1. Introduction: a puzzle for Russellianism

The following two sentences express distinct propositions:

The first, after all, expresses a proposition that’s true according to Moby Dick whereas the second does not. An adequate theory of propositions must accommodate that distinctness. But it turns out that the traditional Russellian theory of propositions is not so accommodating.Footnote ¹ The problem can be succinctly stated as an inconsistent triad:

The first two statements seem independently plausible, and the third seems plausible given the Russellian theory of propositions. Hence, this inconsistent triad constitutes a theoretical puzzle for anyone endorsing it.Footnote ^2, Footnote ³

In this paper, I develop a variant of Russellianism that, when appropriately augmented, is equipped to solve the theoretical puzzle above. This variant – Plenitudinous Russellianism – is a view on which there are distinct propositions that are structurally identical to one another. Plenitudinous Russellianism, augmented with gappy propositions, is equipped to deny (C). For, assuming that ‘Ahab’ and ‘Holmes’ really do fail to refer, the defender of Plenitudinous Russellianism can say that (S1) and (S2) express distinct, yet structurally identical, gappy propositions.Footnote ⁴ In Section 2, I first show how Traditional Russellianism is subject to the theoretic puzzle above and then introduce Plenitudinous Russellianism. There are some key metaphysical and semantic differences between Plenitudinous Russellianism and Traditional Russellianism. In Section 3, I discuss the distinguishing metaphysical thesis of Plenitudinous Russellianism while considering and responding to objections directed at that thesis. In Section 4, I discuss the distinguishing semantic thesis of Plenitudinous Russellianism while considering and responding to objections directed at that thesis. These objections, although quite powerful, are not decisive and I believe that Plenitudinous Russellianism is worthy of further development. Finally, in Section 5, I give a more detailed account of how Plenitudinous Russellianism deals with (S1) and (S2).

2. Traditional Russellianism and Plenitudinous Russellianism

On the Traditional Russellian theory, propositions are made up of constituents: individuals, properties, propositional operators, quantifier meanings, etc. The constituents of a proposition play particular roles in that proposition. On the semantics of Russellianism, declarative sentences express propositions (in a context).Footnote ⁵ The proposition expressed by any particular declarative sentence contains as constituents the semantic contents of the terms that make up that sentence. The semantic contents of proper names are the individuals to which those names refer, if any. The semantic contents of simple predicates are the properties picked out by those predicates, if any. Finally, the semantic contents of the terms that make up a declarative sentence play a role in the proposition expressed that corresponds to the role played by those terms in the sentence.

Consider a straightforward case:

This sentence is made up of a proper name, ‘Barack Obama’, and a simple predicate, ‘is a lawyer’. The name refers to Obama and hence has Obama as its semantic content. The predicate picks out the property being a lawyer and hence has being a lawyer as its semantic content. So, the proposition expressed by (S3) contains Obama and the property being a lawyer as constituents. Moreover, since ‘Barack Obama’ plays the subject role in (S3), Obama himself must play a subject-like role in the proposition expressed by (S3); since ‘is a lawyer’ plays the predicate role in (S3), being a lawyer must play a predicate-like role in the proposition expressed by (S3).Footnote ⁶ We can represent the proposition expressed by (S3) in the following way:

This representation can be understood as an ordered pair. The first member of the ordered pair is that which plays the subject-like role in the proposition represented. The second member of the ordered pair is that which plays the predicate-like role in the proposition represented. I cannot stress enough that this is merely a representation. We could have represented the proposition in question with an ordered pair of unit sets, the first member of which is the unit set containing Obama and the second member of which is the unit set containing being a lawyer; or we could have represented the proposition in question with an ordered pair the first member of which is being a lawyer and the second member of which is Obama; or we could have represented the proposition in question using a structured tree similar to those which are used in diagramming sentences; or we could have just used the English sentence ‘Barack Obama is a lawyer’.Footnote ⁷ None of these representations is objectively better than any others. But some representations more perspicuously convey various semantic and metaphysical facts than others. I will stick with representations like the one above, but with one simple modification to be introduced later.

