An Act-Based Approach to Assertibles and Instantiables

1. Introduction

In recent years, there has been renewed attention to the metaphysics and epistemology of propositions. Several authors such as King (2007; 2014), Soames (2014; 2015), and Hanks (2011; 2015) have argued, on primarily semantic grounds, that propositions must be structured representational entities rather than sets of possible worlds, yet have also argued that traditional platonic conceptions of structured propositions of the sort associated with Frege and Russell face serious metaphysical and epistemological problems. Accordingly, they have attempted to articulate “naturalized” accounts of propositions, understanding such things as in some way dependent upon our cognitive or linguistic activities. All existing such accounts, however, appeal to speakers’ cognitive relations to platonic properties and relations as an essential theoretical ingredient. While King and Soames are unbothered by this appeal, Hanks (2015: 206–207; 2017) seriously worries that many of the same concerns about propositions, traditionally understood, can be raised with respect to properties and relations as well, and Pautz (2016) has explicitly raised this problematic analogy for naturalized accounts of propositions. In this paper, I show how, by integrating an act-based metaphysics of the sort developed by Hanks with a normative functionalist semantics of the sort developed by Wilfrid Sellars (1953; 1954; 1974) and Robert Brandom (1994; 2000), the act-based approach can be radicalized, giving an act-based account of propositional constituents such that no appeal to platonic properties and relations is necessary. I show, moreover, how, beyond just not appealing to our knowledge of properties and relations, this radicalized act-based of propositional constituents provides the resources for a satisfying account of our knowledge of properties and relations in terms of our mastery of linguistic norms.

The paper is structured as follows. In §2, I draw on Peter van Inwagen’s (2006) unified characterization of propositions, properties, and relations as “assertibles,” contrasting this with an alternative conception of states of affairs, properties, and relations as “instantiables.” This sets the target of the paper: giving a unified act-based account of assertibles that will ultimately yield an account of our knowledge of instantiables. On the generalized act-based account of assertibles I provide in §3, token acts of predication are understood as the types of acts that they are not in virtue of a representation relation they bear to a platonic entity but in virtue of how they normatively relate to other such acts, committing one to or precluding one from being entitled to other such acts. In §4, I distinguish between two conceptions of these assertoric acts, and argue that they must, in the first instance, be understood as perspective-relative, individuated in terms of the normative attitudes actually held by speakers, in virtue of which they attribute normative statuses to other speakers. In §5, I deploy this perspective-relative conception to articulate a new account of opacity on the act-based theory. Finally, in §6, I show how, from a normative functionalist account of predicative and propositional acts, one can arrive at a satisfying epistemology of properties, relations, and states of affairs. Coupled with the perspectival account of opacity in §5, this ultimately affords us with a secondary conception of assertoric acts as perspective-neutral, involving the representation of things as instantiating objective properties and standing in objective relations.

2. Assertibles and Instantiables

I start with an account of properties, relations, and propositions put forward by Peter van Inwagen (2006), according to which all such things are broadly classified as “assertibles.”¹ Van Inwagen’s basic thought is that, whereas propositions are things that are asserted (full stop, as it were), properties and relations are things that are asserted of things. For instance, I might assert that the Sun is round. Here, the phrase “that the Sun is round” picks out what I assert: the proposition that the Sun is round. In asserting that the Sun is round, however, I assert of the Sun that it’s round, and this is something that you might assert of Neptune as well. The phrase “that it’s round,” then, might be understood as picking out an “unsaturated assertible,” something that can be asserted of things. More specifically, that it’s round is a 1-place assertible: something that’s asserted of just one thing. There are 2-place assertibles, which are asserted of two things, for instance, that the first is bigger than the second which I might assert of the Sun and Neptune, 3-place assertibles, and so on. So, whereas propositions are 0-place assertibles, properties and $n$-place relations are 1-place and $n$-place assertibles. To call properties, relations, and propositions “assertibles” is simply to identify them as the contents of assertion. That is, they are what one asserts, either of something or full-stop, when one makes an assertion.²

This conception of properties, relations, and propositions as “assertibles” contrasts with a different and perhaps more common way of thinking about properties and relations, most commonly associated with Russell (1903).³ This is to think of them as “ways for things to be.” For instance, being round is a way for things to be, and the Sun and Neptune are two things that are this way. For something to be this way, on this second way of thinking about properties, just is for it to instantiate the property of being round. Thus, the Sun and Neptune both instantiate the property of being round. This way of thinking about properties makes no reference, at least in the first instance, to our assertions, beliefs, or linguistic expressions; we simply refer to things in the world like the Sun and Neptune and the various ways that these things are or might be. Thus, whereas the first conception of properties and relations identifies of them as assertibles, this second conception of properties and relations identifies them as (what we might call) instantiables. Whereas being larger than is a 2-place instantiable, and being larger than Neptune is a 1-place instantiable, the natural continuation of this thought is to say that the Sun’s being larger than Neptune is a 0-place instantiable, something that’s not instantiated by anything, but simply instantiated, once again, full-stop.

