Amphibians and the Particular-Universal Distinction

ABSTRACT

I defend a new conception of the particular-universal distinction based on considerations about what David Lewis calls ‘amphibians’. I argue, first, that given the possibility of amphibians, two recently popular conceptions of the particular-universal distinction, namely the repeatability conception and the duplicability conception, are both objectionable since they are biased in one way or another. I then propose a more flexible conception that solves this problem by regarding amphibians as belonging to a sui generis sort of property distinct from what I call ‘strong universals’ and ‘strong tropes’. Finally, I respond to some objections directed at this new account.

KEYWORDS:

• particular-universal distinction
• universals
• particulars
• tropes
• amphibians

1. Introduction

The distinction between particulars and universals is one of the most fundamental ontological distinctions. It is not clear, however, what this means and how the distinction should be drawn. According to a stronger view, the distinction is fundamental in the sense that it marks off a joint in reality such that every possibly existing entity either belongs to the category of particular or universal, but not both—that is, the two categories are mutually exclusive and jointly exhaustive (Lowe 1998, 2006). To meet this requirement, it is typically proposed that the particular-universal distinction should be characterized as a distinction between the $F$s and the non-$F$s, where $F$ is some capacity of entities. For instance, a naïve Aristotelian conception says that only universals but not particulars are capable of being wholly present in distinct places at the same time. Since nothing both has and lacks the capacity to be multiply located, and everything either has or lacks that capacity, it satisfies the requirement that the two categories are mutually exclusive and jointly exhaustive.

This stronger view, although widely assumed, is far from uncontroversial.¹ Those who find the view unsatisfactory but still wish to uphold a genuine particular-universal distinction might, therefore, question the constraints imposed on it and adopt a more flexible conception according to which particulars and universals fail to be mutually exclusive or jointly exhaustive or both (MacBride 2005: 609). This paper aims at developing this view through considerations about a special sort of property—what Lewis (1986a) calls ‘amphibians’ or what Rodriguez-Pereyra (2017) calls ‘indiscernible universals’. As I will argue, the possibility of amphibians renders two popular conceptions of the stronger view—the repeatability conception and the duplicability conception—biased and thus objectionable. The moral is that amphibians, if genuinely possible, should be classified as neither particulars nor universals. To account for this fact, I propose a fine-grained theory of property categorization from which a novel conception of the particular-universal distinction follows directly. According to this view, the distinction fails to be jointly exhaustive and is fundamental in that there are two categories, universal and particular, each of which has a distinctive metaphysical role played exclusively by its members.

In section 2, I begin by clarifying two popular approaches to the particular-universal distinction and then propose an argument based on amphibians demonstrating that both approaches render unsatisfactory results. I then argue that it is no good to reply by biting the bullet or rejecting the possibility of amphibians outright. In section 3, after briefly discussing two radical alternatives, I propose a novel account of property categorization and derive from it a conception of the particular-universal distinction which nicely solves the problem of amphibians. Finally, in section 4, I respond to two objections, namely that the novel account (i) is arbitrary and (ii) might have some counterexamples.

2. Amphibians: Neither Universals nor Particulars

2.1. The Repeatability Conception and the Duplicability Conception

Let us start by clarifying two popular accounts of the particular-universal distinction.² First, many have attempted to characterize the distinction by whether entities could have repeated occurrences. Universals but not particulars are said to be those that are repeatable according to this conception. I will call this the ‘repeatability’ conception. Depending on what it takes to be repeatable, there are at least two ways to implement this approach:

Multiple Location (ML) For any universal $U$, $U$is repeatable in that there could be distinct$l$ and $l^{\ast }$ such that (i) $U$ is wholly present in $l$ and (ii) $U$ is wholly present in $l^{\ast }$. By contrast, for any particular $P$, $P$is unrepeatable in that there could not be such $l$ and $l^{\ast }$.

