things going:
x thinks in L iff all of x's propositional-attitude states are realized by tokenings of L sentences, where the content of each propositional-attitude state is precisely its realizing sentence's meaning in L.
Thus, if you think in L and believe p, then there is some sentence s that means p in L (i.e., L(s) = p) and your believing p is realized by s's being tokened in you in a certain way. Likewise, if you desire p, then your desiring p is realized by there being tokened in you in some other way a sentence that means p in L. How can one tokening of a sentence realize a belief that the talk will soon be over while another tokening of it (or some other sentence) realizes a desire with the same content? It is useful to think of the matter in the following familiar two-step way.
Step one. To have a belief is to stand in a certain computational relation to a token of a neural sentence, and to have a desire is to stand in a certain other computational relation to a token of a neural sentence, and so on for each primitive kind of propositional attitude. A vivid way to keep this in mind is to pretend that in each person's head there is a box for each type of primitive propositional attitude. To have a belief is to have a neural sentence tokened in your belief box; to have a desire is to have a neural sentence tokened in your desire box; and so on.
Step two. We shall also eventually want this to be the case on the supposition that you think in L: if L(s) = p and s is tokened in your belief box, then you believe p, and if s is tokened in your desire box, then you desire p. Clearly, for this to be the case, s must have some quite substantial property that makes it the case that a tokening of s in your belief or desire box would realize your believing or desiring p. This substantial property cannot, of course, be the mere set-theoretic fact that L(s) = p. What sort of property might it be, and how might having that property realize thoughts with the requisite content? If we can answer this, we can know in what sense the tokening of a neural sentence can "realize" your believing or desiring a particular proposition.
Well, suppose we accept, as we should, this supervenience thesis:
If x believes p, then x has some physical property F such that x's having F is metaphysically sufficient for x's believing p (and likewise, mutatis mutandis, for the other propositional attitudes).
(By a physical property I mean a property specifiable in the language of a correct fundamental physics, for the sustaining idea here is that we have the propositional attitudes we actually have in every possible world that is physically indistinguishable from the actual world.) Then this would license us to say that a tokening of s in your belief box realizes your believing p just in case s has some physical property F such that s's both having F and being tokened in your belief box is metaphysically sufficient for your believing p; and likewise, mutatis mutandis, as regards a sentence's occurrence in your desire box realizing your desiring p. Of course, we are not thereby licensed to say that if s has a physical property that makes its occurrence in the belief box a realization of the belief p, then that same physical property would make s's occurrence in the desire box a realization of the desire p. This further claim may well be plausible, but the hypothesis that we think in a language of thought need not be construed as requiring it. In any case, I want at this point to introduce a further simplification, so that the only line of thought essential to my purposes is not obscured by the technical niceties imposed by the need to get everything exactly right. In order to keep the crucial expositional line as uncluttered as possible, I shall ignore propositional attitudes other than belief, in effect pretending that we are defining the language-of-thought relation for creatures whose only propositional attitudes are beliefs.11 Later, in a note, I shall indicate how I think the more general account of the language-of-thought relation should go.
So, restricting ourselves, for simplicity, to the case of belief, we may reformulate the above first shot at defining the language-of-thought relation thus:
[*] x thinks in L iff "p[x believes p ® $s$F(F is a physical property & Fs & L(s) = p & s is tokened in x's belief box & it is metaphysically sufficient for x's believing p that [Fs & s is tokened in x's belief box])].
In other words, you think in L just in case, for whatever proposition p you believe, your believing p is realized by a tokening in your belief box of a sentence that means p in L, where to say that your believing p is realized by a tokening of s in your belief box is to say that s has some physical property F such that s's both having F and being tokened in your belief box is metaphysically sufficient for your believing p.
What can be said about the nature of these content-determining physical properties, properties determined by the physical properties on which our beliefs supervene? That is a very difficult question, for while it seems clear that our beliefs supervene on physical properties, it is very unclear what more can be said about those properties. In part, this is because it is very unclear what can be said about the naturalistic reducibility of propositional-attitude relations. The supervenience of the mental on the physical is plausible, but it simply is not clear what else is plausible. Notice in this regard that it by no means follows from the fact that my believing p supervenes on my having physical property F, that F is in any sense a composite property made up of a physical correlate of the belief relation and the proposition p. Let me put this in other words. Suppose Ralph believes both that worms have noses and that dandruff is not fatal. Then it is extremely plausible that there is one physical fact on which the first belief fact supervenes and another physical fact on which the second belief fact supervenes. This may then be harmlessly reworded thus: there are physical properties F and Y such that Ralph's having F is metaphysically sufficient for his believing that worms have noses and his having Y is metaphysically sufficient for his believing that dandruff is not fatal. But from this it in no way follows that there is a physical relation R that "realizes" or reduces the belief relation such that (i) F = bearing R to the proposition that worms have noses and (ii) Y = bearing R to the proposition that dandruff is not fatal. In fact, it is pretty hard to see how the physical fact on which believing p supervenes will directly involve the proposition p, since this physical fact--that is to say, this fact statable in the language of fundamental physics--will not require any reference to p for its specification (unless p is itself a proposition specifiable in the language of fundamental physics).
Still, there is a little more that can be said about these physical content-determining properties, especially when they are located, as in [*], in an account of the language-of-thought relation. One obvious thing is that these properties will be extremely "wide," encompassing complex relations that relate the neural sentences in one's head to things far removed in space and time. Another reasonable thing to say about a sentence's physical content-determining property is that it is determined by physical properties of the sentence's parts and structure; but I want to put off saying more about this extremely important feature until a little later, when I shall put it to some real work.
Anyway, it is time to notice that the first shot [*] seems not to provide either a necessary or a sufficient condition for the language-of-thought relation. The necessity problem may be fairly minor; it is that we should probably allow for the possibility that a person uses more than one system of mental representation, just as a speaker may use more than one public language. In other words, we do not want to read 'x thinks in L' as 'x thinks only in L'. Allowing for this seems less urgent than in the public-language case, but it is probably a good idea to take the weaker reading, since it is trivial to explain what it is for a person to think exclusively in a language once we know what it is to think in it either exclusively or nonexclusively. What will have to go, then, is the requirement that to think in L requires that all of one's beliefs are realized by tokenings of L sentences. If you think in a language, then at least some of your beliefs must be realized in that language, but we should not require that all of them are. The account presently to be offered will reflect this.
The failure of [*] to provide a sufficient condition for the language-of-thought relation is considerably more serious than its failure to provide a necessary condition. The problem is subtle, but its appreciation is crucial. Suppose Ralph thinks exclusively in neural English. Then while all of his beliefs are realized by some finite number of English sentences, there will of course be infinitely many English sentences that will never get tokened in Ralph's head: perhaps they are too long or convoluted for Ralph's brain to process, or perhaps they express propositions that he would never believe. Now consider another language, Shmenglish, which is exactly like English as regards the finitely many sentences that might actually get tokened in Ralph's belief box, but which departs radically from English thereafter: maybe it keeps the same sentences as English (i.e., the functions English and Shmenglish share the same domain of arguments) but assigns wild and arbitrary meanings to the infinitely many sentences that have no chance of occurring in Ralph's belief box; or maybe Shmenglish keeps only the English sentences that have some chance of being tokened in Ralph's head and then has infinitely many garbage sentences paired with arbitrary and wild meanings. The infinitely many sentences of Shmenglish which are guaranteed not to be used need have no physical content-determining features whatever. Yet Shmenglish will satisfy [*]'s right-hand side, thus showing that [*] fails to provide a sufficient condition for the language-of-thought relation. It satisfies [*]'s right-hand side because every proposition that Ralph will believe will be realized by a sentence of both English and Shmenglish, with the same meaning in both.12 We can solve this problem, however, by resorting to an inevitable, and lately alluded to, feature of the physical content-determining properties of Mentalese sentences. Let me explain.
If we think in languages of thought, then those languages will have whatever expressive power our natural languages have. They will therefore be infinite languages, languages having infinitely many sentences, each with its own meaning. Consequently, one's language of thought will have infinitely many sentences that will never be tokened in one's head. At the same time, the actually-tokened sentences will belong, with just the same meanings, to infinitely many languages one does not think in: like Shmenglish, these languages will agree with one's Mentalese on the tokened sentences, but they may depart wildly and capriciously on the rest. If x thinks in L, then we need to appeal to features of L that are already instantiated in x's head and that determine all of L. All of L must get nailed down by stuff that is already in x's head. So the task should be clear: we need to find features of the sentences actually tokened in x's head that determine all of x's Mentalese--the tokened and untokened sentences of it--and determine no other neural language. We need some sort of systematicity, in fact a double dose of systematicity: one pertaining to the syntax of x's Mentalese, the other to its sentences' content-determining physical properties.
The first thing we need in play is the plausible assumption that any actual language of thought will have a compositional syntax. For present purposes, a compositional syntax for a language L may be thought of as a finitely statable set of rules which generates all and only the sentences of L; in other words, a finite specification of L's domain of arguments. Such a syntax will construct all the sentences of L from what it recognizes as the finitely many words and primitive structures of L. The assumption in hand that each actual language of thought has a compositional syntax, let me next stipulate that a compositional syntax S of L is realized in x just in case every word and primitive structure recognized by S occurs in some S-generated sentence of L tokened in x's belief box.
