First-Person Propositions

1. Introduction

A central dispute in discussions of self-locating attitudes concerns which of the following two accounts we should accept:¹

propositionalism

Attitude relations such as belief and knowledge are two-place relations between a subject and a proposition, an abstract object that does not vary in truth value across individuals.

proprietism

Attitude relations such as belief and knowledge are two-place relations between a subject and a property, an abstract object that may vary in truth value across individuals.

Lewis famously argued that self-locating attitudes should lead us to reject propositionalism in favour of proprietism, while Stalnaker argued, to the contrary, that the phenomenon of self-locating attitudes does not motivate rejecting propositionalism.² In what follows, we’ll argue that there are good reasons to prefer propositionalism to proprietism, and we’ll show that there are natural accounts of self-locating attitudes that one can provide by appeal to the propositional relations of belief and knowledge.

In §2, we provide our primary argument against proprietism and in support of propositionalism. As a generic label, we’ll refer to the objects of belief and knowledge as contents. Given propositionalism contents are propositions, while given proprietism contents are properties. In this section, we show that, given proprietism, there is a large class of cases in which it is impossible for one agent to know, of any content, that their believing it would suffice for agreement with another agent’s belief. We argue that this implies that there are many cases in which the proponent of proprietism incorrectly predicts that a given agent’s beliefs must be in principle incommunicable to another agent. These sorts of limitations are not, however, imposed given propositionalism. Since we take it that the limitations on successful communication imposed by proprietism are not, in fact, witnessed, this seems to us to provide a strong argument against proprietism and in favour of propositionalism.

In §3, we develop two versions of propositionalism and consider their respective merits. While we think that there is good reason to endorse propositionalism, and so good reason to deny that belief and knowledge are relations between an agent and a property, we argue that there is also good reason to maintain that there are important psychological relations—which we call doxastic and epistemic self-ascription respectively—whose objects are properties. Our two versions of propositionalism provide two different accounts of how the propositional relations of belief and knowledge are related to the proprietal relations of doxastic and epistemic self-ascription. According to our first account, for an agent $x$ to doxastically (epistemically) self-ascribe a certain property $p$ just is for them to believe (know) the de re proposition that $x$ has property $p$, while, according to the second account, for an agent $x$ to doxastically (epistemically) self-ascribe a certain property $p$ just is for them to believe (know) a particular de dicto proposition. We argue that, on balance, the latter provides a more attractive propositionalist account of self-ascription.

2. Agreement and Communication

One common argument in favor of propositionalism is that proprietism yields an inadequate account of interpersonal cognitive relations like agreement and communication.³ In this section, we’ll argue that propositionalists are right about these shortcomings of proprietism. Indeed, we’ll argue that the problem of providing an adequate proprietist account of agreement and communication is, in fact, much more severe than has been appreciated.

We begin by stating certain assumptions that we will hold fixed through the remainder of the paper.

First, we’ll assume that propositions form a complete, atomic Boolean algebra. We’ll call the atoms of this algebra “world propositions” or “worlds” for short. Any proposition that is not an atom may be represented as a set of worlds. Note that, given this view, a proposition is necessary, in the broadest sense, just in case it is identical to the unique proposition that is true at all worlds. We’ll assume a standard S5 logic for this broad form of necessity. We’ll also assume the necessity of identity; given S5, this implies the necessity of distinctness.

Second, we’ll assume that properties also form a complete, atomic Boolean algebra. The atoms of this algebra can be represented by pairs $⟨w,a⟩$ consisting of a world $w$ and an individual $a$ that exists at $w$. Sometimes we’ll refer to such atoms as “centered-possibilities”. We’ll assume that it is non-contingent which individuals exist, and so we take the class of atoms to be simply the set of pairs $⟨w,a⟩$ such that $w$ is a world and $a$ is an individual. Properties that are not atoms can be represented by sets of atoms.

Third, we restrict our discussion to agents whose beliefs and states of knowledge are closed under logical consequence. In a certain sense, such agents know everything that they are in a position to know. Our restriction to such agents, then, will allow us to trade in claims about what individuals could come to know by inference for claims about what agents in fact know.

Note that it follows from this latter assumption together with our preceding assumptions that if propositionalism is true, then an agent’s doxastic (epistemic) state may be represented by a single proposition—the strongest propositions she believes (knows)—while if proprietism is true, then an agent’s doxastic (epistemic) state may be represented by a single property—the strongest property she believes (knows).

