Propositional unity: what’s the problem, who has it and who solves it?

Abstract

At least since Russell’s influential discussion in The Principles of Mathematics, many philosophers have held there is a problem that they call the problem of the unity of the proposition. In a recent paper, I argued that there is no single problem that alone deserves the epithet the problem of the unity of the proposition. I there distinguished three problems or questions, each of which had some right to be called a problem regarding the unity of the proposition; and I showed how the account of propositions formulated in my book The Nature and Structure of Content [2007 Oxford University Press] solves each of these problems. In the present paper, I take up two of these problems/questions yet again. For I want to consider other accounts of propositions and compare their solutions to these problems, or lack thereof, to mine. I argue that my account provides the best solutions to the unity problems.

1 Introduction

At least since Russell’s influential discussion in The Principles of Mathematics, many philosophers have held there is a problem that they call the problem of the unity of the proposition. In a recent paper, I argued that there is no single problem that alone deserves the epithet the problem of the unity of the proposition.¹ I there distinguished three problems or questions, each of which had some right to be called a problem regarding the unity of the proposition; and I showed how the account of propositions formulated in my book The Nature and Structure of Content [2007 Oxford University Press] solves each of these problems.

In the present paper, I wish to take up two of these problems/questions yet again. For I want to consider other accounts of propositions and compare their solutions to these problems, or lack thereof, to mine.² I shall argue that my account provides the best solutions to the unity problems. I take this to be powerful support for my account. Indeed, my main motivation in elaborating and defending my theory of propositions in King (2007) was that I thought it could solve unity problems and that other theories couldn’t. I take it that at least to some extent I have made good on the former claim; it is now time to defend the latter.

First, then, let me state the two “unity questions” that will concern us. Let us for the moment suppose that propositions have constituents, so that the proposition that Michael swims has Michael and the property of swimming as constituents. A proposition so understood presumably is something distinct from a mere collection of its constituents. The collection of Anthony, the loving relation and Cleopatra is not a proposition. And indeed, two distinct propositions have just those constituents, which shows that the propositions in question are distinct from the mere collection of their constituents. Hence, the constituents of a proposition must be combined or “held together” in some manner in the proposition. Thus, our first unity question:

• UQ1: Exactly how are the constituents combined in a proposition such that the resulting combination is something distinct from a mere collection of its constituents?

As to our second unity question, propositions somehow manage to represent the world as being a certain way: they impose conditions that the world must meet in order that they be true. So propositions have truth conditions. But surely these are strange things to have. And so there should be some explanation as to how or why propositions manage to pull this off³:

• UQ2: How do propositions manage to have truth conditions and so represent the world as being a certain way? And how do they have the specific truth conditions they have?

Though I won’t argue the matter here, it seems to me that Russell had both these questions before his mind, perhaps not clearly distinguishing them, in his famous discussion in The Principles of Mathematics.⁴ Whether this is so or not, it seems to me that no serious theory of propositions can fail to address these questions, if only by way of giving some reason for rejecting the questions themselves.

It is perhaps worth noting that in principle there might be lots of ways to answer UQ1. Perhaps the constituents of propositions are combined by being members of an n-tuple that is the proposition or in some other set theoretic way. Indeed, it might appear that there are too many possibilities as to how propositional constituents are combined and that this is itself cause for worry. However, one must answer UQ1 in a way that allows one to answer UQ2.⁵ This is a strong constraint. Many prima facie possible answers to UQ1, including those just mentioned, make UQ2 unanswerable and so are to be rejected.

2 Naturalized propositions: the account in The Nature and Structure of Content

King (2007). The account discussed here will also make use of King (2009).

In order to sketch my account of propositions, let’s begin by looking at a simple sentence and its syntactic structure. Idealizing a lot, let’s consider the sentence ‘Michael swims’ with the syntactic structure as follows⁷:

Let’s call the syntactic relation that obtains between ‘Michael’ and ‘swims’ in the sentence here R. I call relations like R that lexical items stand in to form sentences sentential relations. Because it will be important later, I wish to point out that English speakers interpret R in a certain way: they take R to ascribe the semantic value of ‘swims’ to the semantic value of ‘Michael’. This is in part why the English sentence is true iff Michael possesses the property of swimming. Further, it is a contingent matter that R is interpreted by English speakers in the way it is in the sense that there might have been a language that included the sentence 1, but whose speakers took the sentence to be true iff Michael doesn’t swim. In so doing, they would have been interpreting R differently from the way English speakers do.

Before moving on, let me say a couple things about the idea that English speakers interpret R, and syntactic concatenation generally. That English speakers interpret R as ascribing the semantic value of ‘swims’ to the semantic value of ‘Michael’ consists in the fact that they spontaneously and unreflectively take 1 to be true iff Michael possesses the property of swimming. Similarly, when English speakers confront other cases of syntactically concatenated expressions, they spontaneously and unreflectively compose the semantic values of the concatenated expressions in characteristic ways. For example, when English speakers confront ‘red house’ they do something like conjoin the properties that are the semantic values of the two expressions; when they confront ‘every man’, they do something like saturate an argument of the relation expressed by ‘every’ with the property expressed by ‘man’, resulting in the (relational) property of properties that is possessed by a property A iff every man has A. That speakers interpret syntactic concatenation in the ways they do consists in the fact that they spontaneously and unreflectively compose the semantic values of the concatenated expressions in they ways described. Hence, this is how my talk of R above being interpreted by English speakers as ascribing the property of swimming to Michael should be understood. I’ll put the fact that speakers of English so interpret R by saying that R encodes ascription in English. I hasten to add that the idea that when speakers encounter syntactic concatenation, they spontaneously compose semantic values in certain ways is not some idiosyncratic idea of mine. Any semantic theory has to give rules that speakers employ for assigning semantic values or denotations to nodes in a syntactic tree based on the semantic values of the daughters of that node.⁸ That is all I am doing in saying that R encodes ascription. Assuming that we are doing extensional semantics for a moment, I could put the point about R encoding ascription in the following way: If α is a branching node and {β, γ} is the set of its daughters, where β is a name and γ is a predicate and || || is the function that assigns semantic values to expressions, then ||α|| = 1 if ||α|| possesses ||γ||. Otherwise, ||α|| = 0.