If a person thinks in L, then it is plausible that she realizes some compositional syntax of L. For suppose it were claimed that w was a primitive lexical item (or syntactical feature) in x's lingua mentis but that none of her thoughts--believed, disbelieved, or entertained--was realized by a sentence that contained w, not even trivial tautologies. Then, unless she already had a synonym for w, x would lack the concept determined by w, and I think we should deny that she thought in a language that had w-containing sentences, just as we would deny that a word belonged to a person's spoken idiolect if she could not use the word to formulate some positive or negative or hypothetical or tautological thought.13
Now, it may well be reasonable to deem it a necessary condition for x's thinking in L that some compositional syntax of L is realized in x, but this cannot provide a sufficient condition. Infinitely many distinct languages will have exactly the same sentences as L while differing from L in the meanings they correlate with those sentences. We need a way of assigning properties to the words and structures of a realized syntax for L which will generate content-determining properties for each of L's infinitely many sentences. We already know this about the content-determining property for a Mentalese sentence: it is a physical property F such that the sentence's both having F and being tokened in x's belief box is metaphysically sufficient for x's believing the proposition x's language of thought assigns to that sentence. So suppose the neural sentence s has such a content-determining supervenience property F. Then, to take up a point already touched on, we should expect two things: first, that F is itself determined by physical properties of s's syntax and component words; and second, that each such smaller physical property plays the same content-determining role in each sentence in which a word or structure having it occurs. For example, suppose Bob thinks in English. Then 'The Eiffel Tower is in Paris' will have some wide physical property by virtue of which it can function in Bob as a realizer of the belief that the Eiffel Tower is in Paris. This physical property will be a function of physical properties of the sentence's syntax and component words; and it will be because 'Paris', say, has its wide physical property that whenever a sentence containing it is tokened in the belief box, one believes a proposition about Paris. The alternative to supposing that the physical content-determining properties of Mentalese sentences are compositionally determined in this way is simply too bizarre to contemplate: that there is no finite basis from which the infinitely many physical content-determining properties derive.
In this way, we see how if x thinks in L, then there will be a finitely axiomatized supervenience theory that does the following.
For some compositional syntax S of L which is realized in x, the supervenience theory assigns to each word and primitive structure of S a physical property and, on the basis of this, assigns to each sentence s of L a physical property F such that (1) s's having F is logically equivalent to the parts and structure of s having the physical properties the theory assigns to them and (2) it is metaphysically sufficient for x's believing L(s) that s both has F and is tokened in x's belief box.14
Let us call such a theory a compositional supervenience theory for L with respect to x. It puts us in a position to say what it is for a language to be a person's system of mental representation:
x thinks in L iff there is a true compositional supervenience theory for L with respect to x.
So the idea is this. If x thinks in L, then the words and primitive structures of L (as recognized by some compositional syntax of L) are already tokened in x's head in L sentences tokened in x's belief box. This secures that x has beliefs realized by L sentences, but it does not require that all of x's beliefs are so realized. Thus, [*]'s necessity problem is obviated. Furthermore, these words and structures have physical properties that determine a physical property for each of the perhaps infinitely many sentences of L. And if F is the property determined for the sentence s, then it is metaphysically sufficient for x's believing the proposition L(s) that s both has F and is tokened in x's belief box. In this way, all of L is nailed down by stuff already in x's head, and thus [*]'s sufficiency problem is obviated.15
Now that we know what it is to use a language as a language of thought, we need to return to the question that is driving this whole discussion: Does one's language of thought have features whose explanation requires a compositional meaning theory? A compositional meaning theory for L is a finitely axiomatized theory of L which issues in a theorem of the form
s means p in L (i.e., L(s) = p)
for each sentence of L. It is commonly assumed that a person's language of thought must have a correct compositional meaning theory. For it is argued that without this assumption one will not be able to explain the productivity and systematicity of a person's use of her language of thought.16 In discussing whether one's language of thought has features whose explanation requires a compositional meaning theory, it is expedient to relativize this question to a particular case. So let 'Mentalese' stand for that neural language that is Jane's language of thought, and let us suppose that this language has the same infinite expressive power as Jane's public language (you might even suppose that it is a neural version of her public language). Then our general question becomes: Does Mentalese, or Jane's use of it, have features whose explanation requires, or seems to require, a compositional meaning theory? Productivity and systematicity enter as relevant features in the following way.
Mentalese itself is simply a function from sequences of neural states to propositions, and there is nothing in the notion of such a function which requires it to be finitely specifiable. There can be, then, nothing about the set-theoretic function we are calling 'Mentalese' which per se requires a compositional meaning theory. But although motives for a compositional meaning theory will not arise for Mentalese qua set-theoretic function, they may arise for Jane's use of Mentalese as a system of mental representation. This will be clear if we permit ourselves to speak thus: if L is x's language of thought, then every sentence of L means in x's head what it means in L. Now, s's meaning p in Mentalese is the mere set-theoretic fact that M(s) = p. But if s means p in Jane's head, then that is a quite substantial fact--a substantial fact essentially defined by the account lately offered of the language-of-thought relation, of what it is to think in a language. And the crucial component of this substantial fact is that s has some physical property, one determined by physical properties of its parts and structure, such that s's both having that property and being tokened in Jane's belief box is metaphysically sufficient for her believing p. Here, then, is a substantial productivity fact that demands explanation: What explains the fact that each of infinitely many neural sentences means in Jane's head some particular proposition? Surely this infinity of meaning facts must be explained, at bottom, by some finite physical state of affairs, some nonendless way the world is physically. Does this not suggest the need for a compositional meaning theory for Mentalese, so that we can account for Jane's having it as her lingua mentis?
And Jane's use of Mentalese is also systematic. What a sentence means in Jane's head depends on its words and structure, and those words and structure play the same meaning-determining roles in every sentence in which they occur. It is no accident that whenever '... water ...' is in Jane's belief box she believes that ... water .... This systematicity of Jane's use of Mentalese explains what might be thought of as the systematicity of her thought tout court. This is the fact, made much of by Fodor, that someone like Jane cannot have the capacity to form the thought that John loves Mary without also having the capacity to form the thought that Mary loves John. Perhaps this systematicity of Jane's use of Mentalese, and the systematicity of her thought which supervenes on it, requires a compositional meaning theory for Mentalese to explain it.
It is, however, considerably less than obvious that a compositional meaning theory is needed to explain any of this, for it would seem, first, that both the productivity and systematicity of Jane's use of Mentalese are explained by a correct compositional supervenience theory for Mentalese with respect to Jane, and, second, that such a theory is not a compositional meaning theory. Let me explain.
Since Jane thinks in Mentalese, there is a correct compositional supervenience theory for Mentalese with respect to her. Let us call this theory 'T*'. For each sentence of Mentalese, T* issues in a theorem of the form
s has F,
where F is a physical property such that s's both having F and being tokened in Jane's belief box is metaphysically sufficient for her believing M(s), the proposition M(entalese) assigns to s. So T* does not explain productivity and systematicity by formally entailing that Jane's use of Mentalese is productive and systematic. Indeed, T*, qua supervenience theory, formally entails nothing about what any Mentalese sentence means in Jane's head. But T* does account for this productivity and systematicity in the sense that it metaphysically entails that Jane's use of Mentalese is productive and systematic. In other words, there is no metaphysically possible world in which T* is true and Jane's use of Mentalese fails to be both productive and systematic. Indeed, there is no metaphysically possible world in which T* is true and a sentence of Mentalese means in Jane's head something other than what it actually means there. Clearly, then, we can say that Jane's use of Mentalese is productive and systematic because T* is true. This is simply a result of T*'s assigning to each sentence of Mentalese a physical property on which the meaning the sentence has in Jane's head supervenes. For that supervenience secures that there is no metaphysically possible world in which T* is true and Mentalese is not Jane's language of thought, and there is no metaphysically possible world in which Mentalese is Jane's language of thought and her use of it is not both productive and systematic. This follows from the nature of Mentalese, the definition of a compositional supervenience theory for L with respect to x, and the use of that definition in the proffered account of the language-of-thought relation.
The second thing to notice about T* is that it is not a compositional meaning theory for Mentalese. A compositional meaning theory for Mentalese issues, for each sentence of Mentalese, in a theorem of the form
[m] s means p in Mentalese.
But, we know, a compositional supervenience theory for Mentalese with respect to Jane issues, for each sentence of Mentalese, in a theorem of the form
[s] s has F,
where F is a physical property such that s's meaning the proposition M(s) in Jane's head supervenes, in the way made clear, on s's having F. Obviously, a theory can issue in theorems of form [s] even though it does not have the wherewithal to issue in theorems of form [m]; to pick a trivial reason, it might simply lack the vocabulary to enable it to formulate [m]-type theorems. This shows that a compositional supervenience theory need not be a compositional meaning theory. But we can say something stronger: since the specification of the physical properties the supervenience theory generates will not in general involve reference to the propositions they determine (just think of the physical property, specifiable in the language of fundamental physics, that is the supervenience base for your believing the proposition that 12 + 12 = 2), a compositional supervenience theory is guaranteed not to have the wherewithal also to be a compositional meaning theory.17
Thus, since Jane thinks in Mentalese, there is a correct compositional supervenience theory for Mentalese with respect to her. This theory is not a compositional meaning theory for Mentalese, but it does metaphysically entail the productivity and systematicity of Jane's use of Mentalese.