Finally, we’ll assume that if proprietism is true, then agents may fail to know or to correctly believe, first-personally, who they are. Proponents of proprietism standardly assume that such ignorance is possible, and we think that this is well-motivated.

We now turn to the principal topics of this section: communication and agreement. We begin with the mundane observation that individuals are able to successfully communicate their beliefs—both first-personal and non-first-personal—to one another. For example, if Sam believes that Paris is the capital of France, while you are ignorant of this fact, then Sam can communicate this belief to you, and, as a result, you may come to believe an appropriate content, such that, given your respective beliefs, you and Sam agree. And similarly, if Sam believes first-personally that they are sick, while you are ignorant of this fact, then it would seem that Sam can communicate this belief to you, and, as a result, you may come to believe an appropriate content, such that, given your respective beliefs, you and Sam agree.

Successful communication is a means to agreement. While it is natural to talk about agreement as a relation between individuals, such a relation holds between individuals given particular beliefs that they have. We can think of agreement, then, as a relation that holds between possible states of affairs in which given individuals have beliefs with particular contents. We can represent this relation by introducing a binary sentential connective: ${\equiv }_A$. Letting $Bel(y,q)$ mean that $y$ has a belief with content $q$, we can then take $Bel(y,q){\equiv }_{A}Bel(x,p)$ to mean that $y$’s having a belief with content $q$ constitutes agreement with $x$’s having a belief with content $p$. Note that, as we’re understanding this relation, $Bel(y,q){\equiv }_{A}Bel(x,p)$ may obtain even if $y$ doesn’t in fact have a belief with content $q$ or $x$ doesn’t in fact have a belief with content $p$. Instead, ${\equiv }_A$ is a relation that may hold between the possible states of affairs $Bel(y,q)$ and $Bel(x,p)$, independent of whether or not they obtain, and that explains why $y$ agrees with $x$ if, in fact, $y$ has a belief with content $q$ and $x$ has a belief with content $p$.

What is required in order for the relation ${\equiv }_A$ to obtain? The proponent of propositionalism has a natural and simple answer to this question. In particular, given our assumptions about the structure of propositions, we suggest that the proponent of propositionalism should maintain that for two agents to have beliefs that are in agreement just is for them to have beliefs with the same content. That is, the proponent of propositionalism should endorse:

propositional agreement

Necessarily, for any agents $x$ and $y$ and propositions $p$ and $q$, $Bel(y,q){\equiv }_{A}Bel(x,p)$ just in case $p=q$.

Clearly, believing the same proposition is sufficient for agreement. And, given our assumptions about the nature of propositions, if $p$ and $q$ are distinct, then there is some possibility in which one holds and the other fails to hold. But if $p$ and $q$ may come apart in truth-value, then it would seem that believing one can’t constitute agreement with believing the other. Given propositionalism, then, for two agents to have beliefs that are in agreement just is for them to have beliefs with the same content.

It is much less clear, however, what the proponent of proprietism should say is required for the relation ${\equiv }_A$ to obtain. Consider, for example, the minimal proprietal variant of propositional agreement:

proprietal agreement (first incorrect version)

Necessarily, for any agents $x$ and $y$ and properties $p$ and $q$, $Bel(y,q){\equiv }_{A}Bel(x,p)$ just in case $p=q$.

To see that this misfires, let $p$ and $q$ each be the property of being Hume. The above principle then tells us that the state of Hume first-personally believing that he is Hume would constitute agreement with the state of some other individual—say Mad Heimson—also first-personally believing that he is Hume. But this is clearly incorrect. For, given the actual facts, Hume’s possible belief is correct—he is Hume—while Heimson’s is not—he is not Hume. But an obvious minimal condition on agreement is that if two individuals’ possible beliefs would be in agreement then it can’t be that one of these beliefs is true and the other false.⁴

In light of this sort of counterexample, a natural thought is that, given proprietism, agreement should be understood as the guaranteed absence of divergence in truth value. Thus, one may be tempted to endorse:

proprietal agreement (second incorrect version)

Necessarily, for any agents $x$ and $y$ and properties $p$ and $q$, $Bel(y,q){\equiv }_{A}Bel(x,p)$ just in case necessarily, $y$ has property $q$ just in case $x$ has property $p$.