This distinction between assertibles and instantiables is widely recognized at least in the propositional case. It is common, in standard metaphysical parlance, to distinguish between propositions, denoted by clauses such as “that the Sun is round,” and states of affairs, denoted by clauses such as “the Sun’s being round.”⁴ The standard way of drawing this distinction is to say that propositions, which are true or false, are truth-bearers whereas states of affairs, which obtain or fail to obtain, are truth-makers.⁵ That is, the proposition that the Sun is round is capable of being true or false, it is in fact true, and what makes it true is the obtaining of the state of affairs consisting in the Sun’s being round. For a state of affairs to obtain is, in my terminology, for a 0-place instantiable to be instantiated (full-stop).⁶ So, despite the new terminology, this distinction is familiar in the propositional case. It should be clear, however, that this distinction between truth-bearers (denoted in the propositional case with a clause of the form “that $a$ is $F$”) and truth-makers (denoted in the propositional case with a clause of the form “$a$’s being $F$”) applies just as well to properties and relations. Just as there is a clear distinction in the sense of the clauses “that $a$ is $F$” and “$a$’s being $F$,” there is a clear distinction in the sense of the clause “that it’s $F$,” expressing what one says of something in saying of it that it’s $F$, and the clause “its being $F$,” expressing what makes true what one says of something when one says of it that it’s $F$. So, whereas “that it’s $F$” expresses an unsaturated truth-bearer, “its being $F$” expresses an unsaturated truth-maker. Whereas the former has a single gap to be filled in order to yield a complete truth-bearer, the latter has a single gap to be filled in order to yield a complete truth-maker.⁷

To solidify this distinction between assertibles and instantiables, note that, intuitively, two distinct assertibles can be made true by a single instantiable. Consider first a classic propositional case. At least intuitively, Lois Lane believes that Superman flies, and so she’d say that Superman flies if asked. On the other hand, she doesn’t believe that Clark Kent flies, and so she wouldn’t say that Clark Kent flies if asked. So, it seems that there are two 0-place assertibles here: one that Lois is disposed to assert (because she believes it) and one that she isn’t disposed to assert (because she doesn’t believe it). Unbeknownst to Lois, however, there is a single state of affairs on which the truth of both of these propositions turns: the state of affairs consisting in this guy, the one alternatively known as “Superman” and “Clark Kent,” being such that he flies. So, though there are two 0-place assertibles (two propositions, in the standard sense), there is just one corresponding 0-place instantiable (one state of affairs).⁸ This point is, of course, familiar in the propositional case, but it applies just as well for the case of properties and relations. For instance, before the discovery of the chemical composition of water, Aristotle, say, was disposed to assert of the Ilisos River that it’s filled with water. Aristotle wasn’t, however, disposed to assert of it that it’s filled with H₂O. Nevertheless, the Ilisos’s being filled with water just is its being filled with H₂O.⁹ So, here too, at least intuitively, there are two 1-place assertibles—two different things that can be asserted of a river such as the Ilisos—but just one corresponding 1-place instantiable—one way for a river such as the Ilisos to be.

What, exactly, does the distinction between assertibles and instantiables come to? I’ve just put it in terms of the distinction between truth-bearers and truth-makers. However, to put it in different terms, I take it that it ultimately amounts to the distinction between representings and representeds. Now, identifying assertibles with representings might seem like a surprising identification, since it seems to suggest that assertibles such as that it’s round are acts of representing. That is, indeed, precisely what I want to suggest, as I’ll now explain.

3. The Act-Based Conception, Radicalized

One prominent theory of propositions to emerge in recent years is the so-called “act-based theory of propositions,” put forward most notably by Peter Hanks (2011; 2015) and Scott Soames (2014; 2015). It’s Hanks’s version on which I want to draw here.¹⁰ Consider a case in which Norm says, in English, “The Sun is round” and Maddy says, in Spanish, “El Sol es redondo.” Intuitively, we’re inclined to say that Norm and Maddy said the same thing, albeit in different languages. What they’ve both said is that the Sun is round. The founding thought of the act-based conception of propositions is that, when we say, for instance, “Norm and Maddy said the same thing,” the surface grammar of this phrase is actually a bit misleading. What it is for two people to “say the same thing” is, really, not for them to both stand in the saying relation to some object but to both perform the same type of assertoric act. Now, Hanks has a particular way of articulating what it is to perform an act of a certain type, and I will return to Hanks’s proposal in a moment. The important point for now, however, is that the act-based conception, as developed by Hanks (2011), identifies propositions with these assertoric act types. To say that Norm and Maddy both said that the Sun is round is to characterize both of their acts as being of the same type. On this account, the distinction between token acts of asserting and the types of acts of which those acts are tokens does the philosophical work that is traditionally done by the distinction between acts of asserting and the objects asserted.

Insofar as propositions are assertibles, the act-based theory provides an account of them. The twist is that, on the act-based account, the noun “assertible” is not to be understood by analogy to the noun “eatable,” denoting some extrinsic thing to which one is able to stand in the eating relation, but, rather, as a determinate of “doable,” where the class of doables is the class of things that can be done—the class of act types that can be tokened. One of the most fundamental virtues of this account is epistemological: rather than knowledge of propositions being knowledge of platonic abstracta which exist completely independent of us, knowledge of propositions is understood as a specific sort of self-knowledge, knowledge of our own acts and capacities. This is perhaps the account’s main philosophical appeal. The account, however, is limited to 0-place assertibles; things that can asserted full-stop. Once again, however, not only can Norm and Maddy assert the same thing full-stop, but, for instance, if Norm says “The Sun is round” and Maddy says “Neptune es redondo,” Norm says of the Sun what Maddy says of Neptune, namely, that it’s round. A reasonable question to ask, then, is whether we can apply the very same act-based conception here. Doing so, the thought would be that when we say “Norm said of the Sun what Maddy said of Neptune, namely, that it’s round,” the phrase “that it’s round” here doesn’t function to pick out some object to which Maddy and Norm both stand in the saying-of relation, but, rather, functions to characterize the type of act that Maddy and Norm both perform.¹¹ Is such an act-based conception of 1-place assertibles viable? Most proponents of the act-based conception of propositions, I take it, would think that it’s not.