A compositional supervenience theory is not a compositional meaning theory. The interesting question, however, is whether it is possible for Mentalese to have a compositional supervenience theory without also having a compositional meaning theory. The answer is that it all depends on the nature of the propositions to which our that-clauses refer. If those propositions are compositionally-determined things, then Mentalese will have a compositional supervenience theory and a compositional meaning theory. But if those propositions are noncompositionally-determined things, then Mentalese will have a compositional supervenience theory but not a compositional meaning theory. Either way, the compositional supervenience theory is there to account for the productivity and systematicity of Jane's use of Mentalese.
To say that propositions are compositionally determined is to say, roughly speaking, that there is a finitely definable function from propositional building blocks (the referents words have in that-clauses, on the assumption that the reference of a that-clause is determined by its syntax and the references of its parts) to the propositions they build. Russellian propositions, which are set-theoretically composed of the objects and properties our beliefs are about, are paradigmatically compositionally-determined propositions, and my own view is that if our that-clauses refer to compositionally-determined propositions, then those propositions are Russellian. Anyway, suppose that believing is a relation to compositionally-determined propositions. Then it is reasonable to suppose we would have the wherewithal to construct a compositional meaning theory for Mentalese given that we had the wherewithal to construct a compositional supervenience theory for it. For a vivid picture of how this goes, suppose that the propositions we believe are not merely compositionally determined but also structured, Russellian propositions. Now suppose that the supervenience theory T* assigns the word-size physical property Y to the word w. Then there will be a propositional constituent x such that w's having Y secures that x will be introduced into every proposition expressed by a sentence containing w. In this way, then, we should be able to pair off the word-size physical properties assigned by T* with propositional constituents, and we should also be able to pair off the physical properties T* assigns to the primitive structures of Mentalese with compositional rules that map sequences of propositional constituents onto Russellian propositions containing those constituents. The result would be a compositional meaning theory for Mentalese. Needless to say, the result would be the same even if the compositionally-determined propositions were not Russellian complexes (but were, say, sets of possible worlds). There could still be a pairing of assigned physical properties with semantic values that are propositional determinants, and there could still be a pairing of physical properties assigned to primitive syntactic structures with compositional rules mapping propositional determinants onto propositions, the net result being that the semantic apparatus worked alongside the physical apparatus to yield exactly those propositions that supervene on the physical properties T* assigns to the sentences of Mentalese. To be sure, this is an extremely crude sketch, but I trust that the general point will be readily conceded--that Mentalese will have a compositional meaning theory if it has a compositional supervenience theory and the propositions we believe are themselves compositionally determined.
Now suppose that believing is a relation to propositions that are not compositionally determined: they are propositions by the general gloss of that notion but there is no finite way of constructing those propositions from propositional building blocks. Then it will not be possible to pair off word-size physical properties with semantic values (i.e., propositional determinants) and Mentalese will not have a compositional meaning theory, even though it has a compositional supervenience theory.18 At the same time, the productivity and systematicity of Jane's use of Mentalese will be explained by T*, the correct compositional supervenience theory for Mentalese with respect to Jane, in the sense that T* metaphysically entails that Jane's use of Mentalese is both productive and systematic.
Thus the issue of compositional meaning theories for Mentalese turns on the nature of the propositions to which our that-clauses refer, the propositions, therefore, which Mentalese sentences mean. What can be said at this point about the competition between the conception of propositions as compositionally determined and the conception of them as noncompositionally determined?
Propositionalists have traditionally taken propositions to be compositionally determined, but this may simply be because they have felt the need for a conception of propositions which comports with compositional semantics. That motivation has now been called into question, for we need to suppose that there is a correct compositional supervenience theory for Mentalese with respect to Jane just to explain the fact that she thinks in Mentalese; this theory is not a compositional meaning theory; but it does metaphysically entail that her use of Mentalese is productive and systematic. At the same time, none of this precludes a compositional meaning theory for Mentalese from playing some role in explaining the productivity and systematicity of Jane's use of Mentalese. It might be argued that although a compositional supervenience theory explains the productivity and systematicity of her use of Mentalese, a compositional meaning theory is needed to explain how the supervenience theory is able to play its explanatory role. Alternatively, it might be argued that while the supervenience theory metaphysically entails all the semantic facts about Jane's use of Mentalese, that metaphysical relation is too weak to sustain anything that could properly be called an explanation of why the sentences of Mentalese mean what they do in Jane's head.
To the extent that either of these explanatory roles can be made plausible, then to that extent there would be motivation for compositionally-determined propositions. Now, there is in fact a rather obvious line of reasoning to be pursued here, one concerned with explaining why an infinity of meaning facts should supervene on the infinity of physical facts described by a compositional supervenience theory, and I shall return to it in due course. The present bottom line is that while we have some basis for questioning whether a compositional meaning theory is needed to explain meaning productivity and systematicity, that it does play some such role is consistent with the claims made about a compositional supervenience theory's explanatory role, and this is an issue further to be explored. So the jury is still out on the motivation for compositionally-determined propositions.
As regards the motivation for noncompositionally-determined propositions, there are two things to be said, one supportive, the other probative. The supportive thing is that we have some reason to prefer noncompositionally-determined propositions, for we have some reason to prefer that solution to the paradox, [P], which requires them. I allude, of course, to the solution that locates (2) as the odd man out, thus allowing us to say that, while that-clauses refer to propositions, the reference of a that-clause is not determined by its syntax and the references of its component words. This solution is coherent only if the propositions to which that-clauses refer are themselves noncompositionally determined. At the same time--and this is the probative remark--the conception of propositions as noncompositionally determined faces challenges apart from the issue of compositional semantics. If that-clauses refer to noncompositionally-determined propositions, then (a) those propositions should enjoy some sort of positive motivation independent of our little paradox and (b) answers should be available to challenging questions that test the coherence of this conception of propositions. In the next section, I shall say something in aid of (a), and (b) will be the topic in the section after that.
There is, however, a loose end to attend to before turning to those matters. The ongoing enterprise is to challenge (2) of the paradox [P], and that requires challenging the widely-held assumption that natural languages have compositional truth theories. But the challenge I have been discussing is to the assumption that Mentalese needs a compositional meaning theory. The connection between the two challenges is apparent: motivating a meaning theory for a language is, we noticed, one primary way of motivating a truth theory for the language, and, owing to the way in which one's public language must share its expressive power with that of one's language of thought, it is clear that one's public language will have a compositional semantics if, and only if, one's Mentalese has one. Nevertheless, two questions are naturally raised at this point. First, might there not be a still unconsidered motive for thinking that Mentalese needs a compositional truth theory? Second, might I not have overlooked motivations for compositional semantics that are unique to public language? I think the answer to both questions is no. As regards the first question, the motivation for supposing Jane's use of Mentalese to need a compositional truth theory would be to account for its truth-conditional productivity and systematicity. But this is also explained by the supervenience theory T*, for it is metaphysically necessary that if T* is true, then Jane's use of Mentalese is truth-conditionally productive and systematic. I take this to be obvious, since (a) Jane's use of Mentalese will be truth-conditionally productive and systematic if it is meaning productive and systematic and (b) we have already seen the way in which T* accounts for the meaning productivity and systematicity of Jane's use of Mentalese.
As regards the second question, there is a lot to be said, but I shall say only a little. The public-language-relation problem is the problem of saying what relation must obtain between a person, or population of persons, and a language in order for the person or population to use the language as a public language of communication. Elsewhere19 I have argued that this relation needs to be defined in terms of a language-processing mechanism that maps public-language sentences onto meaning-equivalent language-of-thought sentences in such a way that there are two results: (i) the productivity and systematicity of one's use of one's public language is inherited from the productivity and systematicity of one's use of one's language of thought, and (ii) public-language understanding--the ability to hear an utterance of a possibly novel sentence and know what was said in the utterance--can be accounted for, without invocation of any kind of compositional semantics for one's public language, in terms of processing that maps public-language sentences onto meaning-equivalent language-of-thought sentences. The gist of the idea behind (ii) is that understanding public-language utterances requires not an internally represented compositional semantics for the public language, but rather employment merely of some finitely-based device that maps each public-language sentence onto its language-of-thought translation.
This takes us back to where we left off. A challenge has been raised to the traditional motivation for compositionally-determined propositions, but it remains a still unsettled question whether that conception of propositions, and the compositional semantics that goes with it, is needed to help explain semantic facts entailed by a person's use of her language of thought. On the other hand, the paradox-[P]-generated motivation for noncompositionally-determined propositions is evident, but that conception of propositions wants some sort of motivation apart from the paradox, and it has yet to face specific questions challenging its coherence. These last two matters, I have already announced, are the concerns of the next two sections, and the still-unsettled issue about compositionally-determined propositions will be joined in wondering how the opposite conception of propositions might meet its challenges.
Propositions belong to a class of things that have long been viewed with skepticism. Others in this group include properties, states, and events. What makes them fishy? Some people have a problem with abstract objects generally, but that does not single out our group: events, after all, are in space and time. I think what has worried people about the members of the group I have singled out is, as it were, their ontological shallowness, where this is reflected in two features they appear to have: the something-from-nothing feature and the no-criterion-of-individuation feature.
The something-from-nothing feature. From a true sentence containing no singular term that refers to an entity of the kind in question, we get a singular term that does refer to an entity of the kind in question. Thus, from the truth of 'Fido bit Fi Fi', whose only singular terms are 'Fido' and 'Fi Fi', we get the singular term 'Fido's biting Fi Fi', which we are assured of referring to Fido's biting Fi Fi--an event we may then go on to talk about in sentences such as 'Fido's biting Fi Fi caused a lawsuit'. In the same manner, the true sentence 'Fido is a dog', whose only singular term is 'Fido', yields the singular term 'Fido's being a dog', which we are assured of referring to Fido's being a dog--a state we may then go on to talk about in sentences such as 'Fido's being a dog means he can't vote'.