But now we are in a position to see why statement (C) of our theoretical puzzle is so plausible given Traditional Russellianism. Suppose that neither ‘Ahab’ nor ‘Holmes’ has a referent, as is claimed by the antecedent of (C). If neither of those names has a referent, then, in accordance with Russellianism, neither of those names has a semantic content. But if neither of those names has a semantic content, then (S1) and (S2) are both semantically defective in their subject positions. Now, on some versions of Russellianism, sentences that are semantically defective just don’t express propositions. So, on those versions of Russellianism, (S1) and (S2) just wouldn’t express propositions at all, much less distinct propositions. On other versions of Russellianism, semantically defective sentences express correspondingly defective propositions; semantically defective sentences express propositions that contain unfilled roles or gaps. On those versions of Russellianism, since (S1) and (S2) differ only in their subject positions and since they are both semantically defective in their subject positions, they both express a proposition that has an unfilled subject-like role and has the property being a whaler filling its predicate-like role. Plausibly, then, they both express the same gappy proposition.Footnote ⁸ So, if ‘Ahab’ and ‘Holmes’ both fail to refer, as the antecedent of (C) claims, then either (S1) and (S2) fail to express different propositions because they fail to express propositions at all or they fail to express different propositions because they both express the same gappy proposition.

Admittedly, there are several responses one might give to this puzzle. Some Russellians might be willing to bite the bullet and accept that (S1) and (S2), contrary to appearances, really do express the same proposition. They may try to explain away the appearance of distinctness by appealing, for example, to ways of believing; or by appealing to differences in pragmatic implications.Footnote ⁹ Other bullet biters may say that (S1) and (S2) don’t express propositions at all and hence don’t express the same proposition.Footnote ¹⁰ Still others might be willing to accept a bifurcated view on which fictional names, unlike non-fictional names, have descriptive content.Footnote ¹¹ Finally, some may simply say that fictional names really do refer; they refer to fictional characters and the sentences in question express distinct non-gappy propositions.Footnote ¹²

But Plenitudinous Russellianism offers a novel response to our theoretic puzzle and avoids many of the counterintuitive consequences of its traditional rivals. A Plenitudinous Russellian need not accept a metaphysics of fictional characters, nor endorse a bifurcated semantics of proper names and, yet, may still hold that (S1) and (S2) express distinct propositions. Plenitudinous Russellian is just like Traditional Russellianism in that simple declarative sentences express propositions. If the predicate of a simple declarative sentence picks out a property, then the proposition expressed by that sentence contains the property picked out as a predicate-like constituent. If a name in the subject position of a simple declarative sentence has a referent, then the proposition expressed by that sentence contains that referent as a subject-like constituent. Moreover, I advocate for a version of Plenitudinous Russelianism on which a simple sentence that contains a non-referring name expresses a gappy proposition. However, Plenitudinous Russelianism is distinguished from Traditional Russellianism by two theses. First, that there are distinct propositions that have exactly the same constituents playing exactly the same roles. And, second, the proposition expressed by a simple declarative sentence is not simply determined by the semantic contents of the subject and predicate of that sentence but also by reference relations. In the next two sections, I will spell out these two theses and defend them from objections.

3. Metaphysics of Plenitudinous Russellianism

Let’s start with a definition. Letting ‘p’ and ‘q’ range over simple subject–predicate propositions, let’s say:

What metaphysically distinguishes Plenitudinous Russellianism from Traditional Russellianism is that Plenitudinous Russellianism entails that there could be distinct yet structurally identical propositions whereas Traditional Russellianism does not. In other words, Traditional Russellianism entails that, necessarily, for any p and q, p is structurally identical to q if and only if p is identical to q; Plenitudinous Russelianism entails that, possibly, for some p and q, p is structurally identical to q and yet p is not identical to q.

