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The Nature and Structure of Content$

Jeffrey C. King

Print publication date: 2007

Print ISBN-13: 9780199226061

Published to Oxford Scholarship Online: May 2007

DOI: 10.1093/acprof:oso/9780199226061.001.0001

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Objections to Structured Propositions Generally

Objections to Structured Propositions Generally

Chapter:
(p.102) 4 Objections to Structured Propositions Generally
Source:
The Nature and Structure of Content
Author(s):

Jeffrey C. King (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199226061.003.0005

Abstract and Keywords

This chapter addresses objections to structured propositions generally. For the most part, the objections considered do not depend on difficulties in the account of structured propositions that has been sketched. Thus, this chapter focuses on a sample of challenges it is considered important to address.

Keywords:   structured propositions, objections, truth

Having considered objections to the particular view of structured propositions I am defending, in the present chapter I address objections to structured propositions generally. For the most part, the objections considered here do not depend on idiosyncrasies of the account of structured propositions I have sketched. Of course, not all challenges to structured propositions can be considered. Thus, the present chapter comprises a sampling of challenges that I take to be important to address.

There is one prominent sort of challenge that will not be considered here. It is sometimes argued that structured propositions of the sort I am defending cannot, without some additional machinery, underwrite a proper semantics for verbs of propositional attitude. For, assuming that names and predicates have the sorts of semantic values I have assumed them to have, that verbs of propositional attitude express two‐place relations between individuals and propositions, and that that‐clauses designate propositions, neither of the following two sentence pairs can diverge in truth value:

  1. 1a. Lucy believes that Mark Twain is a great author.

  2. 1b. Lucy believes that Samuel Clemens is a great author.

  3. 2a. Lucy believes that a groundhog is in the shed

  4. 2b. Lucy believes that a woodchuck is in the shed.

In both cases, there is only one proposition to be believed on the present account. And some hold that this is too implausible to accept.1

I don't ignore this sort of challenge to structured propositions here because I take it lightly or think it isn't important. There are two reasons for setting it aside. First, the challenge is well known and has been extensively discussed in the literature, whereas, so far as I know, the objections I will be considering have not received replies. And second, as I said in Chapters 1 and 2, my primary (p.103) concern is not with the constituents of propositions, but rather with how those constituents are bound together. Thus, though I have adopted a view about the constituents of propositions on which 1a and 1b express the same proposition (the same goes for 2a and 2b) and I think the view is a plausible one, I at least in principle remain open to other views as long as they cohere with my account of what binds the constituents of propositions together.

That said, let me begin by considering a very general argument against any theory of structured propositions (either Fregean or Russellian) recently given by Stephen Schiffer (2003). (I'll be primarily concerned with the argument as an argument against Russellian views of structured propositions, on which their constituents are objects, properties and relations, since that is the sort of view I am defending.) Since Schiffer states the argument very concisely, let me quote him in full:

  1. (1) If any theory of structured propositions is true, then (α) ‘barks’ in ‘Ralph believes that Fido barks’ functions as a singular term whose referent is a constituent of the structured proposition to which the that‐clause refers (for all intents and purposes, that referent would either be the property of being a barker or else a concept of that property).

  2. (2) If (α), then the following inference is valid:

    • Ralph believes that Fido barks.

    • ∴ (∃x)(Ralph believes that Fido x)

  3. (3) But the inference isn't even coherent, let alone valid.

  4. (4) ∴ No theory of structured propositions is true.2

Now the natural first reaction to the argument, which I shall argue is correct, is that premise (1) is false. However, Schiffer offers the following defense of premise (1):

Premiss (1) may strike one as surprising, but the theorist of structured propositions seems committed to it. For example, for the Russellian ‘that Fido barks’ in ‘Ralph believes that Fido barks’ is a semantically complex singular term whose referent is, or may be represented as, <Fido, the property of being a barker>. This means that both ‘<Fido, the property of being a barker>’ and ‘that Fido barks’ are co‐referential semantically complex singular terms, in the first of which ‘the property of being a barker’ refers to the property of being a barker, and in the second of which ‘barks’ refers to that property. This isn't a role ‘barks’ could perform if it were functioning as a verb; to perform its referential role in the that‐clause it must be functioning as a singular term on all fours with the co‐referential expression ‘the property of being a barker’. Likewise, mutatis mutandis, for the Fregean, only in her case the reference is not to the property of being a barker but to a concept of it.3

I have to confess that I don't follow Schiffer's reasoning here as to why the structured proposition theorist is committed to premise (1).4 Schiffer says that (p.104) the Russellian is committed to the following claims in defending premise (1) in the above quotation (and suggests that the Fregean is committed to analogues of them):
  1. A. ‘<Fido, the property of being a barker>’ and ‘that Fido barks’ are complex singular terms that both refer to the proposition that Fido barks.

  2. B. ‘the property of being a barker’ in ‘<Fido, the property of being a barker>’ refers to the property of being a barker.

  3. C. ‘barks’ in ‘that Fido barks’ is a singular term referring to the property of being a barker.

Given that ‘barks’ is a referring expression in ‘that Fido barks’, as is claimed in C, it should be legitimate to existentially generalize on it. This gives us the claim in premise (2) that the inference mentioned there is valid.

One thing that puzzles me about Schiffer's defense of premise (1) here is why he brings up ‘<Fido, the property of being a barker>’ at all. Does he think A and B above entail C? He doesn't say this, but if he doesn't think it, why did he bring up ‘<Fido, the property of being a barker>’?

I believe that Schiffer reasons that premise (1) is true as follows.5 Assume you are a structured proposition theorist. Assume ‘that Fido barks’ is a referring expression whose referent is the proposition that Fido barks. Schiffer takes structured proposition theorists to endorse a principle he calls the compositionality hypothesis (CH) according to which ‘the referent of a that‐clause token is determined by its structure and the referents of its component expressions together with whatever implicit references are made in the utterance of the that‐clause.’6 We can safely ignore implicit references in the present case. Schiffer thinks that in an utterance of ‘Wendy believes that it's raining’ the speaker might make implicit reference to a place, say Mammoth Lakes, so that the token of ‘that it's raining’ in question refers to the proposition that it is raining in Mammoth Lakes. In the case of ‘that Fido barks’, we can assume no implicit references are made. So CH tells us that the referent of ‘that Fido barks’ is determined by its structure and the referents of its component expressions. But ‘barks’ is one of the component expressions and must surely help to determine the referent of the that‐clause. So this means that ‘barks’ must have a referent.7 For the Russellian, could this referent be the set (p.105) of barking things? No, because if the set of barking things and the set of things with fleas were the same, it would then follow that ‘that Fido barks’ and ‘that Fido has fleas’ refer to the same proposition. Thus, the Russellian must hold that ‘barks’ is a referring expression in ‘that Fido barks’ that refers to the property of being a barker. In order to do this, ‘barks’ must be a singular term referring to the property of being a barker. But then the inference in premise (2) ought to be valid. I should add that Schiffer correctly assumes that the Russellian doesn't hold that ‘barks’ refers to the property of being a barker in sentences like ‘Fido barks’. Thus, he thinks that Russellians must hold that ‘barks’ functions differently semantically in that‐clauses than it does in sentences like ‘Fido barks’, violating semantic innocence.8

As against Schiffer, I'll argue that there is no good reason to believe premise (1). Worse, I believe premise (1) can be shown to be false. Let me take these points in turn.