A further question here is why English speakers interpret syntactic concatenation in the small handful of ways they do. If, as I suspect, it turns out that speakers of different natural languages interpret syntactic concatenation in the same small handful of ways, a reasonable hypothesis is that this is part of our biologically endowed language faculty. That this is so would make language acquisition significantly easier. When encountering concatenated expressions, speakers would be hard wired to compose the semantic values of the concatenated expressions in a small handful of ways. Hence, speakers would only need to learn which way to do it in specific cases.

Returning to the main theme, in virtue of the existence of the English sentence 1, there is a two-place relation that Michael stands into the property of swimming. The relation is this: ___is the semantic value of a lexical item e of some language L and ___ is the semantic value of a lexical item e’ of L such that e occurs at the left terminal node of the sentential relation R that in L encodes ascription and e’ occurs at R’s right terminal node. Because we also wish to talk about the two-place relation that Michael stands into the property of swimming in virtue of the existence of the English sentence ‘I swim’ taken in a context with Michael as speaker, we should really suppose that in virtue of the existence of sentence 1, Michael stands in the following relation to the property of swimming (boldface indicates new additions): there is a context c such that ___is the semantic value in c of a lexical item e of some language L and ___ is the semantic value in c of a lexical item e’ of L such that e occurs at the left terminal node of the sentential relation R that in L encodes ascription and e’ occurs at R’s right terminal node.⁹ This relation, I claim, is the relation that holds Michael and the property of swimming together in the proposition that Michael swims. As such, I’ll call it the propositional relation of the proposition that Michael swims.

As I did in King (2007, 2009), I’ll call an object possessing a property, or n objects standing in an n-place relation, or n properties standing in an n-place relation or etc. a fact. Then the proposition that Michael swims is the fact consisting of Michael and the property of swimming standing in the two-place relation mentioned above: there is a context c such that Michael is the semantic value in c of a lexical item e of some language L and the property of swimming is the semantic value in c of a lexical item e’ of L such that e occurs at the left terminal node of the sentential relation R that in L encodes ascription and e’ occurs at R’s right terminal node.¹⁰ Note that this fact is distinct from the fact that is Michael possessing the property of swimming. The latter fact makes the former fact qua proposition true.

It should now be clear that I have explained the answer my account of propositions provides to UQ1. For we have specified what holds together the constituents of the proposition that Michael swims. Of course, similar remarks apply to other propositions and their constituents. One might complain here that I have just traded in one problem for another. I have answered the question of what holds the constituents of propositions together by specifying the relations that I claim do that job. But, one might complain, this leaves unanswered the general question of what holds together a relation and its relata when they are so related.¹¹ It is true that I haven’t answered this question, and in this sense I have traded in “the” question of the unity of the proposition (UQ1) for what we might call the question of the unity of the fact. My excuse is that I think that anyone who believes that things stand in relations and possess properties must face the question, if only to dismiss it, of what holds an object and a property together when the object possesses the property or what holds an n-place relation and n objects together when the objects are so related, etc. So I claim to have reduced the mystery of what holds propositions together to a mystery that all of us who think that objects possess properties and stand in relations need to face in any case. Reducing two mysteries to one seems like progress to me. Let’s now turn to UQ2.

I have claimed that the proposition that Michael swims is the fact described above consisting of Michael standing in the two-place relation mentioned to the property of swimming. But in general, such facts aren’t the sorts of things with truth conditions. Consider the fact consisting of me standing in the two-place sitting in front of relation to my computer. This fact, of course, obtains but it doesn’t have truth conditions. So how is it that the fact that I claim is the proposition that Michael swims does have truth conditions and so is the sort of thing that is true iff Michael possesses the property of swimming?

One of the most radical and provocative features of the account of propositions in King (2007, 2009) is the idea that it is something speakers do that endows the fact that is the proposition that Michael swims, and propositions generally, with truth conditions. This will explain why this fact has truth conditions, while many other facts do not. It will also provide our answer to UQ2.

Though the two-place propositional relation binding together Michael and the property of swimming is highly complex (e.g. it has the sentential relation R of 1 as a component or “part”), let’s suppress that complexity for a moment and simply focus on the idea that on the present view the proposition that Michael swims is a fact consisting of Michael standing in the (complex) two-place propositional relation to the property of swimming. We can represent this fact/proposition thus: (where the picture on the left is Michael; that on the right is the property of swimming and the branching tree structure is the propositional relation). Now one way this fact could have truth conditions is if speakers interpreted the propositional relation here as ascribing the property of swimming at its right terminal node to Michael at its left terminal node. Then the fact would be true iff Michael possessed the property of swimming. Recall that the sentential relation of the sentence 1 is interpreted by English speakers as ascribing the property that is the semantic value of ‘swims’ to the semantic value of ‘Michael’, which we expressed by saying that the sentential relation R encodes ascription in English. What we are now saying is that if the propositional relation of 1P were interpreted as ascribing the property at its right terminal node to the individual at its left terminal node, and so itself encoded ascription, the fact/proposition would have truth conditions. Encoding ascription understood in this way, note, is a relational property of the propositional relation itself: the property of being interpreted as ascribing what is at its right terminal node to what is at its left terminal node. So henceforth, let’s understand the proposition that Michael swims to be the fact described above, taken together with the propositional relation having the relational property of encoding ascription (this means that the fact that is the proposition that Michael swims is a slightly “larger” fact than we have taken it to be to this point, since it now includes the propositional relation possessing a certain relational property). In so doing, we can explain why the proposition/fact has truth conditions and so give a preliminary answer to UQ2.