But this too misfires. While the guaranteed absence of divergence in truth value is, we think, a necessary condition for agreement, it would not seem to be sufficient. Given the necessity of distinctness, note that if neither Heimson nor Marcus is Hume, it follows that, necessarily, Heimson has the property of being Hume just in case Marcus has the property of being Hume. And so the above principle tells us that Heimson’s believing first-personally that he is Hume constitutes agreement with Marcus’s believing first-personally he is Hume. But this strikes us as wrong. For just as Hume and Heimson would disagree about who is Hume, were each to believe, first-personally, that he is Hume, so too would Heimson and Marcus also seem to disagree about who is Hume were each to have such a first-personal belief.

It isn’t at all obvious to us what the proponent of proprietism should say about the conditions under which two agents count as agreeing in virtue of their beliefs. We need not, however, survey all of the possible options. For we can show that any account of agreement that the proponent of proprietism may provide will have a significant flaw. In particular, we can show that, given proprietism, there are guaranteed to be certain in principle limitations on the extent to which agents can know, first-personally, that their belief is in agreement with that of another individual. And this, we’ll argue, incorrectly predicts that there is a large class of cases in which successful communication is, in principle, precluded. propositionalism, in contrast, doesn’t predict the same sorts of in-principle limitations on successful communication. This thus provides a good reason to prefer propositionalism to proprietism.

We begin by stating two plausible principles concerning agreement and communication.

The fact that agents, in general, can successfully communicate their beliefs to others motivates the claim that, in general, for any belief that one agent may have there is some other possible belief that another agent may have that would suffice for the two to be in agreement. Given proprietism, then, it seems quite plausible that the following principle holds:

proprietal agreement existence

For any agents $x$ and $y$, and any property $p$, there exists some property $q$ such that $Bel(y,q){\equiv }_{A}Bel(x,p)$.

Successful communication, of the sort that is standardly achieved, does not, however, merely require that there be some content such that the addressee’s adopting a belief with that content would suffice for agreement with the speaker’s communicated belief—it also requires that the addressee know, of some content, that their believing that content suffices for agreement with the speaker’s communicated belief. We assume, then, that the following provides a natural constraint on successful communication:

successful communication

In a case of successful communication, there is a communicated content $p$ and a content $q$ such that the addressee knows first-personally that their believing $q$ constitutes agreement with the speaker’s believing $p$.

This much we take to be clear. There are, however, two natural ways of understanding the requirement imposed by successful communication. On one interpretation, the addressee must have de re knowledge of the speaker. According to this interpretation, if $x$ is the speaker, then successful communication between $x$ and their addressee requires that the addressee know, of some content, that their believing this content suffices for agreement with $x$’s believing the communicated content. On a second interpretation, the addressee must have a piece of de dicto knowledge concerning the speaker. According to this interpretation, successful communication between a speaker and their addressee requires that there be some appropriate mode of presentation of the speaker $f$ such that the addressee knows, of some content, that their believing this content suffices for agreement with $f$’s believing the communicated content.

We won’t try to adjudicate between these two ways of understanding the requirement imposed by successful communication. Instead, we’ll argue that, given either interpretation, the proponent of proprietism incorrectly predicts that there are certain significant limitations on successful communication.

Let’s begin by considering the de re interpretation of successful communication:

successful communication (de re)

In a case of successful communication between a speaker $x$ and an addressee $y$, there is a communicated content $p$ and a content $q$ such that $y$ knows first-personally that their believing $q$ constitutes agreement with $x$’s believing $p$.

For the time being, we’ll assume that successful communication requires this condition to be satisfied. Given proprietism, though, we can show that there is a large class of cases in which this condition is guaranteed to fail. That is, for many agents $x$ and $y$ and propositions $p$, there is no proposition $q$ such that $y$ can know that their believing $q$ constitutes agreement with $x$’s believing $p$. And so proprietism predicts that there is a large class of cases in which it is, in principle, impossible for one agent to successfully communicate their belief to another.

To see this, first consider the following two extremely plausible principles:

proprietal alethic agreement

Necessarily, for any agents $x$ and $y$ and properties $p$ and $q$, if $Bel(y,q){\equiv }_{A}Bel(x,p)$, then $y$ has property $q$ just in case $x$ has property $p$.

proprietal self-agreement

Necessarily, for any agent $x$ and properties $p$ and $q$, $Bel(x,p){\equiv }_{A}Bel(x,q)$ just in case $p=q$.