Existing act-based accounts of propositions (like most contemporary accounts of structured propositions in general) appeal to properties and relations as primitive, articulating the acts with which propositions are identified by way of this appeal.¹² In particular, the act with which Hanks identifies the proposition that the Sun is round is the act of referring (in a specific way) to the Sun, expressing the property of being round, and linguistically predicating (i.e. asserting) the latter of the former. Performing such an act, on Hanks’s account, one represents the Sun as being round, and so one who performs such an act speaks truly just in case the Sun is round. The idea of properties with instantiation conditions which one can linguistically get a hold of and predicate of objects, thus representing those objects as being certain ways, plays a crucial role in the account Hanks provides of the act types with which propositions are identified. It is only in virtue of the appeal to such properties, which can be truly or falsely asserted of objects, that Hanks is entitled to speak the acts with which he identifies propositions as representational acts at all. It’s not at all clear how, in the context of this account, one could eliminate talk of such properties for talk of acts. Nevertheless, Hanks expresses serious concern about the appeal to properties in his theory of propositions, recognizing that many of the same problems that motivate the act-based conception of propositions apply just as well to properties, and concluding that he “would like to have a non-Platonic story to tell about property expression” (2015: 207).¹³ Fortunately, there is such a story to be told. One can indeed provide an act-based account of such predicative acts as saying of something that it’s round, without any appeal to platonic properties, as I will now show.

What is it to say of something that it’s round? For Hanks, it is to “latch onto” (207) some platonic entity—the property of being round—and predicate it of something. But this is not the only way to understand what this act is. An alternative way to go is to understand the act of saying of something that it’s round simply as a certain type of linguistic act, one that plays a certain role in a linguistic practice, articulating what it is to token an act of this type in terms of the relations such a tokening bears to the tokening of other assertoric act types.¹⁴ Thus, we can say, for instance, that saying of something that it’s round is an act such that, if one tokens it in the context of a propositional act involving reference to some thing, one is precluded from being entitled to say of that thing that it’s square, one is committed to saying of that thing that there is some central point of it from which surface points are (relatively) equidistant, and so on. To articulate what it is to say of something that it is round in this way is to articulate what it is to token this assertoric act type in terms of the role this act plays in a space of other such acts; precluding one from being entitled to token some such acts, committing one to tokening others, and so on. No extrinsic platonic entities are needed.

This general idea here is, of course, a familiar one. It is perhaps most familiar in the context of functionalist accounts of mental content according to which the content of a mental state is understood in terms of its causal role among a space of other such states (Lewis 1972). This specific version of this idea I’m appealing to here, developed most notably by Wilfrid Sellars (1953; 1956; 1974) and Robert Brandom (1994; 2000), has been called “normative” (rather than causal) functionalism (O’Shea 2007; Maher 2012), since the role of an assertoric act is understood in terms of the specifically normative relations that it bears to other such acts. I will say more about the metaphysics of these normative relations shortly. For the moment, I’ll take these normative relations as primitive and illustrate the work they can do.

There are two sorts of normative relations on which I’ll focus. First, an assertoric act (or set of assertoric acts) might commit one to another assertoric act. For instance, if I say of something that it’s a sphere, I’m committed to saying of it that it’s round. This is not to say, of course, that if I say of something that it’s a sphere, I must actually say of it that it’s round (this requirement would lead to us saying way more things can possibly be said). Rather, saying of something that it’s a sphere commits one to saying of it that it’s round in that one must be prepared to make this latter move (and defend it) if appropriately prompted, at least insofar as one retains one’s commitment to the claim that it’s a sphere. The second normative relation on which I’ll focus here is that an assertoric act (or set of assertoric acts) might preclude one from being entitled to another assertoric act. For instance, if I say of something that it’s round, I’m precluded from being entitled to say of it that it’s square. So, if I perform or am committed to performing the first act, the second act is normatively ruled out. I refer to these two types of normative relations as relations of “committive” and “preclusive” consequence. As the example I’ve just given shows, in articulating what it is to say of something that it’s round, we look both upstream, at the assertoric acts that stand in relations of committive and preclusive consequence to this act, and downstream, at the assertoric acts to which this act stands in relations of committive and preclusive consequence. On this account, articulating these upstream and downstream normative relations that the act of saying of something that it’s round bears to other such acts is sufficient to say what this act is. Thus, we articulate what it is not by relating it to some extra-linguistic object but by articulating the normative functional role it plays in the practice in which it can be tokened.