But the answer is still preliminary and unsatisfying until we explain what constitutes our interpreting the propositional relation of 1P as ascribing the property of swimming to Michael. What exactly makes it the case that we so interpret the propositional relation? Let me sketch my explanation, which comes in two steps.

Call the fact that I claim is the proposition that Michael swims FAST. What we first need to explain is why it is FAST, rather than some other fact, whose propositional relation we interpret as ascribing the property of swimming to Michael so that it is true iff Michael swims. I believe that there are a number of conditions a fact must satisfy in order to be the one whose propositional relation we so interpret, including being a fact consisting of Michael standing in a two-place relation to the property of swimming.¹² But a crucial condition is that we must be able to make sense of the idea that speakers have some sort of cognitive connection to the fact in question. Surely it would be bizarre to hold that speakers are interpreting the propositional relation of a fact in a certain way, where we claim that they have no cognitive connection or access to it. Further, since we want speakers of different languages to in some cases grasp the same proposition, we must be able to make sense of speakers of different languages interpreting the propositional relation of the same proposition/fact. And this requires them to be cognitively connected to the same fact in order that we can make sense of their interpreting its propositional relation.

In addition, it seems reasonable to hold that the required cognitive connection to the fact that is the proposition that Michael swims comes about in virtue of speakers deploying sentences of their languages. For by the time speakers deploy sentences of their languages, they presumably must have propositional attitudes whose contents are the semantic contents of the sentences they are using. But this means that propositions must exist by that time. That in turn means that speakers must be interpreting the propositional relations of the facts that are propositions in certain ways by that time. And in turn, this means that speakers at that time must be cognitively connected to the relevant facts. The most straightforward explanation of why speakers have cognitive connections to the facts that are propositions as soon as they deploy sentences of languages is that by deploying sentences of their languages they thereby have cognitive access to the relevant facts.¹³

To summarize, then, for a fact to be the proposition that Michael swims, we must be able to make sense of the idea that speakers of different languages all have cognitive access to it and do so in virtue of deploying the relevant sentences of their languages. I’ll now argue that FAST is preeminently a fact of this sort.

To see this, note first that sentences (types) themselves are likely facts in my sense. For it seems plausible that word types are properties and hence that sentences are properties standing in sentential relations. Obviously, speakers of e.g. English and German have cognitive access to the facts that are sentences in their languages, like ‘Michael swims’ and ‘Michael schwimmt’. More importantly, as a result, they also have access to the following “interpreted sentences”: These are just the sentences, together with the semantic relations the lexical items bear to their semantic values (including the semantic values themselves—these relations are represented by vertical lines connecting ‘Michael’ to Michael and ‘swims/schwimmt’ to the property of swimming). Hence these interpreted sentences are just “bigger” facts than the sentences themselves in virtue of including the semantic relations between lexical items and their semantic values, as well as the semantic values themselves. We can describe the fact 1 IE as follows: there is a context c such that Michael is the semantic value of ‘Michael’ in c, which occurs at the left terminal node of the syntactic relation R that in English encodes ascription and the English word ‘swims’ occurs at the right terminal node of R and has as its semantic value in c the property of swimming.¹⁴ It seems to me that by having cognitive access to the sentences ‘Michael swims’ and ‘Michael schwimmt.’ and being competent with them, English and German speakers thereby have cognitive access to the facts that are the interpreted sentences 1IE and 1IG respectively.

Let’s say that the fact of object o possessing property P is a witness for the fact of there being P’s (i.e. the fact of the property P having the property of being instantiated); similarly for the fact of o bearing R to o’ and the fact of there being an x and y such that xRy, and so on. The facts 1IE and 1IG are both witnesses for the fact that I claim is the proposition that Michael swims, namely, FAST. FAST is the result of “existentially generalizing” on the words in 1IE/1IG and the languages involved.

The crucial point for current concerns is that that having cognitive access to a witness for a fact is a way of having cognitive access to the fact witnessed: having cognitive access to the fact of o possessing P is a way of having cognitive access to the fact of there being P’s. But then having cognitive access to 1IE or 1IG above suffices for having cognitive access to FAST, the fact I claim is the proposition that Michael swims. Thus we can see how English and German speakers can all have access to FAST in virtue of deploying the relevant sentences of their languages. Hence, we are in a position to make sense of their interpreting its propositional relation as encoding ascription, and so make sense of the claim that it is FAST whose propositional relation we so interpret.

But even if we are now convinced that it is FAST’s propositional relation that we interpret as ascribing the property of swimming to Michael, we need to say what constitutes our so interpreting it. That is, what is it we do that amounts to our so interpreting it? It is simply that we compose the semantic values at the terminal nodes of the propositional relation in the way we do. In the end, this is just a reflex of the sentential relation R having the semantic significance it does. When we entertain a proposition, we work our way up the propositional relation, combining semantic values to yield new semantic values for further combining. Obviously we must combine or compose those semantic values in some way. In the case of FAST, were we to do anything other than ascribe the property of swimming to Michael, we would not be combining semantic values in a manner that is consistent with the way we interpret the syntax of the sentence 1. It just isn’t coherent to interpret the sentential relation R as ascribing the semantic value of ‘swimming’ to the semantic value of ‘Michael’, while composing the semantic values Michael and the property of swimming in some other way as one moves up the propositional relation of FAST. Semantic values only get composed once in understanding the sentence 1, and hence entertaining the proposition FAST. We either do so in the way dictated by the way we interpret the sentential relation R or not. To do so in the way dictated by our interpretation of the sentential relation R just is to interpret the propositional relation as encoding ascription.