Unless the following claim is true there is no reason to believe premise 1:

  1. i. (Putting implicit references aside) Structured proposition theorists, including Russellians, are committed to the claim that the referent of a that‐clause is determined by the referents of the expressions in it and how they are combined syntactically (CH), and so all the expressions in a that‐clause (including ‘barks’ in ‘that Fido barks’) must be referring expressions.9

For it is the claim that structured proposition theorists hold that ‘that Fido barks’ is a referring expression whose referent is determined by the referents of its parts, including ‘barks’, that allows Schiffer to conclude that structured proposition theorists are committed to the claim that ‘barks’ is a singular term with a referent in the that‐clause. I'll argue that i is false, and so there is no reason to believe premise (1).

Second, premise (1) entails at least the following claims:

  1. ii. Structured proposition theorists, including Russellians, are committed to the claim that that‐clauses are referring expressions.

  2. iii. Structured proposition theorists, including Russellians, are committed to the claim that ‘barks’ functions semantically differently in that‐clauses than it does in sentences such as ‘Fido barks’.

(Premise (1) entails iii in conjunction with the obvious truth that ‘barks’ in ‘Fido barks’ does not function as a singular term.) I'll show that ii and iii are false, and hence that premise (1) must be as well.

(p.106) Taking i first, note that if ii is false, then i is false. If Russellians are not committed to the claim that that‐clauses are referring expressions, then neither are they committed to the claim that the referent of a that‐clause is determined by the referents of the expressions in it and how they are combined syntactically (CH), nor to the claim that all the expressions in a that‐clause (including ‘barks’ in ‘that Fido barks’) are referring expressions. Hence since I will show that ii is false, it follows that i is false. I should add that though the Russellian is not committed to these claims, she may well hold that in some sense the semantic value of a that‐clause is a function of the semantic values of its parts and how they are combined. It's just that because she is not committed to that‐clauses being referring expressions, she is not committed to the referent of a that‐clause being a function of the referents of its parts and how they are combined.

But I also wish to emphasize that even a Russellian who takes that‐clauses to refer should reject both the claim that the referent of a that‐clause is determined by the referents of the expressions in it and how they are combined syntactically, and the claim that all the expressions in a that‐clause are referring expressions. To see this, consider the case of complex demonstratives. I have argued elsewhere that they are not referring expressions, but suppose one held that they are referring expressions.10 Would one hold that the expressions in ‘that man in the corner talking’ are all referring expressions and that the referent of the demonstrative is a function of the referents of its parts and how they are combined?11 Surely not! Otherwise, one would presumably have to admit that the following inference is valid: John knows that man in the corner talking. Therefore, (∃x)(John knows that man in the corner x). Hence, even if one held that complex demonstratives are referring expressions, one should deny that all the expressions in a complex demonstrative are referring expressions. Those Russellians who hold that that‐clauses are referring expressions should do the same. Hence, even those who accept the view that that‐clauses refer should reject the claim that the referent of a that‐clause is determined by the referents of the expressions in it and how they are combined syntactically (CH), and the claim that all the expressions in a that‐clause (including ‘barks’ in ‘that Fido barks’) are referring expressions. So contrary to i, not only are Russellians not committed to these claims, but no Russellian should endorse them.

Turning now to ii, aren't Russellians committed to the view that that‐clauses are referring expressions? They clearly are not. I think that Russellians should hold that a belief ascription such as ‘Lucy believes that Fido barks’ is true iff Lucy stands in the belief relation to the proposition that Fido barks. And I myself hold this. But this doesn't at all require the Russellian to hold that that‐clauses are referring expressions. To see this, simply note that holding that a sentence (p.107) like ‘Michelle loves the tallest California congressman’ is true iff Michelle bears the loving relation to the unique thing o that is a tallest California congressman doesn't require one to hold that ‘the tallest California congressman’ is a referring expression that refers to o. For example, one could maintain that ‘the tallest California congressman’ is a quantifier. In just the same way, the Russellian can hold that a belief ascription like ‘Lucy believes that Fido barks’ is true iff Lucy stands in the belief relation to the proposition that Fido barks, while holding that ‘that Fido barks’ is not a referring expression. It is true that such a person must hold that in some way the that‐clause here has the effect of making the proposition that Fido barks and the relations it stands in relevant to the truth conditions of the sentence ‘Lucy believes that Fido barks.’ But she need not hold that it does so by referring to the proposition that Fido barks.

It is worth adding that there are some reasons for doubting that that‐clauses are referring expressions. First, there are expressions that do appear to be singular terms referring to propositions, such as ‘logicism’. Given that one believes in propositions, it is hard to think of what such expressions could be except referring expressions whose referents are propositions. Such expressions exhibit distributional differences with that‐clauses:

  1. 3. Robin embraced logicism/*that arithmetic reduces to logic.

  2. 4. Robin is sure of logicism/*that arithmetic reduces to logic.

  3. 5. Robin hoped *logicism/that arithmetic reduces to logic.

  4. 6. It is necessary *logicism/that arithmetic reduces to logic.

Admittedly, the distributional differences don't show that that‐clauses aren't singular referring terms. But they should give us pause. After all, we don't find these distributional differences between expressions that are widely acknowledged to be singular referring terms, such as names, indexicals, and demonstrative pronouns. But then if that‐clauses and terms like ‘logicism’ are all referring expressions, why would we get distributional differences here?

Second, there seem to be semantic differences between ‘logicism’ and ‘that arithmetic reduces to logic’. The following apparently could diverge in truth value:12

  1. 7a. Glenn knows that Frege believed logicism.

  2. 7b. Glenn knows that Frege believed that arithmetic reduces to logic.

Suppose that Glenn knows that logicism is a view about the relation between arithmetic and logic, and he knows that according to it they are intimately related somehow but he isn't sure exactly how. He knows that a number of philosophers held the view in the late nineteenth and early twentieth centuries. Finally, he learns that Frege held this view. Then arguably, 7a is true and 7b is false. But to hold that we must hold that there is some semantic difference between the (p.108) that‐clause ‘that arithmetic reduces to logic’ and ‘logicism’. If ‘logicism’ is a referring expression, the that‐clause must not be.13

Finally, consider a sentence in which a universal quantifier binds pronouns in a that‐clause:

  1. 8. Everyone believes that he is smart.

The occurrence of the that‐clause here doesn't simply refer to a proposition. At most, it could be held to refer to a proposition relative to an assignment of values to variables. In any case, it does not refer to a proposition in the sense that it cannot contribute a (single) proposition to the proposition expressed by 8. The truth of 8 requires people to believe different things! Hence the that‐clause here cannot make the sort of contribution to the proposition expressed by 8 that singular referring terms make: a single referent. Further, the fact that all other expressions in natural language that one can quantify into in this way appear to be quantificational (or at any rate, not referring expressions) provides some reason for thinking that that‐clauses are not referring expressions:
  1. 9. Every man loves some women he used to date.

  2. 10. Most swimmers remember the fastest swim they ever had.

In any case, the main point here is that ii is false. Russellians need not hold that that‐clauses are referring expressions. I myself am a Russellian who is at least skeptical of the claim that that‐clauses refer for reasons such as those just canvassed.

