Unity through truth
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Abstract
Renewed worries about the unity of the proposition have been taken as a crucial stumbling block for any traditional conception of propositions. These worries are often framed in terms of how entities independent of mind and language can have truth conditions: why is the proposition that Desdemona loves Cassio true if and only if she loves him? I argue that the best understanding of these worries shows that they should be solved by our theory of truth and not our theory of content. Specifically, I propose a version of the redundancy theory according to which ‘it is true that Desdemona loves Cassio’ expresses the same proposition as ‘Desdemona loves Cassio’. Surprisingly, this variant of the redundancy theory treats ‘is true’ as an ordinary predicate of the language, thereby defusing many standard criticisms of the redundancy theory.
Keywords
Structured propositions Unity of the proposition Deflationism Redundancy theory Truth Ramsey1 Introduction
 (1)
Desdemona loves Cassio.
 (2)
That Desdemona loves Cassio is true.
Recently, this question has been raised under the guise of a renewed worry about “the unity of the proposition”. Those pushing the worry ask how a proposition manages to have truth conditions. That is, why does the truthvalue of the proposition that Desdemona loves Cassio necessarily covary with whether she loves him?^{1} The need to associate a proposition with its truth condition is meant to be an important check on the theory of what propositions are. Standard theories of the nature of propositions are judged inadequate because they cannot explain why a proposition has truth conditions. So, it is contented that what Othello believes cannot be (a) a structured whole, (b) a primitive abstract entity, or (c) a set of possible worlds on pain of failing to deliver a crucial explanation.^{2} Some have taken this unity worry to be so severe as to mandate the psychologicstic conclusion that propositions are dependent on mental acts or linguistic vehicles.^{3}
In this paper, I isolate two formulations of the new problem of the unity of the proposition. One formulation asks for an explanation of why propositions have truth conditions. Why is the proposition that Desdemona loves Cassio true if and only if Desdemona loves Cassio? The other formulation begins with an attempted explanation. A proposition has truth conditions because it represents in some independent sense. On this view, the proposition that Desdemona loves Cassio represents that Desdemona loves Cassio. This fact purportedly explains why the proposition’s truthvalue varies with whether Desdemona loves Cassio. On this formulation of the unity worry, the puzzle is to explain why propositions are representational, whereas mere lists or aggregates are not.
I argue, however, that supposing that propositions are representational in this independent sense is no explanatory advance. Thus, we should prefer a formulation of the problem in terms of truth conditions to a formulation in terms of representation. We need to explain why a proposition and the claim that it is true are, in general, equivalent; that is, why is it that the proposition that Desdemona loves Cassio is true if and only if Desdemona loves Cassio. Since I accept this demand, my position differs significantly from others who deny that propositions are representational such as Speaks (2014a, b, c) and Richard (2014).
The worry is to explain why the truthvalue of a proposition varies with the state of the world. Those pushing the unity objection tend to frame this as a problem about contents. They say that there is something about propositions which explains this variation. I propose a change of view: the problem should be solved by our theory of truth and not our theory of content. To this end, I develop a form of the redundancy theory of truth delivering the needed explanation. On this theory, a simple sentence and a corresponding truthascription such as (1) and (2) express the same proposition. The claim that Desdemona loves Cassio just is the claim that the proposition that Desdemona loves Cassio is true. This explains why they are equivalent. In other words, the puzzle is to explain why Desdemona’s loving Cassio covaries with the seemingly distinct state of the world that the proposition that Desdemona loves Cassio is true. The redundancy theory replies that these states of the world are not as distinct as they might seem.
 = \(\lambda p\) . p

As a result, the new problem of the unity of the proposition does not call for the radical revisions to the traditional conception of propositions contemplated in the literature.[I]f we have analysed judgment we have solved the problem of truth; [...] the truth or falsity of this depends only on what proposition it is that is judged[.] (Ramsey 1927, p. 158).
2 Unity problems: old and new
The renewed worries about the unity of the proposition arise against the backdrop of more traditional concerns about propositional unity. These more traditional worries tend to target conceptions of propositions as structured wholes. I am attracted to one such conception, deriving from Moore and Russell. This view construes propositions as structured complexes containing objects, properties, and relations as constituents. The proposition that Desdemona loves Cassio is a structured whole containing Love, Desdemona, and Cassio. We may represent this structure as \(\langle \)Love, \(\langle \)Desdemona, Cassio\(\rangle \rangle \), where the settheoretic relations go proxy for corresponding structural facts about the proposition. Importantly, I assume only that propositions can be represented in terms of set theoretic constructions, not that propositions are identical to ntuples. Rival theories also identify propositions with structured wholes, but differ as to the constituents of these wholes. According to one alternative picture, due to an interpretation of Frege, propositions are structured wholes containing representations of these objects, properties, and relations.
Advocates of structured propositions have faced a formidable challenge concerning the unity of the proposition. The challenge is to explain how the proposition is a unity. The problem has come in many guises. Some have asked how the diverse constituents—Desdemona, Cassio, and love—come together to make up the structured proposition. Bradley (1893/2002) charged that complexity is itself mysterious. Others have inquired about the relationship between the structured complex and these constituents. Thus, Lewis (1986) and Keller (2014) charge that structured complexes require a mysterious kind of complexity.^{4}
What is special is that propositions must be—inherently and without further interpretation by us—capable of being true or false. (Soames 2014b, p. 32)
The problem we need to solve [...] is not to find some relation born by the constituents of a proposition to one another that ‘holds them together’ as parts of a single complex entity; the problem is to explain the intentionality of propositions. (Soames 2014b, p. 32)
Understood as a problem about truth conditions, the unity of the proposition asks why a proposition’s truthvalue varies with the world at large. That is, why is the proposition that Desdemona loves Cassio true just in case Desdemona loves Cassio? Similarly, why is the proposition that Richard killed Henry true just in case Richard killed Henry? The question can be repeated for any nonparadoxical case. One might understand this covariation as a kind of representation.^{6} The proposition that Desdemona loves Cassio represents that Desdemona loves Cassio insofar as it is true just in case Desdemona loves Cassio. The proposition that Richard killed Henry represents that Richard killed Henry insofar as it is true just in case Richard killed Henry.
