Is L.A. Paul’s Essentialism Really Deeper than Lewis’s?

1. Introduction

Let us take essentialism to be the doctrine that at least some non-trivial property is determined to be essential to some objects, where trivial properties are properties such as being either F or non- F, for any property F.1 L.A. Paul distinguishes between “deep” and “shallow” essentialism. Deep essentialism is the thesis according to which properties are determined to be essential to an object O independently of the context.2 Shallow essentialism opposes deep essentialism: it rejects the view that properties can be determined as essential to O independently of the context. David Lewis is said to be a shallow essentialist.

Paul argues that standard forms of deep essentialism face a range of issues (mainly based on an interpretation of Quinean skepticism) that shallow essentialists à la Lewis do not. However, she claims, deep essentialism is what gives us those properties that define the real, ultimate, nature of the objects, while shallow essentialism eliminates the very heart of what motivates essentialism. Therefore, as Paul states, “it is better to be deep than to be shallow” (Paul 2006, 347). Accordingly, she proposes a very sharp novel account of essentialism, which, while attempting to preserve some of the advantages of shallow essentialism over the classical forms of deep essentialism, can be deemed to be deep.

While I concur with Paul regarding the challenges traditional forms of deep essentialism encounter in addressing skepticism, I will not delve into this matter. My focus in this paper will be on comparing Paul’s proposal for a kind of deep essentialism with Lewis’s account as presented by Paul. I will demonstrate that the differences between the two approaches in terms of depth are not as significant as Paul takes them to be, and that Paul’s account can be taken to be deeper than Lewis’s only at the cost of sacrificing the very idea at the bottom of deep essentialism.

This might be taken to suggest that, if Paul is correct in asserting that shallow essentialism is better equipped to address some skeptical challenges (as I think she is), but it is preferable to be deep than shallow, then Lewis’s account should be re-evaluated, since, as shallow as it can be, it might be deeper than it looks.

Before moving on, some quick terminological clarifications. Given an object O, I will distinguish between “the properties that are said/determined to be essential to O” and “the essential properties of O”. Unlike the latter, the first are those properties that are characterized as “essential” to O, only according to some context. For the sake of clarity, I will sometimes use expressions like “context-independent essential properties” or “essential properties determined independently of the context”, even though they are only redundant ways to say “essential properties”. Claims that attribute essential properties to objects, or properties that are said/determined to be essential, are “essentialist claims”.

2. Deep essentialism

Paul (2004, 2006) aims to defend a kind of deep essentialism (from now on “DE”). She writes that, according to DE: “essential properties are absolute, i.e., are not determined by contexts of describing (or thinking, etc.) about the object, and truths about such properties are absolute truths” (Paul 2006, 333). Similarly, she says that “deep essentialism takes objects’ natures and claims about them to be independent of context (…)” (Paul 2006, 358).

From these definitions, it seems reasonable to infer that DE, for Paul, is a thesis that holds at two levels of analysis: semantics and metaphysics. Indeed, Paul claims that the properties that define objects’ natures as well as “the truths about such properties” or the “claims about [objects’ natures]” are supposed to be “absolute”, namely, context-independent. However, in a footnote to the first quote, Paul claims that DE “should defend a certain sort of semantic indeterminacy consistent with this view (…)” (Paul 2006, 366). And, in some other places (for instance, see Paul 2004, 180), she clearly admits that, in her account, the truth-values of essentialist claims are inconstant.

I believe that, in order to understand what is really at stake here, we should clearly distinguish between the two different understandings of DE. Broadly speaking, semantics is about the semantic values of expressions. Semantically speaking, DE might thus be intended as the thesis that the truth-values of essentialist sentences must be context-independent (I will refer to the semantic understanding of DE as “DE semantical”). Metaphysics can be thought to concern the nature of the facts in the world, which are the truth-makers for sentences (the potentially truth-making properties, if we are going in for the truth-maker talk). Therefore, metaphysically speaking, DE might be interpreted as the thesis that what makes essentialist sentences true must be facts in the worlds, which are independent of the context (I will refer to the metaphysical reading of DE as “DE metaphysical”). In the following, I will compare Lewis’s stance towards these theses with Paul’s.

3. Lewis’s account

Let us consider essentialist sentence type 1):3

According to Lewis, the truth-conditions for 1) are given in terms of counterpart relations of Socrates. Counterpart relations are similarity relations that Socrates entertains with objects of (usually) other worlds, namely, counterparts (see, for instance, Lewis 1968, 1986).