Finally, let's turn to iii. To show that iii is false, we'll construct a toy theory of the semantics of that‐clauses that is available to the Russellian and according to which ‘barks’ behaves semantically in the same way in ‘Shirley believes that Fido barks’ and in ‘Fido barks.’14 Suppose we have a language containing n‐place predicates (for arbitrary values of n); let B be a two‐place predicate (“believes”). Suppose our language contains names of individuals. For any expression e, let e* be the semantic value of e. If b is a name, b* is an individual; and B*, the semantic value of B (‘believes’), is a two‐place relation between individuals and propositions. For other n‐place predicates P, P* is an n‐place relation between individuals. Assume our language contains truth functional sentential connectives, quantifiers and the complementizer ‘that’. Assume the obvious syntax (an n‐place predicate followed by n names is a sentence, etc.), with the addition that placing ‘that’ in front of a sentence yields a that‐clause. We then add:

If α is a name, and C is a that‐clause, then α(B(C) ) is a sentence.15

(p.109) Because nothing hangs on it here, we represent propositions by ordered tuples. In what follows, let S be a sentence, let Π be an n‐place predicate, and let α,α1,. . .,αn be names. Then some of the clauses specifying the propositions expressed by sentences are as follows:

  1. 1. Πα1,. . .,αn expresses the proposition <Π*, <α1*,. . .,αn*>>.

  2. 2. α(B(that S) ) expresses the proposition <α*, <B*, <g, Prop S>>>, where g is the function that maps every proposition to itself and Prop S is the proposition expressed by S, where the constituents of Prop S are constituents of <α*, <B*, <g, Prop S>>>.

The force of the comment that the constituents of Prop S are constituents of <α*, <B*, <g, Prop S>>> can be made clear as follows. Consider a one‐place predicate of the language ‘R’ (“barks”) and names ‘f’ (“Fido”) and ‘s’ (“Shirley”).16 Now consider the sentence:
  1. 11. s(B(thatRf) ) (“Shirley believes that Fido barks.”)

Instead of rendering the proposition expressed by this sentence as an ordered n‐tuple, let's represent it in tree form. It looks thus:
  1. 11'.

                       Objections to Structured Propositions Generally

Note that R* and f*, the constituents of the proposition expressed by ‘Rf’, are at terminal nodes in this tree. That is to say, they are constituents of the proposition 11’, which 11 expresses. By contrast, suppose we introduced into our language a singular term referring to the proposition expressed by ‘Rf’, say ‘dogicism’. Call such a singular term a proposition name (PN). We then add to the syntax:

If α is a name and D is a PN, then α(B(D) ) is a sentence.

Now consider the sentence
  1. 12. s(B(dogicism) )

(p.110) It expresses the following proposition:
  1. 12'.

                       Objections to Structured Propositions Generally

Note that though the proposition <R*, f*> is a constituent of this proposition (since it occurs at a terminal node), neither R* alone nor f* alone is. What the last part of clause 2 tells us is that a sentence containing a that‐clause expresses a proposition in which the proposition expressed by the sentence ‘that’ fronts occurs, and where the constituents of the latter occur as constituents of the larger proposition. Finally, our definition of truth for propositions includes the following clause:
  1. 1. A proposition of the form <α*,<B*,<g, Prop S>>> is true at a circumstance of evaluation e iff <α*,g(Prop S)> is in the extension of B* at e.17

I take it that on the account I have sketched words function the same way semantically in and out of that‐clauses (and terms like ‘barks’ do not function in that‐clauses as referring terms that refer to properties). To see this, consider the proposition expressed by

  1. 13. Fido barks. (Rf)

It is:
  1. 13'. <R*, f*>

Now consider the proposition expressed by
  1. 14. Shirley believes that Fido barks. (s(B(thatRf) )

It is (this time as an ordered n‐tuple):
  1. 14'. <s*,<B*,<g,<R*,f*>>>>

In both cases, ‘barks’ contributes to the proposition expressed by the sentence in question R*, the property of being a barker, and it does so in the same way in both cases. So ‘barks’ functions the same way semantically in both sentences. Thus on (p.111) the present view, the inference Schiffer claims the Russellian is committed to (in premise(2) ):
  • Shirley believes that Fido barks

  • ∴ (∃x)(Shirley believes Fido x)

is no better than this one
  • Fido barks.

  • ∴ (∃x)(Fido x)

And Schiffer has offered no reason for thinking the Russellian is committed to the latter inference.

The account of that‐clauses I have sketched shows that there are accounts available to the Russellian on which words like ‘barks’ function semantically the same way in and out of that‐clauses. Hence iii above is false.

In summary, unless i above is true, there is no reason to believe premise (1) of Schiffer's argument against structured propositions. Further, Schiffer's premise (1) entails claims ii and iii mentioned above. I have now argued that i–iii are all false. I conclude that not only is there no reason for holding premise (1) of Schiffer's general argument against structured propositions (since i false), but in addition it is false (since ii and iii are). For this reason, the argument fails.

Max Cresswell (2002) has also given a general argument against structured propositions.18 Cresswell's argument employs four “assumptions”, as he calls them. First, there is what Cresswell calls the principle of effability (PE):

Propositions are the semantic values of sentences, and for every proposition p there is a possible language V in which there is a sentence α such that V(α)=p.19

The rough idea behind the generalized version of this principle (see note 19) is that for any particular thing that is of the sort to be a semantic value of a certain kind of expression, there is a possible language in which it is the semantic value of an expression of that kind. The second assumption is functional compositionality:

The semantic value of a whole sentence if obtained by functions which are the semantic values of parts of that sentence operating on the semantic values of other parts.20

(p.112) As we'll see, for our purposes the important feature of FC is that it entails that if α is a one‐place sentential connective that attaches to a sentence β to form the complex sentence <α, β>, then the semantic value of <α,β>, V(<α,β>), = V(α)(V(β) ). That is, the semantic value of the complex sentence is the output of the semantic value of α, a function, taking the semantic value of β as argument. The third assumption Cresswell employs is the principle of truth conditions(TC):
  1. (a) If p is a proposition and I a set of indices, then there is an associated set, I(p), which is the set of indices at which p is true.

  2. (b) For any a subset of I, i.e. any set of indices, there is a proposition p such that I(p)=a.21

Indices, of course, are the circumstances at which propositions are evaluated. We don't worry here about what such circumstances of evaluation are (worlds? world/time pairs?, etc.).22 TC claims simply that every proposition is associated with the set of indices at which it is true; and for every set of indices, there is some proposition that is true at exactly the indices in the set. The final assumption Cresswell employs is the principle of classical negation (PCN):

If there are two (sentence) operators ∼ and ∼* in language V such that for any sentence α, ∼α is true at index i iff it is not the case that α is true at index i and ∼*α is true at index i iff it is not the case that α is true at index i, then V(∼)=V(∼*).

Essentially, PCN says that any sentential operators in a given language that obey the truth table for negation have the same semantic value.

Cresswell proves that if a language obeys his four assumptions PE, FC, TC and PCN, the propositions expressed by sentences of that language that are true at exactly the same indices are identical. Cresswell dubs this result Theorem 1. Cresswell claims, and I agree, that for present purposes anyway, we might as well take Theorem 1 as showing that the propositions expressed by sentences of such a language just are sets of indices. Thus, if Cresswell's four principles hold for natural language, it follows that the propositions expressed by sentences of natural language are sets of indices. Thinking of sets of indices for the moment as sets of possible worlds, this would mean that propositions expressed by sentences of natural languages are sets of possible worlds. Cresswell writes:

The importance of Theorem 1 resides in the assumption that the conditions mentioned [PE, FC, TC and PCN] should be satisfied by any acceptable semantics for natural language which makes use of intensional entities like propositions . . .23

Of course, structured proposition theorists like me will want to resist this conclusion. Precisely the motivation for structured propositions is that sets of (p.113) worlds are not fine grained enough to play the role of propositions expressed by sentences of natural languages. If propositions are only as fine grained as sets of worlds, there are no structured propositions.