To summarize, FAST has truth conditions because speakers interpret its propositional relation as ascribing the property of swimming to Michael. The account of what constitutes speakers doing this is in two steps. First, reason was given for thinking that it is FAST’s propositional relation that gets interpreted as ascribing the property of swimming to Michael. Second, an account was given of what so interpreting FAST’s propositional relation consists in. There are facts closely related to FAST that probably satisfy these conditions as well, so here we would have to claim that FAST is the most eligible to be the proposition that Michael swims of the facts satisfying all relevant conditions.¹⁵ This completes the answer to UQ2.

Finally, I have already mentioned a provocative positive feature of my account of propositions: on this account, it is something speakers do that endows propositions with truth conditions. There is a corresponding negative feature of my account: the claim that propositions cannot be things that by their very natures and taken independently of minds and languages have truth conditions and so represent the world as being a certain way. There ought to be some explanation as to how propositions manage to have truth conditions. My account provides such an explanation. If you hold that propositions are just the kinds of things that independently of minds and languages have truth conditions, I don’t see that you can provide any explanation for how/why they manage to do this other than to say it is a primitive feature of propositions. Note that the issue is not one of whether propositions have truth conditions intrinsically.¹⁶ Propositions as I understand them have their truth conditions intrinsically: the fact that is the proposition that Michael swims includes its propositional relation having the relational property of encoding ascription. As such, any duplicate of this fact will have the same truth conditions it does and so the fact/proposition has its truth conditions intrinsically. But on my account there is an explanation of how it has them by way of things speakers did to make it so. This is why I say that my account is one of naturalized propositions. By contrast, as I’ve said, I cannot see how any account that holds that propositions have truth conditions independently of minds and languages can provide such an explanation. But then, it seems to me, on such accounts, that propositions have truth conditions is utterly mysterious.

3 Possible worlds accounts of propositions

Let’s now turn to accounts of propositions that take them to be sets of worlds or the characteristic functions of such sets: functions from worlds to T or F. I’ll call such accounts of propositions worlds accounts. For the sake of definiteness, I’ll consider Stalnaker’s version of this view, but I believe the points I am going to make apply quite generally to other versions.

The first thing I want to ask about worlds account is: which is it? Are propositions sets of worlds or characteristic functions of such sets? These are different things and something must be said about which are the propositions (or perhaps they both are?). So right off, worlds accounts are saddled with a Benacerraf problem.

Waiving this concern, the second thing I want to ask is: on the functions version of the view, what are T and F, the values of the relevant functions? Stalnaker (1984) answers:

A proposition is a function from possible worlds into truth values…. There are just two truth values—true and false. What are they: mysterious Fregean objects, properties, relations of correspondence and noncorrespondence? The answer is that it does not matter what they are; there is nothing essential to them except that there are exactly two of them…a proposition may be thought of as a rule for selecting a subset from a set of possible worlds. The role of the values true and false is simply to distinguish the possible worlds that are members of the selected subset from those that are not.¹⁷

This sounds to me like Stalnaker takes the idea that propositions are sets of worlds to be fundamental, and then thinks that you can talk about propositions as functions from worlds to any pair of exactly two things, which latter two things are used by us to say which worlds are in the set that is the proposition and which are not. In any case, Stalnaker is very clear that he does not view true and false as “mysterious Fregean objects” or etc. Any two things will do. Below I’ll criticize both versions of worlds accounts (set vs. characteristic function).

Turning now to UQ1, worlds accounts will be quick to dismiss this question. The proposition that Michael swims does not have as constituents Michael and the property of swimming, so there can be no question here of how they are combined in the proposition. Perhaps worlds accounts raise other questions, but they are right by their own lights to dismiss this one. I myself think that not having Michael (or a Michael-sense, etc.) be a constituent of the proposition that Michael swims is counterintuitive and so a strike against the worlds account. But I am prepared to admit that this does not by itself carry a lot of weight.

Turning now to UQ2, let’s ask whether the worlds account can answer it. First, let’s consider the functions version: propositions are functions from worlds to exactly two arbitrary elements, say 1 and 0. But why/how would such a function have truth conditions or represent the world as being a certain way? Certainly, there are lots of functions from a set of elements to {0,1} that don’t have truth conditions. But then why do functions from a set of worlds to {1,0} have truth conditions? Certainly we could view such functions as having truth conditions. This would then be a matter of us interpreting such functions in a certain way. However, worlds accounts don’t generally seem to hold that we endow propositions with their truth conditions by interpreting them in certain ways. (Of course if some advocate of worlds accounts were to embrace the view that we endow functions from worlds to {0,1} with truth conditions by interpreting them in certain ways, the onus would be on such a theorist to explain what our so interpreting them consists in. I have a hard time seeing what that story would be; but I would then have to compare her story to mine. As might be imagined, I think I am going to get the better of that comparison.) And there just isn’t anything in the functions themselves, taken independently of minds and languages, that determines that they have truth conditions.