Now, similarity is defined in terms of properties sharing. The fact that two individuals have some properties in common, that they are similar in some way, does not depend, in general, on the context;4 it depends on how the world(s) is(are) made. In other words, it is the business of metaphysics to establish similarity relations between objects. S imilarity, as it has been defined, is very easy to get: almost anything is similar to anything else, under some respect (see, for instance, Goodman 1972). Therefore, given an individual like Socrates, there are a lot of similarity relations that he entertains with possible objects, and such similarities are established independently of the context.

Then, there is the further question of which similarity relations are relevant, and relevance is a matter of context. Accordingly, as Divers puts it, what may change from one context to another “ are facts about which [similarity] relations are relevant in a context, not the facts about the obtaining or otherwise of [similarity] relations” (Divers 2007, 18).

Now, retracing Paul’s (2006, 344ff.) distinction between an “evaluative” and an “antiessentialist” kind of shallow essentialism, there are two plausible readings of how Lewis intends that we think of similarity relations and their selection , when it comes to essentialist claims:5

Paul is more inclined to interpret Lewis according to A, though she is not firm about this point (Paul 2006, 370).6 In this paper, I will discuss both interpretations, and I will call the Lewisian who accepts A “ Lewis_A ”, and the Lewisian who endorses B “Lewis_B”. If I do not specify the interpretation, it means that I am referring to both and, in order to do that, I will use the devise of putting between brackets what holds only for Lewis_B.

Lewis_A and Lewis_B give different truth-conditions for essentialist claims, such as 1). According to Lewis_A :

For Lewis_B:

However, in both cases, the same counterparts matter in order to determine the truth-values of essentialist claims: given a context C, the possible objects whose similarity to Socrates is relevant according to C. Therefore, 1_A and 1_B end up being equivalent for determining the truth-conditions of 1). This implies, as we will see presently, that there are no significant differences between Lewis_A and Lewis_B, when it comes to the evaluation of the truth-values of essentialist claims. >

Let us call “de re representations” of an object O the similarity relations that determine the de re modal properties of O. Therefore, in Lewis’s view, the de re representations of O are the similarity relations that are relevant in a context.

4. Lewis and DE semantical

Let us go back to 1):

As we saw, for Lewis, 1) is true iff all the (relevant) counterparts of Socrates are human. This means that the general form of the truth-conditions for an essentialist sentence type is incomplete: it needs to be completed with the input of a (relevant) counterpart relation, and we know that that is a contextual matter: O is a (relevant) counterpart of Socrates iff O is similar enough to him under relevant respects, but it is a matter of context which respects of similarity are salient and which grades of similarity are enough under such respects. The (relevant) counterparts of Socrates are therefore determined to a large extent by the contexts in which 1) is produced and evaluated. Therefore, Lewis gives complete truth-conditions only for specific tokens of 1). Different tokens of the same sentence type about Socrates might be produced and evaluated in different contexts and, thus, evoke different (relevant) counterparts of him. So, according to different contexts, different de re representations may figure in the content of the utterance of 1), and, hence, 1) might have different truth-values in different contexts. Accordingly, Lewis rejects the semantic constancy of essentialist claims, namely, he rejects DE semantical.

This means that, for Lewis, according to different contexts, different properties are said to be essential to an object. Note that I am not saying that an object is said to have different essential properties according to different contexts. Indeed, if essentialist claims are semantically inconstant, it would be misleading to talk about “essential properties”, since there are only properties that, according to a context, are said to be essential to an object.

5. Lewis and DE metaphysical

DE metaphysical is the thesis that what makes essentialist sentences true (the truth-making properties, if you like) must be facts in the worlds which are independent of the context.

So, let us see, in Lewis’s view, what ultimately makes essentialist sentences, such as 1), true. We know that what would make sentence 1) true is the fact that all the (relevant) counterparts of Socrates are human. Let us suppose that, in a context C, Socrates’s (relevant) counterparts are Socrates, O and P. Well, if 1) is true in C, this is so by virtue of the fact that Socrates, O and P are all human, that is by virtue of the fact that they are all similar by being all human. However, we saw that it is the job of metaphysics to establish similarity relations between objects, since they are based on the fact that objects have the properties they have, which, in turn, depends on how the worlds are made. So, it is a matter of metaphysics if O and P are similar to Socrates under some respect (they all share the property of being human) that happens to be contextually relevant. Therefore, 1), if true, is made true by facts in the worlds which are independent of the context.