As Cresswell himself says, ‘ . . . if you don't like the conclusion, then you must reject one of the assumptions . . . ’,24 and so the question arises as to which of Cresswell's four assumptions I will want to reject. I am not completely sure about some of the other principles (especially PCN), but I am sure that I want to reject functional compositionality (FC). I believe that whether or not FC holds for natural language is the main issue between Cresswell and structured proposition theorists. Thus in responding to Cresswell I will focus solely on the question of whether a semantics for natural language must adhere to FC. If the answer is no, the proof of theorem 1 doesn't go through for natural language, and so we have no reason to think that sentences of natural language don't express structured propositions. Thus, if it can be argued that FC doesn't hold for natural language, Cresswell's argument against structured propositions fails.

The structure of my response to Cresswell runs as follows. First, I'll briefly indicate why structured proposition accounts like mine (and those of others) violate FC. Then I'll consider Cresswell's defense of FC and will respond to that defense. As we'll see, in the end Cresswell and I agree on most substantial claims at issue in his paper. It seems, however, that we view the claims in question in somewhat different terms.

Let's recall Cresswell's statement of FC:

FC: The semantic value of a whole sentence is obtained by functions which are the semantic values of parts of that sentence operating on the semantic values of other parts.

Now consider a negated sentence like:
  1. 15. It is not the case that Squaw Valley is in New Jersey.

Assume that ‘It is not the case that’ in 15 is a sentence operator expressing the truth function for negation or, as on Cresswell's treatment, a function from a set of indices to the complement of that set. On a structured proposition view of the sort I'm defending, 15 expresses a structured proposition that looks something like this:
  1. 15a. Neg (p)

where Neg is the truth function for negation or Cresswell's function from sets of indices to their complements, and p is the structured proposition expressed by the embedded sentence in 15. Now 15a is the semantic value of 15 on my view, but it is not obtained by functions that are the semantic values of the relevant parts of 15 operating on the semantic values of other parts of 15, as FC requires. In particular, 15a is not the result of applying the function Neg to p. Indeed, (p.114) the function Neg, either a function from truth values to truth values or from sets of indices to sets of indices, can't operate on p since p is not a truth value or a set of indices. p, of course, is a big, structured entity. So the claim that 15 expresses the structured proposition 15a is incompatible with FC. Obviously, since I think 15 does express or have as its semantic value 15a, I am committed to denying FC.

Now what does Cresswell say in defense of FC? He writes:

. . . without supplementation non‐functional semantic theories cannot deliver the truth conditions of sentences. There are semantic theories which are not functionally compositional, but these theories cannot of themselves preserve the link with truth.25

Cresswell goes on to consider a theory of structured propositions that violates FC and assigns to the sentence 15 something like the proposition 15a.26 Cresswell worries about how the proposition 15a determines the intuitively correct truth conditions for the sentence 15. He suggests that one could make 15a have this effect by stipulation as follows:27
  1. 16. i ∈ I(Neg (p) ) iff i ∉ I(p).

where i is an index and I(p) is the set of indices at which the proposition p is true. This says that Neg(p) is true at an index i iff p is not true at i.28 Cresswell then makes the following complaint about 16:

What makes [16] unsatisfactory is that it turns I into an interpretation function, which gives a meaning to [Neg], whereas the whole point of structured propositions is supposed to be that they are not things which have meanings, but are things which are meanings. The semantic work is now done by the fact that I satisfies [16], and provided it does that, [Neg] could be anything at all.29

Cresswell's point is that nothing in the nature of Neg results in 15a having the truth conditions it does. 16 enforces the proper truth conditions, but the function Neg itself plays no role in the truth conditions coming out right. And so Neg could be anything at all, e.g. Mount Everest instead of a function, and the truth conditions would still come out right as long as 16 remains in force. Because the nature of Neg plays no role here, and 16 in effect “interprets” Neg, Cresswell complains that Neg, and the whole structured proposition 15a, acts like a linguistic expression that is interpreted by a clause like 16. Nothing in (p.115) the natures of linguistic expressions themselves determine the truth conditions of a sentence—it is how they are interpreted by semantic clauses. Similarly, Cresswell says, for Neg here and its interpretation 16. This, I take it, is the sense in which theories that aren't functionally compositional require supplementation to deliver the truth conditions of sentences, according to Cresswell in the above quotation. The supplementation takes the form of clauses like 16 that serve to interpret and hence in effect assign meaning to things like Neg. But, Cresswell says, Neg is supposed to be a meaning.

In response, I wish to emphasize that 16 is not the sort of clause for negation I use. In Cresswell's notation and on his approach, it would be rather:

  1. 16a. i ∈ I(Neg p) ) iff i ∈ Neg(I(p) ).

Again, p is itself a structured proposition in 16a. It says that the structured proposition Neg (p) is true at an index i iff Neg maps the set of indices at which p is true to a set of indices that contains i. We can put this point another way, letting Neg now be the truth function for negation:
  1. 16b. Neg (p) is true at circumstance i iff Neg maps the truth value of p at i to true.

16a/16b get the right truth conditions for 15a, and here Neg does play a substantial role in the derivation of those truth conditions: we get the truth conditions right because Neg maps a set of indices to the right set of indices (16a) or because Neg maps truth values to the right truth values (16b). So the fact that Neg is the relevant function in 16ab/16b plays a crucial role in the derivation of the proper truth conditions for the proposition 15a and hence the sentence 15. Hence Cresswell can't complain here that the nature of Neg plays no role in determining truth conditions and that the clause for negation in the definition of truth for structured propositions interprets Neg. I think this addresses Cresswell's argument to this point against structured proposition theories that violate FC. Because things are about to become more complicated, let me pause to note that to this point, we have been given no reason to reject structured proposition accounts that violate FC and we have been given no reason to think that a semantics for natural language must obey FC.

Now in discussing Lewis' (1970) account of structured meanings, Cresswell notes that it violates FC in just the way that an account of structured propositions like mine does.30 Cresswell gives a response to his argument on Lewis's behalf that is exactly similar to the one I just gave to Cresswell's argument (invoking a semantic clause for negation like 16a/16b instead of 16). Cresswell then provides a response to the response he provides on Lewis' behalf. I'll sketch a (p.116) modified version of Cresswell's response that applies to my response to Cresswell's argument. For the remainder of my discussion of Cresswell, I shall ignore the differences between a Lewisian structured meaning account and an account of structured propositions like mine. Both violate FC and the question I am interested in is whether this is a problem.

To recap, recall that the initial worry about theories like mine that hold that 15 expresses something like 15a was that it wasn't clear how 15a could get the right truth conditions for 15. Invoking a clause like 16 for negation was claimed to be illegitimate, because the nature of Neg played no role in getting the truth conditions right. Thus, Neg could be anything at all, so long as it was governed by 16. But then Neg, the constituent of a proposition, behaves like a linguistic expression, being interpreted by or given a meaning by 16, rather than itself being the meaning of an expression. My response was that the clause for negation I use (and Lewis uses) is 16a/16b, and here the nature of Neg, what sort of function it is, plays a crucial role in getting the truth conditions of 15a and hence 15 right.