Multiple Instantiation (MI) For any universal $U$, $U$ is repeatable in that there could be distinct $x$ and $y$ such that (i) $x$ is an instance of $U$ and (ii) $y$ is an instance of $U$. By contrast, for any particular $P$, $P$is unrepeatable in that there could not be such $x$ and $y$.

The multiple location formulation (ML), sometimes called the ‘Aristotelian’ formulation, explains the repeatability of universals and the unrepeatability of particulars, a fundamental—and indeed for its supporters the definitive—feature of such entities, in terms of their capacity to occupy multiple locations. By contrast, the multiple instantiation formulation (MI) explains the repeatability of universals and the unrepeatability of particulars in terms of their capacity to have multiple instances.

The other popular conception of the particular-universal distinction is what I call the ‘duplicability’ conception, which can be traced back to Wisdom (1934: 208–9) and Williams (1986: 3). Ehring (2011: 32), a recent defender, explains its central idea as follows: ‘[the] potential for having a wholly distinct duplicate is what makes something a particular and the absence of that capacity makes something a universal.’ We can implement it in the following way:

Duplicability (D) For any particular $P$, $P$ is duplicable in that there could be at least one distinct particular $P^{\ast }$such that $P$ and $P^{\ast }$ are perfect duplicates of each other. By contrast, for any universal $U$, $U$ is non-duplicable in that there could not be any distinct universal $U^{\ast }$such that $U$and $U^{\ast }$are perfect duplicates of each other.

An equivalent way to formulate the duplicability conception is to define universals as those conforming to the principle of the identity of indiscernibles and particulars as those not conforming to it, where the relevant version of the principle says that for any entities $x$and $y$, if they are exactly similar, then they are identical.

This ends my exposition of the two popular conceptions. Both regard the particular-universal distinction as a fundamental distinction without restriction, applying to both objects and properties. For the sake of argument, however, I will confine my discussion to universal and particular properties only. Fortunately, this won’t affect the generality of the conclusion. Given that the particular-universal distinction makes the categories of particular and universal jointly exhaustive, the distinction between particular properties (henceforth tropes) and universal properties (henceforth universals) also makes the two subcategories jointly exhaustive in the following derivative sense: every possibly existing property is either a trope or a universal. And if it could be shown that the trope-universal distinction is not jointly exhaustive in this derivative sense, it is implied that the more general particular-universal distinction cannot be jointly exhaustive either. Given this, we can write down three corresponding formulations of the trope-universal distinction:

Multiple Location for Properties (ML-P) For any universal $U$, $U$is repeatable in that there could be distinct $l$ and $l^{\ast }$ such that (i) $U$ is wholly present in $l$and (ii) $U$ is wholly present in $l^{\ast }$. By contrast, for any trope $T$, $T$ is unrepeatable in that there could not be such $l$ and $l^{\ast }$.

Multiple Instantiation for Properties (MI-P) For any universal $U$, $U$ is repeatable in that there could be distinct $x$ and $y$ such that (i) $x$ is an instance of $U$ and (ii) $y$ is an instance of $U$. By contrast, for any trope $T$, $T$ is unrepeatable in that there could not be such $x$ and $y$.³

Duplicability for Properties (D-P) For any trope $T$, $T$ is duplicable in that there could be at least one distinct trope $T{}^{\mathbf{\ast }}$such that $T$ and $T{}^{\mathbf{\ast }}$ are perfect duplicates of each other. By contrast, for any universal $U$, $U$ is non-duplicable in that there could not be any distinct universal $U^{\mathbf{\ast }}$ such that $U$ and $U^{\mathbf{\ast }}$ are perfect duplicates of each other.

Note that for any two properties to be perfect duplicates here is for them to ‘confer perfect similarity in a respect’ (Rodriguez-Pereyra 2017: 604) and whether these properties themselves share any properties is not directly relevant (Rodriguez-Pereyra 2017: 605).