Some people might find the distinctive metaphysical thesis of Plenitudinous Russellianism incredible. After all, it seems to violate a plausible principle about the grounds of identity between propositions. It seems that, necessarily, the structural indistinguishability of propositions grounds the identity of those propositions. But if that’s the case, then there cannot be distinct yet structurally identical propositions. We can formalize this argument as follows:

• (1) Necessarily, for any p and q, if p is structurally identical to q, then the fact that p is structurally identical to q grounds the fact that p is identical to q.

• (2) If so, then it is necessary that for any p and q, if p is structurally identical to q, then p is identical to q.

• (3) So, necessarily, for any p and q, if p is structurally identical to q, then p is identical to q.

Line (2) is impeccable. First, it’s necessary that if one fact grounds another, then both facts obtain. So, if (1) is true, then it’s necessary that for any p and q, if p is structurally identical to q, then the fact that p is structurally identical to q and the fact that p is identical to q both obtain. Second, facts obey a redundancy principle: necessarily, if the fact that p obtains, then p. So, if (1) is true, then it’s necessary that for any p and q, if p is structurally identical to q, then p is structurally identical to q and p is identical to q. By simple logic it follows that if (1) is true, then it’s necessary that for any p and q, if p is structurally identical to q, p is identical to q. But that’s just line (2).Footnote ¹⁴

The crux of the argument lies with premise (1). (1) might be supported by some general metaphysical principle. For example, one might think that all abstract objects are generated by abstraction principles, which give the conditions that ground identity facts about particular abstract objects. Since propositions are abstract objects, they must also be generated by abstraction principles, which give the conditions that ground identity facts about propositions. But the only plausible abstraction principle is one that grounds the identity of propositions in structural indistinguishability. Or one might, slightly less stringently, believe that any abstract objects or (perhaps) any theoretical posits must be accompanied by a principle that gives the identity grounding conditions for those objects or posits. Since propositions are abstract objects and (on some views) theoretical posits, then they too must be accompanied by a principle that gives their identity grounding conditions. Again, the only plausible such principle for propositions is that their structural indistinguishability grounds their identity.

It seems to me that there are two plausible responses to the above argument. First, one might reject premise (1) and endorse some alternative identity grounding conditions for propositions (or at least give some reason to believe that there are alternative conditions). Second, one might reject premise (1) and reject the demand for identity grounding conditions. Let’s consider each of these in turn.

Suppose we want to reject (1) and endorse some alternative identity grounding conditions. Then, of course, we must come up with some plausible alternatives. But some potential alternatives are too course-grained for any form of Russellianism. For example, some might believe that necessarily, for any propositions, p and q, if p is true in exactly the same possible worlds as q, then that fact grounds the fact that p is identical to q. But given those course-grained identity grounding conditions, the proposition that 2 + 2 = 4 and the proposition that everything green is extended must be identical, since both are necessarily true. If any form of Russellianism is true, though, then those two propositions are distinct. After all, they have different constituents. The first has the numbers 2 and 4 as constituents whereas the second does not. So, the course-grained identity conditions are off the table.Footnote ¹⁵

Since the identity grounding conditions noted above are too course-grained for our purposes, one might opt for the following fine-grained alternative: necessarily, for any propositions, p and q, if it’s necessary that one has a propositional attitude towards p iff one has that attitude towards q, then that fact grounds the fact that p is identical to q. But this alternative has at least two problems. First, it seems that modal facts should be grounded in non-modal facts rather than vice versa. But if the fine-grained alternative were correct, then the non-modal fact that one proposition is identical to another would be grounded in a modal fact. Second, there are several propositions toward which no possible being can have any attitudes.Footnote ¹⁶ But if the fine-grained alternative given above were correct, then there would at most be one such proposition.