Accordingly, Lewis accepts DE metaphysical: for Lewis, what makes an essentialist sentence true in a context are facts in the worlds which are independent of the context. This means that metaphysics can establish the properties that, according to some context, are determined to be essential to Socrates. Note that I am not saying that metaphysics can establish which essential properties Socrates has, because (and again) it would be misleading to talk, in this view, about “essential properties”: metaphysics can only establish which properties the objects (Socrates, O and P) exemplify; then those properties, according to some context (namely, when O and P are deemed to be (relevant) counterparts of Socrates), are required by the truth-conditions of 1) and, hence, are determined to be essential to Socrates. In other words, there are only properties (that are exemplified independently of context) that, according to a context, are determined to be essential to objects.

Saying that Lewis accepts DE metaphysical means to say that, at the level of metaphysics, no contextual facts are involved in the attributions of essentiality to some properties of individuals. And, in this sense (maybe a shallow sense), DE survives in Lewis’s metaphysics. Note also that, not even at the metaphysical level, there are relevant differences between Lewis_A and Lewis_B. 7

6. Paul’s account

Let us see now Paul’s account of how objects have properties as a matter of de re modality, which is crucial to her defence of DE (I will refer mainly to Paul 2004, 2006).

Paul takes ordinary objects to be nothing more than bundles of properties, such that bundling is a type of mereological fusion. The sum of the basic non-modal properties of an object O is its “ core” (the composition that gives rise to the cores is called “qualitative composition”, that is a fusion of properties). The fact that O’s core is in a counterpart relation (namely, a similarity relation) to some possible object which has a property F, generates the relational property ( Rprop) of being de re represented as having F ( RpropF). In this way, O is de re represented as having F. The Rprops are thus monadic relational properties ontologically generated by the core of the object standing in a counterpart relation to possibilia, and they are included in the sum that is the object (the composition between a core and the Rprops it generates is called “modal composition”, which is a kind of qualitative composition). Therefore, O is a sum of its core properties plus the Rprops of being de re represented in certain ways.

Then, if O includes F and the Rprop of being represented as not- F, then O is accidentally F. If O includes F and lacks the Rprop of being represented as not- F, then O is essentially F.

Therefore, in this perspective, for an object to have a de re modal property, both the core and the Rprops must be included in the sum that is the object. That is to say that, while we would intuitively take an object to be only its core (and Lewis with us), for Paul objects are sums of their cores plus the Rprops. The de re modal properties of an object supervene on the sum of object’s core plus the Rprops and, as such, they are included as well in the sum that is the object (see Paul 2006, 353).

Paul then claims that modal composition is unrestricted. Therefore, given a core (what we would take to be the object), and given that anything is similar to anything else under some respect, there are many objects composed by that core. In other words, where we thought there was only one object, there are instead many more objects. By having the same basic non-modal properties, namely the same core, these objects have a lot in common: they occupy precisely the same spatiotemporal region. Nonetheless, they occupy different regions of “modal space”: they differ from each other in terms of inclusion or exclusion of some Rprop and, so, in which de re modal properties they include. Therefore, we have a proliferation of objects and modal profiles (these different sums are different objects with different natures): many different objects with clear modal boundaries, metaphysically carved at their joints. However, Paul claims, in most non-philosophical contexts we would deny the existence of many of these objects. Nonetheless, according to her, they exist.8

Let “ O” be the name of an object. Since the sum of that object’s core and the Rprops generated by the core is unrestricted, then there are many sums which share the same core, and they are all plausible candidates to be the denotation of “ O”. Hence, there are many different sums that we can pick out when we use “ O”: for instance, the maximal sum of core properties and all the Rprops generated by that core, or some proper parts of this maximal sum. Paul maintains that it is the context that helps us to determine the denotation of “ O”.

Paul claims that, thanks to her theory of objects, she can disagree with Lewis about an important point that marks the passage from a shallow to a deep kind of essentialism. For Paul, the reason why Lewis is a shallow essentialist is that he accepts the inconstancy of de re representations. And Lewis overtly admits that he endorses inconstancy of de re representations. We have seen, indeed, that the reason why Lewis rejects DE semantical is precisely because objects, according to different contexts, may have different (relevant) counterparts and, so, the de re representations that figure in the content of the utterance of an essentialist sentence may change according to different contexts. Paul claims that, unlike Lewis, she is able to take de re representations to be constant.

Before delving into Paul’s strategy for achieving the hoped constancy of de re representations, it is useful to stress what I take to be the key moves of such a strategy. The first key move is semantical: Paul postulates that ordinary names such as “Socrates” are vague inasmuch they can refer (in this world) to different objects. The second key move is metaphysical: she includes in the sums she takes to be the objects the Rprops and the de re modal properties and, from this assumption, she derives that there exist many more objects that we thought, metaphysically carved at their joints.