To this Cresswell responds as follows. The primary business of semantics is assigning intensions to sentences. To do this for simple sentences such as 15, nothing more is required than that the intension of the sentence is derived from the intensions of the parts of the sentence in the function/argument way dictated by FC in accordance with the syntax of the sentence. A Lewisian structured meaning or a structured proposition like my 15a can only get the truth conditions for 15 right by having entities at the terminal nodes that either are or determine intensions corresponding to the parts of the sentences, and allowing these things to combine in such a way that the right intension for the sentence is derived. But all that is needed to derive the right intension for 15, and hence all that semantics requires, is the intensions of the parts of the sentence combining in a function/argument way, that is, according to FC, as determined by the syntax of the sentence. There is no need for a Lewisian structured meaning or a structured proposition here. Recall that on my view of structured propositions, the structure of a proposition like 15a mirrors the syntactic structure of the sentence 15 at the level of LF or at the level of whatever syntactic representations are the inputs to semantics. Suppose, as Cresswell assumes, that the intension of a complex expression is derived from the intensions of its parts in a function/argument way. Then as Cresswell notes, if you take a structured proposition like my 15a expressed by a simple sentence like 15, replace the propositional constituents by their intensions (which essentially gives you a Lewisian meaning), and let the intensions combine in a function/argument way, you will get the proper intension for the sentence 15. In this sense, what is primary for semantics, at least for a semantics of simple sentences like 15, is that it assigns intensions to sentence parts and obeys FC.

Cresswell stresses that he is not concerned to deny that there may be metaphysical reasons for holding that some entities, say properties and relations, are more basic than, but determine, intensions of expressions. Thus Cresswell writes: (p.117)

I am not concerned in this paper to deny that there may be metaphysical reasons for saying that this or that kind of favoured entity is more basic, but as far as semantics is concerned anything that does determine an intension will do the job, and anything which does not will not. All semantics requires is the intensions themselves.31

Especially given this last qualification, I can't find much of substance to disagree with so far. For simple sentences like 15, of course I agree that all that is needed to derive its intension is the intensions of its parts combining in a function/argument way, as FC requires. But of course, those of us who favor the view that natural language sentences express structured propositions do so because of the semantics of sentences containing verbs of propositional attitude. Here, people like me think that we need more than the intensions of the parts combining in a function/argument way to get the intension of the whole sentence. A verb of attitude is sensitive to more than the intension of the sentence it embeds. Those of us who endorse structured propositions think that a verb of attitude is precisely sensitive to the structured proposition expressed by the sentence it embeds. So while I can agree with Cresswell's view that all that is required to derive the intensions of sentences like 15 is the intensions of their parts combining in a function/argument way, that is not so for sentences in a fragment of natural language that contains verbs of propositional attitude. In particular, to get the intension of a sentence containing a verb of propositional attitude, we need the structured meaning of or structured proposition expressed by the sentence it embeds.

Given this, consider the following sentence:

  1. 17. That first order logic is complete is necessarily true and believed by Cresswell.

If the that‐clause here must have as its semantic value a structured meaning or structured proposition so that the semantics of the belief ascription comes out right, it would seem that being necessary and being true must also be predicated of a structured entity in 17.32 But then it would appear that natural language sentences containing that‐clauses in which truth or modality is ascribed, as well as sentences containing verbs of propositional attitude, must have parts whose semantic values are structured meanings or structured propositions. But since having expressions whose semantic values are structured meanings or propositions violates FC, it appears that FC fails for a large part of natural language. Indeed, it seems reasonable to think that FC fails for any fragment of natural language containing that‐clauses.

Now I would have thought that this is game over: FC fails for a large portion of natural language, hence Theorem 1 doesn't go through for natural language, (p.118) and so it provides no reason to hold that sentences of natural language express unstructured propositions. But Cresswell, the author of Structured Meanings after all, agrees with everything I've just said! He writes:

Does the need for structured meanings to account for propositional attitude sentences count against FC? For the semantics of such a sentence is not obtained by the meaning of the attitude verb operating on the intension of the complement sentence. If this violates FC then it would seem that English may not after all be a ‘well behaved’ language in the sense introduced earlier, and that Theorem 1 might therefore not apply to it.33

And later, after considering examples similar to my 17 above, :

But if the preceding observations are correct, it would seem that almost any contexts involving truth, necessity or what have you, which can make sentences out of that‐clauses would seem to require structured meanings. If so, it would seem that FC fails for far more of a language than just propositional attitudes.34

Despite our agreement on these points, Cresswell insists that the violations of FC are deviant exceptions and that in some important sense, most of natural language does obey FC, so that Theorem 1 does apply to natural language and unstructured propositions are “primary”. If Cresswell and I have any substantive disagreement regarding the issues he raises that I've discussed, it is here.

As I understand it, Cresswell's defense of the claim that in some sense FC governs natural language in spite of the violations to it engendered by verbs of attitude, modality and truth is three‐pronged. First, Cresswell claims that in a language without propositional attitudes but containing modal operators and a truth predicate, FC would apply unrestrictedly.35 So there is a sense in which verbs of propositional attitude provide the only exception to FC. Second, Cresswell claims that FC itself predicts that there will be exceptions to it.36 Consider a language for which FC is stipulated to hold. Such a language will have syntactic structures that are the inputs to semantics and an assignment of intensions to basic expressions, where the intensions of complex expressions are determined in a function/argument way from the intensions of its parts and how they are put together. But then such a language essentially generates structured meanings, which after all are just syntactic structures whose terminal nodes are occupied by intensions. So, Cresswell thinks, since a language obeying FC essentially generates structured meanings, it isn't surprising that users of the language would want to talk about them. In so doing, they develop mechanisms that violate FC, since they will develop sentences whose intensions depend on these structured meanings, and not simply intensions, of their parts. So, again, Cresswell claims that FC itself predicts that violations to FC will occur.37 Third, and related to the second point just mentioned, Cresswell (p.119) claims that unstructured meanings, sets of indices, are primary.38 In his most explicit statement regarding what he means by this, he writes:

Semantic structures . . . are not an end in themselves and owe their existence to their contribution to the determination of sets of indices which are the end.39

Cresswell's remark here is immediately preceded by a reiteration of the second point above: that in any linguistic system governed by FC, its users will inevitably develop means for talking about structured meanings, leading to a violation of FC. I think the point about the primacy of unstructured meaning is that structured meanings come into play only because in some cases the intension, unstructured meaning, of a sentence depends on the structured meaning/proposition of one of its parts. Thus, the determination of sentences' intensions/unstructured meanings is the important point, and structured meanings are only justified to the extent that they contribute to the determination of unstructured meanings. In this sense, unstructured meanings are primary.

For the sake of argument, let me grant all of this. Cresswell sees in these claims a vindication of the claim that in some important sense, natural language obeys FC. But I am inclined to view things differently. The first point, that a language without verbs of propositional attitude would be governed by FC, is irrelevant. Structured proposition theorists can happily agree to this, since they think precisely that the semantics of verbs of propositional attitude require structured propositions. Their arguments in favor of structured propositions have to my knowledge always invoked this claim.40 The third point is irrelevant as well. Again, the structured proposition theorist can happily agree that the justification for structured propositions is that they contribute to the determination of the intensions of some sentences. Indeed, the structured proposition theorist will see in this a point in favor of structured propositions: they are required to determine the intensions of some sentences. Isn't that precisely the point structured proposition theorists have been insisting on all along?