Necessarily, p is true if and only if Desdemona loves Cassio. Necessarily, proposition q is true if and only if Richard murdered Henry. And so on. End of theory.
But such a theory feels unsatisfactory. This theory is worse—all other things being equal—than a theory that explains these equivalences.

Intensionalism: Propositions are intensions in that (i) they determine functions from pointsofevaluation to truthvalues and (ii) two propositions that determine the same functions are identical.^{7}

Primitivism: Propositions are fine grained, simple objects with no internal structure.^{8}
I first examine an approach that attempts to explain this connection in terms of the theory of content. Specifically, the thesis that propositions are representations and that truth is accurate representation. I then argue that the covariation can be explained by our account of truth rather than our account of content. My own proposal will be developed in a framework which identifies propositions with structured wholes composed of objects, properties, and relations. But nothing I say will depend essentially on this framework. Indeed, everything I say could be adopted by proponents of almost any conception of propositions so long as it can be developed in conjunction with certain semantic assumptions that I discuss below.
3 Unity through representation
why is the proposition that snow is white true? It is true because (a) it represents snow as white, and (b) snow is white.
Returning to our examples: proposition q—that Richard murdered Henry—represents that Richard murdered Henry. Richard did murder Henry. So q is true. On the other hand, proposition p—that Desdemona loves Cassio—represents that Desdemona loves Cassio. Desdemona did not love Cassio. So p is not true.
[S]ome elements have the property: representing that a donkey talks, or being an element according to which a donkey talks. It is in virtue of these representational properties that some elements are selected and some or not. For instance, there is one element that has the aforementioned property of representing that a donkey talks, and no other properties. Necessarily, that one is selected iff a donkey talks. (Lewis 1986/2001, p. 177)
On this view, a certain element is “selected” because it represents that Richard murdered Henry and Richard did murder Henry. The analogous position about propositions—defended by Hanks (2007), Soames (2014a), and Merricks (2015, ch. 6)—says roughly that the proposition that Richard murdered Henry is true because it represents that Richard murdered Henry and Richard did murder Henry.
We have not the slightest idea what the ‘representational properties’ are; except that they are properties whereby a vast flock of abstract simples differ from one another. Lewis (1986/2001, p. 178)
By way of contrast, Lewis allowed that we can understand linguistic or pictorial representation.^{10} He would, presumably, also say the same about mental representation. If we are to have representation (as something beyond covariation) it must be explained in terms of the same mechanisms by which we explain linguistic, pictorial, or psychological representation. To a certain extent, Soames, Hanks, and King all agree. They attempt to explain representation in psychological or linguistic terms. The representational properties of propositions are due to the abilities of agents, psychological states, or sentences to represent.

RepresentationThat: The proposition that Desdemona loves Cassio represents that Desdemona loves Cassio.

RepresentationAs: The proposition that Desdemona loves Cassio represents Desdemona as loving Cassio.
3.1 Representationthat
Those who think that propositions have their truth conditional properties on account of their representational properties posit an explanatory connection between truth and representation. Namely, a proposition that represents that \(\phi \) is true just in case \(\phi \). Above, we saw Lewis construe his opponents’ view as asserting that a certain primitive element represents that a donkey talks and that this element is selected just in case a donkey talks. The analogous position about propositions says that a certain proposition represents that Desdemona loves Cassio. This proposition is true just in case Desdemona loves Cassio. Many philosophers do indeed use this terminology to refer to the representational properties of propositions or their features, including King (1995, p. 526), Richard (2014, p. 2), and Jago (2015, p. 4). The aim of this section is to suggest that one cannot explain the truth conditional properties of propositions in terms of their representational properties construed as properties of representationthat.
 (3)
Proposition p represents that Desdemona loves Cassio.
 (4)
Othello believes that Desdemona loves Cassio.
 (5)
Margaret knows that Richard killed Henry.
I have argued that the ‘that’clause in (3) should be construed as specifying or describing some object just as the analogous ‘that’clauses do in (4) and (5). One might push the analogy with propositional attitude ascriptions to argue that the entity specified in (3) must be a proposition. But, then, it is hard to see how we have a satisfactory explanation of a proposition’s possession of truth conditions in terms of its being representational. It is unilluminating—from the point of view of explaining why propositions have truth conditions—to say that the proposition has truth conditions because it represents itself.^{12}
I will not here go through the entire literature on alternative views as to what the ‘that’clause in (3) might represent. Rather I divide the potential candidates into two categories. The two options I consider are: (\(\alpha \)) the proposition that Desdemona loves Cassio represents something which may exist regardless of whether Desdemona loves Cassio and (\(\beta \)) this proposition represents something that exists if and only if she loves him.