Further, it does not seem like the functions taken independently of minds and languages determine specific truth conditions either. If a function maps w to 1, is it true or false at w? Recall that Stalnaker thinks that it doesn’t matter what T and F are so long as there are exactly two of them. Ok, let’s use L.A. and New York instead. If a function maps w to L.A., is it true or false at w? Surely, it is hard to take this question seriously—as a question that has some determinate answer in the absence of stipulation. I conclude that the functions version of the worlds account doesn’t have an answer to UQ2: it doesn’t explain why propositions have truth conditions in general, nor why a specific proposition has the truth conditions it has.

Let’s now consider the set version of the worlds account: propositions are sets of possible worlds. Lots of sets presumably don’t have truth conditions. So why do sets of worlds have truth conditions? Again, we could view them as having truth conditions. But as before, this would be a matter of us interpreting them in certain ways. However, again, defenders of worlds accounts don’t seem to hold that we endow propositions with truth conditions. (And again I claim that if the worlds theorist tries to tell a story as to what our interpreting sets of worlds consists in, it will be inferior to my story about how we endow the relevant facts with truth conditions.) Finally, again, it just doesn’t seem that there is anything in sets of worlds themselves, taken independently of minds and languages, that determines that they have truth conditions.

Further, as with the functions version, there doesn’t seem anything about sets of worlds themselves, taken independently of minds and languages, that determines specific truth conditions. Consider a set of worlds S. If w is in S, is S true at w? Why not say that it is false at w? What about S determines that if w is in it, S is true at w instead of false at w? Again, it is hard to believe that this question has any non-stipulative answer. I conclude that the sets version of the worlds account has no answer to UQ2: again it neither explains why in general propositions have truth conditions nor why a specific proposition has the truth conditions it has.

Hence, contrary to what I have sometimes heard in casual conversation, the worlds account of propositions does have a problem with the unity of the proposition: neither version of the worlds account has a plausible answer to UQ2.¹⁸

4 Propositions as world properties

Some philosophers have wanted to identify propositions with properties of possible worlds.¹⁹ Call such properties world properties. I’ll call propositions-as-world-properties views world properties accounts. World properties accounts come in different versions, depending on what views of properties and possible worlds are adopted and which world properties are claimed to be propositions. Much of what I’ll have to say about world properties accounts will be neutral as between these different versions.

So how will world properties accounts answer UQ1? Here differences in views about properties will make a difference. On some views of properties, properties like disdaining George W. Bush are complex and have as components the disdaining relation and George W. Bush (I use the term ‘components’ for the “parts” of complex properties and facts, reserving the word ‘constituents’ to talk about constituents of propositions). On views of this sort, a world property like being such that George W. Bush is a fool will have George W. Bush and the property of being a fool as components. These will also then be the constituents of the world property qua proposition. On such a view, the answer to UQ1 is that since propositions are just complex (world) properties, their constituents are held together however components of complex properties are held together in those complex properties. As with my own answer to UQ1, some might complain that the question of what holds together the constituents of propositions has simply been traded in for the equally difficult question of what holds together the components of complex properties. But I think the world property theorist can respond along the lines I did. Anyone who thinks complex properties have components in the way suggested is going to have to face the question of how the components are held together in the complex property. So the world properties theorist can claim to have reduced the mystery of what holds propositions together to a mystery that anyone who believes in complex properties with components must address anyway.

On the other hand, on views of properties where properties like disdaining George W. Bush do not have George W. Bush and the disdaining relation as components, world properties presumably won’t have components either.²⁰ Hence, presumably it would be denied that world properties qua propositions such as being such that George W. Bush is a fool have George W. Bush and the property of being a fool as constituents. Thus, the advocate of this sort of world properties account will simply dismiss UQ1 as a bad question. By her lights at least, she is right to do so.

Hence, I think the versions of world properties accounts mentioned can provide some response to UQ1. Let’s now think about UQ2.

What explanation can world properties accounts offer of the fact that propositions have truth conditions and that specific propositions have the truth conditions they have? Well, on world properties accounts what it is for a proposition qua property to be true at a world is for the world to instantiate the property. So from the standpoint of such accounts, the question of why propositions are the kinds of things that are true and false (at worlds) is the question of why properties (of worlds) are the kinds of things that are instantiated and not instantiated (by worlds). At first, the latter sounds like a very hard question to answer. In general, given properties of some kind of entity K, what in the world could be said about why those properties are the kinds of things that are instantiated and not instantiated by K’s? What could be said about why having unit charge is the kind of thing that is instantiated by electrons and not instantiated by many other things? As is often the case in philosophy, I think a sensible thing to say here is that the question seems so difficult because it isn’t a good question. It seems reasonable to think that properties generally just are the kinds of things that are instantiated and not instantiated by various things. This is just a primitive, basic feature of properties. There is no further explanation or account as to why/how they are things that are instantiated and not instantiated beyond saying that’s the kind of things they are. So, the world properties advocate responds to UQ2 by rejecting it as a bad question.²¹ Surely this is sometimes the right thing to say about philosophical questions and the advocate of the world properties account insists that this is one of those times. Such a response seems to me not unreasonable.²²

So it seems that the world properties account has defensible responses to both UQ1 and UQ2.²³ Of course, those responses are only plausible to the extent that it is plausible to identify propositions with world properties and truth with instantiation. The problem for the world properties theorist is that these identifications are not plausible, as I will now argue.