The sentence 'Fido is a dog', whether or not it is true, also yields the singular term 'the property of being a dog', which we are assured of referring to the property of being a dog, and the singular term 'that Fido is a dog', which we are assured of referring to the proposition that Fido is a dog. That the property and proposition singular terms and their references are thus secured is displayed in the way we can move back and forth between 'Fido is a dog' and its pleonastic equivalences 'Fido has the property of being a dog' and 'That Fido is a dog is true' (more colloquially, 'It is true that Fido is a dog').20
Some have taken the something-from-nothing feature to indicate that the singular terms in question are not referential singular terms. Since 'My birth was on a Tuesday' is a stylistic variant of 'I was born on a Tuesday', why not just say that all the ontological commitments are owned by the more parsimonious version, the ostensible singular term 'my birth' not having a genuinely referential function? And likewise with the ostensible references to states, properties and propositions. But we know that there are two problems with this nonexistence line. First, one cannot always paraphrase the problematic singular term away. This is especially apparent for the use of that-clauses in propositional-attitude ascriptions: there is no paraphrase for 'Ralph believes that Fido is a dog' which eliminates the ostensible reference to the proposition that Fido is a dog. Second, occurrences of the singular terms in question are subject to existential generalization, and, as I earlier remarked, there are problems with the idea that the resulting existential quantifications ('There is something Ralph believes', 'Something happened on a Tuesday', 'Fido has some attribute', etc.) can all be read as involving uses of a suitably "nonobjectual" quantifier. Perhaps a better response to the something-from-nothing feature is to allow the existence of the entities seemingly miraculously brought into existence by a manner of speaking, but to treat their existence in a suitably deflationary, or minimalist,21 manner. States, events, properties, and propositions exist all right, but in acknowledging this we are merely playing along with the language games that introduce these notions, and there is nothing more to the natures of these things than these little language games determine. Such a doctrine of cheap ontology might reasonably be read into the view of propositions I am in the process of sketching with an eye toward motivating a conception of noncompositionally-determined propositions.
The no-criterion-of-individuation feature. A second thing that has bothered philosophers about the kinds of entities in question is that we seem not to have criteria of individuation for them. The contrast is with ordinary physical objects, where it is reasonable to suppose we do have such criteria. For example, horse x = horse y iff their spatio-temporal worms coincide. In the case of propositions we can perhaps say that p = q iff necessarily, one believes p just in case one believes q, but what is lacking is the analogue of the property of being a horse having such-and-such spatio-temporal worm. By this I mean, to take the case of propositions, a kind of property K such that (i) every proposition must have a property of kind K, (ii) properties of kind K are intrinsically specifiable without reference to any propositions that might have them, and (iii) necessarily, if F is of kind K and p has F, then, for any proposition q, q = p iff q has F. In this sense of criterion of individuation, I think our suspicious entities have nothing close to criteria of individuation. But this is not to say that we cannot make judgments of identity or difference. We can ascribe some kinds of properties to these entities, and these ascriptions can sometimes be used to establish identity or difference. For example, if proposition p is believed by Al while proposition q is not, then p q, and if your wedding made you happier than any other event ever made you, then your wedding = the happiest event in your life. It may also be that judgments of identity and difference do not figure very importantly in the use we make of the notions in question.
The something-from-nothing and no-criterion-of-individuation features suggest a certain deflationary picture of the nature of these ontologically suspect entities. It is as though someone introduced the notions of a state (e.g., Fido's being a dog), of an event (e.g., Fido's biting Fi Fi), of a property (e.g., the property of being a dog), and of a proposition (e.g., that Fido is a dog) by:
(1) Giving their grammar.
(2) Giving the something-from-nothing transformations. For events these take us from 'a Fed' to the singular term 'a's Fing'. For states, properties, and propositions they take us from 'a is F' to, respectively, the singular terms 'a's being F', 'the property of being F', and 'that a is F'.
(3) Giving criteria, or "rules of use," for ascribing to propositions et al the sorts of properties we clearly do have procedures for ascribing to them.
(4) Giving nothing more.
And if these notions were introduced in this way, it would have important implications for philosophical views about their essential nature and individuation. In the case of states and events, for example, it would be hard to see how one could accept the Davidsonian line that, although mental properties are irreducibly mental, mental state and event tokens are identical to physical state and event tokens. For nothing would have been determined for events and states which offered any sort of empirical procedures for discovering such identities, and in the absence of such procedures it should seem puzzling how any such identity claim could be determinately true. There would apparently be nothing in the explicitly introduced concept of a state to enable one to determine that, say, a particular pain was identical to a particular neural state. Knowing that one was in pain, one would also then know, by the trivial transformation, that one had a pain. One might then set out to discover whether this pain state had various other features; for example, whether it was caused by something one ate. But no procedures would be available to determine whether the pain state was also a neural state, and in the absence of such concept-determined procedures, it is apt to seem that there could not really be any hidden identity fact to be discovered. At the least, it would seem that a coherent notion of event/state had been introduced that did not require any such identities.
Another likely consequence of the explicit-introduction story, at least when fleshed out in the way I have in mind, is a diminished epistemological status for our fishy entities. We can imagine people discovering the existence of horses or electrons even before they had those notions,22 but I think that nothing could count as discovering propositions in a possible world where the notion of a proposition had not already been introduced. In such a world, the only way someone could rationally come to believe in the existence of propositions would be via the introduction of the notion of a proposition, and this notwithstanding the fact that on our conception of propositions they exist in all possible worlds. Likewise, mutatis mutandis, for properties, states, and events.
And I find it plausible that a further consequence of the explicit-introduction story is that there would be nothing in the explicitly introduced notion of a proposition to determine that the introduced propositions were compositionally determined. A coherent conception of propositions would have been introduced which was consistent with propositions' not being compositionally determined. I realize that this is not obvious because step (3) of the introduction appeals to intuitions about what properties we are clearly in a position to ascribe to propositions, and one might try to argue that something could be appealed to here that would demonstrate a requirement that the introduced propositions be compositionally determined. I shall not try to argue against this, but shall simply go on record with my own bet. What I am primarily fixing on is the way nothing relevant about the nature of that Fido is a dog is determined by the way we are told we can get to it merely from the sentence 'Fido is a dog'. I am not, however, claiming that the explicit-introduction story implies that referents of that-clauses are not compositionally determined. It could not be ruled out that, although the introduction per se made no demand on propositions' being compositionally determined, nevertheless some ingeniously constructed recursively defined function secured that in fact they were. I am merely trying to tell a little story that suggests a positive conception of propositions which requires the existence of propositions and is conceptually consistent with their not being compositionally determined.
It should come as no surprise now if I were to suggest that the concept of a proposition was such that in relevant respects it was as though it were introduced in the forgoing way. And if this suggestion is correct, then we would have a sort of positive motivation for noncompositionally-determined propositions; we would have, as I just suggested, a positive conception of propositions which was conceptually consistent with their not being compositionally determined.
Now I do want to recommend the gist of the minimalist conception of propositions et al that we would have if those notions had been stipulatively introduced in the imagined way; I think it is pretty much as if propositions et al were introduced in that way. Consequently, there can be nothing more to the nature of a proposition--the thing, that S, we get from the sentence 'S'--than is determined for it by the little concept-fixing language game we play with the notion of a proposition, the one corresponding to the imagined stipulative introduction. At the same time, I do not think that we can say that it is exactly as if propositions et al had been introduced in the forgoing way. The problem is that there appear to be entities of each of the relevant kinds which cannot be obtained via the something-from-nothing transformation. In the case of events, I have in mind "objectless" events, such as flashes of lightning, and in the case of states, properties and propositions I have in mind the apparent conceptual possibility of things of those kinds for which we lack linguistic means of expression. For example, we find intelligible the idea that there are truths that cannot now be expressed in any natural language. Regrettably, I do not have a fully worked-out line for these cases. I would like to think they were in some way parasitic on the primary case of entities generated by the something-from-nothing transformation. My recommendation is that we see these exceptions not as undermining the minimalist story already sketched but rather as requiring a slight emendation to it: the practices determinative of our concepts of a proposition, property, state, and event are a little more complicated than the practices determined by the fictional introduction. Yet the main point about propositions stands, I would suggest: the practices determinative of their nature determine, in the trivial way sketched, that our sentences express propositions, but they do not determine, and are consistent with its not being the case, that those propositions are compositionally determined.
Fortified (alas, however weakly) with a deflationary conception of propositions, let us now consider specific questions that challenge the hypothesis that the references of that-clauses are noncompositionally-determined propositions.
1. If the reference of a that-clause is not compositionally determined in the standard truth-theoretic way, then in what way is it determined? What makes the proposition that Superman flies the referent of 'that Superman flies'?
This question most naturally arises in connection with one's public language, which in our case is English; but let us first consider it in connection with Mentalese, one's language of thought. So suppose Jane thinks in neural English. Then what secures that the Mentalese 'that Superman flies', as it occurs in 'Lois believes that Superman flies', refers to the proposition that Superman flies?