This leaves us with the second of Cresswell's points, and the one that he seems to stress the most. If Cresswell is right that FC itself correctly predicts that there will be exceptions to it, in the sense that a language initially governed by FC will inevitably evolve into a language in which FC is violated, then it seems to me that the proper conclusion to draw is that FC is self undermining. A language governed by it will inevitably cease to be governed by it. In short, suppose Cresswell is right about a language governed by FC inevitably giving rise to violations of FC via some expressions coming to have structured propositions or structured meanings as their semantic values. Then had I written Cresswell's paper, instead of being called ‘Why Propositions (p.120) Have No Structure’ it would have been called ‘Why Propositions Must Have Structure’!

In conclusion, as I said earlier, Cresswell and I appear to agree on most of the answers to the substantive questions raised by his paper that I have discussed. However, we seem intent on spinning those answers somewhat differently. Cresswell sees the claim that languages governed by FC will inevitably evolve into languages violating FC as vindicating FC. I see it as undermining FC. In my view, then, since FC doesn't govern natural language, Theorem 1 doesn't hold for it. But then Cresswell has no argument against structured propositions.

Let me turn to a different objection to structured propositions.41 It might be thought that accounts according to which propositions are structured commits one to the view that distinct propositions may have exactly the same parts. Or at any rate, it might be thought that the current account so commits one. For consider the proposition that Carl loves Wendy and the proposition that Wendy loves Carl. If we suppose that the relation R binding together the constituents of both propositions is the same (as I believe), and we suppose that the constituents of both propositions are the same (as I believe), then it looks like we have two propositions made of exactly the same things. Both propositions are facts with precisely the same components: R, Wendy, Carl and the loving relation. Now I take the facts that are these propositions to be built out of these components, so that they are present in the proposition and so are parts of the proposition.42 But then it looks as though I am committed to the claim that two things, the fact that is the proposition that Wendy loves Carl and the fact that is the proposition that Carl loves Wendy, are composed out of the same parts. This contradicts a principle I've touched on at a couple of points in previous chapters, which I'll call uniqueness of composition or fusion. According to the principle, there is only one whole composed of given parts. Now Lewis (1986b) for one finds the idea that distinct things are composed of exactly the same parts unintelligible.43 If the present account of propositions is committed to denying uniqueness of composition and if composition that doesn't obey uniqueness is unintelligible, that spells real trouble for the account.

There are two things one might say in response to this concern. First, one might maintain uniqueness of composition and adopt a view on which the propositions that Carl loves Wendy and that Wendy loves Carl have different (p.121) parts and so are distinct. But how could the propositions have different parts? Consider both propositions in tree form:

  1. 18.

                       Objections to Structured Propositions Generally

  2. 19.

                       Objections to Structured Propositions Generally

Suppose we held that 18 has only two parts, namely
  1. 18a.

                       Objections to Structured Propositions Generally

and
  1. 18a'.

                       Objections to Structured Propositions Generally

Of course, 18a and 18a' themselves have parts. Call the relation binding loves* and Carl together in 18a R’. Then 18a is the fusion of loves*, Carl and R’. Call the relation in 18a’ R”. Then 18a’ is the fusion of Wendy* and R”. But though 18a and 18a’ have the parts mentioned, these aren't parts of 18. 18 has only two parts, 18a and 18a’. Thus, we deny that parts of parts of x are themselves parts of x (e.g. Wendy* and R” are parts of 18a’, and 18a’ is part of 18, but Wendy* and R” are not parts of 18). That is, we deny that parthood is transitive. But we maintain uniqueness of fusion. Wendy* and R” have a unique fusion (18a’), as do loves*, Carl* and R’ (18a). And 18 is the unique fusion of 18a and 18a’. Thus, on this view, 18 is distinct from the fusion of all the parts of both 18a and 18a’: Wendy*, R”, loves*, Carl* and R’. For that fusion has parts not had by (p.122) 18 (e.g. Wendy*). Finally, on this sort of view 19 is the fusion of the following two parts:44
  1. 19a.

                       Objections to Structured Propositions Generally

and
  1. 19a'.

                       Objections to Structured Propositions Generally

Since neither 19a nor 19a' is a part of 18, 18 and 19 are distinct. Though I don't see anything wrong with this proposal in principle, it has the effect of making the constituents of propositions not be parts of those propositions, which to my mind is unfortunate. For example, though intuitively Wendy* is a constituent of the proposition that Wendy loves Carl, she is not a part of it on the present view.45

A second way of addressing the present worry, which I favor, is to deny uniqueness of fusion or composition for facts and hence propositions, and hold that both 18 and 19 have exactly the same parts: Wendy*, R”, loves*, Carl* and R’. Those parts are simply composed differently in the two propositions. Now is composition that denies uniqueness of fusion unintelligible, as Lewis asserts? I don't want to claim that I can make completely clear what composition of this sort is, but it seems to me the claim that it is unintelligible is clearly too strong. In the first place, there are those who think that in the case of material constitution, a statue and piece of bronze might share all the same parts and yet be distinct.46 In this case, the parts are even arranged in the same way. But still, there must be two things made of the same parts because they have different properties. (p.123) Theorists who hold this view then try to explain how two things made of the same parts arranged the same way can nonetheless have different properties. Now I reject such accounts of material constitution, but I feel as though I understand the accounts. They aren't literally unintelligible!

Secondly, I think we have an intuitive idea of what non‐unique composition is like. I think this intuition is reflected in recurring talk of facts or states of affairs in philosophy. The intuitive idea is something like this. There are relations and things stand in them to other things. A given two‐place relation R may be such that though a stands in R to b, b doesn't stand in R to a. Consider such a relation R and suppose c stands in R to d and d stands in R to c. c standing in R to d is one fact and d standing in R to c is a different fact, as witnessed by the fact that the former could have existed without the latter existing. However, these facts have exactly the same parts: c, d and R. Somehow, these parts combine two different ways to yield different facts. At this point, one is likely to picture R having argument places—literally positions things can occupy—and to think that one fact results from c occupying the “first” argument position in R and d occupying the second; whereas the other fact results from d occupying the first argument position and c the second. We can make intuitive sense of how the same parts can combine to yield multiple complexes by invoking some notion of a relation having different positions that the relata can occupy. Different complexes can result from the same relata occupying different positions. But if we can make some sort of intuitive sense of the idea that the same parts can be combined to yield different objects, the idea cannot be unintelligible. Let me add that if, never having thought about it before, one were asked whether combining a given group of parts always yields a unique object, I suspect one would not be certain what to answer. But if the claim that two different objects could be composed out of exactly the same parts is really unintelligible, one should on reflection think the answer to the above question has to be ‘yes’. But many people do not think that this is so even on reflection.