There is one more fine-grained alternative, which I will mention shortly, but for now let’s consider a different response to the argument above. Instead of rejecting premise (1) and advancing some alternative identity grounding conditions, one might reject premise (1) and reject the demand for identity grounding conditions. It may be that, necessarily, for any x and y, if x is identical to y, then the fact that x is identical to y is a brute fact (there’s no further fact that grounds it). It seems that necessarily, for any x and y, if x is identical to y, then the fact that x is identical to y is the same as the fact that x is identical to x. But that latter sort of fact seems to be a brute fact. After all, any fact about x that could ground the fact that x is identical to x would presuppose that x is identical to x. But if one fact presupposes another, then the first fact cannot also be a ground for the other. So, no fact could be a ground for the fact that x is identical to x. So, the fact that x is identical to x is a brute fact. Hence, the fact that x is identical to y is a brute fact as well.Footnote ¹⁷ Thus, one might simply reject the demand for identity grounding conditions in the first place.

Another argument against the distinctive metaphysical thesis of Plenitudinous Russellianism exploits the putative connection between constituency and parthood. Here is a formal presentation of the argument:

• (4) No two objects can have the same parts, at some level of decomposition, playing the same structural roles.

• (5) If (4), then no two propositions can have the same constituents playing the same structural roles.

• (6) So, no two propositions can have the same constituents playing the same structural roles.

We have already encountered the notion of a structural role. The structural roles in propositions are characterized grammatically. But what exactly could a structural role be in an ordinary object? It doesn’t really matter for our purposes. But let’s just assume that the structural roles in an ordinary object are characterized by the spatio-temporal and causal interactions between the parts of an object. For any x and y, if there is a one-one correspondence between the parts of x and the parts of y that preserves spatio-temporal and causal relations, then each of the parts of x plays the same role in x as the corresponding part in y.

So, then, it follows from premise (4) that if one object has some parts, at a particular level of decomposition, standing in particular spatio-temporal and causal relations to one another, then no distinct object has exactly those parts standing in exactly those spatio-temporal and causal relations.Footnote ¹⁸ Premise (4) is not only intuitively plausible, but also assumed in the standard logic of parthood; Classical Extensional Mereology entails that no two objects can have exactly the same parts at a given level of decomposition. In fact, even if we drop the most controversial axiom of Classical Extensional Mereology, the axiom of Unrestricted Composition, the resulting system still entails that no two objects can have exactly the same parts at a given level of decomposition.Footnote ¹⁹ It clearly follows that no two objects can have the same parts, at some level of decomposition, playing the same roles.

Line (5) draws an analogical connection between parthood and constituency. Some people might defend line (5) on the grounds that since parthood and constituency are analogically related, they ought to obey roughly the same logical principles. But, as we’ve seen already, it follows from the logic of parthood that no two objects can have the same parts, at some level of decomposition, playing the same roles. So, one might think it must also follow from the logic constituency that no two propositions can have the same constituents playing the same roles. Alternatively, some might defend (5) on the grounds that constituents just are parts. Some people believe that for any proposition, p, any constituent of p is a part of p and any part of p shares a part with at least one of its constituents.Footnote ²⁰ This kind of view might be supported by a kind of mereological monism according to which all parthood relations, including constituency, are partially analyzed by one fundamental parthood relation. In any case, it’s clear that if the constituents of a proposition are all parts of that proposition and any part of that proposition shares a part with at least one of the constituents, then the constituents of that proposition are all the parts of that proposition at a particular level of decomposition. It follows straightforwardly, then, that if no two objects can have all the same parts at some level of decomposition, playing the same roles, then no two propositions can have the same constituents playing the same roles. So, premise (5) would be true.

So, what might be wrong with this argument? Some people might reject premise (5) on the grounds that constituency is very different from parthood. One might think that the constituents of a proposition are constituents not in the sense that they are parts of the propositions, but rather in the sense that they are represented by the proposition. Think of the constituents of U.S. senator Chuck Schumer. His constituents are not part of him, but are rather represented by him. Perhaps the same is true of the constituents of propositions; they are not literally parts of the proposition but are merely represented by the proposition.Footnote ²¹

Even if we were to accept an analogical connection between parthood and constituency, there are serious doubts about (4). It seems like a statue and a lump of gold from which it is formed might be distinct objects that have the same parts, at some level of decomposition, playing the same roles. Moreover, it’s possible that, in a future epoch, you have a doppelganger who will have at that later time all the same subatomic parts as you currently have, playing the exact same roles. If that being were to time travel to the present, then there would be two beings with the same parts, at some level of decomposition, playing the same roles.