Suppose (\(\alpha \)) that the proposition that Desdemona loves Cassio represents something which—like the proposition itself—may exist even if Desdemona does not love Cassio. This category includes states of affairs, as some construe them. On these construals, the state of affairs that Desdemona loves Cassio exists regardless of whether she loves him. If she does love him, then the state of affairs has an additional feature: it is the case or obtains. If the proposition that Desdemona loves Cassio represents some entity in this category, then the truthvalue of the proposition is explained by both the entity it represents and whether the entity has the additional feature. If propositions represent states of affairs, then the proposition that Desdemona loves Cassio represents the state of affairs that Desdemona loves Cassio. The proposition is true if the state of affairs is the case or obtains.^{13}
The problem is that the notion of being the case or obtaining introduces the same sort of worry we had about truth. The state of affairs that Desdemona loves Cassio may be the case or it may fail to be the case. But it does not have these features—being the case or failing to be the case—in isolation from the world at large. In particular, when Desdemona loves Cassio, that Desdemona loves Cassio is the case. And when she fails to love him, it is not the case. It is natural to ask why the obtaining of this state of affairs covaries with the world at large in this way. Thus, this proposal purports to explain why propositions have truth conditions in terms of the structurally similar fact that states of affairs have obtaining conditions. Given the precise structural similarity, I fail to see how this is a genuine explanatory advance.
Now suppose (\(\beta \)) that the represented entity cannot exist unless the proposition is true. Under this category, we might include states of affairs or facts, as they are sometimes conceived.^{14} On such a view, the proposition that Richard killed Henry represents the fact that Richard killed Henry. And this fact could not exist unless Richard did kill Henry. This approach, then, can provide an account of truth along the lines of classical truthmaker theory.^{15} For a proposition to be true is for it to represent a fact.
Note that on this proposal, false propositions fail to represent anything. The proposition that Desdemona loves Cassio is false. As a result, it represents nothing on this picture. Yet, if Desdemona were to love Cassio, then necessarily there would come into existence a fact F that Desdemona loves Cassio. And the proposition that Desdemona loves Cassio would come to represent F. The proposal, therefore, posits two modal connections where before we only had one. First, whenever Desdemona loves Cassio, F comes into existence.^{16} Second, whenever Desdemona loves Cassio and F comes into existence, the proposition p that Desdemona loves Cassio comes to represent F. It is far from obvious that jointly explaining these two connections will be easier than explaining why the proposition that Desdemona loves Cassio becomes true when Desdemona loves Cassio.^{17}
3.2 Representationas
Recently, it has been popular to offer an alternative formulation of what a proposition represents. Rather than saying that a proposition represents that such and such is the case, proponents of this alternative formulation say that a proposition represents an object as being a certain way. Thus, it might be suggested that the proposition that Desdemona loves Cassio represents Desdemona as loving Cassio.^{18} The proposition that Richard killed Henry represents Richard as killing Henry.
[Propositions] represent things in the world as being certain ways; thus they have truth conditions. Since the proposition that o is red represents a certain object as red (while doing no further representing) it is true iff o is the way it is represented to be—red. (Soames 2014a, p. 95)
The idea is that if something represents an object as having a property, then the representation is true (or accurate) just in case the object has the property.
We might think of this connection as a general law relating representation to truth. Presumably, this law is meant to be part of our pretheoretic conception of representing an object as having a property. That is, representing a as F is not some new unstructured monadic property P or relational property R(a as F), between a proposition and what it represents. Rather, the notion of representation invoked is meant to be something pretheoretically available and expressible in natural language using one of these ‘as’ constructions. If it were not, then the purported explanation would be no better than that of a traditional structured propositionalist who says that the fact that the proposition that Desdemona loves Cassio stands in interesting constituency relations to Desdemona, love, and Cassio explains why it has truth conditions.
 (6)
The proposition that Desdemona loves Cassio represents Desdemona as loving Cassio
 (7)
The department represented Mary as a syntactician.
 (8)
The department regarded Mary as a semanticist.^{19}
 (9)
The linguistics department represented Mary as a syntactician and Sam as a semanticist.
 (10)
The department considered Mary a semanticist.
Of course, any account of the nature of these ‘as’clauses will be controversial, and my preference is no exception. I don’t need to defend my preference here. Rather, I note that on many accounts ‘as’clauses will represent something. And whatever they represent will lead to issues similar to those discussed above.^{22} I take this as sufficient motivation to explore another option.
3.3 Properties and representation
I believe, however, that we still must explain why propositions are representational in this minimal sense: why does their truthvalue depend on what happens in the world? Why is the proposition that Desdemona loves Cassio true if and only if she loves him?Propositions [...] are what is represented. They are representational in the minimal sense that they are true or false[.]^{23}
Richard and also Speaks (2014a) think that they have a satisfactory explanation that does not derive from any purportedly representational properties of propositions. Richard and Speaks both identify a proposition—say the proposition that Desdemona loves Cassio—with an entity that according to them unproblematically varies with whether Desdemona loves Cassio. In particular, both identify the proposition that Desdemona loves Cassio with a certain property, the property of being such that Desdemona loves Cassio.^{24} This property is instantiated just in case Desdemona loves Cassio. Very roughly, they claim that for a proposition to be true is for it to be instantiated.