What secures this is the compositional supervenience theory for Mentalese with respect to Jane. The basic idea is simple: the referent of 'that Superman flies' is the meaning of 'Superman flies', and the compositional supervenience theory assigns physical properties to the parts and structure of that sentence in a way that secures a physical property for the entire sentence which secures that in Jane's head the sentence means the proposition that Superman flies. There are two ways to elaborate this. (a) We know that the Mentalese sentence
'Superman flies' means in Mentalese that Superman flies
is true, and we are assuming that that-clauses are referential singular terms. So it follows that the displayed that-clause, 'that Superman flies', refers to the meaning of 'Superman flies'. And we also know that the physical property that the compositional supervenience theory assigns to the Mentalese 'Superman flies' determines that in Jane's head it means the proposition that Superman flies. Since the sentence's meaning-determining physical property is itself determined by the physical properties the theory assigns to the sentence's parts and structure, it follows that the reference of the Mentalese that-clause is determined by the physical properties the compositional supervenience theory assigns to the parts and structure of the sentence contained in the that-clause.
(b) Consider the Mentalese sentence
[#] Lois believes that Superman flies
and before asking what makes it the case that its that-clause refers (in Jane's head) to the proposition that Superman flies, let us first ask what makes it the case that 'Lois' refers (in Jane's head) to Lois. Well, the first thing to say is that the compositional supervenience theory for Mentalese with respect to Jane assigns to [#] a physical property that determines it to mean the proposition that Lois believes that Superman flies. This proposition is about Lois in that it is true iff Lois believes that Superman flies. But [#]'s meaning-determining physical property is in turn determined by the physical properties that the compositional supervenience theory assigns to its parts and structure, and the physical property the theory assigns to 'Lois' is precisely what makes the ultimately determined proposition about Lois. That is why 'Lois' refers in Jane's head to Lois. Similarly, the proposition that Lois believes that Superman flies is also about that Superman flies--i.e., the proposition that Superman flies. That [#] expresses a proposition that is about the proposition that Superman flies is due to the physical property the supervenience theory assigns to 'that Superman flies', and this is why the that-clause refers to the proposition that Superman flies. But that physical property is in turn determined by physical properties that the compositional supervenience theory assigns to the words and structure of the that-clause. Now it should be clear that the real work is done by the that-clause's content sentence, 'Superman flies', the word 'that' merely serving, as it were, to indicate that a singular term is being formed. Thus, in this way, we see again that the reference of the Mentalese that-clause is determined by the physical properties the compositional supervenience theory assigns to its content sentence's parts and structure.
Notice, by way of further clarification, that even when the reference of a Mentalese complex singular term (e.g., 'the capital of France') is determined by its syntax and the references, or semantic values, of its parts, it is also the case that its reference is determined by physical properties assigned to its parts and structures by a compositional supervenience theory. Mentalese must have a compositional supervenience theory whether or not it also has any sort of compositional semantics, and a fortiori whether or not any fragment of Mentalese has a compositional truth theory. I hasten to add, however, that if Mentalese has no compositional meaning theory, then while some fragment of it may have a compositional truth theory, no fragment of it will have a compositional meaning theory. If the reference of a that-clause is a noncompositionally-determined proposition, then its reference cannot be determined by its syntax and the references of its components words, and hence no that-clause-containing sentence can be accommodated in a compositional truth theory. But this leaves it open that fragments of the language not containing that-clauses might be so accommodated. At the same time, since the reference of 'that S' is the meaning of 'S', this means that if the references of that-clauses are noncompositionally-determined propositions, then the meaning of no sentence can be compositionally determined in the way required by a compositional meaning theory. The moral is that, for all intents and purposes, a compositional theory of that-clause reference simply is a compositional meaning theory for all the sentences occurring in that-clauses.
I am emphasizing this in order to correct a misleading impression that the case against compositional truth theories is apt to create. Suppose one were to deny that natural languages had compositional truth theories because, say, sentences containing certain kinds of adverbs could not be accommodated in such a truth theory. No other constructions present a problem, but those adverbs are recalcitrant. Naturally, one ought to be suspicious of such a claim, even if one could not see how to accommodate the adverbs, and this because there is nothing theoretically special about the problematic sentences except for their being problematic. Well, one might have the same reaction to a denial of compositional truth theories based on a claimed impossibility of accommodating sentences containing that-clauses in a truth theory. Yet here the complaint, legitimate against the adverb-based argument, would be wrong. There is something principled and extraordinarily special about that-clauses: they refer to propositions, and propositions are meanings. That-clause-containing sentences are not just one more kind of sentence; the failure of that-clauses to be accommodatable in a compositional truth theory would be a manifestation precisely of the noncompositional nature of meaning.23
So much for the reference in Jane's head of Mentalese that-clauses. Now that we see that the question about the accommodation of that-clauses in a truth theory is really the question about the accommodation of any sentence in a meaning theory, we can see what to say about the reference of Jane's public language that-clauses. One needs only to repeat the translational story told toward the close of section IV about the relation between inner and outer languages with respect to the issue of a compositional meaning theory: the semantic features of public-language expressions are inherited from those of one's Mentalese expressions via the language-processing mechanisms that account for one's understanding of public-language utterances by mapping them onto appropriate formulae in one's inner system of mental representation. This is further elaborated in Schiffer 1993.
2. What individuates propositions? What makes the proposition that Superman flies distinct from the proposition that Clark Kent flies? And how do we get--as indeed we may have to get, if our theory is to cover the data--two distinct propositions as the referents of distinct tokens of 'that she is a philosopher' when both tokens of 'she' refer to the same person?
There are, I have suggested, no nontrivial criteria of individuation for propositions. At the same time, we are able to make confident judgments of nonidentity, for we have criteria for ascribing properties to propositions, and we are often in a position to know that two propositions are indeed two, because one has a property the other does not have. Just think of all the differences between the proposition that Harry Truman had toes and the proposition that the Eiffel tower is in Paris. In a sense, what "makes" the proposition that Superman flies distinct from the proposition that Clark Kent flies is that someone can believe one of them without believing the other. According to the deflationary conception of propositions earlier sketched, there is simply nothing more to the nature of propositions than is determined by our use of the notion of a proposition, by, if you like, the "language games" we play with that notion. This is not true of rocks and people. They have complex natures to be studied and discovered, natures that go considerably beyond anything determined by our concepts of rocks and people. We know what there is to know about the proposition that Superman flies by knowing such things as when it would be correct to say that someone believes it. Ascriptions of belief are attuned to what the person to whom the belief is ascribed would say. A fluent English speaker who is willing to assert 'Superman flies' but unwilling to assert 'Clark Kent flies' counts as believing that Superman flies and as not believing that Clark Kent flies.
I am not trying to say something trivial. If Al kissed Betty but did not kiss Carla, then Betty Carla, and if Lois believes that Superman flies but does not believe that Clark Kent flies, then the proposition that Superman flies the proposition that Clark Kent flies. I find it difficult to be precise about the asymmetry I want to articulate, but let me try to grope for it in the following way. Suppose you were wondering whether Betty and Carla were the same person. You could hardly hope to determine that they were not by determining that Al kissed Betty but not Carla. Imagine saying, "Well, I saw that Al kissed Betty and that he didn't kiss Carla, so I knew Betty wasn't Carla." The absurdity, of course, is that you could not rationally conclude in this case that Al kissed Betty but not Carla unless you already knew that Betty was not Carla. But you can determine that Lois believes that Superman flies and that she does not believe that Clark Kent flies without any prior opinion, as it were, about the identity or difference of the two propositions. It is because the criteria for the truth of these belief statements are independent in this way that we can first determine the different truth-values of 'Lois believes that Superman flies' and 'Lois believes that Clark Kent flies' and then conclude that the proposition that Superman flies the proposition that Clark Kent flies. Part of what is going on here is a further asymmetry. Criterial evidence for the truth of a statement of the form 'A kissed B' requires, so to say, prior identification of A and B: you identify A, you identify B, and then you see if they are requisitely related by the kiss relation. It is not like this, however, with statements of the form 'A believes that S'. Here we do not identify A, then identify the proposition that S, and then see whether A is belief related to the proposition. Instead, we base this ascription ultimately on nonintentional facts whose specifications require no reference to propositions, facts pertaining to linguistic and nonlinguistic behavior, functional organization, and placement in a largely shared environment.
The other example mentioned in the question that began this discussion was of two tokens of 'that she is a philosopher' referring to different propositions, even though both tokens of 'she' referred to the same woman. I have in mind a familiar sort of case. During a break from the APA convention in Washington D.C., a group of philosophers are visiting the National Gallery when one of them, Nigel, is asked whether a certain woman also touring the galleries is a philosopher. Nigel replies that he has no idea, he neither believes that she is a philosopher nor that she is not a philosopher. One member of the group mishears Nigel's reply and says to another, referring to the woman, 'Nigel believes that she is a philosopher'. Intuitively, this utterance is false, even though, unbeknown to everyone, Nigel did encounter the same woman earlier in the day and took her to be a professor of philosophy. At the same time, back at the convention hotel, someone says 'Nigel believes that she is a philosopher', referring to the woman Nigel spoke with earlier at the hotel. Intuitively, this utterance is true. Since my hypothesis holds that believing is a two-place relation between a person and a proposition, I am committed to holding that the two tokens of the that-clause refer to different propositions. Actually, the same sort of phenomenon also arises in cases not involving indexicals. For example, to borrow from Saul Kripke (1979), Ralph may think there were two Paderewskis, one a statesman, the other a famous pianist. Playing on this, we can imagine two utterances of 'Ralph believes that Paderewski played at Carnegie Hall', one true, the other false.