We’ve already had occasion to appeal to proprietal alethic agreement, and it strikes us as being clearly correct. In particular, this was what established that Hume and Heimson do not agree by each believing that he is Hume. The natural thought here is that any divergence in truth value between two beliefs is sufficient to show that the agents in question are not in agreement in virtue of holding those beliefs.

proprietal self-agreement also strikes us as being clearly correct. Obviously, the right-to-left direction holds. Each agent agrees with their own belief by having that belief. And the left-to-right direction also seems to be clearly true. For, given our assumptions about properties, any two distinct properties have different possible patterns of application. But if something could instantiate a property $p$ but not a property $q$ or vice versa, then taking oneself to have property $p$ would seem to constitute a different opinion from taking oneself to have property $q$.

Given these minimal constraints on agreement, we can now show that proprietism imposes a significant limit on successful communication.

Given proprietism, for an agent to know first-personally that they have some property just is for the agent to stand in the knowledge relation to that property. We’ll use the standard device of lambda abstraction to form property-denoting terms. Given proprietism, then, for $y$ to know, first-personally, that their believing some content $q$ constitutes agreement with $x$’s believing some content $p$ just is for $y$ to know $\lambda z.Bel(z,q){\equiv }_{A}Bel(x,p)$.

Our first result establishes that, given proprietism, for many agents $x$, $y$, and contents $p$, there is no content $q$ such that $y$ knows $\lambda z.Bel(z,q){\equiv }_{A}Bel(x,p)$. In particular, we can show that if an agent $y$ doesn’t know whether they are some agent $x$ in one world or some other agent $z$ in another, then there are many contents that $x$ may believe such that there is no content that $y$ could know would suffice for agreement with $x$’s belief.

first limitative agreement result

Let $y$’s epistemic state include the following centered-possibilities: $⟨x,w_1⟩,⟨u,w_2⟩$, where $x\ne u$, and let $p$ be such that $\{⟨x,w_1⟩,⟨u,w_2⟩\}\subseteq p$ but $⟨x,w_2⟩\notin p$. Given proprietal self-agreement and proprietal alethic agreement, it follows that, for each property $q$, $y$ does not know $\lambda z.Bel(z,q){\equiv }_{A}Bel(x,p)$.

Proof: We consider two cases:

Case 1: $q\ne p$. Since $q\ne p$, it follows from proprietal self-agreement that $Bel(x,q){\not\equiv }_{A}Bel(x,p)$ at $w_1$. So $x$ lacks the property $\lambda z.Bel(z,q){\equiv }_{A}Bel(x,p)$ at $w_1$. Since $⟨x,w_1⟩$ is an element of $y$’s epistemic state, it follows that $y$ does not know $\lambda z.Bel(z,q){\equiv }_{A}Bel(x,p)$.

Case 2: $q=p$. Since $q=p$ and $⟨u,w_2⟩\in p$, it follows that $u$ has property $q$ at $w_2$. Since $⟨x,w_2⟩\notin p$, it follows that $x$ lacks property $p$ in $w_2$. So given proprietal alethic agreement, it follows that $Bel(u,q){\not\equiv }_{A}Bel(x,p)$ at $w_2$. Since $⟨u,w_2⟩$ is an element of $y$’s epistemic state, it follows that $y$ does not know $\lambda z.Bel(z,q){\equiv }_{A}Bel(x,p)$.

The above result shows that if an agent $y$ doesn’t know whether they are some agent $x$ in one world or some other agent $z$ in another, then there are many contents that $x$ may believe such that there is no content that $y$ could know would suffice for agreement with $x$’s belief. And given this, it follows from successful communication (de re) that if $y$ doesn’t know whether they are some agent $x$ in one world or some other agent $z$ in another, then there are many beliefs that $x$ may have that, in principle, $x$ cannot successfully communicate to $y$.

This strikes us as a bad prediction. For, given proprietism, there should be many possible cases in which an agent is unsure about who they are. And yet it would not seem that there are, in such cases, significant limitations on the extent to which an agent $x$ may successfully communicate with an agent $y$, when $x$ happens to be one of the individuals that $y$ thinks that they could be.