Though we agree that propositions are not representational except insofar as they are true or false, I disagree with Speaks and Richard that they have offered a satisfactory explanation of why propositions possess these truth conditions. As I conceive of the worry over truth, it is essentially the same as the one Lewis raises against “magical ersatzism” in Lewis (1986/2001). Why is a certain proposition true—or, why is a given ersatz world “selected”—just in case Desdemona loves Cassio? I conceive of these same worries as applying to complex properties: why is the property of being such that Desdemona loves Cassio instantiated just in case Desdemona and Cassio instantiate the loving relation (in the right order)? The initial explanatory demand concerned why a proposition’s truthvalue covaries with what happens to the world at large. It is answered by appealing to properties whose instantiation covaries with the instantiation of other properties. But I believe it is reasonable to ask why the instantiation of these properties covaries with the instantiation of simpler universals. And I believe that this is Lewis’s (1986) worry as well, especially as developed by Hawley (2010). This is why Lewis’s objections to ersatz possible worlds so closely resemble his objections to “structural universals” whose instantiation conditions vary with those of simpler properties. So from my point of view, the shift from propositions to properties makes little explanatory advance.^{25}
4 A solution through truth
The task is to explain why the truthvalue of a proposition varies with the world at large. Why does the proposition that Desdemona loves Cassio come to be true just in case she loves him? As we have seen, it has recently been popular to attempt to explain this covariation in terms of the nature of contents: there is something special about propositions such that their truthvalue varies with the world at large. I suggest an alternative approach. I propose that there is something special about truth such that the ascription of truth to a proposition will necessarily covary with the world at large.
The truth about truth, so far as propositions are concerned, is a long but simple story. A proposition is true iff
it is the proposition that a donkey talks, and a donkey talks; or
it is the proposition that pigs fly, and pigs fly; or
it is the proposition that cats purr, and cats purr; or
it is the proposition that servitude to the state is perfect freedom, and servitude to the state is perfect freedom; or....
For Lewis, the easy task is to explain the equivalence between the truth of the proposition that Desdemona loves Cassio and Desdemona’s loving Cassio. The hard task, by way of contrast, is to explain why a given proposition p gets to be named “the proposition that Desdemona loves Cassio”.^{26} This hard task is a version of the traditional problem of unity, and I shall not address it here.
The basic idea behind the redundancy theory—that sentences of the form S and \(\ulcorner \)that S is true\(\urcorner \) say the same thing—is shared by distinct views of truth. For instance, some interpreters of Ramsey such as Soames (1999, p. 238) take him to hold that constructions involving ‘is true’ are always eliminable or paraphrasable into constructions that do not involve truth. Advocates of the prosentential theory of truth follow this line, but allow that these paraphrases can be developed in an expanded version of English.^{27} The idea is also present in Strawson’s (1950) performative theory.^{28}The proposition to which they are ascribed may be either explicitly given or described. Suppose first that it is explicitly given; then it is evident that “it is true that Caesar was murdered” means no more than that Caesar was murdered[.] (Ramsey 1927, p. 157)
In the remainder of this paper, I will defend a particular implementation of Ramsey’s idea, according to which the truth predicate has a definite meaning that can be incorporated into a standard compositional semantics. In what follows, I first explain why I develop a compositional version of the theory. I then sketch a semantics that assigns each sentence (in context) to a Russellian structured proposition. I show how a truth predicate exhibiting these features can be smoothly integrated into this semantics. As I mentioned above, the crucial move is to regard ‘is true’ as expressing an identity function restricted to propositions. This function takes a proposition as argument and returns that very proposition. Although I develop my solution in a broadly Russellian framework, the basic structure of this proposal could be adopted by rival views so long as the semantic value of a predicate is treated as determining a mapping from individuals into propositions, whatever these turn out to be on the theory.^{29}
4.1 Why a compositional redundancy theory?
According to the minimalist thesis, all of the facts whose expression involves the truth predicate may be explained in such a way: namely by assuming nothing more about truth than instance of the equivalence schema.
 (11)
Everything John said is true.
Classical interpretations of the redundancy theory that attempt to make do without assigning a compositional meaning to ‘is true’ have also been charged with these difficulties.^{30} In particular, if the only semantic claim about ‘is true’ is that sentences of the form S and \(\ulcorner \)that S is true\(\urcorner \) express the same proposition, it is unclear what a claim such as (11) might mean.^{31} Prosentential theorists attempt to understand Ramsey as offering a paraphrase of these sentences into a language which allows propositional quantification. The intelligibility of these interpretations is itself hotly disputed.^{32}
My version of the redundancy theory, however, sidesteps these worries. I assign a standard predicate meaning to ‘is true’. This standard predicate meaning nonetheless delivers the result that S and \(\ulcorner \)that S is true\(\urcorner \) express the same proposition. I do not hold that all facts whose statement involves ‘is true’ are entailed by propositions expressed in nonalethic terms together with instances of the schema, the proposition that p is true if and only if p. Rather, I hold that I can assign a meaning to every sentence in context containing the predicate ‘is true’. Because ‘is true’ functions analogously to any other predicate of the language, there is no difficulty in understanding quantified claims so long as we have a reasonable understanding of the meaning of the quantifier. I present this theory in the next few sections, beginning with the background propositionalist semantics.^{33}
4.2 Propositionalist semantics
As I mentioned above, I take Russellian structured propositions to be the semantic values of sentences in context. Thus, sentence (1) ‘Desdemona loves Cassio’ denotes a structured proposition which I represent as \(\langle \)Love, \(\langle \)Desdemona, Cassio\(\rangle \rangle \). A propositionalist semantics aims to compositionally map the sentences of a language onto their semantic values. Following a proposal briefly mentioned by Dummett (1981, p. 294) and developed in Pagin and Pelletier (2007), Elbourne (2011, pp. 104–107), and Pickel (forthcoming), I suggest—contra some leading proponents of structured propositions—that sentences are functionally compositional: the semantic value of a sentence in context is the result of applying the function denoted by one component in context to the argument denoted by the other component in context.^{34}
 (1a)
Love(Desdemona, Cassio).