Paul’s proposal is clever, captivating, ambitious, and deserves careful consideration. Despite my forthcoming arguments that Paul can (partially) eliminate the inconsistency of de re representations only by sacrificing the very idea at the core of deep essentialism, I believe it is her great merit to have acknowledged the significance of including contextual factors in the analysis of essentialism.

In the following pages, I will analyze what we can derive from Paul’s key moves with regard to the coveted constancy of de re representations, by starting from Paul’s stance toward DE semantical.

7. Paul’s semantic move and DE semantical

Let us go back to our essentialist sentence type 1):

According to Paul, context helps us to determine which object the name “Socrates” refers to, among the multitude of sums (in this world) that are eligible candidates for the denotation. Therefore, the general form of the truth-conditions for 1) is incomplete: it needs to be completed with the input of the denotation of “Socrates”. However, different tokens of the same term type “Socrates” might refer to different objects (in this world), which have different de re modal properties. This means that, in Paul’s view, 1) is such that in some contexts is true, and in some other context may be false.9 Therefore, Paul also embraces the inconstancy of the truth-values of essentialist claims. In other words, Paul also rejects DE semantical.10

However, since Paul is not totally clear about her rejection of DE semantical, it is important to see if there is any relevant difference between Paul and Lewis’s accounts, when it comes to semantics.

Let us consider Paul’s semantic move of postulating the vagueness of ordinary names. Well, the first semantic consequence that such a move has is to shift the source of the semantic inconstancy of essentialist sentences (I will simply refer to it as “the shift”): while in Lewis’s case the semantic inconstancy is due to the variability of Socrates’s de re representations, in Paul’s view, it is due to the semantic indeterminacy of “Socrates” (see Paul 2004, 180). Might it be the case then that, even if Paul rejects DE semantical, she can still guarantee, by virtue of the shift, the constancy of de re representations, as she claims? No, she cannot.

Indeed, in her view, given the semantic vagueness of the name “Socrates”, different contexts can pick out different objects as the reference for that name. However, by selecting an object, the context also selects its Rprops (which are included in the object). But, since the Rprops are generated from the object’s core standing in some de re representations, then, by selecting an object, the context also selects the object’s de re representations. Therefore, de re representations figure in the content of the utterance of an essentialist sentence for Paul as well as they do for Lewis. And, in both accounts, their inconstancy is the source of the rejection of DE.

So far, the only way in which Paul can get constancy is to say that, once we have specified which object “Socrates” denotes, the same de re representations will figure in all the utterances of essentialist claims about that object. Indeed, as we saw, once the context picks out one object, it also selects the object’s de re representations. Then, of course, in all the essentialist claims about that object, the same de re representations will figure. But the same happens with Lewis. Once a context is fixed, we know which de re representations figure in the content of the utterance of an essentialist claim about, say, Socrates. Hence, the same de re representations will figure in all the essentialist claims about Socrates. For instance, let us suppose again that, in the context of evaluation of 1), Socrates’s (relevant) counterparts are Socrates, O and P. Well, given that context, the same de re representations will figure in all the utterances of essentialist claims about Socrates.

So, for instance, Paul can claim that:

But, in this quote, the only difference between the two cases is that Paul supplies the context only for the latter example (her case). Indeed, by saying “Suppose that the person I refer to as ‘Humphrey’ is essentially descended from his parents”, Paul is supplying the context: she is individuating the reference of the name “Humphrey” as that sum that includes Humphrey’s core and does not include the Rprop for different origins. Of course, given a context and, with it, the object that the context picks out, then, in every essentialist claim about that very same object, the same de re representations that the object’s core entertains will occur. But the same would apply to the first case (Lewis’s case) if we supply a context: given a context and, with it, Humphrey’s (relevant) counterparts (say that they all have the same origins as Humphrey), in every essentialist claim about that very same object, the same de re representations will figure.

Therefore, so far, the difference between the two approaches is quite superficial. Paul maintains that de re representations are constant; however, what she really believes is that, once a context is supplied and, with it, the object that is the reference of the name (and, with it, the counterpart relations that the object’s core entertains) they are fixed. Lewis explicitly claims that de re representations are inconstant; nonetheless, what happens is that, once a context is supplied and, with it, the (relevant) counterparts, they are fixed. And it is precisely because they both accept, at the end of the day, the inconstancy of de re representations that they both reject DE semantical.