2.2. The Problem of Amphibians

Behind each of the above two conceptions is something intuitive about what we thought of as universals and tropes. The repeatability conception captures our belief that a universal, a ‘one-over-many’ as it is often put, is something capable of repeated occurrence—either in the sense of having multiple locations (ML-P) or in the sense of having multiple instances (MI-P). By contrast, a trope, being a particular, is either particular to the location which it occupies (ML-P) or particular to the object which instantiates it (MI-P). In other words, they are unrepeatable. On the other hand, the duplicability conception captures our belief that a trope, being a particular instance or instantiation of an aspect of reality, exists independently of other instances or instantiations of that aspect, if there are any. This means that it may have perfect duplicates. By contrast, a universal, being the aspect of which such perfect duplicate tropes are instances, cannot itself have perfect duplicates.

Ideally, our preferred conception would account for both of these intuitions about tropes and universals—or more precisely, intuitions about the particularity of tropes and the universality of universals. However, as I shall now demonstrate, the possibility of a special sort of property shows that neither the repeatability conception nor the duplicability conception could do this. First, note that since being repeatable and being duplicable do not seem to exclude each other in any apparent sense, there might be a sort of property that has both of these capacities. If we interpret being repeatable as ML-P does, then such properties are those that could be wholly present in more than one place yet coexist with their perfect duplicates. And if we interpret being repeatable as MI-P does, then such properties are those that could be instantiated by more than one object yet coexist with their perfect duplicates. Although being an unfamiliar sort of property, there seems to be no prima facie reason to rule out the possibility of such entities. David Lewis seems to be the first who explicitly considers such possibilities:

A universal recurs; a trope has duplicates. We could also imagine an intermediate thing that sometimes recurs and sometimes has duplicates. (Lewis 1986b: 65)

In another place, he calls them ‘amphibians’ (Lewis 1986a: 39). Rodriguez-Pereyra (2017) provides a similar argument for the possibility of such properties and calls them ‘indiscernible universals’ instead. I’ll stick with the term ‘amphibians’ (for reasons that will become clearer below).

Once we accept the possibility of amphibians, neither the repeatability conception nor the duplicability conception can account for both of the intuitions we wish to maintain. On the one hand, supporters of the repeatability conception, no matter whether they adopt ML-P or MI-P, are forced to regard amphibians as belonging to the category of universal since they are, by definition, repeatable. This implies that not only tropes but universals could also be duplicated, violating one of the above-explained intuitions. On the other hand, supporters of the duplicability conception are forced to regard amphibians as belonging to the category of trope since they are, by definition, duplicable. But then not only universals but tropes are also repeatable, violating another of our intuitions.

This is what I call the ‘problem of amphibians’, which shows that both the repeatability conception and the duplicability conception are biased in some way, not capable of accounting for the double requirements explained above at the same time. Faced with this difficulty, there seem to be three possible responses. First, one might bite the bullet and give up one of the intuitions to maintain either the repeatability conception or the duplicability conception. Second, one might posit a law ruling out the possibility of amphibians. Finally, one might argue that amphibians should, in some sense to be clarified, neither be seen as universals nor as tropes. As we shall see, this is the most promising view.

2.3. Amphibians: Indiscernible Universals or Scattered Tropes?

Universal theorists and trope theorists may opt for the first route, challenging one or other of the intuitions. But others may pursue this route too. Rodriguez-Pereyra, for instance, adopts the repeatability conception and argues that nothing in the concept of universals as repeatable properties ‘rules out the possibility of indiscernible universals’ (2017: 606). Arguably, what he calls ‘indiscernible universals’ are just amphibians—properties that are repeatable yet duplicable.⁴ However, such entities do not draw him away from the repeatability conception. On the contrary, he embraces it and objects to the duplicability conception (2017: 621–22).