The same functionalist strategy just appealed to with respect to simple predicative acts like that of saying of something that it’s round, can be applied to predicative acts which take propositional acts as objects. On the standard act-based conception, “It’s not the case that” expresses the property of being false, and so, when one says “It’s not the case that the Sun is square,” one performs a complex act in which one expresses the property of being false, expresses the proposition that the Sun is square, and predicates the former of the latter. For Hanks, who takes the acts with which propositions are identified to be ones with assertoric force, this requires a complex (and potentially problematic) story about “force cancellation.”¹⁵ No such story is required here. Just as we can radicalize the act-based account so as to remove an appeal to the expression of standard properties like the property of being round, we can radicalize it here too so that no appeal to expression and predication of properties like being false is required. We simply ask, what is it to perform the act one performs in assertorically uttering “It’s not the case that $\phi$”? Well, minimally, it is to perform an act that precludes one from being entitled to assert that $\phi$. Conversely, if one performs an act $\psi$ that precludes one from being entitled to asserting that $\phi$, then $\psi$ commits one to asserting that $\neg \phi$. In this way, one can specify precisely what it is to perform an act of negating some proposition directly in terms of the functional role of the act, without any appeal to an act of expressing the property of being false which is then predicated of that proposition. The same can be done for conjunction, disjunction, and other logical operators. The result is a recursive specification of the normative significance of the propositional acts tokened by uttering sentences of arbitrary logical complexity.¹⁶

The normative functionalist account of content I’ve just sketched is, of course, controversial, and I will not give a sustained independent defense of it here.¹⁷ What I hope to show here, providing only the general contours of this sort of account, is that if the normative functionalist account of content can be made to work, then it can be put to work to radicalize the act-based theory of propositions in order to account for assertibles—all of them—intrinsically in terms of their functional roles, without any appeal to such extrinsic entities as properties or relations. 0-place assertibles are understood as propositional acts, whereas 1-place and many-place assertibles are understood as predicative acts. The term “predicative act,” in this context, however, must be used with some caution, since “predication” is not what Hanks takes it to be—an act of getting cognitive hold of some property and attaching it to an object in the way that one might grab a sticker and attach it to an object. Rather, predicative acts, paradigmatically expressed by clauses such as “that it’s round,” are understood by abstracting what stays constant in propositional acts, expressed by complete sentences such as “The Sun is round,” “Neptune is round,” and so on, as different singular terms are substituted into the sentences used to token these propositional act types. This constitutes an important difference between the version of the act-based account articulated here and the standard act-based account, enabling us to respond to one recent objection to the view put forward by Speaks (2020).

As we’ve already said, on the standard act-based account, the act of saying that the Sun is round is analyzed as a tripartite act in which one refers to the Sun, expresses the property of being round, and predicates the former of the latter. In the context of the standard account, these constituent acts are understood as primary relative to the complete act of saying that the Sun is round. That is, the complete act of saying that the Sun is round is understood as a composite of self-standing building blocks—acts of reference, property expression, and predication—that are combined in some way so as to constitute a propositional act. As Speaks (2020) has recently argued, such an analysis faces problems directly analogous to the traditional problem of the “unity of the proposition” that act-based theories are advertised by their proponents as solving. On the radicalized act-based conception offered here, we adopt the opposite order of explanation. We start with a conception of what it is to token a complete propositional act, understanding such an act as being the particular propositional act type that it is in terms of its playing a certain functional role. We then understand the referential and predicative components which might be common to various propositional act types by abstraction. So, while we can still speak in terms of propositional acts containing referential acts and predicative acts as component parts, as the standard act-based theorist does, we should maintain, following Ryle (1960), that, ultimately, these referential and predicative acts “are not proposition components but propositional differences. They are distinguishables, not detachables; abstractables, not extractables” (436).¹⁸

4. Normative Attitudes and Normative Relations

On the account offered here, assertibles are understood as types of propositional or predicative acts, and what it is to perform a propositional or predicative act is understood in terms of its normative role—what tokening it commits one to, precludes one from being entitled to, and so on. But how, exactly, should we conceive of the normative relations constitutive of an act’s normative role? Let me now distinguish between two ways of thinking about this normative role, and, accordingly, two conceptions of “the act” one performs in assertorically uttering some sentence or predicate.

The first conception individuates an assertoric act in terms of the subjective normative attitudes actually held by speakers, in virtue of which they attribute normative statuses to other speakers upon their performance of that assertoric act, taking them to be committed to certain acts, precluded from being entitled to others, and so on. Such normative attitudes can be thought of as speakers’ “scorekeeping principles,” the principles in accordance with which they keep discursive score, updating the “scorecards” wherein they keep track of the normative statuses that they’ve attributed to other players. Thus, insofar as a speaker has the principle of scoring anyone who says that something’s spherical to be committed to saying that it’s round, if someone performs the first assertoric act, they’ll be attributed a commitment to the second assertoric act. On this first conception, an assertoric act, understood in terms of the normative attitudes actually held by speakers, is individuated in terms of how its performance changes the set of scores actually kept by those speakers. Importantly, the normative attitudes actually held by speakers may differ from speaker to speaker, and so, on this first conception, the significance of an assertoric act is determined only relative to some scorekeeping perspective.