First, properties, even properties of worlds like being such that snow is white, just don’t seem to be things that are true or false. To say that they are true or false seems like some sort of category mistake. Perhaps someone would respond that despite this, the property in fact is true. They might add that when we consider the claim that snow is white, we take it to be true; and the ‘that’ clause here designates the property in question. So we do take properties like being such that snow is white to be true and false. The problem with this is that properties are most transparently expressed by predicates. If propositions really are properties as the world properties theorist claims, why when we consider the predicate ‘being such that snow is white’ that allegedly expresses the proposition in question are we not inclined to say that it expresses something true or false? It looks like the world properties theorist will have to claim that when we encounter a proposition qua property as the thing designated by a ‘that’ clause, we treat it as something that is true or false. But when we encounter it as the thing expressed by a predicate, we don’t do so. This is made all the more peculiar by the fact that, as indicated above, it is predicates that canonically and transparently express properties. Hence, when we encounter a proposition qua property as the thing expressed by a predicate, we will be more aware that it is a property. If propositions are properties, why when we encounter them via the linguistic devices that most make clear that they are properties do we precisely not want to treat them as things that are true and false? Why must we encounter propositions via linguistic devices that disguise the fact that they are properties (e.g. ‘that’ clauses) in order to treat them as things that are true and false? I can’t see how the advocate of the world properties account can answer this question.

Second, there are conjunctive propositions, negated propositions, and disjunctive propositions.²⁴ If propositions are properties as the world properties theorist claims, there must be conjunctive, negated and disjunctive properties.²⁵ However, as is well known, many who believe in properties do not think there are conjunctive, and especially negated and disjunctive, properties.²⁶ One reason for this is that it is widely thought that when two things both possess the same “real” property, they should resemble each other or have a common nature; but common possession of negated and disjunctive properties does not in general make for similarity or possession of a common nature. Hence, because the world properties account commits one to negated and disjunctive properties, it can only be adopted by the most promiscuous in their views about what properties there are. I would have hoped that a theory of propositions could remain neutral on this question.

A third and final objection concerns the world properties theorist’s identification of truth and instantiation for propositions.²⁷ It is generally thought that in having truth conditions, a proposition in some sense specifies conditions that have to be met by a world for the proposition to be true there. Consider a proposition P specifying such conditions and a world w that meets them. Surely, we want to say in such a case that P is true at w because w is a certain way. Indeed, this seems like a truism. However, one would also think that a thing’s possessing an intrinsic property generally explains why the thing is a certain way. That I possess the property of being 6 feet tall explains why I am a certain way. Possession of the property constitutes my being a certain way. Now surely the same should be true of worlds possessing intrinsic properties: that the world possesses an intrinsic property constitutes its being a certain way. Suppose a world w possesses the property being such that snow is white. This is an intrinsic property of w.²⁸ Then just as in other cases, that should explain why w is a certain way. However, the world properties theorist claims that w possessing or instantiating a property like being such that snow is white is just this property qua proposition being true at w. But then on this account, we should say w is a certain way, because the property/proposition being such that snow is white is true at w (i.e. is instantiated at w). Unfortunately, this precisely reverses what we said was the proper order of explanation mentioned above: the proposition that snow is white is true at w because w is a certain way. Surely, this is the right order of explanation. Hence, that the world properties account has it that w is a certain way because a proposition is true there is a strong reason for rejecting the account.

In summary, then, by identifying propositions with properties of worlds and truth with instantiation, the world properties account of propositions is able to give prima facie reasonable answers to UQ1 and UQ2 and so appears not to have problems with the unity of the proposition. However, these answers are only plausible to the extent that the above identifications are plausible. I’ve argued that they are not plausible. Indeed, each of the difficulties I’ve highlighted suggests either that propositions just aren’t like properties or that truth just isn’t like instantiation. So I conclude that the world properties account cannot successfully answer UQ1 and UQ2, since the superficially reasonable answers the account offers presuppose the implausible identifications mentioned.

5 Soames’ “cognitive realist” account of propositions

In discussing the account of naturalized propositions in King (2007), I mentioned a radical negative feature of the account, which was novel to this account at the time of writing. The view that propositions are things that are representational, and so have truth conditions, by their natures and independently of minds and languages was rejected as ultimately mysterious. In a recent series of works,²⁹ Scott Soames follows King (2007) in embracing this negative point. Like me, Soames thinks that the fact that propositions are representational must ultimately be explained in terms of the representational capacities of agents. As a result, I view Soames as in the same camp as I am in and so am sympathetic to his approach. However, Soames’ positive account of how/why propositions have truth conditions differs in important ways from mine; and I believe the account has serious difficulties when it comes to answering UQ1 and UQ2.

Soames begins with the notion of the mental act of predication, which he takes to be primitive. However, by way of illustration, if an agent perceives an object o as red, and so has a perceptual experience that represents o as being red, the agent predicates redness of o. Similarly, if an agent “thinks of” o as red,³⁰ or “form[s] the nonlinguistic perceptual belief that o is red”.³¹ For Soames, predicating redness of o does not amount to believing that o is red. To believe that o is red, one must predicate redness of o and do something like endorse the predication. Unfortunately, it is hard to say precisely what predicating amounts to since the notion of predicating is primitive for Soames.

I should note in passing that the claim that there is some one primitive mental act, predicating, involved in each of: understanding the sentence ‘o is red’, thinking of o as red and perceiving o as red strikes me as highly speculative and quite dubious. However, I won’t dwell on this point, as we are concerned with Soames’ answers to UQ1 and UQ2 and not other difficulties with his view.

An agent predicating redness of o is an event token. Of course there may well be many event tokens of agents predicating redness of some object o by an agent perceiving it as red, an agent thinking of it as red and so on. Soames claims that the proposition that o is red is the event type of an agent predicating redness of o. Other more complex propositions are identified with events types of agents performing sequences of primitive mental acts.³² Soames doesn’t provide an account of what events (types or tokens) are. But since he thinks that propositions are structured entities with constituents, he must think that event types are structured entities with constituents. Presumably, the proposition that o is red—the event type of an agent predicating redness of o—has o and redness as constituents.