To motivate a theory of amphibians, Rodriguez-Pereyra (2017: 607–16) argues that various useful philosophical works could be done if we posit such entities, which I take to be mostly successful and will not query here. Interestingly enough, the really serious and, according to him, the most common objection to his theory is that ‘on it universals collapse into tropes’ (2017: 620). To this, Rodriguez-Pereyra replies by resorting to the repeatability conception, claiming that universals can still be distinguished from tropes since only the former are repeatable (2017: 620). I believe that he is right in claiming this, but misses the real concern the objectors probably have in mind. Their worry is rather that classifying what he calls ‘indiscernible universals’ as a sort of universals contradicts our intuition that universals—being aspects of reality capable of having multiple instances—are not themselves duplicable like their instances. The objectors have presumably implicitly assumed something like the duplicability conception and thus cannot coherently imagine the possibility of duplicated universals, as they are ruled out a priori by such an account. According to them, amphibians, if genuinely possible, should be classified as a sort of tropes, and insisting that they are universals is thus collapsing universals into tropes. Now we seem to have reached a stalemate since supporters of both conceptions would insist on their own way of distinguishing universals from tropes, and the problem returns to whether we should adopt the repeatability conception or the duplicability conception in the first place. The moral of this, as I take it, is that although we should take seriously the possibility of amphibians, it is less clear that they should be regarded as universals. Therefore, without independent reasons, we’d better not reply to the problem of amphibians by biting the bullet.⁵

A trope theorist might also reply by biting the bullet. Recall that Ehring (2011) adopts the duplicability conception according to which tropes are properties that can coexist with perfect duplicates. Nothing in this concept precludes the possibility of certain tropes—call them ‘scattered tropes’—that could be multiply located.⁶ Obviously, scattered tropes are nothing but a sort of amphibians. However, this does not draw him away from the duplicability conception. Instead, he embraces the trope’s capacity for repetition (2011: 91).⁷

Ehring’s view faces a similar difficulty to that of Rodriguez-Pereyra. For one might object that allowing tropes to have multiple locations is to confuse the notion of tropes with that of universals and thus collapsing tropes into universals (Allen 2016: 58). Of course, Ehring could reply by insisting that what distinguishes tropes from universals is their duplicability and not their repeatability. But then the debate will, again, end in a stalemate. The lesson is that although we should take seriously the possibility of amphibians, it is less clear that they should be seen as a sort of tropes.

We can build a similar argument if repeatability is understood as properties’ capacity to be multiply instantiated, albeit things get a little more complicated here. Assume, once again, that we adopt the duplicability conception and regard tropes as duplicable properties. Nothing in this rules out the possibility of some tropes being multiply instantiable as well. In a sense, such tropes are also scattered, as they are possessed by multiple objects. Given this, proponents of the repeatability conception would object that permitting tropes to be multiply instantiated violates a crucial feature of tropes, namely that they are particular to, or dependent on, the specific objects they constitute.⁸ And the proponents of the duplicability conception would presumably reply by insisting that what distinguishes universals from tropes is their duplicability, and the above-mentioned argumentative impasse resurfaces. Then we could draw the same conclusion as in the case of multiply-located tropes.

However, one might worry that this argument rests on the controversial assumption that tropes can be instantiated. The idea here is that tropes aren’t the sort of entities apt for being instantiated in the first place.⁹ According to certain trope theorists, such as Keinänen and Hakkarainen, instantiation is simply the wrong conception to characterize the connection between tropes and objects built from them.¹⁰ In response, first note that there are certain concepts of tropes, such as what Garcia (2016) calls ‘modifier tropes’, that appear to be more suited to be instantiated.¹¹ Therefore, the argument has at least some limited force. Second, even if tropes are not apt for being instantiated in a strict sense, trope theorists might still require some notions in the vicinity, such as inherence or characterization, to capture the connection between objects and their tropes. Given this, an analogous case for the possibility of scattered tropes can still be made by using the term ‘instantiation’ in a more neutral sense which does not assume any particular account of objects and properties.¹² Finally, even if the trope theorists reject a primitive notion of instantiation or inherence, perhaps by reducing it to other primitives such as parthood and exact colocation, they would still want an account of repeatability—they would want to say that tropes, as opposed to universals, are in some sense unrepeatable. And a natural move here is to adopt ML-P. If this is the case, then the argument against Ehring’s view applies.