This means that, semantically speaking, Paul’s stance mirrors Lewis’s: (i) the selection of the de re representations is a contextual matter, therefore (ii) essentialist claims are inconstant, and (iii) according to different contexts, different properties are said to be essential to objects. Let us move on, now, to the metaphysical level, in order to see if, at that level, there are significant differences between the two approaches.

8. Paul’s metaphysical move and DE metaphysical

We know that similarity relations are metaphysically determined, and that they are easy to get. According to Paul, the similarity relations simpliciter can enjoy the status of counterpart relations. This means that, given Socrates’s core, (CoreS), such a core can be fused with many different Rprops. For instance, since there is a similarity relation between CoreS and a cat, under some respect, CoreS will also generate the Rprop for being represented as the cat (RpropC). Modal composition is unrestricted, so CoreS can combine with the Rprops that it generates in many different ways. So, for instance, we have the maximal sum of CoreS plus all the Rprops that it can generate (Sum_n), and all the proper subsets of Sum_n (Sum₁, Sum₂, and so on). Sum_n will have all its properties accidentally, while its subsets, by ruling out some Rprop, will have some properties essentially.

Let us take one of these subsets: Sum₁, which has CoreS plus the Rprop for being represented as a musician (RpropM). Sum₁ will be accidentally a philosopher and essentially human (there is no Rprop for being represented as non-human: for instance, the RpropC is not included in this sum). The fact that Sum₁ is essentially human, and here is Paul’s metaphysical move, is determined by virtue of constant de re representations. Indeed, Sum₁ is carved at its joints, metaphysically speaking. Surely, metaphysics cannot establish if Sum₁ is the best reference for “Socrates”. As Paul says (see 2006, 362), there is nothing that allows us to select one object rather than another, when we talk about Socrates: no object stands out as the privileged reference of “Socrates”. Nonetheless, metaphysics can establish the boundaries between Sum₁ and, say, Sum_n: these objects are carved at their joints. This means that it is not the context that determines which de re representations of Sum₁’s core are relevant: they are all at the same level. And, since metaphysics distinguishes between Sum₁ and Sum_n, and since Sum₁ includes only some of the Rprops generated by its core (only the RpropM), then we get metaphysically selected de re representations, namely constant de re representations. And such constant de re representations are able to determine the essential properties of Sum₁.

Let me stress the point that, in Paul’s view, should make the difference: Sum₁ has essential properties independently of context. That is, we are no longer talking about properties that, according to a context, are determined to be essential to Sum₁, but about its essential properties. And this can happen because such properties are established by virtue of constant de re representations: similarity relations, whose relevance is metaphysically determined. Indeed, the RpropM is the only Rprop included in Sum₁, which metaphysics carves at its joints; so, the similarity relation that Sum₁’s core entertains to the musician is metaphysically picked out, among all the similarity relations that that core entertains, since only the Rprop that it generates is included in Sum₁.

However, does this really amount to saying that Paul can guarantee constant de re representations, as she intends to? Does this make any relevant difference with Lewis for what regard DE metaphysical?

Well, recall that, in Lewis’s view, according to different contexts, different de re representations of Socrates are deemed to be relevant. Because of this, essentialist claims are inconstant and, hence, according to different contexts, different properties are said to be essential to Socrates. However, and here is Lewis’s acceptance of DE metaphysical, it is the business of metaphysics to establish the properties that, according to some context, are determined to be essential to Socrates.

Is the situation really different on Paul’s view? Well, I just said that metaphysics can establish essential properties of Sum₁, inasmuch they are determined by constant de re representations. However, only according to some context, Sum₁ is the reference of “Socrates”. This means that we are back where we were: according to different contexts, different de re representations of Socrates are deemed to be relevant (since different objects are regarded as relevant). Because of this, essentialist claims are inconstant and, hence, according to different contexts, different properties are said to be essential to Socrates. And Paul accepts DE metaphysical, for the very same reasons why Lewis accepts it: metaphysics establishes the properties that, according to some context, are determined to be essential to Socrates.

This means that, in both accounts, de re representations are inconstant and, in neither account, metaphysics can determine the essential properties of Socrates, but only the properties that, according to some context, are required by the truth-conditions of an essentialist sentence about him and, thus, are determined to be essential to him.

The only way to make a difference between the two accounts, therefore, is to insist on focusing on what happens to, say, Sum₁, which is an object for Paul, and, as I said, does have essential properties, determined by constant de re representations. Indeed, when Paul says that she can guarantee that objects have essential properties and are de re represented in a constant way, she does not intend to talk about what we would take to be objects (like Socrates), rather she means to talk about objects like Sum₁. And, surely, Lewis cannot guarantee that any of his objects have any of those characteristics.