Let’s see how Soames answers UQ1. One might think that Soames doesn’t take UQ1 to be a good question, and so doesn’t answer it, given that he criticizes Russell (1903) and King (2007) for taking it seriously. Soames (2010b) writes

The error in both accounts [King (2007) and Russell (1903)] comes from taking the question “What holds the constituents of a proposition together?” too seriously. The misnamed problem of propositional unity isn’t that of making one object out of many. Sets, sequences, and trees are each single things with multiple constituents of various sorts. The reason they aren’t propositions isn’t that their constituents keep falling out. They aren’t propositions because they don’t represent anything as being any particular way. The real problem for which we have, as yet, no answer is “How is it that propositions are able to represent the world, and so have truth conditions?”³³

Setting Russell (1903) aside, Soames misrepresents King (2007) here. Soames suggests in this quotation that King (2007) took the problem of the unity of the proposition to be (just) the question of what holds the constituents of propositions together. But, as I suggested at the outset, King (2007) makes clear that the problem he is concerned with is to give an answer to the question of what holds the constituents of propositions together such that the resulting account allows us to explain how/why propositions have truth conditions.³⁴ In short, King (2007) is an attempt to answer UQ1 and UQ2. And the question that Soames says is the important one in the quotation above is just UQ2. So King (2007) addresses the question that Soames says is “the real problem”, contrary to what the quotation suggests.³⁵

In any case, given Soames’ remarks here it is rather surprising that he gives an answer to UQ1, if only implicitly, and that the answer is quite similar in kind to that of King (2007). Recall that King (2007) specifies the relations that bind together the constituents of propositions. The result is that propositions are what I call facts. Hence, a quick version of my answer to UQ1 is that the constituents of propositions are held together in propositions the way the components of facts are held together in facts. Soames identifies propositions with event types. As we saw above, event types presumably have constituents on Soames’ view. Further, it appears that different event types could have the same constituents. This presumably is the result of the events’ constituents being combined differently in the event types. For Soames, then, the answer to UQ1 is that the constituents of propositions are held together in propositions the same way the constituents of events are held together in events.³⁶

Soames gives no account of how the constituents of events are held together, and so one might object to Soames’ answer to UQ1 here on the grounds that we really don’t know how propositions are held together, and hence we really don’t have an answer to UQ1, until we are given an account of how the constituents of events are held together. But I think that Soames can respond here the same way I and advocates of the world properties account responded to similar objections. Many philosophers believe that there are events and that they have constituents. Hence, any such philosopher must confront the question of what holds the constituents of events together, if only to dismiss it. So Soames can claim to have answered UQ1 in such a way that it leaves us with a question that many of us would have had to face in any case.

Turning now to UQ2, how does Soames explain the fact that propositions have truth conditions? In addressing this question, Soames (2010a) writes:

Also unlike the Frege-Russell account, the cognitive- realist conception [Soames account] doesn’t face the metaphysical pseudo- problem of “the unity of the proposition,” which—though traditionally described as that of explaining how the constituents of propositions “hold together”—serves only to mask the real problem of explaining how propositions can be representational, and so have truth conditions…. The key is to reverse our explanatory priorities. Propositions, properly conceived, are not an independent source of that which is representational in mind and language; rather, propositions are representational because of their intrinsic connection to the inherently representational cognitive events in which agents predicate some things of other things. ³⁷

So it appears that Soames’ explanation (in boldface) of why propositions have truth conditions involves two steps. For illustrative purposes let’s stick with the proposition that o is red. First, it is claimed that event tokens of agents predicating redness of o are “inherently representational” and so “inherently” have truth conditions. They are true iff o is red. Second, the event type of an agent predicating redness of o, which Soames claims is the proposition that o is red, is “intrinsically connected” to the aforementioned event tokens that have truth conditions inherently; and so the event type itself has truth conditions. I’ll argue that Soames’ explanation here as to why propositions have truth conditions fails at both steps.

The first step of Soames’ explanation is the claim that event tokens of agents predicating redness of o inherently have truth conditions. However, Soames gives no argument for this claim nor does he explain how/why such event tokens have truth conditions inherently. Further, the claim that the event tokens in question inherently have truth conditions is just mysterious. I can see how event tokens could have truth conditions in virtue of agents interpreting them in certain ways. But how could an event token inherently have truth conditions? How could an event token have truth conditions by its very nature? That seems as mysterious as the claim that propositions are sui generis abstract entities that have truth conditions by their natures and independently of minds and languages, which I and Soames himself both reject as unintelligible. Given that it is a mystery how event tokens could have truth conditions inherently, in the absence of any argument for the claim that the event tokens of agents predicating redness of o inherently have truth conditions or any explanation of how this could be so, we should reject the claim.

Second, what evidence there is suggests that the event tokens in question do not have truth conditions. Suppose Vicky is perceiving o as red and that this event token is quite salient to us. Suppose o is in fact red. If I say nodding at Vicky ‘What is occurring is true.’ or ‘The event of Vicky seeing o as red is true.’, this just sounds like a category mistake. (Indeed, the second sounds like a misguided attempt to say that the event occurred.) However, if Soames is right these sentences are true. And any attempt to predicate truth or falsity of an event token of an agent predicating (in Soames’ sense) redness of o sounds like a category mistake.³⁸ But if Soames is right that such event tokens are inherently things with truth conditions, why would predicating truth or falsity of them sound so anomalous as to seem like a category mistake?³⁹ I conclude that what evidence there is suggests that event tokens in which agents predicate redness of o do not have truth conditions inherently.