Here is an example that illustrates the sort of limitation that holds given the above result. Suppose that the famous amnesiac Lingens is in the Stanford library in the actual world $\mathrm{@}$, and that another amnesiac Lauben is also in this library in $\mathrm{@}$. Suppose, moreover, that it’s compatible with what Lingens knows that he is Lauben in $\mathrm{@}$ and that it’s also compatible with what Lingens knows that he is some other amnesiac Harold in the Harvard library in a world $w$. And suppose that Lauben believes, first-personally, that either he is Lauben in $\mathrm{@}$ or that he is Harold in $w$. The above result tells us that, given proprietism, there is no content that Lingens could know, first-personally, would suffice for agreement with this belief of Lauben’s. And so, assuming successful communication (de re), it follows that Lauben’s belief that he is Lauben in $\mathrm{@}$ or that he is Harold in $w$ cannot, in principle, be successfully communicated to Lingens.

It seems to us, though, that even if Lingens and Lauben are ignorant of their identities in the manner that we’re imagining, they may still successfully communicate their respective beliefs to one another. For example, if Lingens and Lauben were to speak to one another in the Stanford library, it would seem that Lauben could inform Lingens that he thinks that he is either Lauben in $\mathrm{@}$ or Harold in $w$, and, given this, Lingens could know what sort of belief would suffice to agree with his interlocutor.

How should the proponent of proprietism respond to the preceding limitative result? One possibility would be for the proprietist to maintain that successful communication (de re) doesn’t capture the true interpretation of successful communication. In particular, they may maintain that successful communication between a speaker and their addressee doesn’t require the sort of de re knowledge required by successful communication (de re), but instead it merely requires that there be some appropriate mode of presentation of the speaker $f$ such that the addressee knows, of some content, that their believing this content suffices for agreement with $f$’s believing the communicated content.

Formally, we can think of a mode of presentation $f$ as a function that picks out a unique individual in a possible world. We’ll say that $f$ is a mode of presentation of an individual $x$ just in case $f$ as a matter of fact picks out $x$. In what follows, we’ll let $Bel(y,q){\equiv }_{A}Bel(f,p)$ mean that $y$’s having a belief with content $q$ constitutes agreement with $f$’s having a belief with content $p$. This proposition is true at a world $w$ just in case the unique $u$ such that $f(w)=u$ is such that $Bel(y,q){\equiv }_{A}Bel(u,p)$ holds at $w$. Given proprietism, then, for $y$ to know, first-personally, that their believing some content $q$ constitutes agreement with $f$’s believing some content $p$ just is for $y$ to know $\lambda z.Bel(z,q){\equiv }_{A}Bel(f,p)$.

If, then, the proponent of proprietism is inclined to reject successful communication (de re), we suggest that they should instead accept the following weaker principle:

successful communication (de dicto)

In a case of successful communication between agents $x$ and $y$, there is a communicated content $p$, a content $q$, and a mode of presentation $f$ of $x$ such that $y$ knows first-personally that their believing $q$ constitutes agreement with $f$’s believing $p$.

Given this alternative principle, however, the proponent of proprietism still incorrectly predicts that there is large class of cases in which one agent’s belief is, in principle, incommunicable to another agent. Indeed, we can show that there are such limitations, even in cases in which an agent knows who they are and knows that they are distinct from their interlocutor.

To show this, we’ll appeal to a third plausible principle concerning agreement:

modalized proprietal alethic agreement

Necessarily, for any agents $x$ and $y$ and properties $p$ and $q$, if $Bel(y,q)$ ${\equiv }_{A}Bel(x,p)$, then, necessarily, $y$ has property $q$ just in case $x$ has property $p$.

modalized proprietal alethic agreement is a strengthening of proprietal alethic agreement, but it follows from that weaker principle given the plausible principle that truths of the form $Bel(y,q)$ ${\equiv }_{A}Bel(x,p)$ are necessary.⁵

Now given just this minimal constraint on agreement, we can show that proprietism implies that there are a number of limitations on the conditions under which an agent can know, first-personally, that they are in agreement with another agent under a given mode of presentation. In particular, our second result establishes that, given proprietism, for many agents $x,y$, properties $p$, and modes of presentation $f$ of $x$, there is no property $q$ such that $y$ knows that their believing $q$ constitutes agreement with $f$’s believing $p$.

second limitative agreement result

Let $y$’s epistemic state include the following centered-possibilities: $⟨u,w_1⟩,⟨u,w_2⟩$, where $w_1\ne w_2$. And let $f$ be a mode of presentation of $x$ and $p$ a property such that: $\{w:⟨f(w_1),w⟩\in p\}\ne \{w:⟨f(w_2),w⟩\in p\}$. Given modalized proprietal alethic agreement, it follows that, for each property $q$, $y$ does not know $\lambda z.Bel(z,q)$ ${\equiv }_{A}Bel(f,p)$.