Admittedly, one might reject the principle that no two objects can have the same parts, at some level of decomposition, playing the same roles and accept that no two propositions can have the same constituents playing the same roles. Such a position might be motivated on the grounds that propositions can satisfy their theoretical role, in particular their role as the contents of declarative sentences, only if no two propositions could have the same constituents playing the same role. This worry is intimately connected to the semantic principle under discussion in the next section. I hope the following discussion will help to mitigate the worry.Footnote ²²

4. The semantics of Plenitudinous Russellianism

The discussion that follows will be simplified by ignoring context sensitivity, tense, structural ambiguity, and the parts of sentences that have no meaning in isolation. Let’s say that:

What semantically distinguishes Plenitudinous Russellianism from Traditional Russellianism is that, on the Traditional Russellian view, the proposition expressed by a declarative sentence is the unique proposition that is structurally isomorphic to that declarative sentence whereas on Plenitudinous Russellianism it is not. Remember that, on Plenitudinous Russellianism, there are some distinct yet structurally identical propositions. Suppose that P and Q are two arbitrarily chosen distinct yet structurally identical propositions and that there’s some sentence, S, which expresses P. Since P and Q are structurally identical, then S is structurally isomorphic to P if and only it S is structurally isomorphic to Q. So, although S expresses P, it is not the case that P is the unique proposition that’s structurally isomorphic to S. So, unless propositions that have structurally identical twins are just inexpressible, Plenitudinous Russellianism cannot simply adopt the Traditional Russellian semantic thesis.Footnote ²³ Instead, the Plenitudinous Russellian must adopt some slightly less committal view according to which the proposition expressed by a declarative sentence is some proposition that is structurally isomorphic to that declarative sentence.

There is, however, a strong reason to favor the semantic thesis of Traditional Russellianism. Here’s the rough idea. If some sentence expresses a proposition that is not uniquely structurally isomorphic to that sentence, then it must be a brute fact that sentence expresses that proposition. But it cannot be a brute fact that a particular sentence expresses a particular proposition. Semantic facts, after all, can’t be brute facts. Here is a formulation of that argument:

• (7) Necessarily, if for some sentence, S, and some proposition, P, S expresses P and P is not the unique proposition that’s structurally isomorphic to S, then for some sentence, S, and some proposition, P, S expresses P and it’s a brute fact that S expresses P.

• (8) Necessarily, for any sentence, S, and any proposition, P, if S expresses P, then it’s not a brute fact that S expresses P.

• (9) So, necessarily, for any sentence, S, and proposition, P, S expresses P only if P is the unique proposition that’s structurally isomorphic to S.

I take this to be one of the most powerful objections to Plenitudinous Russellianism. After all, propositions are supposed to be the semantic contents of sentences and so there should be a plausible story to tell about how particular propositions become the semantic contents of particular sentences. Plenitudinous Russellianism seems to undermine our ability to tell such a plausible story. There are, though, two responses which I will discuss below.

First, one might object to (9) and claim that some semantic facts are brute facts. Some views already seem to require brute semantic facts. Epistemicism, for example, is the view that vague predicates express particular properties and yet, in most cases, it is unknowable which properties they express.Footnote ²⁴ But this seems to imply that nothing grounds that a particular vague predicate expresses one property rather than one of the others.Footnote ²⁵ After all, if something did ground that fact, then we would simply have to discover whether that grounding fact obtains in order to know what that vague predicate expresses.Footnote ²⁶ Hence, it’s a brute semantic fact, in most cases, that vague predicates express the properties they do rather than some other nearby property.