The second conception individuates an assertoric act in terms of the objective normative relations, which determine what one is ultimately really committed to, in performing that assertoric act, whether or not anyone in the actual discursive practice is disposed to attribute such commitments. Thus, for instance, suppose there is some mathematical fact about spheres that is yet to be discovered, according to which all spheres are necessarily $F$s. Plausibly, there is an objective sense of “commitment” such that, in saying that something is a sphere, one is committed to saying that it is an $F$, since one is committed to the claim that the thing of which one is speaking has the nature of a sphere, whatever that nature happens to be. According to this objective sense of “commitment,” one is so committed, even though no one is disposed to attribute this commitment. On this second conception, unlike the first conception, the normative significance of an assertoric act is objective and does not vary from perspective to perspective.

It will be crucially important that this account has room for the second conception of an assertoric act, since it is only in virtue of that latter conception that we can speak of an assertoric act as an act of representing things as instantiating objective properties and relations. We will arrive there by the end of this paper. However, it is methodologically important to start with the first conception in thinking about the normative significance of assertoric acts. Only by thinking first about the attribution of commitments, and how these attributions can vary from perspective to perspective, can we ultimately make sense of the thought that what one is really committed to, in making some claim, outstrips the set of commitments attributed to one by any actual set of speakers. To key in on this crucial structural feature of the practice of commitment attribution, let me show how, drawing on this feature, this normative functionalist account of propositional content enables us to make sense of tricky cases of propositional attitude ascriptions (something that, of course, has substantial independent interest as well).¹⁹

5. Propositional Attitude Ascriptions

Let us consider the case of Lois Lane, who believes that Superman flies but doesn’t believe that Clark Kent flies. In distinguishing between two propositional acts here so as to make sense of Lois as not being subjectively irrational, we are thinking of the propositional acts tokened in assertorically uttering “Superman flies” and uttering “Clark Kent flies” as Lois understands their discursive significance. Lois takes it that one undertakes different commitments in tokening these respective acts. For instance, relative to Lois’s perspective, tokening the first act commits one to saying that a caped superhero flies, that a Kryptonian flies, and so on, whereas tokening the second act commits one to saying that the son of Jon and Martha Kent flies, saying that a normal human being flies, and so on. We can distinguish between two propositional acts here by indexing the normative attitudes relative to which the significance of these acts are assessed to Lois’s perspective. In principle, we can specify a different propositional act for each sentence/speaker pair—the act one performs in assertorically uttering that sentence, according to that speaker. There is generally sufficient widespread agreement among speakers that, when we analyze what one says, we don’t do this, generally just speaking of “the” proposition expressed by that sentence, but, in cases in which there is disagreement, it is important that we can distinguish between the different propositional acts, relativized to different perspectives, in this way.

To see how shifting between perspectives enables us to make sense of our judgments of the truth-values of sentences attributing beliefs, consider first the following two sentences:

• 1.  

  Superman flies.

• 2.  

  Clark Kent flies.

Relative to our perspective—we who know of the identity of Superman and Clark Kent—these two sentences have the same semantic value. Since we take “Superman” and “Clark Kent” to refer to the same person, we take it that someone who utters (1) undertakes just the commitments that someone who utters (2) undertakes, whether they know it or not. Relative to Lois Lane’s perspective, however, (1) and (2) have different semantic values, since she does not take it that someone who utters one undertakes the same commitments as someone who utters (2). When we say, then,

• 3.  

  Lois believes that Superman flies, but she doesn’t believe that Clark Kent flies.

we appeal to Lois’s understanding of the semantic significance of those propositional acts—the semantic values of those sentences relative to Lois’s perspective. This is how we are capable of understanding how it could be that she believes the first without believing the second. We can say, precisely, the content of her two beliefs by articulating the commitments and preclusions of entitlements she takes one to take on in saying that Superman flies or that Clark Kent flies, where these acts are individuated relative to her perspective. Her believing only one of these two things, on this account, is her taking herself to be committed to only one of these two propositional acts which are, at least from her perspective, distinct.

Though my main aim in articulating this account of propositional attitude ascriptions here is to develop this perspectival conception of semantic content, it’s worth noting that, formally, this account can be straightforwardly integrated into a standard truth-conditional semantic framework of the sort proposed by Heim & Kratzer (1998).²⁰ All one needs to do is add a perspectival index in the way suggested by Asudeh & Giorgolo (2016: 15–18).²¹ On their proposal, intensional verbs such as “believes” or “loves” (unlike extensional verbs like “punch”) require that the semantic value of the grammatical object be determined relative to the perspective index of the subject of those verbs. Though I won’t go into the formal details here, the result is that semantic contents of “Superman flies” and “Clark Kent flies,” as they occur unembedded in (1) and (2), are distinct from the contents of those sentences, as they occur embedded in (3). Spelling out this difference on the account provided here, unembedded, the content is determined by the commitments we take one to take on in uttering either sentence, and so there is a single content shared by both sentences, whereas, embedded in the clause “Lois believes that,” the content is determined by relativizing the commitments one takes on to Lois’s perspective, and so there are distinct contents possessed by the two sentences. In this way, we can make the fine-grained distinctions in meaning that the Fregean can. However, there are no mysterious Fregean senses that are posited as primitive in this account. Rather, we simply have the idea of speakers who have differing normative attitudes in terms of which they differently assess the significance of same assertoric acts.

The same account can be given to make sense of our judgments regarding the truth of sentences like the following:

• 4.  

  Aristotle believes of the Ilios that it’s filled with water, but he doesn’t believe of it that it’s filled with H₂O.