However, is there really any improvement if we focus on objects, like Sum₁, which have essential properties and constant de re representations? I say no. I will claim that, far from being an improvement, it goes to Paul’s disadvantage that she guarantees that. Before going there, a little detour might be useful.

9. Lewis_A and Lewis_B

We need to go back to the distinction between Lewis_A and Lewis_B. Recall that the main difference between them lies in the fact that only Lewis_B accepts counterpart relations simpliciter. I said that, from this difference, we cannot infer any significant consequence with regard to their stances toward DE, neither semantical or metaphysical. However, Paul draws an important consequence.

From Lewis_B’s perspective, and from the fact that anything is similar to anything else under some respect, we inferred that there will be as many counterparts of Socrates as many relations of similarity there are. Now, according to Paul’s understanding of Lewis_B , such counterparts simpliciter determine the de re modal properties of O (see Paul 2006, 344ff.).11 I claim that, if Paul so interprets Lewis_B, then she should accept that Lewis_B has constant de re representations as well. Especially because this does not change her supposed advantage over Lewis_B.

Indeed, if counterparts simpliciter determine the de re modal properties of O, then such de re modal properties are individuated once and for all, independently of the context : they are determined by similarity relations, whose relevance is established independently of context. Indeed, we know that, in this view, metaphysics cannot distinguish among O’s counterparts, since no one stands out as the privileged counterpart . However, if they are all kept at the same level, without any arbitrary privileging, then they are all determined to be equally relevant, from a metaphysical point of view. This means that Lewis_B too has constant de re representations. 12 However, I do not call such properties “essential”, despite their being context-independent, for an important reason. O will have so many counterparts (and metaphysics cannot privilege one over another) that almost no property will come out as essential to it: they all will turn out to be accidental. So, O will have context-independent accidental properties.13

Therefore, here is the difference between Paul and Lewis_B, that is relevant for Paul. In both cases, we have constant de re representations: de re representations that determine the de re modal properties of objects, whose relevance is determined independently of context. However, Paul has constant de re representations by virtue of the fact that metaphysics can pick out some de re representation as relevant, by carving the objects at their joints. By contrast, Lewis can have constant de re representations only because, since metaphysics cannot discriminate among them, then it establishes that they are all equally relevant. The consequence is that only in Paul’s case, constant de re representations can determine essential properties of objects (recall Sum₁, which is metaphysically determined to be essentially human), while in Lewis’s view, metaphysics establishes that all the properties of Socrates come out as accidental, and we need to appeal to the contextual selection of the relevant de re representations in order to talk, in some context, of properties that are determined to be essential to him.14

So, Paul is entitled to claim that, only according to her account, (some) objects have essential properties that are determined by constant de re representations. In the next Section, I am going to argue that, rather than being an asset to Paul’s account of essentialism, this aspect actually worsens the situation (in Section 11, I will discuss other problems for Paul’s account).

10. A problem with Paul’s account of DE

I explained why Paul’s metaphysical move of having objects (cores plus Rprops) carved at their joints is relevant for her account of DE: since metaphysics establishes the boundaries between one sum and another, Paul can have objects (like Sum₁) with constant de re representations that determine essential properties.

Therefore, Paul needs to be cautious about the question as to whether modal composition, namely the fusion of a core with the Rprops it generates, is unrestricted or restricted. Indeed, if metaphysics must establish the boundaries between objects, then it must be a matter of metaphysics if a composition between a core and some Rprops is admissible or not. Therefore, either (i) modal composition is unrestricted and, hence, any sum is allowed, so that there is no arbitrary privileging of some sum over another, or (ii) if modal composition is restricted and, hence, not all the sums are allowed, there must be some metaphysical justification for limiting the composition.

Despite the fact that Paul clearly recognizes how important this matter is for her defence of DE (Paul 2006, 359), I do not find her discussion about this point very clear.15 In the following, I raise a problem for modal composition that has to do with sums of “modal incompatibilities”. I will argue that (i) if modal composition is totally unrestricted, then there are sums with modal incompatibilities, to the effect that the very idea at the bottom of DE is jeopardized; (ii) if modal composition is somehow restricted, the restrictions we would need in order to avoid those sums are either not metaphysically justified, or somehow available to Lewis too, so to cancel the differences between the two accounts.