\(\llbracket \)Love(Desdemona, Cassio)\(\rrbracket \) = \(\llbracket \)Love\(\rrbracket \)(\(\llbracket \)Desdemona\(\rrbracket \), \(\llbracket \)Cassio\(\rrbracket )\) = \(\langle \)Love, \(\langle \)Desdemona, Cassio\(\rangle \rangle \).

\(\llbracket \lnot \phi \rrbracket \) = \(\langle NEG, \langle \llbracket \phi \rrbracket \rangle \rangle \)
 = \(\lambda q \)\(\langle NEG, \langle q \rangle \rangle \)
 \(\llbracket \lnot \phi \rrbracket \) = = \(\langle NEG, \langle \llbracket \phi \rrbracket \rangle \rangle \)
The quantifiers raise additional complications. Let us understand a quantifier as syntactically applying to a complex predicate. That is, a quantified sentence of the form \(\ulcorner \)for each x, \(\phi \urcorner \) (abbreviated \(\forall \widehat{x} \phi \)) will be understood as resulting from composing the quantifier \(\forall \) with the complex predicate \(\widehat{x}\phi \). This predicate itself results from applying the variable binder \(\widehat{x}\) to a formula \(\phi \). Following Soames and Salmon (and ultimately Russell), the complex predicate will be taken as a propositional function which maps individuals to propositions. Essentially, \(\widehat{x} \phi \) denotes the propositional function that maps an object o onto the proposition expressed by the formula \(\phi \), but with x reinterpreted to designate o.^{36}

\(\llbracket \forall \widehat{x} \phi \rrbracket \) = \(\langle ALL, \langle \llbracket \widehat{x} \phi \rrbracket \rangle \rangle \).
 = \(\lambda g \)\(\langle ALL,\langle g \rangle \rangle \)
4.3 The truth predicate

\(\llbracket \)That\(\phi \)is true\(\rrbracket \) = \(\llbracket \phi \rrbracket \).
 = \(\lambda p\) . p
 (12)
That Desdemona loves Cassio is true if and only if Desdemona loves Cassio
 (13)
Desdemona loves Cassio if and only if Desdemona loves Cassio
 = \(\lambda g \)\(\langle ALL, \langle g \rangle \rangle \)
 = \(\langle ALL, \langle \lambda p\) . \(p \rangle \rangle \)
So here, Ramsey is saying that the propositional function which I write as ‘\(\lambda p\).p is true’ and the propositional function which I write as ‘\(\lambda p\).p’ are identical. For any input, they give the same output. My view combines this basic insight with a semantics that compositionally assigns structured propositions by treating ordinary predicates as mappings from individuals onto structured propositions. As a result, the truth predicate can be treated as an ordinary predicate of the language.[When] the proposition is described and not given explicitly, [...] we get statements from which we cannot in ordinary language eliminate the words “true” and “false.” Thus if I say “he is always right” I mean that the propositions he asserts are always true, and there does not seem to be any way of expressing this without using the word “true.” But suppose we put it thus “For all p, if he asserts p, p is true,” then we see that the propositional function p is true is simply the same as p, as e.g. its value “Caesar was murdered is true,” is the same as “Caesar was murdered.” (Ramsey 1927, p. 158)
5 Objections
I have offered a new redundancy theory of truth in order to solve the renewed problem of the unity of the proposition. Traditional redundancy theories have faced a variety of objections. I believe that my implementation is largely immune to these objections. However, in a few cases, I adopt standard solutions to them. In this section, I briefly outline my response to these standard challenges to the redundancy theory.
5.1 Meaning
Horwich’s idea seems to be that the meaning of a component of a sentence must be a component of the meaning of the sentence. I believe that this is wrong. On my semantic framework, the semantic value of an expression is generally not a component of the semantic value of a sentence that contains it. Consider, for instance, the predicate ‘loves’ as it occurs in ‘Desdemona loves Cassio’. I suggested that the semantic value of ‘loves’ was a function from pairs of individuals to the proposition that one loves the other: \(\llbracket \)Loves\(\rrbracket \) = \(\lambda o_1, o_2\)\(\langle \)Love, \(\langle o_1, o_2\rangle \rangle \). The semantic value of the sentence ‘Desdemona loves Cassio’ is the value of applying this function to arguments Desdemona and Cassio. In general, a function is not a constituent of its value and this case provides no exception. So, I see no reason to endorse Horwich’s claim.[One] respect in which minimalism improves on the original redundancy theory is not claiming that ‘p’ and ‘The statement (belief,...) that p is true’ have exactly the same meaning. This claim is implausibly strong; for those meanings would appear to be, in some sense, ‘components’ of the meaning of ‘The statement that p is true’ but not of ‘p’. (Horwich 1998, p. 124)

BNEC: Two sentences express the same proposition only if there is no concept whose mastery has to be exercised only in understanding utterances of one of them. (Künne 2003, p. 47)
Note first that nothing as strong as BNEC is required to account for the substitution failure Künne considers. That is, Künne’s example may show that BNEC has an advantage over views saying that necessarily, a priori, or cognitively equivalent sentences express the same proposition. But on its own, it fails to show that BNEC is required to explain these substitution failures.[BNEC is necessary] if we want to make sense of our practice of ascribing attitudes and reporting speech by means of thatclauses: ‘Our youngest daughter believes (said) that she has ten fingers, but she does not believe (did not say) that the number of her fingers equals ten multiplied by one’ may be a correct report, but if the embedded sentences were to express the same proposition, such a report would be inconsistent. (Künne 2003, p. 48)
 (14)
That dog is a cat.