Here again, our primary deployment of the concept of belief with respect to predicative acts concerns what we take someone to take themself to be committed to, not what we ourselves take them to actually be committed to. Thus, the predicative acts that are relevant for making sense of our natural inclination to judge that (4) is true are the ones defined relative to the perspective of Aristotle, who takes water to be a simple substance and so, when he says of something that it’s filled with water, does not take himself to be committed to the claim that it is filled with a composite substance like H₂O.²² It should be clear, in this case, that, articulated in a truth-conditional theory, the semantic content of “filled with water,” as it occurs embedded in (4), is not the property of being filled with water. Rather, it is the predicative act one tokens on uttering this predicative phrase, as its significance is assessed by Aristotle. By contrast, when we consider the same predicate occurring unembedded in the following sentences:

• 5.  

  The Ilios is filled with water.

• 6.  

  The Ilios is filled with H₂O.

We evaluate the significance of this predicative act relative to our perspective, and so these two sentences are taken to have the same semantic content.

This act-based account of opacity, based on the proposal Brandom puts forward in Chapter 8 of Making It Explicit, is a major advance on Hanks’s own act-based account of opacity on several counts. First, Hanks’s account involves individuating “semantic reference types” in terms of a primitive notion of “semantic competence” with respect to names. However, the criteria for specifying what, exactly, semantic competence requires is unclear at best.²³ Second, Hanks is committed to providing a different solution to Kripke’s (1979) puzzle with Peter, since he cannot say that the different tokenings of “Paderewski” in two different contexts constitute two different semantic reference types. But it seems clear that any solution at all to these puzzles about belief should be a unified solution that applies equally to Lois Lane’s contradictory beliefs about Clark Kent and Peter’s contradictory beliefs about Paderewski. The account here provides such a unified solution. Finally, as we’ve seen, we can generate precisely the same sorts of puzzles with respect to predicative acts and properties. For all that Hanks says about semantic reference types, he says nothing about “property expression types” and how to individuate them with respect to semantic competence regarding predicates, and, even if the strategy does work for referential acts, it’s not at all clear that it can be carried over to predicative acts. The account here, by contrast, once again, offers a unified account of both phenomena. All we appeal to, in order to account for all of these cases, is the different discursive significance of propositional and predicative acts, as these acts are assessed and individuated from different perspectives.

6. Our Grasp of Instantiables

I began this paper with a distinction between assertibles and instantiables. I’ve now given an account of assertibles as types of acts of asserting (either full-stop or of things), and I’ve shown how, by thinking of the normative significances of these acts as varying from perspective to perspective, we can give account for ascriptions of propositional (and predicative) attitudes. It is now time to return to instiantables to articulate the final and I believe most philosophically significant upshot of this act-based account of assertibles: by not presupposing knowledge of instantiables on the part of speakers, it enables us to provide a satisfying account of speakers’ knowledge of instantiables in terms of their mastery of linguistic norms. Let me explain.

Standard act-based theorists such as Hanks and Soames (as well as other theorists of structured propositions such as King, Speaks, and many others) want to explain semantic norms in terms of the instantiation conditions of properties and relations that linguistic expressions stand for. For instance, in a case of saying of something that it’s round, it is as Hanks says: “The correctness conditions for your act of predication …flow directly from the satisfaction conditions of the property you latch onto” (2015: 207). So, it is in virtue of grasping properties such as being round, which have the instantiation conditions that they do, that one grasps the correctness conditions of predicative acts, and, thus, the norms governing those acts. Now, such theorists typically say relatively little about the nature of properties such as being round, though it is typically assumed that they are, as King says, “entities in the external world” (2018: 784) “existing quite independently of minds and languages” (2007: 450). Such worldly properties are what I have identified in the opening section of this paper as “1-place instantiables,” and, as I’ve just explained, standard act-based theories appeal to speakers’ cognitive relations to such entities in their accounts of assertibles.

By contrast, in the account of assertibles that I have provided, worldly properties, such as being round, instantiated by such things as the Sun and Neptune, do not show up at all. This, I claim, is a major a benefit. Insofar as we do not need to appeal to any epistemic relations that we bear to mind-independent abstract objects such as properties in order to explain our grasp of the norms governing the use of predicates, this opens the door for explaining our knowledge of properties and relations in terms of our grasp of the norms governing the use of predicates. That is, our knowledge of properties and relations is not a prerequisite of but a product of our mastery of the norms governing the use of predicates.

To spell out this epistemological thesis, consider our knowledge of the property of being a sphere. In what does this knowledge consist? We have given an account of what is to say of something that it’s a sphere; this is to perform an act that commits one to saying of it that it’s round, precludes one from being entitled to say of it that it’s square, and so on. What, however, is it for something to be a sphere? I suggest we endorse a completely analogous answer: it is to be a certain way, such that, if something’s this way, then its being this way necessitates its being round, excludes its being a square, and so on. Here, “necessitation” and “exclusion” express alethic modal relations, relations specifying how things in the world must necessarily be or can’t possibly be, given certain conditions. In specifying these alethic modal relations, we specify the distinctive “modal profile” possessed by a spherical thing. The property of being a sphere, on this account, is identified with this modal profile. In general, a property can be identified with the distinctive modal profile possessed by a thing that instantiates it: what something’s being this way necessitates that it be or excludes it from being. While a full account of the metaphysics of properties along these lines is beyond the scope of the current paper, I take this to be a perfectly plausible structuralist account of what properties are, and if one goes in for the normative structuralist account of assertibles I have articulated above, one might as well go in for a corresponding modal structuralist account of instantiables.²⁴ The core epistemological thought advanced here, made possible by this correspondence, is that it is through mastering the norms governing the use of “sphere” that we get a grip on the modal profile with which the property of being a sphere is identified. In general, our grasp of properties, relations, and states of affairs is understood in terms of our mastery of semantic norms.