Let us start by assuming that modal composition is unrestricted. Recall the previous example, in which metaphysics establishes both Sum_n and Sum₁’s de re modal properties, and while Sum₁ is essentially human, Sum_n is accidentally human. Now, it is bad enough that it is metaphysically established that a human being could have been a cat. However, as bad as it is, it is nothing new for us. We saw that Lewis_B, according to Paul’s interpretation, also accepts that (and this holds regardless of whether or not I am right in saying that Lewis_B has constant de re representations). In addition, Lewis_B has no way to say that, metaphysically speaking, some human is essentially human. Therefore, so far so good for Paul: her account is deeper than Lewis’s.

However, let us take the sum of CoreS (Socrates’s core) plus the RpropC (the Rprop for being represented as a cat) and nothing else (we are assuming that composition is unrestricted, therefore, there must be such a sum). This sum (Sum₂) is carved at its joints. So, metaphysics can establish which de re modal properties Sum₂ has. Well, Sum₂ will be accidentally human (being represented as a cat). However, it will be essentially, say, intelligent and hairy. Here, I am assuming that CoreS is composed by non-modal properties such as “being intelligent”, “being hairy”, “being a philosopher” and so on. Since it has only a cat as a counterpart, it is represented by this counterpart as not-human, perhaps as not-philosopher and so on. However, it is not represented as not-hairy and not-intelligent (and here I am assuming that the cat is intelligent and hairy). Therefore, metaphysics allows for the existence of a human being (recall that we cannot call it “Socrates”, otherwise we are back to semantics), which is accidentally human but, at the same time, essentially hairy. Therefore, Paul has objects with essential properties determined by constant de re representations. However, such essential properties are not the properties we expected them to be. And they are not even the properties Paul wanted.

Indeed, Paul aims to defend DE because she wants essential properties to define the nature of things. For this reason, Paul claims, such properties cannot be context-dependent (Paul 2006, 345). But what do we have now that DE is back? We do have context-independent essential properties of objects, but they do not always define the nature of things. Indeed, if there is something that defines the nature of a human being, it should be his being human, and certainly not his being hairy. Using her own words, “there is very little content in the idea that object has to be a certain way in order for it to exist” (Paul 2006, 346).

To sum up, totally unrestricted modal composition allows for sums of modal incompatibilities. The fact that metaphysics allows for the existence of a human being that has all of his properties accidentally, the property of being human included, is bad enough, both for Lewis_B and Paul. But saying that metaphysics allows for the existence of a human being that could have been a cat but not bald is definitely worse.

Let us suppose, then, that modal composition is minimally restricted. Are there metaphysical justifications for limiting modal composition to the effect that sums of modal incompatibilities are not admissible?

Note that it might be said that, if a sum combines incompatible properties, then it simply does not exist: metaphysics does not carve its joints. Therefore, the thought goes, there is no need to put restrictions on what sums there exist in order to avoid such sums: they simply are impossible. Accordingly, modal composition can be unrestricted, since such sums cannot exist. In response to such a thought, I would like to say that DE, as an account of the nature of objects, should explain why the nature of an object stops it from being essentially hairy and accidentally human: DE should explain why the combination of CoreS only with RpropC would make for an impossible object (Sum₂). If DE’s explanation were only that, if the combination of CoreS only with RpropC makes for an impossible object, then there is no fusion of them, there would be no explanation of what DE was supposed to explain. So, it cannot be simply said that Sum₂, since it is impossible, it does not exist: we need to know why CoreS cannot combine only with RpropC. Therefore, if there are metaphysically justified restrictions on modal compositions, and if, according to these restrictions, Sum₂ does not exist, only then could it be claimed that Sum₂ is impossible.16

So, let us see if there are metaphysically justified restrictions that can be imposed on modal composition, to the effect that Sum₂ is ruled out:

Therefore, (i) if modal composition is unrestricted, then sums of modal incompatibilities are admissible, to the effect that the very idea at the bottom of DE gets lost; (ii) if modal composition is restricted, the restrictions put in place in order to avoid sums of modal incompatibilities are either not metaphysically justified or available to Lewis too, to the effect that the difference between the two accounts would be lost.

What happens, instead, from Lewis_A and Lewis_B’s perspectives, with regard to objects with incompatible modalities? Well, also Lewis might say that a human being is essentially hairy but accidentally human. This happens if there is a context that makes it true. However, Lewis does not intend to say that such de re modal properties metaphysically define the object’s nature: it is only a matter of context.