The situation is essentially the same as that which led us to see 'that Superman flies' and 'that Clark Kent flies' as referring to distinct propositions. Criteria for the ascription of beliefs tell us first that one utterance of 'Nigel believes that she is a philosopher' may be true while another is false, notwithstanding that both occurrences of 'she' refer to the same person. Then this tells us that what Ralph believes in the one case is different from what he believes in the other. Since what he believes is what the that-clauses refer to, we get the result that the two tokens of the that-clause refer to different propositions. What there is to our individuation of propositions is simply consequent on the criteria we have for making belief assertions, criteria that do not themselves rely on a prior individuation of propositions. To put this loosely, our propositional-attitude language game, which governs the conditions under which we can correctly utter propositional-attitude sentences, is not keyed to an antecedently established distinction among neatly individuated types of propositional-attitude states of affairs; rather, what individuation there is to these states of affairs is consequent on our linguistic practices. Since we know that one utterance of 'Nigel believes that she is a philosopher' is true while another is false, we know there is one thing he believes and another he does not believe, and both propositions may be referred to by the same that-clause. It is also true that these propositions may perhaps be referred to by other that-clauses. Perhaps in the first case one could as well have said, 'Nigel believes that that woman over there is a philosopher', this not being something one could have said in the circumstance of the second imagined utterance. And likewise, perhaps in that second circumstance the speaker could as well have said, 'Nigel believes that the woman he was talking to by the book display is a philosopher', this not being something one could have said in the circumstance of the first imagined utterance. Yet it would be another mistake to suppose that these new singular terms referred to anything more than the woman in question. According to the hypothesis being entertained, the propositions these that-clauses refer to are not structured entities individuated by their constituents. They are individuated by no general criteria of individuation, but only by the truth-values attaching to actual belief ascriptions. We deem there to be two propositions, both true just in case a certain woman is a philosopher, because we first accept that there are true and false utterances of 'Nigel believes that she is a philosopher', where both occurrences of 'she' refer to the same woman. To be sure, this conception of propositions goes against a heavy-duty Platonism and invites the metaphor of propositions as mere shadows of that-clause occurrences. But that is the point.
3. We know how to define truth for the familiar sorts of propositions that comport with compositional semantics, but how are we to define truth for these new creatures?
If propositions are sets of possible worlds, then a proposition is true just in case the actual world belongs to it. If propositions are Russellian complexes composed of an n-ary property and an n-tuple of things, then a proposition is true just in case its n-tuple component instantiates its n-ary property component. No such neat definition of truth for propositions is possible if they are not compositionally determined. But so what? What interesting notions can be defined? Indeed, the fact that standard and familiar conceptions of propositions allow truth to be so easily defined for them should make one suspicious. It should make one suspect that these are not the objects of belief to which our ordinary conceptual and linguistic practices commit us but rather philosophical constructions tailor-made to suit preconceived philosophical ends.
Although we cannot define truth as a property of propositions, we have no trouble knowing how to ascribe the property, and no trouble accounting for our conception of it. For it belongs to our conception of truth that, subject to a certain qualification, every proposition of the form
That S is true iff S,
It is true that S iff S
is necessarily true. For any instance of this form that we entertain, we know it a priori and noninferentially. No one who has our concept of truth can fail to know, merely upon consideration, that it is true that snow is white iff snow is white. Such a thought, for such a person, is a trivial truism.24 It is a truism that is a reflection of the earlier-noticed (section V) something-from-nothing transformation that introduces propositions into our ontology, the pleonastic transformation that allows us to move back and forth between 'S' and 'It is true that S'.
The alluded-to qualification pertains to the notorious semantic paradoxes, for evidently we do not, on pain of contradiction, want to count the proposition that, say, it is true that 'heterological' is heterological iff 'heterological' is heterological as true (where, of course, a predicate is heterological just in case it is not true of itself). So instances of the propositional truth schema must be restricted in some way in order to avoid contradiction. I have nothing useful to say about how this restriction should be stated, but however it is stated, the points just made about our a priori knowledge of instances of the restricted schema, and of the role of that schema in our mastery of the notion of propositional truth, should stand (cf. Horwich 1990, pp. 41-2).
4. It is clear that singular terms may have referential occurrences in that-clauses. But how can this be accounted for on the requisite conception of that-clauses, which denies that the referent of a that-clause is a function of the references of its parts?
Singular terms in that-clauses do indeed sometimes occur with their "customary" references. This is most obvious when demonstratives and pronouns are used, as in 'Ralph believes that I stole this hubcap', but there are clear examples involving every kind of singular term. This fact, however, is consistent with the claim that the reference of a that-clause is not determined by its syntax and the references of its parts. If there is puzzlement on this score, it may be partly due to conflating the distinction between the commonsense notion of singular term reference and the technical notion of reference that goes with a compositional truth theory.
The technical concept, a philosopher's invention, is such that terms in a that-clause could not have reference unless there was a compositional, truth-theoretic determination of the reference of a that-clause as a function of the references of its parts. This is because the technical notion of reference just is the notion of semantic values assigned to expressions in a correct compositional truth theory for the language to which those expressions belong. As such, the technical notion is theory relative, in that if there is one way of assigning semantic values to words in a correct compositional truth theory, then there will also be alternative ways. For example, if we have a truth theory that assigns sets as semantic values to predicates, then there will be equivalent theories in which predicates are assigned properties rather than sets or no semantic values at all (the theory will instead use a recursive definition of satisfaction for predicates). So, in the technical sense, it really makes no sense to ask about the reference of an expression, except relative to the supposition that a particular kind of formulation of a compositional truth theory is in question. In any case, the hypothesis under consideration holds that that-clauses cannot be accommodated in a compositional semantics, and thus denies that words in that-clauses have any reference in the technical sense of "semantic value assigned by such-and-such compositional truth theory."
The commonsense notion of reference evidently allows us to recognize a singular term's having reference in a that-clause without requiring us to say that the reference of that that-clause is a function of the references of its component words. Thus, Al says, 'Nigel believes that she is a philosopher', and his utterance of 'she' refers to Louise Peters. What makes this so? Well, thanks to Al's referential intentions with respect to 'she', he is saying that Nigel believes a certain proposition about that woman. The proposition is about her in two related respects: first, it cannot be specified except by reference to her, and second, it is a necessary truth that the proposition is true if and only if that woman, Louise Peters, is a philosopher. Now, notwithstanding the truth of Al's utterance, Betty, in another context, might say 'Nigel doesn't believe that Louise Peters is a philosopher', and her utterance might also be true. Her utterance of 'Louise Peters' also refers to Louise Peters, and this by virtue of the fact that she is denying that Nigel believes a certain proposition about that woman. This proposition, that Louise Peters is a philosopher, is about Louise Peters again in two respects: the proposition cannot be specified except by reference to Louise Peters, and, necessarily, the proposition is true if and only if that woman, Louise Peters, is a philosopher. So, we have the proposition referred to by Al's utterance of 'that she is a philosopher' and we have the proposition referred to by Betty's utterance of 'that Louise Peters is a philosopher'. These are two propositions by virtue of Nigel's believing the first but not the second; but they are both about same person, and both have the same truth condition. Propositions, to repeat what was earlier said, are not (on the hypothesis being entertained) to be identified and individuated by the propositional building blocks that construct them. Although abstract and language-independent, propositions are really conceptual products of the conceptual and linguistic practices governing our use of that-clauses. They are, if you like, abstractions from our ways of ascribing beliefs, and their properties are those implicitly determined by those ascriptions.
5. If Mentalese sentence meanings are noncompositionally-determined propositions, then how are we to account for the supervenience of meaning properties on physical properties?
Jane thinks in Mentalese, so each of infinitely many Mentalese sentences has some physical property that secures that in her head the sentence means the proposition it means in Mentalese. How is this infinite correlation of physical properties and propositions to be explained? What explains how just those meanings come to supervene on just those properties? It might seem that this cannot be explained on the assumption that propositions are noncompositionally determined and, even worse, that it can be explained on the assumption that they are compositionally determined.
Notice, to begin, that the infinite correlation is not explained by the compositional supervenience theory for Mentalese with respect to Jane. That theory gives a finite way of correlating each sentence of Mentalese with the physical property on which its meaning supervenes, but it does nothing to explain why any given meaning should supervene on the physical property that is its supervenience base. If the sentence s means the proposition that snow is white in Jane's head, then the supervenience theory will assign to s a physical property F such that s's meaning that proposition supervenes on s's having F; but nothing will have been done to account for why that particular meaning property should supervene on that particular physical property.
At this point it may seem puzzling how this puts the noncompositionalist at a disadvantage vis-à-vis the compositionalist. For is not the problem at issue simply the extraordinarily difficult one of explaining the supervenience of the intentional on the physical, and who has a convincing story to tell about that? This is a problem for all theorists, and, one might think, puts the advocate of compositionally-determined propositions at no advantage. For, to continue the thought, that theorist might account for the supervenience of s's meaning p on s's having F in terms of other supervenience relations between parts of F and constituents of p, but how are those other supervenience relations to be explained? If Jane thinks in English, then the compositionalist might explain the fact that 'Fido is a dog' means in Jane's head the singular proposition <Fido, doghood> partly in terms of the fact that 'Fido''s meaning Fido in Jane's supervenes on 'Fido''s having the physical property Y and the fact that 'dog''s meaning doghood in Jane's head supervenes on 'dog''s having the physical property Y'. But then those supervenience relations must be explained, and no explanation whatever is forthcoming merely from the assumption of compositionally-determined propositions or its concomitant compositional meaning theory.