Finally, Lewis (1986b) writes the following about a notion of composition that denies uniqueness of composition (which he calls unmereological composition in virtue of it violating uniqueness of composition—see p. 96) :

What is the general notion of composition, of which the mereological form is supposed to be a special case? I would have thought that mereology already describes composition in full generality. If sets were composed in some unmereological way out of their members, that would do as a precedent to show that there can be unmereological forms of composition: but I have challenged that precedent already.47

There are two important points here. The first is that Lewis thinks he is owed an account of the general notion of composition of which composition obeying uniqueness of fusion is a special case. Very well: composition is the combining (p.124) of parts to form an object with those parts. Composition obeying uniqueness is a special way of doing this that results in the complex object being unique. As to the second point, Lewis suggests that sets are not composed by means of a mode of composition that violates uniqueness of composition, and so cannot serve as a precedent showing that there are such modes of composition. What is not clear to me is whether Lewis means to be claiming that there must be such a precedent if composition violating uniqueness is to be accepted. Does he mean to suggest that unless we can give an uncontroversial example of something that is composed in a way that violates uniqueness of composition, we should not accept that there is such composition? Whether Lewis is suggesting this or not, it would be wrong to do so. Suppose one were to claim that qualia don't supervene on the totality of purely physical facts about the world. For this claim to be acceptable, should one be required to give an uncontroversial example of something that doesn't supervene on the totality of purely physical facts? Obviously not. Or suppose you are arguing with someone who denies that mereological composition ever occurs. This person holds that there are only mereological atoms, so that nothing is a part of anything else. Can such a person demand of those who hold that mereological composition occurs that she be given an uncontroversial example of a case in which things are composed mereologically as a precedent? Obviously not. Similar remarks apply in the present case. Those who deny that composition violating uniqueness of fusion occurs cannot require that those who hold that it does provide an uncontroversial example of things composing in a way that violates uniqueness of fusion as a precedent.48

In conclusion, then, composition that violates uniqueness of fusion is not unintelligible. Hence the advocate of the account of propositions I am defending may embrace it without fear.

I wish to close this chapter with a brief discussion of a very different sort of concern about structured propositions when they are taken to be the objects (p.125) of certain attitudes.49 David Kaplan and Richard Montague (1960) consider a language L that contains Robinson's Arithmetic (Q) and assume some scheme of Gödel numbering that allows one to say things in the language about expressions of the language. Where A is an expression of the language, <A> is the numeral in the language that stands for the Gödel number of A. Assume we add to the language a one‐place predicate K. The intended interpretation is that K is true of a number just in case that number is the Gödel number of a sentence that is known. Since L contains Q, we know by the Diagonal Lemma that there is a sentence D such that the following is provable in L:

  1. 20. D ⇔ (K(<∼D>)

But then Kaplan and Montague are able to show that given the following three assumptions, we are able to derive a contradiction:
  1. A1 K(<∼D>) → ∼D

  2. A2 K(<K(<∼D>) → ∼D>)

  3. A3 [I(<K(<∼D>) → ∼D>, <∼D>) & K(<K(<∼D>) → ∼D>)] → K(<∼D>)

where the predicate I(x,y) in A3 means that the sentence with Gödel number y is derivable in L from the sentence with Gödel number x. (This relation is definable in L.) A1 intuitively says that if ∼D is known, it is true. A2 says that A1 is known. And A3 is a single instance of a closure principle. It says that if ∼D is derivable from A1 and A1 is known, ∼D is known. Again, taking A1–A3 as assumptions allows one to derive a contradiction in L.

As interesting as this is, so far there is no problem for me, since K is a predicate of (Gödel numbers of) sentences. But I, of course, take the things to be known to be propositions, and so have no commitment to predicates that say of sentences that they are known. Hence I thus far have no need to decide which of A1–A3 I must give up. However, Rich Thomason (1980, ms.) considers a language (again containing Q) that has a predicate K* of structured propositions whose intuitive interpretation is ‘It is known that’. Given certain assumptions that are hard to deny (e.g. the expression relation between a sentence and the proposition it expresses is recursive), Thomason is able to show that one can use K* to define a predicate of sentences K such that A1–A3 hold.50 Thus, it appears that the structured proposition theorist does have to say which of A1–A3 he would deny.

The obvious first thought is to deny the instance of the closure principle A3. Since it seems that quite often I know something A that entails something B, but I don't know B, denying an instance of this seems to come with virtually (p.126) no price.51 However, Cross (2001) appears to show that there is a closely related paradox that makes use of only (the analogues of) A1 and A2, so that denying closure won't rid us of paradox here. Though Uzquiano (2004) challenges Cross' conclusion by arguing that Cross' new paradox requires a more controversial assumption than A3, Cross' argument is sufficiently worrisome to make me uncomfortable resting the resolution here on the denial of A3 or its analogue.52 Further, Anderson (1983) has offered a spirited defense of the claim that Closure (A3) can't be the problem. What else to do?

I don't see that A1 (or its analogue) can be denied. To do so seems tantamount to giving up the claim that if a sentence is known, then what it says is true. Surely we can't deny that! But then, assuming we are banning blaming closure at least for the moment, A2 must be the problem. But what exactly is the problem? Following Anderson (1983), one might reason as follows. Just as one may think that the Liar paradox showed that ‘true’ has some sort of hidden hierarchical structure, so the paradox of the knower shows this about ‘It is known’. Anderson shows how to implement a resolution of the paradox of the knower by introducing different subscripted predicates K0, K1, . . . . On Anderson's treatment, A2, on which the subscripts on K must be the same, comes out false. Anderson advocates thinking of the subscripted predicates not as actually distinct lexical items (it certainly doesn't seem we have those in English), but rather as representing different extensions of the expression ‘It is known’ as fixed by features of context. If this is right, essentially the resolution of the paradox involves giving up the view that ‘It is known’ has a fixed, context independent interpretation.53 I assume, then, that the advocate of the view that structured propositions are the objects of knowledge can avoid paradox either by denying closure (A3) or by adopting a hierarchical/context sensitive view of ‘It is known’ on which A2 (where K has the same index twice) comes out false.

Notes:

(1) For example, both Schiffer (2003) and Matthews (2002) give arguments of this sort against Russellian structured propositions. Interestingly, though Schiffer thinks Russellian propositions aren't what that‐clauses in sentences like 1a/1b and 2a/2b designate, he nonetheless tends to think that Russellian propositions are needed because possible worlds are constructed out of them. See p. 96.

(2) P. 30.

(3) P. 30.

(4) A minor problem with his reasoning is that he seems to assume that Russellians will claim that ‘the property of being a barker’ is a referring expression whose referent is the property of being a barker. I, like I think most Russellians, take definite descriptions to be quantificational expressions and so hold that they don't have referents at all. Or perhaps, following Fara (2001), definite descriptions should be understood as predicates. In any case, they aren't referring expressions. Because this is a minor problem, I'll set it aside.

(5) My belief is based in part on how Schiffer defends a closely related premise in a similar argument against (only) Fregeans. See pp. 27–8.

(6) P. 17. Schiffer seems to take structured proposition theorists to be committed to CH because he thinks that adherence to CH is what motivates the view that propositions are structured in so far as it is difficult to hold both CH and the view that proposition are unstructured. See pp. 1–2; 18; 31; 46; and 88.

(7) Note that to this point, we are considering any sort of structured proposition theorist, including Fregeans. Thus, Schiffer thinks that any such theorist must hold that ‘barks’ has a referent in ‘that Fido barks.’ Of course what the referent is depends on whether one is a Fregean or Russellian. In any case, the conclusion that ‘barks’ is a referring expression in that‐clauses is enough to render the inference in premise (2) valid.

(8) P. 45. Presumably, Schiffer thinks Fregeans will be stuck with this conclusion as well, since he thinks they will be forced to hold that ‘barks’ is a referring term in ‘that Fido barks’ and they will not hold that it is a referring terms in ‘Fido barks’.

(9) See note 6.

(10) King (2001).