This basic epistemological thesis has recently been defended for specifically modal properties and relations by Amie Thomasson (2020).²⁵ On Thomasson’s “modal normativist” view, in assertorically uttering a modal sentence such as “If something’s spherical, then it’s necessarily round,” one expresses a semantic norm. In the normative vocabulary deployed here, this would be the norm that asserting of something that it’s “spherical” indefeasibly commits one to asserting of it that it’s “round.” Thomasson claims that “the most important advantage of the normativist view” is that it provides a satisfactory epistemology of our knowledge of metaphysical modal facts, properties, and relations, such as our knowledge of the relation of necessitation that obtains between something’s being spherical and something’s being round, in terms of our knowledge of semantic norms (17). On the account here, we can extend this epistemological advantage to a much wider class of traditionally problematic metaphysical knowledge: that of properties and relations in general. Insofar as properties and relations themselves are identified as modal profiles, as I’ve suggested here, the modal normativist position can be extended beyond just modal properties and relations, to ordinary properties and relations such as being round or being larger than. Insofar as something’s being round just is its having certain modal profile, the knowledge of the property that we have is nothing other than a grasp of a certain set of modal relations, and, on the modal normativist picture, our knowledge of these modal relations is grounded in our mastery of the norms governing the use of predicates such as “sphere,” “round,” “square,” and so on. Since there is a straightforward story to tell of how this mastery is achieved through linguistic training, this account demystifies our knowledge of properties and relations.

Now, a modal normativist view of this sort is widely thought to entail anti-realism about modal relations, and, extended in this way, one might think it entails a problematic sort of anti-realism about properties and relations in general.²⁶ However, as I’ve spelled it out here, there is no such entailment. Endorsing an act-based epistemology of properties, according to which our knowledge of properties is grounded in our knowledge of the norms governing predicative acts, does not require endorsing an act-based metaphysics of properties, according to which properties themselves are in some way grounded in our assertoric acts or our normative attitudes through which we assess their significance. Thus, it is perfectly compatible with this account to say that the Sun instantiates the modal profiles that it does (such as being round, being a sphere, being a star, being primarily composed of hydrogen and helium, and so on) independently of us and our linguistic practices, and, moreover, that these modal profiles themselves, instantiated by the Sun and many other things, are what they are independent of us and our linguistic practices. That is, it is compatible with this account to say that the world has the modal structure that it does, articulated in terms of the properties and relations (modal profiles) instantiated by things, independently of our linguistic practices. Indeed, not only can we say this, but we are finally in a position to bring together the various pieces assembled here to account for our grasp of this very independence, once again, entirely in terms of our mastery of linguistic norms.

Recall, in §4, we drew a distinction between two conceptions of assertoric acts. The first conception conceived of them in terms of the subjective normative attitudes actually held by speakers, in virtue of which they attribute commitments and preclusions of entitlements upon someone’s assertorically uttering some sentence or predicate. In §5, we saw how this first conception enabled us to make fine-grained distinctions between assertoric acts by individuating these acts relative to the perspectives of different speakers, who take themselves to take on different commitments in assertorically uttering certain sentences or predicates. We also saw in §5, that, when speakers use some sentence or predicate, we can, given our differing set of scorekeeping principles, attribute commitments to them that they do not themselves acknowledge.

Thus, we can say, for instance, that, in saying that Superman flies, Lois has in fact committed herself to the claim that Clarke Kent flies, even though she does not take herself to be so committed. Likewise, we can say that, in saying of the Ilisos that it’s filled with water, Aristotle has in fact committed himself to the claim that it’s filled with H₂O, even though he does not take himself to be so committed. Now, on Brandom’s account of opacity on which I’ve drawn here, de re ascriptions of beliefs and assertions function to explicitly mark such commitments that we attribute to someone, in tokening some assertoric act, that they may not themselves acknowledge. In the case of Lois, to explicitly mark the commitments we attribute to her in tokening her referential act that she does not herself acknowledge, we use the following familiar sort of de re ascription:

• 7.  

  In saying that Superman flies, Lois said of Clarke Kent that he flies.

Here, “of” introduces an extensional context in the attribution of an assertion to Lois, understood here as a context in which, in specifying her act in terms of its inferential consequences, we can freely substitute in accordance with our own scorekeeping principles, rather than being refined to her own. How do we do the same sort of thing in the case of Aristotle, explicitly marking the commitments we attribute him in tokening his predicative act that he does not himself acknowledge? I take it that one way in which we can do it is by specifying them with the use of “property” talk. Thus, we can say:

• 8.  

  In saying of the Ilisos that it’s filled with water, Aristotle ascribed the property of being filled with H₂O to the Ilios.