It is true that the compositionalist has to explain her basic supervenience correlations, and in this regard the problem of explaining the supervenience of the intentional on the physical is as hard for her as it is for anyone. But the compositionalist has finitely many basic supervenience correlations to explain, and therein lies her apparent explanatory advantage. Whether one's conception of propositions is as compositionally determined or as noncompositionally determined, one must accept that Jane's use of Mentalese has a compositional supervenience theory, and one must confront the task of accounting for why the infinitely many physical properties the supervenience theory assigns to sentences should subvene the infinitely many meaning properties that depend on them. One must explain that infinity of, so to say, F/p correlations. The apparent advantage of the compositionalist is simply this. If Jane's use of Mentalese has a compositional supervenience theory and Mentalese sentence meanings are compositionally-determined propositions, then, we have seen, Mentalese will also have a compositional meaning theory. This meaning theory can be combined with the supervenience theory to get a finitely-based theory that will generate each of the infinitely many F/p correlations operative in Jane's head. This theorist will still have finitely many basic supervenience relations to account for, but those relations can be used in a finitely axiomatized theory that specifies, for each sentence, exactly which propositional meaning supervenes on the physical property assigned to that sentence by the supervenience theory. Such a further theory, if one had it, might reasonably be claimed to be both a superior explanation of the meaning facts of Jane's use of Mentalese and also a partial account of how the compositional supervenience theory is able to metaphysically entail the productivity and systematicity of Jane's use of Mentalese. This is why I earlier (on p. 000) said that even though a compositional supervenience theory was bound to provide its account of the productivity and systematicity of Jane's use of Mentalese, this did not preclude a compositional meaning theory from playing, in one or another of the two ways mentioned, its own explanatory role.
The advocate of noncompositionally-determined propositions can offer no similar account of the infinity of F/p correlations. He can have no finitely-based formal deduction of them. But each such supervenience dependence must in some way be explained, and it is surely absurd to suppose that we must settle for an infinity of equally basic, unconnected explanations, one for each dependency. If that is the best that can be hoped for from noncompositionally-determined propositions, then the contest is over.
So the question is whether there is something reasonable to be said by way of explaining the infinity of F/p supervenience correlations on the assumption that sentence meanings are noncompositionally-determined propositions. I think there may be a story to be told here, one that belongs to a deflationary account of meaning to go along with the already sketched deflationary account of propositions. The details of the story may be negotiable, but its basic plot is straightforward. Let me convey that plot in a very simple fiction so that the explanatory strategy I have in mind is not obscured by the complexities of the real story.
We may imagine a possible world pretty much like ours except that the language we both speak and think in is nonindexical, indicative, and unambiguous English. Our concept of meaning in this world is determined by two things. The first is the privileged status of the disquotational meaning schema (DMS),
'S' means for me that S.
This privileged status consists in the fact that the conceptual role of our notion of meaning is such that nothing could count against the truth of any substitution instance of DMS. Merely to entertain an instance is to believe it, and nothing can count as evidence against any such belief. One's knowledge that 'Snow is white' means (for one) that snow is white is noninferential and indubitable. That is simply a brute fact about one's concept of meaning. At the same time, however, instances of DMS are not regarded as necessary, and this brings us to the second thing determinative of our concept of meaning: the concept-generated intuitions about what our sentences would mean in counterfactual situations. One recognizes that it is an entirely contingent fact that 'Snow is white' now means for one that snow is white, and that, therefore, the sentence does not have that meaning in various counterfactual circumstances. One knows, for example, that if one used 'snow' in the way one now uses 'coal', then 'Snow is white' would not mean for one that snow is white. These implicit judgments about counterfactual situations, determined by the conceptual role of our notion of meaning, are very complex and not easily codified. They might also be very coarse-grained and murky, so that even in principle it is impossible to be very precise and fine tuned about how meaning would vary across relevant possible situations. One's actual and potential intuitions about meaning in counterfactual situations might be a clumsy, blunt instrument, and, if so, that fact about one's concept of meaning would be compatible with the point of having the concept. I mention this without actually building it into my fiction because I think it reflects our actual concept, but my fiction does not need this embellishment. All that is crucial is that our concept of meaning commits us to an array of determinate judgments about whether our sentences would or would not mean what they now mean in various counterfactual situations. Our intuitions may be entirely indeterminate for a vast array of other counterfactual situations.
In the fictional world I have been describing, we would have a way of explaining the infinity of F/p supervenience correlations. Our concept of meaning would afford us an answer to why our meaning properties have the physical supervenience bases they have. Given the privileged status of DMS, one knows that each sentence of one's language has the meaning ascribed in DMS. Given further that the departures from DMS determined by one's concept of meaning--i.e., the circumstances in which one's sentences would not determinately mean what they mean--are all possible worlds that are physically different from one's actual world (one uses one's words differently in those worlds), one can conclude that one's sentences will have exactly the meanings they now have for one in every possible world that is physically indistinguishable from one's actual world. Thus, one can conclude that the infinitely many instances of DMS supervene on one's present total physical state of affairs. Then, in principle, one could use the counterfactually-relevant aspects of one's concept of meaning to whittle away at this total physical state of affairs to arrive at a finite physical basis and, in this way, a compositional supervenience theory for one's use of one's language. The whittling process would secure, in principle, that the finite physical basis thus determined was not any larger than it needed to be in order determinately to determine every instance of DMS. But in having all this, one would have a concept-based explanation of why one's meanings supervened on just the physical properties specified in the compositional supervenience theory. Given the described nature of one's concept of meaning and the present physical state of affairs, the F/p supervenience correlations could be no other than what they are.
This would be, I think, a suitable explanation, or at least demystification, of why one's meaning properties should supervene on the physical properties on which they happen to supervene, and there are two things to notice about this explanation. First, it affords no finitely axiomatized way of formally deducing the infinity of F/p correlations, and second, it is evidently conceptually and logically consistent with sentence meanings' being noncompositionally-determined propositions. What we seem to have, then, is a just-so story of how in a certain possible world we can account for the supervenience of meaning properties on physical properties on the assumption that sentence meanings are noncompositionally-determined propositions.
But what about the real world where, owing to indexicals and nonindicatives, we cannot appeal to DMS; where it cannot be assumed that one thinks in one's public language; and where the concept-determining conceptual role of one's notion of meaning is considerably richer than the one in the fiction, especially since it is a notion applicable to speakers of languages other than one's own? I cannot hope to answer these questions here. I can hope that a version of DMS will still provide the conceptual anchor to one's notion of meaning, ascriptions of meaning to others based on similarity to one's own case. Most of all, I hope I have said enough to indicate how in principle there might be a concept-based demystification of the F/p supervenience correlations consistent with the ps being noncompositionally determined.
This has been a modest paper. I have simply tried to describe a genuine position in logical space and to offer some motivation for taking it seriously. The initial part of that motivation is the way the position in question, the thesis of noncompositionally-determined propositions, yields a solution to the paradox, [P], with which I began. This part of the motivation can hardly seem compelling. For one thing, I was not able to lay out the entire case for taking (2) of [P] as the odd man out while retaining (1) and (3). For another thing, even if I had been able to lay out that entire case, it would be far from immediately compelling. The argument is long and complex, each step of it inviting several possible responses. This is no arena for knockdown arguments or quick-and-easy solutions.
The other part of my motivation is a rearguard defense of noncompositionally-determined propositions against positive objections to, or worries about, that position. This defense has three parts. The first is the stuff about compositional semantics. If that-clauses refer to noncompositionally-determined propositions, then natural languages will not have compositional semantics, and that seems to be a problem. But to this there may be a good reply. Given that we think in an inner system of mental representation, one's public language needs a compositional semantics only if one's lingua mentis does; but the inner system must have a compositional supervenience theory, and this explains the productivity and systematicity of one's language of thought. A compositional supervenience theory is itself no kind of compositional semantics, although there is a legitimate question whether a language can have a compositional supervenience theory without also having a compositional semantics. But the answer to that question turns entirely on the nature of propositions: a language can have a compositional supervenience theory without also having a compositional semantics if, but only if, the propositions in the ranges of our propositional-attitude relations are not themselves compositionally determined.
The second part of the rearguard defense was my effort to provide something of a positive motivation for noncompositionally-determined propositions. The idea was to tell a deflationary story about the nature of propositions which did not require propositions to be compositionally determined and made it unmysterious how they well might not be compositionally determined. I did the best I could with this story, but I wish I could have done a lot better. I would like to think there is a better story to be told, if only I were better equipped to find it.
The final part of the defense was my attempt to formulate and to answer some prima facie difficult questions for the hypothesis of noncompositionally-determined propositions. Here, too, I wish that I could have done better. I suspect that others will think of questions I should have considered, and I doubt that my brief (and too often impressionistic) answers will silence concern about the questions I did consider.