(11) Presumably speaker intentions or some such thing would figure in the determination of reference as well.

(12) I believe this point is due to Richard (1993).

(13) Putting it this way is a little contentious, since Richard himself holds that‐clauses refer. But they function differently semantically on his account than expressions like ‘logicism’ and as a result there is a sense in which they do more than refer in the way ‘logicism’ does.

(14) The account I'll sketch is essentially that of Richard (1993).

(15) Of course we would want to allow quantifiers to occur in place of α here as well, but I'll ignore that. Further, I'll not attempt to formulate things in such a way as to allow quantification into that‐clauses. This is in part why I call the theory a toy theory. My main concern here is simply to show that there are theories of the semantics of that‐clauses available to Russellians on which words like ‘barks’ in them function semantically in the same way they function outside them. I'm not claiming the theory I sketch in the text is ultimately precisely the correct one. Again, it is a toy theory. However, I do tend to think that something like this theory is correct.

(16) ‘R’ is intended to call to mind ‘rrrufff’.

(17) It would be easy enough to introduce a quantifier ‘something’ into our language and allow sentences such as ‘something: x(s(B(x) )’. This sentence would express a proposition that is true at a circumstance e iff there is something ϕ such that <s*,ϕ> is in the extension of B* at e (i.e. iff s* believes something in e). We would then get the result that if ‘Shirley believes Fido barks’ (‘s(B(Rf) )’) expresses a proposition true at e, so does ‘Shirley believes something’ (‘something: x(s(B(x) )’).

(18) I commented on an earlier version of Cresswell (2002) at the Rutgers Semantic Workshop in 2002. Much of what follows is drawn from that comment. I thank both Max Cresswell and the audience for comments on my comment.

(19) P. 643. Actually, Cresswell needs a strengthened version of what he calls the generalized principle of effability. Specifically, he needs the claim that for any two functions ω and ω* from propositions to propositions, there is a language V with functors δ and δ* such that V(δ)=ω and V(δ*)=ω* (see p. 645 and his note 8). Cresswell uses ‘V’ to mean both a language and the interpretation of the language (the function that maps expressions of the language to their semantic values). See his notes 3 and 8.

(20) P. 645.

(21) P. 646. Actually, instead of (b), Cresswell only needs the weaker claim that for any proposition p, there is a proposition r such that I(r)=I‐I(p). See his note 8.

(22) As we'll see in Chapter 6, I think they are worlds.

(23) P. 649.

(24) P. 644.

(25) P. 651.

(26) Pp. 651–2.

(27) I have changed the numbering of the principle here to accord with the numbering in the rest of the chapter.

(28) Here I will for the moment adopt Cresswell's treatment of Neg as a function from a set of indices to its complement to make things easier for the reader who wishes to look at Cresswell's paper—I actually prefer an account on which it is the truth function for negation or the property of propositions of being false.

(29) P. 652; bracketed expressions indicate changes I made to make Cresswell's quote in order to reflect my notation and numbering.

(30) Roughly, on Lewis' account, a sentence expresses a (structured) meaning consisting of the intensions of its lexical items occurring at the terminal nodes of the sentence's syntactic tree in the places where those lexical items themselves occurred in the sentence.

(31) P. 654.

(32) In saying that the that‐clause has a proposition or structured meaning as its semantic value, I mean only that the that‐clause is used to ascribe properties to propositions or meanings or to assert that they stand in relations to other things. See my remarks earlier in this chapter and in Chapter 5.

(33) Cresswell characterizes a ‘well behaved language’ as one for which his four assumptions, including FC, hold. See p. 649.

(34) Pp. 656–7.

(35) P. 657.

(36) P. 657.

(37) Of course it isn't really true that FC predicts violations to itself. Rather, the claim is that if we stipulate that a linguistic system is governed by FC, this very fact will lead us to predict that the system will eventually produce violations to FC. When I (or Cresswell) say(s) that FC predicts that FC will be violated, I (he) should be understood as meaning this.

(38) P. 643, 658, and 659.

(39) P. 658.

(40) See e.g. Soames (1987).

(41) Thanks to David Manley for useful discussions of and suggestions regarding the issues about to be addressed.

(42) One could investigate the idea that components are not parts of propositions, but I'll set aside the issue of fully articulating the relation between componenthood and parthood. Though I claim here that all components of the facts that are propositions are parts of propositions, this leaves open whether all parts are components. Assuming transitivity of parthood, Wendy's nose is a part of the proposition that Wendy loves Carl. If all parts are components, this would mean that Wendy's nose is a component of that proposition. I find nothing objectionable about this. Thus, I am sympathetic to the idea that componenthood is parthood.

(43) Pp. 94–7.

(44) I assume that the relations holding together the parts of 19a and 19a’ are the same as those holding together the parts of 18a and 18a’.

(45) Delia Graff Fara pointed out to me that another way to get 18 and 19 to have different parts is to assign semantic values to non‐terminal nodes in certain ways and claim these actually occur in the propositions. So, for example, one could assign to the non‐terminal (non‐root) node on the right side of 18 the relational property of loving Carl and claim it occurs in that proposition; and assign to the corresponding node in 19 the relational property of loving Wendy and claim it occurs in that proposition. Then the proposition 18 would have a part (the relational property of loving Carl) that the proposition 19 doesn't have (and vice versa). However, I don't see any reason to claim that such properties occur in propositions except to get this result. Thus, doing so looks somewhat ad hoc to me.

(46) E.g. Doepke (1982) holds that you and your body are distinct but share all the same parts. See pp. 10 and 17.

(47) P. 97.

(48) Some might feel that there is a tension between my claim that those who endorse composition violating uniqueness of fusion are not required to give an uncontroversial example of it as a precedent and my claim in Chapter 3 that absent uncontroversial examples of things possessing properties at times when they don't exist, those who claim that things can possess properties at times when they don't exist shoulder the burden of proof and so must give some argument for their claim. But there is no tension for two reasons. First, in Chapter 3 I pointed out that there are uncontroversial examples of properties that require a thing to exist at a time in order to be possessed at that time, whereas there are no uncontroversial examples of things possessing properties at time when they don't exist. Further, I pointed out that the idea of a thing not existing at a time and possessing a property then is puzzling. This generated the burden of proof. I don't think either of these claims is true in the present case. I don't think that there are uncontroversial examples of composition obeying uniqueness of fusion. And I don't think that the idea of composition not obeying uniqueness is very puzzling (as I have discussed). Second, and more importantly, in Chapter 3 I merely argued that the lack of an uncontroversial example of a thing possessing a property at a time when it doesn't exist shifted the burden of proof to those who think this can happen. Here I am asking whether an uncontroversial example of composition violating uniqueness of fusion is required for the doctrine to be accepted. The answer is no, both in this case and in the case of things allegedly possessing properties at times when they don't exist. Thanks to an anonymous referee for raising this issue.

(49) Thanks to Rich Thomason for raising this worry.

(50) Thomason actually considers the slightly different paradox in Montague (1963). But as far as I can tell, his reasoning goes through for the paradox in Kaplan and Montague (1960) which uses only A1–A3.

(51) Max Cresswell (1985) takes Thomason's argument to show that in a community of beings for whom closure holds (or for whom the instance A3 holds), the objects of knowledge are not structured meanings/propositions (see. p. 41).

(52) See also Cross' (2004) response to Uzquiano.

(53) Cross (2001) notes that this is one way to avoid the paradox as well.