 (15)
Fido is a cat.
 (16)
Sam said that that dog is a cat.
 (17)
Othello believes that Desdemona loves Cassio.
 (18)
Othello believes that it’s true that Desdemona loves Cassio.
 (19)
Iago says that Desdemona loves Cassio and Othello believes that it’s true.
 A:
Quine thinks that there are no propositions.
 B:
That’s a striking position. Does anyone else think that’s true?
 A:
Yes. Davidson does/thinks that’s true as well.
5.2 Truth and singular terms
 (1)
Desdemona loves Cassio.
 (2)
That Desdemona loves Cassio is true.
 (20)
Something is true.
 (21)
Everything Mary said is true.

\(\llbracket \exists \widehat{x}\)xis true\(\rrbracket \) = \(\llbracket \exists \rrbracket \)(\(\llbracket \widehat{x}\)xis true\(\rrbracket \)) = \(\langle SOME\), \(\langle \lambda p.p \rangle \rangle \)
Soames (1999, pp. 48–49) offers a related set of challenges concerning singular terms. The charge is that one can assert a sentence of the form \(\ulcorner \alpha \) is true\(\urcorner \) where \(\alpha \) is a directly referential term for a proposition without thereby asserting the proposition to which \(\alpha \) refers. Let me divide the potentially problematic cases into two. First, \(\alpha \) might be a pronoun that refers to a proposition that is somehow supported by the discourse context, whether by propositional anaphora or propositional deixis. Second, there are cases where \(\alpha \) purportedly refers to a proposition that is absent from discourse context, as when \(\alpha \) is purportedly a proper name.
 (22)
 a.
Desdemona loves Cassio.
 b.
That’s true.
 a.
 (23)
 a.
Every even natural number greater than 2 is the sum of two primes.
 b.
Goldbach’s Conjecture is true.
 a.
The matter is not this simple. Unlike core cases of proper names, the expressions at issue such as ‘Goldbach’s Conjecture’ are morphologically complex, which makes Kripke’s arguments already considerably less forceful. Moreover any of these views deploy constructions whose semantic composition rule is highly underspecified. For instance, ‘Goldbach’s Conjecture’ is a possessive construction which leaves highly underspecified what, if any, connection there is between Goldbach and the conjecture.If names were equivalent to definite descriptions, this might not be so since they might then be assimilated to the quantificational case. However, the convincing refutation of descriptive theories of names by Saul Kripke and others makes this strategy unpromising. (Soames 1999, p. 49)
 (24)
 a.
Sam believes Goldbach’s Conjecture.
 b.
Sam believes that every even natural number greater than 2 is the sum of two primes.
 c.
Sam believes that every natural number greater than 2 into which 2 divides evenly is the sum of two primes.
 a.
Nothing I have said here is specific to the fact that ‘Goldbach’s Conjecture’ is a possessive construction. Rather, it is a striking fact about propositions that we normally refer to them using morphologically complex expressions. Many of the constructions seem to be some sort of explicit definite description such as ‘The First Law of Thermodynamics’ (Künne 2003, p. 72), ‘The Riemann Hypothesis’, and so on. Other expressions are morphologically complex in a different way, including Soames’s (1999, p. 49) example of a thesis he labels ‘Extensionalism’. The morpheme ‘ism’ attaches to a root node ‘extensional’ to form the name of a thesis or condition. The relation between the thesis and the root is highly underspecified as can be seen by contrasting: ‘Logicism’, ‘Pythagoreanism’, ‘Utilitarianism’, and ‘Extensionalism’. Given that these names are morphologically complex, I have no qualms about positing that they are highly underspecified descriptions of propositions rather than directly referential names. Propositions are rarely given syntactically simple names, except in highly idiosyncratic circumstances, as in the course of a mathematics proof. These simple names rarely seem to stick beyond a local practice, which suggest they function analogously to anaphoric pronouns discussed above.
Still, the proponent of the compositional redundancy theory need not go this far. I am proposing that the proposition expressed by an inexplicit truth attribution such as (i) \(\ulcorner \)something is true\(\urcorner \) or (ii) \(\ulcorner \alpha \) is true\(\urcorner \) may differ from the proposition expressed by a corresponding explicit truth attribution such as \(\ulcorner \)that \(\phi \) is true\(\urcorner \) due to the fact that the quantifier ‘something’ or the singular term \(\alpha \) may specify the proposition expressed by \(\phi \) in an inexplicit manner. I have done so by suggesting that many singular terms purporting to refer to propositions are descriptions.
But to resist Soames’s arguments, it suffices that purported names of propositions are not Millian. They must have semantic contents other than the proposition named. The crucial point is that the proposition to which truth is attributed is only indirectly specified, it does not exhaust the semantic content of the name. Any difference in semantic values of \(\ulcorner \alpha \) is true\(\urcorner \) and \(\ulcorner \)that \(\phi \) is true\(\urcorner \) must be grounded in a difference in the semantic values of \(\alpha \) and \(\ulcorner \)that \(\phi \urcorner \).^{47}
6 Conclusion
We began with an explanatory demand: why does the truthvalue of a proposition covary with what’s happening in the world at large? I have argued that this puzzle is to be solved by our theory of truth and not our theory of content. A redundancy theory purports to explain the covariation by narrowing the gap between the truth of a proposition and the reality that makes it true. The truth of the proposition that Desdemona loves Cassio amounts to nothing more than that Desdemona loves Cassio. Unlike many other broadly deflationist theories of truth, the form of the redundancy theory which I advocate The Compositional Redundancy Theory, predicts this identity of content in the context of a functionargument conception of compositionality and therefore integrates rather smoothly with contemporary formal semantics. There are many avenues left for exploration, however. One important further test will be to see how well The Compositional Redundancy Theory integrates with existing solutions to the semantic paradoxes such as the Liar. Another will be to investigate its relation to other theories of truth. But, insofar as the theory brings a true proposition and the reality that makes it true closer together, it already has one significant advantage: it solves the renewed problem of the unity of the proposition.^{48}
Footnotes
 1.