Similarly, sometimes we introduce names with arbitrary referents. For example, when I wish to prove that the power set of any set has strictly more members than that set, I might start the proof by saying ‘Let “S” name an arbitrary set’, then go on to prove that the power set of S has strictly more members than S before generalizing. On one view of arbitrary reference, the name introduced, ‘S’, has a particular referent. Moreover, it is partly because the referent of ‘S’ is arbitrary that the generalization at the end of the proof preserves truth. But if ‘S’ has a particular referent, then the fact that it has that referent is a brute fact. Hence, on this view of arbitrary referents, there are some brute semantic facts.Footnote ²⁷

If there are brute semantic facts, as the two views above seem to imply, then the second premise cannot be supported by the general claim that there are no brute semantic facts. Moreover, if there are brute semantic facts, then one might plausibly claim that when there’s no unique proposition structurally isomorphic to a particular declarative sentence, it’s a brute fact which proposition that sentence expresses.

Some, including me, are uncomfortable with brute semantic facts. Luckily, there is a second, stronger, response to the argument. On this second response, (8) is false; although some sentence expresses some proposition that is not uniquely structurally isomorphic to that sentence, it's not a brute fact that sentence express that proposition. My favorite version of this view employs a causal or historical explanation theory of reference (Donnellan Reference Donnellan1974) and the claim that structurally identical propositions are distinguished by their intimate connection to reference relations. Before I sketch out that story, though, let’s look at a simpler case.

Consider, again, our sentence (S3):

This sentence expresses a particular proposition, which we are (temporarily) representing as follows:

But the fact that (S3) expresses (P3) is partly grounded in the fact that the semantic content of ‘Barack Obama’ is Obama. Moreover, the fact that the semantic content of ‘Barack Obama’ is Obama is either identical to, or grounded in the fact that ‘Barack Obama’ refers to Obama. Now, on the causal/historical explanation theory of reference, the fact that ‘Barack Obama’ refers to Obama is either identical to, or grounded in the fact that ‘Barack Obama’ and Obama appear at different ends of a chain of causal or historical explanations. So, it seems to follow that the fact that (S3) expresses (P3) is at least partly grounded in the fact that ‘Barack Obama’ and Obama appear at different ends of a chain of causal or historical explanations. Clearly, then, causal or historical explanations come into the story about what grounds certain expression facts.

Now I’d like to extend this idea. When there are two propositions that are structurally isomorphic to a particular sentence, then if the sentence contains a proper name, the fact that it expresses one of those propositions (rather than the other) is partly grounded in the fact that the name in that sentence appears at the end of some particular chain of causal or historical explanations to which that proposition is intimately related. How might a particular proposition be intimately related to a particular chain of causal or historical explanations? Here are two ideas that seem promising to me. First, a certain causal or historical explanation might be intimately connected to a certain proposition in that the explanation partly grounds the existence or identity of that proposition. An added benefit of this idea is that anyone who endorses it can reject premise (1) of the first argument of the previous section by endorsing alternative identity grounding conditions for propositions. Second, a certain causal or historical explanation might be intimately connected to a certain proposition in that the initial event in the explanatory chain causes that proposition to come into existence or, if the proposition already existed, causes it to be tokenable for the first time.Footnote ²⁸ The Plenitudinous Russellian can then say that the proposition expressed by a simple declarative sentence is the unique proposition that both is structurally isomorphic to that declarative sentence and that is intimately connected, either by causation or by grounding, to the causal or historical chain that makes the subject of the sentence refer to the individual playing the subject-like role in the proposition if there is such an individual or makes the subject of the sentence refer to nothing. Causal or historical explanations can thereby play a role in grounding which proposition is expressed. It’s important to emphasize, though, that the chain of causal or historical explanations is not a constituent of the proposition expressed, it is merely intimately related, by causation or by grounding, to the proposition expressed.

Once we’ve accepted this view it’s easy to see how we might reject premise (8). Suppose that S is a sentence that’s structurally isomorphic to two distinct propositions, P and Q. The expressions in S stand in certain chains of causal or historical explanations and those chains are intimately related to one of the propositions, let’s say P, and not the other. That fact partly grounds that S expresses P rather than Q. Moreover, there might be another sentence, S*, that is also structurally isomorphic with P and Q. But maybe S* expresses Q rather than P because the expressions in S* stand in different chains of causal or historical explanation than those in S, chains that are intimately related to Q rather than P. This is all a bit abstract, though. So, let’s take a closer look at our ‘Ahab’ and ‘Holmes’ sentences to get a better sense of how this all works.