Proof: Consider the two epistemic centered-possibilities for $y$: $⟨u,w_1⟩,$ $⟨u,w_2⟩$. Letting $q$ be an arbitrary property, if $y$ knows that they have the property $\lambda z.Bel(z,q){\equiv }_{A}Bel(f,p)$ then it must be that this property is had by $u$ at $w_1$ and by $u$ at $w_2$. We can show that this can’t be so, given modalized proprietal alethic agreement.

Given modalized proprietal alethic agreement, for $u$ to have the property $\lambda z.Bel(z,q){\equiv }_{A}Bel(f,p)$ at $w_1$ it must be the case that $\{w:⟨f(w_1),w⟩\in p\}=\{w:⟨u,w⟩\in q\}$. And for $u$ to have that same property at $w_2$ it must be the case that $\{w:⟨f(w_2),w⟩\in p\}=\{w:⟨u,w⟩\in q\}$. But given that $\{w:⟨f(w_1),w⟩\in p\}\ne \{w:⟨f(w_2),w⟩\in p\}$, it follows that at least one of these identities must fail, and so there must be at least one epistemic centered-possibility for $y$ such that the individual in that centered-possibility lacks the property $\lambda z.Bel(z,q){\equiv }_{A}Bel(f,p)$ at the world of that centered-possibility. It follows that, for arbitrary property $q$, $y$ does not know $\lambda z.Bel(z,q){\equiv }_{A}Bel(f,p)$.

The above result shows that there is no property $q$ such that an agent could know, first-personally, that their believing $q$ would suffice for agreement with $f$’s believing $p$, for any mode of presentation $f$ that varies between two of the agent’s epistemic centered-possibilities that are alike with respect to their center, and any property $p$ whose pattern of instantiation differs between the two relevant individuals that may be picked out by $f$ at the worlds of those centered-possibilities.

This imposes quite severe constraints on knowledge of agreement. If an agent is certain of who they are but uncertain which individual $f$ picks out, then there is large class of properties $p$ for which there is no property $q$ that the agent could first-personally know would suffice for agreement with $f$’s belief with content $p$. In particular, if an agent is certain of who they are but uncertain which individual $f$ picks out, then any property $p$ whose possible pattern of instantiation differs between any two individuals will be such that there is no property $q$ that the agent could first-personally know would suffice for agreement with $f$’s belief with content $p$. But, plausibly, any qualitative property $p$ will be such that, for any two individuals $x$ and $z$, there is some possibility in which $x$ has $p$ but $z$ lacks $p$. It follows that if an agent is certain of who they are, but uncertain which individual $f$ picks out, then, for any qualitative property $p$, there is no property $q$ that the agent could first-personally know would suffice for agreement with $f$’s belief with content $p$.

This strikes us as a bad prediction. For example, suppose that Lingens is again speaking to Lauben. But this time suppose that Lingens knows that he is Lingens but does not know whether his interlocutor is Lauben or Harold. If Lauben believes that he has some qualitative property—e.g. the property of being tired—then that seems to be the sort of thing Lauben could successfully communicate to Lingens in this scenario. But the above result shows that, given successful communication (de dicto) and modalized proprietal alethic agreement, proprietism conflicts with this possibility.

The proponent of proprietism, then, predicts that there are significant limitations on the extent to which agents can communicate with each other—limitations that do not seem to be witnessed. The proponent of propositionalism, however, is not forced to predict the same sorts of limitations on successful communication. For the proponent of propositionalism does not predict the same sorts of in principle limitations on the extent to which agents can know, first-personally, that their belief is in agreement with that of another individual, either de re or under a given mode of presentation. Suppose a speaker $x$ utters something which thereby reveals that they believe proposition $p$. Is there a proposition $q$ such that addressee $y$ knows that their believing $q$ constitutes agreement with the speaker’s believing $p$? The answer to this question is ‘yes’, for proposition $p$ will itself be such a $q$. For recall that the propositionalist accepts the following principle:

propositional agreement

Necessarily, for any agents $x$ and $y$ and propositions $p$ and $q$, $Bel(y,q){\equiv }_{A}Bel(x,p)$ just in case $p=q$.