In summary, Soames give no argument for the claim that event tokens of an agent predicating redness of o inherently have truth conditions nor does he explain how this could be so. Further, not only is the claim mysterious, but what evidence there is suggests such event tokens do not have truth conditions. Hence, the first step in Soames’ explanation of how/why propositions have truth conditions fails. This, I believe, is the most serious flaw in Soames’ attempt to answer UQ2.⁴⁰

However, the second step of his answer to UQ2 fails as well. Recall that the second step was to say that the event type of an agent predicating redness of o, which recall Soames identifies with the proposition that o is red, itself has truth conditions because of its “intrinsic connection” with event tokens of agents predicating redness of o, which inherently have truth conditions. Of course, we have seen reason to reject the claim that such event tokens do inherently have truth conditions. But even if we were to grant that they did, why would this insure that the event type of which they are tokens has truth conditions? Perhaps some properties had by all tokens of an event type are had by the type (e.g. perhaps event tokens of Shane skiing and the event type both have Shane as a constituent). But there are clearly properties had by all event tokens of a given event type that are not properties of the type. For example, all event tokens of an agent predicating redness of o occur at some particular time. But it doesn’t seem as though the event type occurs at some particular time. So Soames needs to give us some reason for thinking that the event type has truth conditions because of being “intrinsically connected” to its tokens, all of which he claims have truth conditions inherently. But no reason has been given.

In addition, the reason Soames gives for thinking that event tokens of an agent predicating redness of o represent, and so have truth conditions, doesn’t apply to event types. For Soames, the reason an event token of predicating redness of o represents o as being red is that predication is occurring: the agent predicates redness of o.⁴¹ According to Soames, since each such event token involves predication and so representation, the event token itself represents o as being red by predicating redness of o and so is true iff o is red.⁴² However, the event type of an agent predicating redness of o doesn’t predicate redness of o. Compare: the event type of an agent hitting Alan doesn’t hit Alan.⁴³ But then this is reason for thinking that by Soames’ lights, event types lack precisely what is required for representation and so having truth conditions.

Further, as was the case with event tokens of agents predicating redness of o, what evidence there is suggests that the event type of agents predicating redness of o does not have truth conditions. To see this, note first that we can speak of event types as occurring or happening. Thus, if I see a pedestrian get hit by a car at the corner of Amsterdam and 87th, I can say ‘That happens every week.’ and mean that the event type of a pedestrian getting hit at Amsterdam and 87th has instances every week. So the demonstrative ‘that’ here picks out an event type.⁴⁴ Similarly, for locutions like ‘what just happened’ (e.g. my electricity goes off and I say ‘what just happened happens every day at this time.’). So by indicating a token of an event type and using expressions like those just mentioned, I can talk about the event type. And by talking about an event type happening, I am talking about its having instances.

Now according to Soames, entertaining a proposition is simply tokening an event of the type that is the proposition (by performing the acts of predication involved in tokening the type).⁴⁵ So suppose I ask Vicky to entertain the proposition that arithmetic is incomplete, if consistent, and she complies. Hence she tokens an event that is of the type that is the proposition that arithmetic is incomplete, if consistent (roughly, by predicating being incomplete if consistent of arithmetic). I now say ‘What just occurred is true.’ This, again, is bizarre to the point of being incoherent. But if Soames is right, this should sound fine and be true, at least on one reading. For the expression ‘what just occurred’ should be capable of being used to talk about the event type that Soames claims is the proposition that arithmetic is incomplete if consistent. And of course since Godel proved this proposition, it is true.

Finally, evidence similar to the above strongly suggests that the event types that Soames identifies with propositions are not propositions.⁴⁶ As before, imagine that we ask Vicky to entertain the proposition that arithmetic is incomplete if consistent and she complies by tokening the event type that Soames claims is the proposition. Again, we should be able to talk about the event type using the expression ‘what just happened.’ I say ‘What just happened was proved by Godel.’ Again, this is incoherent and surely is a category mistake. But again, if Soames were right this should be true: Godel did prove the proposition that arithmetic is incomplete if consistent. Similar remarks apply to predicating of the relevant event types many things that can sensibly be predicated of the propositions Soames identifies with these event types.⁴⁷ Further, if we predicate of propositions properties that are had by the event types that Soames claims are propositions, again the predications are bizarre to the point of incoherence: ‘What Godel proved occurred twice today.’; ‘What Godel proved just happened.’; ‘What Godel proved occurred all over the world today.’⁴⁸

All of this strongly suggests that the relevant event types do not have truth conditions, and are not propositions contra Soames.

6 Conclusion

I began by claiming that contrary to the way many philosophers talk, there is no single question or problem that alone merits the title of the problem of the unity of the proposition. I claimed that there are at least two questions, UQ1 and UQ2, that deserve that appellation. Further, a successful theory of propositions should provide some answer to both questions or provide reasons for dismissing them. I claimed that my account of propositions offers promising answers to both questions and I sketched those answers. I then argued that all other theories of propositions considered stumble on these questions in one way or another. Worlds accounts fail to answer UQ2. World properties accounts prima facie seem to provide reasonable answers to both questions, but only do so by the implausible identifications of propositions with world properties and truth with instantiation. Soames’ cognitive realist account fails to successfully answer to UQ2. As I said at the outset, a main motivation for the view of propositions outlined in King (2007) was that it could successfully answer UQ1 and UQ2 and that other theories could not. I hope to have made a good case for these claims here.⁴⁹