5. Plenitudinous Russellianism and fiction

Clearly, if Plenitudinous Russellianism is true, then we must amend our method of representing propositions; we must be able to represent distinct yet structurally identical propositions as being distinct. I recommend that we add subscripts to our pointy bracket representations. So, for example, we can represent the proposition that Obama is a lawyer as follows:

The subscript is no more a constituent of the proposition expressed than the comma or the pointy brackets themselves. Officially, I remain neutral about whether or not there are any propositions that are structurally identical to (P3). Plenitudinous Russellianism, it should be pointed out, is consistent with the view that there are such propositions and also consistent with the view that there are no such propositions. However, for consistency, I will put subscripts on all the official propositional representations regardless of whether there are propositions structurally identical to the ones represented.

Now, we can see how Plenitudinous Russellianism deals with the two sentences from our introduction:

Recall that on Traditional Russellianism, augmented with gappy propositions, (S1) and (S2) express the same gappy proposition. However, Plenitudinous Russellianism allows for structurally identical gappy propositions. In particular, Plenitudinous Russellianism allows for structurally identical propositions each of which has a subject-like position that’s unfilled and a predicate-like position that’s filled by the property being a whaler. Those gappy propositions are structurally isomorphic to (S1) and (S2). So, it’s compatible with Plenitudinous Russellianism that (S1) expresses one of those propositions and (S2) expresses another. We might represent the propositions expressed by (S1) and (S2) as follows:

Here, again, the subscripts represent the distinctness of those propositions, but do not represent any of their constituents.

Following up on the discussion of the previous section, one might ask the following questions: What grounds the fact that (S1) expresses (P1) rather than (P2)? And, what grounds the fact that (S2) expresses (P2) rather than (P1)? Well, if the first response to argument (8)-(10) is correct, then it might just be a brute semantic fact that (S1) expresses (P1) and a brute semantic fact that (S2) expresses (P2). But many people won’t find that answer very satisfying. I prefer to say that the fact that (S1) expresses (P1) rather than (P2) is partly grounded in the fact that ‘Ahab’ appears at the end of a particular chain of causal or historical explanations. That chain happens to end in what Donnellan (Reference Donnellan1974) calls a ‘Block’, a point at which no particular thing was successfully dubbed with that name. In this case, the block at the end of the chain involves certain of Herman Melville’s authorial activities.Footnote ²⁹ Now, that chain is intimately connected to (P1) and not to (P2), which is why (S1) expresses (P1) and not (P2). The chain might be connected to (P1) in that it grounds the existence or identity of (P1); it does not ground the existence or identity of (P2). Alternatively, the chain might be connected to (P1) in that Melville’s authorial activities cause (P1) to exist or be tokenable; it does not cause (P2) to exist or be tokenable. Hence (S1) expresses (P1) rather than (P2). Similarly, the fact that (S2) expresses (P2) is partly grounded in the fact that ‘Holmes’ appears at the end of a particular chain of causal or historical explanations the other end of which contains a block involving certain of Arthur Conan Doyle’s authorial activities. That chain is intimately connected, by grounding or by causation, to (P2) and not to (P1).

If Melville had chosen to use the name ‘Holmes’ instead of ‘Ahab’ and Conan Doyle had chosen to use name ‘Ahab’ instead of ‘Holmes’, then maybe (S1) would have expressed (P2) and (S2) would have expressed (P1).Footnote ³⁰ Similarly, if Melville had chosen to use the name ‘Ahab’ in a story significantly different from Moby Dick, then (S1) might have expressed a completely different proposition altogether. After all, Melville would then have been involved in very different authorial activities which would have been intimately connected to different propositions.

Funding

This research was supported in part by funds provided by the University of Wisconsin-Milwaukee.