The use of “property” talk here plays the same basic expressive role as the “of” in “Lois said of Clarke Kent that he flies,” licensing attributions of commitments to Aristotle that he does not himself acknowledge. Understanding that this structure of commitment attribution applies to our own acts as well, we understand that, in assertorically uttering some predicate, the commitments that we actually undertake—those that can be rightly attributed to us by other speakers—can outstrip those that we ourselves acknowledge. Such other speakers could likewise mark this sort of attribution with “property” talk. Likewise, other speakers could do the same with respect to them. Insofar as talk of “properties” can be understood as playing this expressive role, we can understand the modal profiles with which properties are identified as objective, being what they are independently of anyone’s subjective attitudes.

This brings us, finally, to the second conception of assertoric acts discussed in §4, individuated in terms of the normative relations specifying what someone is really committed to, in assertorically uttering some sentence or predicate, regardless of anyone’s attribution of such commitments. The notion of such normative relations is arrived at negatively, through, first, grasping our own normative attitudes which we’ve acquired through induction into the linguistic practice and, second, through grasping the cross-perspectival structure of scorekeeping just articulated, understanding that the commitments that may be rightly attributed to us can outstrip those that we ourselves acknowledge, given our normative attitudes. It is in virtue of this structural feature of scorekeeping that the discursive practice in which such scorekeeping takes place can be understood as one in which the norms governing assertions are objective, settled not by anyone’s subjective attitudes but by the objects themselves. And our concept of the instantiables we ascribe to things in using predicates just is the concept of the determinants of such objective normative relations. These are just those aspects of the objective world to which we are ultimately beholden, in saying the things that we do. In this way, assertoric acts, conceived in accordance with this second conception, are understood acts of representing things as instantiating objective properties and standing in objective relations. Maintaining the epistemological account just given in this section, our knowledge of these instantiables is still grounded in our normative attitudes, acquired through linguistic training. However, insofar as we recognize the possibility of our being rightly attributed commitments that we do not ourselves acknowledge, a crucial structural aspect of our knowledge of instantiables is our recognition that our grasp of the modal relations that constitute them is often only partial. It is in recognizing this limitation of our own knowledge of instantiables that our understanding of their objectivity consists.

Before concluding, one more point must be noted. Insofar as one is a realist about worldly properties and relations in the way I’ve just suggested we ought to be, it is a genuine question of how the normative structure of our linguistic practices comes to correspond to the modal structure of independent reality (at least, in the cases in which there really is such a correspondence). It’s worth being explicit that one sort of answer that’s ruled out by the epistemological account I’ve given is the standard representationalist one mentioned at the beginning of this section, according to which speakers first grasp properties and relations, which stand in various modal relations to one another, and then deploy linguistic expressions to conventionally stand for these properties and relations. On that sort of story, the normative relations between predicates—for instance, that commitment to “$x$ is circular” precludes entitlement to “$x$ is square”—simply follows from the fact that these predicates conventionally stand for the properties that they do. I submit, however, that an answer of this form, insofar as it precludes us from being able to provide the normativist account of our knowledge of properties and relations that I have just articulated, will leave us forever in the dark about our epistemic access to properties and relations. Thus, when faced with the question of explaining how, through the course of natural history, the norms of our linguistic practices come to be structured in such a way that they correspond to aspects of the objective world, an alternate story, or, rather, set of stories must be told. I take it that the specific explanatory stories to be told will vary considerably depending on the sort of semantic norms we’re considering, for instance, whether there those governing observational vocabulary such as “round” or theoretical vocabulary such as “hydrogen.” Actually providing any such metasemantic explanatory stories is beyond the scope of the current paper.²⁷ The point that deserves emphasis, however, is that, far from precluding us from providing such explanations, this account opens the door for genuine explanations of how we, as language speakers, achieve knowledge of the structure of objective reality.

7. Conclusion

I have given an act-based account of assertibles. Assertibles are understood as assertoric act types, identified in terms of their normatively-articulated functional role. These act-types are understood, in the first instance, as perspective-relative. For each predicate or sentence and each speaker who can assess the normative significance of assertorically uttering that predicate or sentence, we can in principle specify the act-type tokened in assertorically uttering that predicate or sentence in terms of its normative profile, assessed relative to the perspective of that speaker. Yet, through the perspectival structure of the attribution of normative statuses, we arrive at the idea of a set of normative relations that specify what one is really committed to, in uttering that sentence or predicate. Our notion of the corresponding instantiable, articulated in alethic modal terms, just is our notion of the determinant of such objective normative relations. Thus, while assertibles are understood in the first instance as perspective-relative, the corresponding instantiables are perspective-neutral; they are constituents of the objective world. The world, as Wittgenstein (1922) says, is the totality of facts. That is, the world is all the things that there are being all the ways that they are and standing in all the relations that they do.²⁸ The facts that constitute reality and the properties and relations that in part constitute these facts are the things to which we are ultimately beholden in saying the various things that we do, either full-stop or about particular things in the world.

Acknowledgments

For helpful discussions and/or comments on earlier drafts of this paper, many thanks to Mack Sullivan, Jeff Speaks, Peter Hanks, Till Hoeppner, Luz C. Seiberth, Johannes Haag, Robert Brandom, Ulf Hlobil, Daniel Nolan, and two anonymous referees for this journal.