By this, I just mean to ask why the proposition is true or is false depending on whether she loves him. (I do not mean to construe truthvalues as objects.) King (2009, p. 258) articulates this worry as follows: “How does [...] the proposition that [Desdemona loves Cassio] manage to have truth conditions and so represent [Desdemona] as [loving Cassio]?”.
 2.
A thorough recent presentation of this argument can be found in Soames (2014b).
 3.
 4.
Hawley (2010) contains an important related discussion concerning complex properties.
 5.
MacBride (2013b, p. 212) frames some of the worries about unity in Frege and Russell in essentially similar terms: “Propositions are entities possessed of that distinctive unity that enables them to bear truthvalues.”
 6.
This is something like the “deflated” sense in which propositions are representational of Richard (2014, p. 716).
 7.
 8.
 9.
 10.
Lewis (1986/2001, p. 174).
 11.
Dyke (2012) also offers an argument against the idea that propositions are representational. Her conclusions also resonate with those of this paper insofar as we agree that the proposition that it is true that Desdemona loves Cassio is just the proposition that she loves him, though my argument does not lend support to the idea that propositions should be extruded from the world.
 12.
Nothing I say here is meant to criticize the identity theory of truth according to which, roughly, a true proposition is identical to a fact. The positive view I develop bears interesting relations to the identity theory that will need to be explored in further work. The view does not require that proposition represent the relevant facts; propositions are the facts. See defenses of the identity theory of truth in McDowell (1994), Hornsby (1997, 1999), and Dodd and Hornsby (1992). Criticism can be found in Baldwin (1991), Candlish (1999a, b), and Johnston (2013).
 13.
Hanks (2011) often glosses his view as though he construes propositions as representing states of affairs. For instance, in describing the renewed unity puzzle he says that traditional views face an obligation: “An account has to be given of how these contents represent states of affairs that does not make any appeal to the intentional actions of speakers” (143). Similarly, he describes his own view—that a proposition is a mental act type—as one on which a proposition represents a state of affairs: “Because any instance of a speaker applying the property of tallness to Smith represents a certain state of affairs, the type [=proposition] that unites these instances also represents that state of affairs” (159ff). While I doubt that Hanks would endorse this as the final statement of his view, it is important to see why it is an undesirable stopping place.
 14.
 15.
 16.
 17.
We might conjoin this approach with a reductive account of truth: truth just is representing a fact. This view, like my own, attempts to explain why truth covaries with the world in terms of the theory of truth and not in terms of the theory of representation. There remain, however, worries about explaining why the existence of the represented entity covaries with the state of the world. For instance, Russell (1913/1992, 144ff) builds toward this sort of picture in his definition of truth for a “nonpermutative belief”.
 18.
 19.
The last two examples are or are based on examples from Bowers (1993).
 20.
 21.
See, for instance, Radford (1997, p. 105). Bowers (1993, p. 602) presses this argument most clearly when he says: “A powerful empirical argument in support of the theory of clause structure proposed in this article is the fact that phrases each consisting of an object and its complement can, quite generally, be conjoined [‘John regards professors as strange and politicians as creepy’].” Landman (1989, p. 732) offers a similar argument. Szabó (2003) is a forceful critic of the view that ‘as’phrases are constituents in sentences such as ‘John as a judge makes a lot of money’. He regards the phrase ‘as a judge’ as an adjunct. But, when considering examples of the form (7), Szabó (2003, p. 395) seems to concede that ‘as’ indicates predication. It is unclear to me what his ultimate view is on sentences of this kind.
 22.
It might be that the proponents of representationas mean the clauses of the form \(\ulcorner a\) as \(F\urcorner \) to denote higherorder entities. This would involve them in complications which I avoid in my preferred theory, as I discuss in my discussion of the prosentential theory in §4.1.
 23.
Speaks (2014b, pp. 145–146) makes similar claims.
 24.
 25.
Speaks (2014a, p. 76) responds to those who want to explain the instantiation of the property of being such that Desdemona loves Cassio in terms of the truth of the proposition that Desdemona loves Cassio by suggesting that the order of explanation proceeds the other way. But he offers no explanation, as far as I can tell, for why the property is instantiated just in case Desdemona loves Cassio. I believe that I can offer an explanation for why the truthvalue of the proposition that Desdemona loves Cassio covaries with whether she loves him. I can then offer an explanation of why the property of being such that Desdemona loves Cassio covaries with whether she loves him as deriving from its connection to the proposition that Desdemona loves Cassio. For this reason, I prefer not to reverse the order of explanation, as Speaks recommends.
 26.
Lewis (1986/2001, pp. 177–179, 182).
 27.
 28.
On Ramsey’s own view, the objects of thought are the diverse entities that the thought is about. So Ramsey’s own view is an implementation of Russell’s multiple relation theory of judgment. But this aspect of his view is motivated by the original problem of the unity of the proposition and related problems about facts and is therefore separable from his account of truth.