Therefore, in order to draw a relevant difference between Paul’s account and Lewis’s, modal composition must be taken to be unrestricted and, so, sums of modal incompatibilities are to be accepted. In this way, it can be said that Paul, unlike Lewis, accepts that some of the sums that she takes to be objects have context-independent essential properties determined by constant de re representations. However, such an achievement plays against Paul herself: it would have been better if it were only a matter of context. Indeed, what Paul can really guarantee is that some of the things she takes to be objects have essential properties, and such essential properties, only in some case, define their natures. Therefore, the sense itself of DE is lost.

In the following, I will briefly discuss some other aspects of Paul’s theory that make, in my opinion, her account worse than Lewis’s. Perhaps, some of the following disadvantages could have been acceptable for the benefit of having DE, if DE had not had the consequence just discussed.

11. Lewis’s view is in better shape than Paul’s

Let us start from semantic aspects. I said that, from a semantic point of view, both authors reject DE semantical. However, I think that the context-dependence that Paul hypothesizes is more problematic than the one postulated by Lewis. Indeed, Paul seems to be relying on the hypothesis that names are vague in ways that we do not expect them to be. That is, she needs to convince us that ordinary names are candidates for semantic indeterminacy. By contrast, Lewis’s postulation that the relevance of an object’s similarity relations changes according to different contexts leaves the reference theory unchanged. That is, according to this perspective, ordinary names, such as “Socrates”, are not treated as candidates for semantic indeterminacy, precisely as we do not expect them to be.

Moreover, it is not only that we are said that ordinary names, contrary to what we expect, are vague. But we are also said that such a vagueness is very pervasive: all the ordinary names come out as semantically vague. Indeed, in Paul’s view, vagueness would be a matter of any name whatsoever insofar as it denotes an object that is eligible for having accidental properties. Perhaps, “God” would not be a vague name in this perspective, as long as the object that it is supposed to denote might be expected to have all of its properties essentially. So, Paul should convince us to believe in a semantic vagueness so pervasive that basically all ordinary names in our language are vague.

Finally, ordinary names tend to occur in the superficial form of the essentialist sentences. Yet we do not have any evidence of such alleged indeterminacy. For Lewis, instead, the indeterminacy concerns a predicate (the predicate for the counterpart relation) that emerges only when the sentence is analyzed in counterpart theoretic terms. Therefore, since such a predicate does not occur in the superficial form of the essentialist sentences, it is less surprising that there are not evidences of its indeterminacy.17

From a metaphysical point of view, the alleged multiplication of entities in Paul’s account is replaced by a multiplicity of counterpart relations in Lewis’s view, which seems to be a less expensive ontological commitment. Note also that Paul’s strategy to make us accept such a proliferation of objects is the standard strategy to distinguish between the things that exist and the things over which we quantify in usual contexts: such a multitude of objects does exist, but we usually ignore them. And by “usual contexts” she mainly means “non-philosophical contexts” (see for instance, Paul 2004, 183; 2006, 361). However, Paul seems to disregard the fact that, since these objects occupy different regions of modal spaces, we would be confronted with such a multitude every time we want to talk about the de re modal properties of objects. But, far from being specific of philosophical contexts, modal talk is everyday talk. I agree with Paul that, in non-philosophical contexts, we would not select as relevant references for “Socrates” those objects according to which Socrates could have been non-human. However, there are many other sums that we would have to take into account in our everyday talk.

Therefore, not only is Paul able to (partly) rule out from her account of essentialism the context-dependence only with high costs, but also the place where she puts such a dependence, namely, the reference theory, with all the consequences that derive from such a move, worsens the situation.

12. Conclusion

In this paper, I discussed Paul’s proposal for a form of deep essentialism that, according to her expectations, retains some of the advantages of shallow essentialism while being classified as deep. The key difference, according to Paul, between her proposal and Lewis’s should revolve around the postulation of constant de re representations.

I argued that, ultimately, Paul’s proposal either is not effectively different from Lewis’s account, as Paul assumes, or, if there are indeed substantial differences, they are to Paul’s own detriment. Moreover, there are difficulties that her proposal faces, both from a semantical and a metaphysical perspective, that Lewis’s account does not encounter.

Therefore, if Paul is correct (and I think she is) in asserting that certain sceptical challenges pose problems for standard forms of deep essentialism that they do not for shallow essentialism, but it is better to be deep than to be shallow, then the arguments presented in this paper could be interpreted as suggesting that Lewis’s account should be reconsidered, since, as shallow as it can be, it might be deeper than it looks.

Acknowledgments

I am deeply grateful to Giorgio Lando, Daniele Sgaravatti, Pasquale Frascolla, and Andrea Bottani for dedicating their time to help me enhance this paper. I would also like to thank the anonymous reviewers of this journal for their valuable remarks.