Thus, even if $y$ doesn’t know who they are or who their interlocutor is, if $y$ knows that their interlocutor believes $p$, then $y$ knows that their believing $p$ will constitute agreement with their interlocutor’s believing $p$. This is because, given propositional agreement, $y$ knows that for any pair of agents $a$ and $b$, $b$’s believing $p$ constitutes agreement with $a$’s believing $p$. Given this, the proponent of propositionalism can endorse successful communication, on either way of understanding this principle, without predicting the sorts of limitations on successful communication predicted by the proponent of proprietism.

3. Two Versions of Propositionalism

We take the preceding to constitute a strong argument for propositionalism—the claim that belief and knowledge are propositional relations. However, despite there being good reason to maintain that these particular psychological relations have propositions as objects, we don’t want to deny that there are important psychological relations whose objects are properties. For we think that agents do have distinctive first-personal beliefs and states of knowledge. And while an agent’s first-personal beliefs and states of knowledge have propositions as their objects, such beliefs and states of knowledge nonetheless determine certain relations to properties. We’ll say that an agent “doxastically (epistemically) self-ascribes” a property $p$ just in case they believe (know) first-personally that they have $p$.⁶

In the remainder of the paper, we develop two accounts of which propositions play the role of being the objects of such first-personal beliefs and states of knowledge, and we develop two corresponding accounts of doxastic and epistemic self-ascription. On both accounts, facts about which properties an agent doxastically (epistemically) self-ascribes are determined by facts about which propositions the agent believes (knows), together with certain additional facts. A more ambitious project would be to reduce facts about about which properties an agent doxastically (epistemically) self-ascribes solely to facts about which propositions the agent believes (knows). We think, however, that such a project must fail. To see this, consider the following case described in Stalnaker, 2016, op. cit.:

Albert is in the kitchen and Boris is in the basement. Each knows who and where he is, and who and where the other is, so there is no self-locating ignorance. They each know all the same objective facts about their respective locations in the house, but there is still a difference in their epistemic states, a difference in their perspectives on the world. To see that this difference is not reflected in their impersonal beliefs, consider any representation of the contents of their common state of belief… All that matters for the point is that propositions are things with absolute truth conditions. That is, they are things whose truth conditions are invariant with respect to time, place, and person. Suppose such a representation contained all the information about the beliefs of any person who is in the cognitive state that Boris and Albert are both in. Let $x$ be any person in that state. Where does $x$ believe himself or herself to be? It is clear enough from the description of the scenario that Boris believes he is in the basement and Albert believes he is in the kitchen, but these are further facts that are not reflected in the common set of propositions that is what each of them believes, or in the set of possible worlds that are compatible with the way they take the world to be. (Stalnaker, 2016, op. cit., 70)

Stalnaker’s point here is that if propositions are common currency between agents, then it would seem that there may be two agents, such as Albert and Boris, who believe (know) all the same propositions while differing with respect to which properties they doxastically (epistemically) self-ascribe. Given this, the minimal conclusion to draw is that which propositions an arbitrary agent believes (knows) doesn’t itself determine which properties they doxastically (epistemically) self-ascribe.

This point strikes us as being both correct and important. The proponent of propositionalism may, however, accept this conclusion but still maintain that the facts about which properties an agent doxastically (epistemically) self-ascribes are determined by the facts about which propositions they believe (know) together with certain additional facts. The two versions of propositionalism that follow will appeal to different sets of additional facts to determine which properties a given agent doxastically (epistemically) self-ascribes given the facts about which propositions they believe (know).