 29.
The view can be embedded in an intensionalist framework, for instance, if the semantic values of predicates are the compositional intensions of Lewis (1970).
 30.
See Soames (1999, pp. 39–49, 232–238).
 31.
 32.
 33.
The strategy resembles an argument of MacFarlane (2014, §4.8) purporting to show that semantic relativism can support the truth schema. A crucial difference is that the underlying semantics of this paper proceeds by assigning only meanings to sentences in contexts, whereas MacFarlane’s semantics appeals to underlying notions of truth at a parameter which demand further explanation.
 34.
I take the term from Cresswell (2002). As King and Stanley (2005, p. 134) observe, standard advocates of structured propositions—Soames (1987), Salmon (1986, Appendix C) and King (2007, Appendix)—posit “no significant composition of semantic contents” in the mapping from a sentence to the structured proposition it expresses in context. In particular, King and Stanley observe that in typical cases, the proponents of structured propositions take the semantic value of a complex to be the result of pairing the semantic values of its components. In Pickel (forthcoming), I argue that this result is undesirable, since it threatens to undermine almost the whole of contemporary formal semantics. The semantics, as sketched below, also reveals that the proponent of structured propositions can accept functional composition.
 35.
 36.
See Pickel (forthcoming, §7) for a discussion of variable binding and the semantics for complex predicates in a propositionalist semantics.
 37.
 38.Soames (2010, pp. 122–129) suggests that treating ALL as a universal leads to difficulties in deriving the truth conditions for the propositions expressed by the sentences of a language. For instance, Soames (2010, p. 125) argues that an account as to the nature of propositions must deliver the following equivalence.According to the worry, if ALL is a simple universal, then the equivalence is an ad hoc meaning postulate. I believe that the redundancy theory developed below will go some way towards substantiating these equivalences. For instance, the semantics will deliver the following identities.

A proposition that predicates being always true (ALL) of a propositional function g is true iff g assigns a true proposition to every object.
Allowing substitution of identical propositions, the identities entail that, concerning a propositional function g, the proposition \(\langle ALL\), \(\langle g \rangle \rangle \) is true if and only if for every o, g applied to o is true.
\(\langle ALL\), \(\langle g \rangle \rangle \) = \(\langle ALL\), \(\langle \lambda o. g(o) \rangle \rangle \) = \(\langle ALL\), \(\langle \lambda o. \lambda p.p(g(o)) \rangle \rangle \) = \(\langle ALL\), \(\langle \lambda o. \llbracket \)is true\(\rrbracket ( g(o)) \rangle \rangle \)

 39.
That is, there is no need for such quantification issuing from the theory of truth. I have said nothing foreclosing the need for such quantification to resolve other problems.
 40.
Note that Ramsey himself explicitly denied that the truth predicate was similarly eliminable in natural language from cases in which the proposition to which truth is ascribed is not explicitly given). Thus, Ramsey endorsed only what Künne (2003) calls the redundancy thesis and not what he calls the redundancy theory, that truth is everywhere redundant. Given that Ramsey is a prototypical proponent of the redundancy theory, I will call the weaker thesis the redundancy theory.
 41.
Thanks to an anonymous referee from Synthese for making me consider this example.
 42.Compare the equally acceptable dialogue:
 A:
Bealer thinks that there are propositions.
 B:
Quine thinks that that’s not the case. He thinks that it’s not true that there are propositions.
 A:
 43.
Asay (2013, §§5.2.2–3) offers a nice example defending this “omnipresence” thesis, remarking: “Think to yourself, ‘I wonder whether there are any kangaroos in Africa, though I do not wonder whether it is true that there are any kangaroos in Africa.’ I for one cannot do it” (155).
 44.
Soames (1999, pp. 39–43, 232–234).
 45.
 46.
Soames (1999, pp. 48–49) writes: “There are other, related problems with the redundancy theory. One familiar kind of case in which true is used is one in which we refer demonstratively in a propositioned say, ‘That’s true.’ Typically, in such cases, the proposition said to be true is expressed by an assertive utterance or inscription in the context, so it is transparent what proposition we have referred to. In these cases, the redundancy theory may seem tempting. However, not all cases of referring to a proposition are like this.” The cases Soames considers are those of the second type, to which I now turn.
 47.
In a recent paper, Rattan (2015) articulates—but does not defend—a limited redundancy theory that accounts for the cognitive value of “inexplicit” truth attributions as “grounded in the cognitive value of generalization” (22) and other mechanisms of indirect specification. Rattan suggests that there is nonetheless a tension in limited versions of the redundancy theory such as the compositional redundancy theory advocated here. I believe that this challenge can be resisted, but leave this project to future work.
 48.
This paper was improved as a result of feedback from Derek Ball, Ray Buchanan, Matthew Chrisman, Manuel GarcíaCarpintero, Ephraim Glick, Bjørn Jespersen, Colin Johnston, John Keller, Lorraine Juliano Keller, Jeff King, Peter Pagin, Brian Rabern, Anders Schoubye, Wolfgang Schwarz, James Shaw, Alex Skiles, Scott Soames, Patrick Todd, Giuliano Torrengo, and anonymous referees for Synthese. It also benefited from feedback from audiences at the Edinburgh Philosophy of Language Reading Group, at the University of Milan, at the University of Stirling, and at the LOGOS Basic Workshop on the Unity and Individuation of Structured Propositions. Research related to this project was partially funded by a project FFI201680636P, supported by the Spanish Ministry of Economy and Competitiveness.
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