At the same time, there is more to be said in favor of the entertained hypothesis. It can be shown that Mentalese has a compositional semantics only if a fairly heavy-duty reduction thesis obtains, and some will be skeptical of such a reductionist commitment.25 In Schiffer 1990, I proposed an account of moral propositions that is of a piece with the deflationary account of properties and propositions sketched in section V. I hope in the future to show how the thesis of noncompositionally-determined propositions is aided by considerations pertaining to conditionals and to vagueness and indeterminacy. And there are broadly logical considerations against compositional semantics of the kind lately detailed by Haim Gaifman (1992). So even if the approach I have sketched has some merit, a lot remains to be said about it.26
1. That-clauses do not function as referential singular terms when they are being quantified into, as in 'Nearly everyone believes that he or she is virtuous'. The paradigmatic occurrences in question are those where that-clauses occur as self-contained units, so to speak, as in 'Ralph believes that Fido is a dog'.
2. The cautious wording, which hesitates to ascribe
validity to all tokens of these types, is in order to leave open the possibility
of the "hidden-indexical theory" of belief ascriptions, which
requires a contextually determined reference to a type of mode of presentation,
thus making the inference type 'Ralph believes that Fido is a dog; so, Ralph
believes that Fido is a dog' no more valid than 'It's raining; so, it's
raining'. See Schiffer 1992 and the discussion below.
3. For an interesting critical discussion of my appeal to nonobjectual quantification, see Tomberlin 1990 and 1992. My own reasons for questioning this approach are more philosophical than technical, and I hope to set them out in some future publication.
4. One view of this sort treats that-clauses on analogy with a Russellian treatment of extensional occurrences of definite descriptions, the "denotation" of the that-clause being the proposition uniquely characterized by the that-clause. For present purposes, this does not really differ relevantly from the position that that-clauses are referential singular terms. A view of this sort that is relevantly different is, e.g., any variation on the line that 'Ralph believes that Fido is a dog' means that Ralph believes some Fregean proposition or other that is true iff Fido is a dog. See Schiffer 1992, p. 506, fn. 10, where I suggest that such a view cannot be extended to sentences like 'Ralph said that Fido is a dog'.
5. The last item of this list alludes to the view that propositional attitudes are relations to "interpreted logical forms." See Higginbotham 1986, Segal 1989, and Larson and Ludlow forthcoming.
6. In my 1987a I argue against both the Mentalese version of sententialism (§ 4.2) and some public-language versions, including Davidson's paratactic theory (ch. 5).
7. Salmon replies in his 1989.
8. As James Higginbotham pointed out to me, this puts the implausibility of the hidden-indexical theory on a par with that of a description-theoretic treatment of "incomplete" definite descriptions. That treatment has it that one uttering 'The dog has fleas' must mean that the thing that is uniquely a dog and F has fleas, for some contextually-determined property F . The trouble with this is that there will typically be a number of potentially completing descriptions that are equally salient in the context--the dog that I own, the dog chewing your slippers, the dog lying on your coat, the thing that is either a dog that I own or the dog lying on your coat, and so on. This makes it highly implausible that there will be one such description that is the one contained in the proposition the speaker meant (cf. Schiffer 1981 pp. 77-78). It is just the same problem that I have raised for the meaning claim required by the hidden-indexical theory. To be sure, this shared problem is not decisive, and a response appealing to referential (or meaning) indeterminacy comes to mind: no determinate type of mode of presentation (completing description) was intended, but that is because what was meant was somehow vague or indeterminate. I no longer feel that this response is as easily dismissed as I once did, but I am still inclined to think that it cannot succeed. I discuss the issue in Schiffer forthcoming.
9. In 1969, 1983a, and 1992. See also Schiffer 1993.
10. What I am now calling the language relation has also been called the actual-language relation. This designation, however, anachronistically adverts to David Lewis's formulation of the problem in his 1969, in which he defined a possible language in the way a language has just been defined and then asked what it is for a possible language to be the actual language of a given population of persons. This way of formulating the problem was later dropped by Lewis, and this, I suspect, for two reasons: the erst while possible languages are actual things--functions of the kind described; and French would not cease to be a language if people stopped using it (it would rather become a language that people no longer used).
11. Needless to say, the propositional-attitude-box metaphor already involves a considerable simplification in the way it ignores degrees of belief and desire. A more realistic account of the language-of-thought hypothesis would need to appeal to something like an agent's subjective probability and desirability functions. It is not exactly clear how this refinement should be incorporated, and I am glad that my own purposes do not require it.
12. This is a version of a problem that I raised against Lewis (in conversation) years ago and which he first discussed in his 1983a, p. 187. He now calls it the problem of meaning without use and discusses it again in his 1992. The solution I am about to offer to this problem, as it arises for the language-of-thought-relation problem, is also discussed in Schiffer 1993, where I also offer to solve the problem as it arises for the public-language-relation problem.
13. To be sure, there may be conditions under which a person would have a thought realized by a sentence containing a new lexical primitive, but this may be construed as an instance of language enrichment, which, on our conceptualization of languages, would be a trivial instance of language change.
14. It is permissible to read in the further condition that these content-determining F s are minimal supervenience bases in the following sense: if the theory assigns F to s , then there is no nondisjunctive property Y that is entailed by F but not logically equivalent to it such that s also has Y and x's believing L( s ) also supervenes on s 's both having Y and being tokened in x's belief box.
15. Let me now say how the restriction to belief,
imposed at the outset to simplify the exposition, should be lifted. The
idea is to leave the just proffered account of the language-of-thought relation
untouched while complicating the account of a composit ional supervenience
theory. Let us pretend that belief and desire are the only primitive propositional
attitudes, all others definable in terms of them. Then we should recognize
three kinds of compositional supervenience theories. The kind using belief
already defined. The kind we get from that by substituting desire for belief.
And one that combines them by replacing (2) with:
(2') it is metaphysically sufficient for x's believing/desiring L( s ) that s both has F and is tokened in x's belief/desire box.
We should allow for the single-attitude versions, since having such a compositional supervenience theory for L with respect to x would evidently be sufficient for x's using L as a system of mental representation. But one would surely expect the (2') version to be what fits most if not all actual languages of thought (assuming there are some). Certain worries about this can be forestalled by noticing that nothing precludes both the neural sentences and their physical content-determining properties from being disjunctively defined, thereby allowing that one tokening of a neural sentence can realize a belief p while another realizes a desire p, even though the two occurrences are physically dissimilar.
16. See Fodor 1990a; Schiffer 1991 and 1993. Notice that as regards one's language of thought, there is no counterpart to the claim that a compositional meaning theory is needed to explain one's language-understanding ability. In the case of a public language, understanding consists in one's ability to hear the utterance of a novel sentence and know what was said in its utterance, and it is not unreasonable to think that these transitions rely on one's tacit knowledge of a meaning theory. But understanding a neural language is simply a matter of thinking in it, and it would seem that motivations here for a compositional meaning theory are exhausted by the motivations provided by productivity and systematicity.
17. Given the loose way I defined a compositional supervenience theory, this admits of a trivial exception: the conjunction of a compositional supervenience theory for L with respect to x and a compositional meaning theory for L would be a compositional supervenience theory for L with respect to x. Please consider me to have given a tighter definition that rules out this trivial exception.
18. Why not a compositional theory that simply took the physical properties assigned by T* as its "semantic values"? Because there would be no way of stating a finitely definable function that mapped those properties onto the propositions they determined unless one could first pair off the properties with things, such as propositional constituents, out of which the propositions could be defined.
19. Schiffer 1993; see also Schiffer 1987a, ch. 7.
20. Apropos of the equivalence in meaning between
'That S is true' and 'It is true that S', Paul Horwich suggests that
We can construe 'It is true that p', on a par with 'It is true, what Oscar said', as an application of the truth predicate to the thing to which the initial 'It' refers, which is supplied by the subsequent noun phrase, 'that p'. (1990, p. 17, n. 1)
21. Cf. Johnston 1988.
22. In 1897, J.J. Thomson discovered the electron. Prior to this there had been speculation about subatomic particles, but no one really had the concept of an electron. What Thomson discovered was that so-called cathode "rays" were not waves of radiation, as they had been thought to be, but rather minute particles of matter each carrying an electric charge. He also found that they weighed far less than hydrogen atoms. But it took some years for scientists to realize that these particles could be emitted from atoms themselves, or to realize that atoms were not simple but had these new particles as constituents. Here there was the discovery of electrons, and then the gradual introduction of electron talk into the language.
23. One would still be entitled to wonder why there could be correct compositional truth theories for certain language fragments if a compositional truth theory was not needed to explain how the truth-value of any sentence was determined by features of its words and syntax. I am inclined to suppose this question will have an informative answer if its hypothesis is correct, and I wish I knew it.
24. Horwich proposes that "a person's understanding
of the truth predicate, 'is true'- -his knowledge of its meaning--consists
in his disposition to accept, without evidence, any instantiation of the
(E) 'The proposition that p is true if and only if p',
by a declarative sentence of English (including any extensions of English)" (1990, p. 36).
25. In Schiffer 1991 I argued that what I there called the Reduction Principle must be true if Mentalese is to have an explanatory compositional meaning theory. But this was to put the point in an unnecessarily weak way. Since there must be a compositional supervenience theory for L with respect to x merely to account for x's thinking in L, the basic argument of that paper shows that if any actual language of thought has a compositional meaning theory, then the Reduction Principle is true.
26 . Thanks to Kent Bach, Paul Boghossian, John Carroll, Mark Crimmins, Russell Dale, Hartry Field, Jerry Fodor, Jean Kazez, Brian Loar, William Lycan, Raul Orayen, Greg Ray, Mark Richard, Margarita Valdes, Takashi Yagisawa, and Umit Yalcin.