While we think that the propositionalist should allow that there are proprietal relations of doxastic and epistemic self-ascription, there is good reason to think that the propositionalist will accept certain constraints on these relations that proprietists will not generally accept. In particular, both of the accounts we develop below entail the following substantive constraint on self-ascription:

self-ascriptive symmetry

Necessarily, for any agents $x$ and $y$ and property $p$, if $p$ is the strongest property that $x$ self-ascribes and the strongest property that $y$ self-ascribes, then $x$ has $p$ iff $y$ has $p$.

proprietists, we take it, will generally reject this claim. For example, Lewis, op. cit., 525–526 takes it that when two agents $x$ and $y$ get their heads into ‘perfect match’—that is, when they are, in a certain sense, psycho-functional duplicates—we should say that the strongest property $x$ self-ascribes is identical to the strongest property $y$ self-ascribes. Given this, we should expect that it is possible for there to be two agents $x$ and $y$ such that $p$ is the strongest property each self-ascribes though one has $p$ and the other lacks $p$.

However, while proprietists will naturally reject this principle, propositionalists are well-motivated to endorse it. For this principle follows from three principles which we think propositonalists are well-motivated to accept.

We’ll say that two agents $x$ and $y$ completely agree just in case (i) for every content $p$ that $x$ believes there is a content that $q$ that $y$ believes such that $x$ and $y$ are in agreement given these beliefs, and (ii) for every content $q$ that $y$ believes there is a content that $p$ that $x$ believes such that $x$ and $y$ are in agreement given these beliefs. Then, given this definition, propositional agreement entails:

complete belief agreement

Necessarily, for any agents $x$ and $y$, $x$ and $y$ completely agree just in case the strongest proposition that $x$ believes is the same as the strongest proposition that $y$ believes.

In addition, we think that the proponent of propositionalism should accept the following two principles:

strongest proposition

If $p$ is the strongest property $x$ self-ascribes, then $p^{\prime }=\{w:⟨y,w⟩\in p$ for some individual $y$} is the strongest proposition $x$ believes.⁷

complete proprietal agreement

Necessarily, for any agents $x$ and $y$, and properties $p_1$ and $p_2$, if $p_1$ is the strongest property that $x$ self-ascribes and $p_2$ is the strongest property that $y$ self-ascribes and $x$ and $y$ completely agree, then $x$ has $p_1$ iff $y$ has $p_2$.⁸

Together these three principles entail self-ascriptive symmetry. Each of the two versions of propositionalism developed below provides a natural explanation of why self-ascriptive states are subject to this additional constraint.

Both versions of propositionalism discussed below are parametric on an initial version of proprietism. In keeping with our initial assumptions, the version of proprietism that we’ll assume takes the class of propositions to form a complete, atomic, Boolean algebra, and the class of properties to be isomorphic to the class of sets of ordered-pairs $⟨x,w⟩$, where $x$ is an individual and $w$ is an atomic proposition. To have useful labels, we’ll call these classes the “base propositions” and “base properties”, and we’ll call the propositions that are atoms amongst the class of base propositions “base atoms”.⁹

In §4.1, we describe a version of propositionalism that agrees with our initial version of proprietism about what the space of propositions looks like. According to this account, for an agent $x$ to self-ascribe some property $p$ just is for that agent to believe a particular base proposition. In §4.2, we describe a second version of propositionalism that admits more propositions than our initial version of proprietism admits. According to this account, it will not in general be true that for an agent $x$ to self-ascribe some property $p$ just is for that agent to believe a particular base proposition. While we’re inclined to think that both accounts have their merits, we think that there are certain reasons to prefer the second version of propositionalism to the first.

4. Conclusion

We began with an argument in favor of the thesis that the contents of the attitudes of belief and knowledge are propositions rather than properties. While proponents of the former view can give a very simple account of agreement, proponents of the latter would not seem to be able to provide any similarly simple and principled account. Even worse, we argued that, given some plausible assumptions, proprietism predicts that successful communication cannot take place in certain cases in which there would not, in fact, appear to be any such limitations. propositionalism, on the other hand, results in no similar predictions.

We then examined two versions of propositionalism according to which both facts about epistemic and doxastic self-ascription may be determined by facts about propositional knowledge and belief, together with certain other facts. These two versions of propositionalism, however, differ in important ways. de dicto propositionalism allows that an agent $x$ might be ignorant of their identity in the sense of failing to self-ascribe the property of being $x$, while de re propositionalism does not. And de dicto propositionalism implies that there are no essential differences between the nature of proprietal self-ascription for distinct agents, while de re propositionalism implies that there are. These differences arguably favor de dicto propositionalism over de re propositionalism.¹⁷