To summarize, saving the repeatability or duplicability conceptions by biting the bullet would be biased or tendentious and fail to fully account for the distinctive features associated with universals and particulars.

2.4. Amphibians: Ruling out by a Law?

Another response to the problem of amphibians concedes that the concept of repeatable yet duplicable properties is indeed coherent but claims that there are independent reasons to reject their possible existence. One might, for instance, argue that the possibility of amphibians should be rejected since a law excluding them is required to account for the intimate relationships between the repeatability and duplicability of properties.

Suppose that certain objects $o_1,o_2,o_3,\dots ,o_n$ have the same quality $Q$. Consider now the property $U$ which, according to the universalists, confers $Q$ to the objects that instantiate it. Given that $U$ is non-duplicable, that is, given that $U$ is the only property that could confer $Q$, it appears to follow that $U$ must be multiply instantiable. Otherwise, universalists cannot explain attribute agreement in their usual way, namely, by saying that $o_1,o_2,o_3,\dots ,o_n$ instantiate the same one universal, $U$. Or consider some trope $T$ which confers $Q$ according to the tropists. That $T$ is unrepeatable seems to entail that it is duplicable, capable of having indiscernible twins $T^{\ast },T^{\ast \ast },T^{\ast \ast \ast }$, $\dots$ that also confer $Q$. Otherwise, the tropists cannot explain attribute agreement by saying that each of $o_1,o_2,o_3,\dots ,o_n$ has its own $Q$-conferring trope.

So, the argument goes, the repeatability and the duplicability of properties are not strictly independent, and there must be something in virtue of which such a connection holds. It is then suggested that we postulate a law¹³ that makes true that for every property $F$, $F$ is repeatable if and only if $F$ is non-duplicable, or equivalently, that for every property $F$, $F$ is unrepeatable if and only if $F$ is duplicable. The existence of such a law guarantees the alleged intimate relationships between the repeatability and duplicability of properties: that a universal is non-duplicable entails that it is multiply instantiable and that a trope is unrepeatable entails that it is duplicable. It also allows one to accept the repeatability conception and the duplicability conception at the same time since they will now render the same results concerning what counts as universals and tropes. Therefore, this view could account for our intuitions that universals are not only repeatable but also non-duplicable while tropes are not only unrepeatable but also duplicable. Overall, this seems to be a better response than biting the bullet.

How plausible is this view? Note firstly that the connection between the repeatability and duplicability of properties may not be as strong as one had thought. Although the phenomenon of attribute agreement is widely accepted, claiming that it holds is still to demand a specific shape of reality in addition to claiming that there are non-duplicable universals or unrepeatable tropes. Suppose we make the assumption that it is possible that attribute agreement fails to hold—that is, assume that there exists some possible world in which no two objects ever resemble each other in any aspect. Then the alleged intimate relationship between the repeatability and duplicability of properties is immediately lost. There is no reason to suppose that the repeatability of universals follows from their non-duplicability, or that the duplicability of tropes follows from their unrepeatability, in such worlds. Note that what is crucial here is not that attribute agreement might possibly fail to hold. The point is rather that the repeatability and duplicability in themselves do not seem to entail one another. This is true even if attribute agreement turns out to hold of necessity. To strengthen the case, recall that both Rodriguez-Pereyra (2017) and Ehring (2011) demonstrate that the contrapositive entailments from repeatability to non-duplicability and from duplicability to unrepeatability do not hold. Given this, the two features are further disentangled.

Second, the argument for the alleged law, if valid at all, shows nothing but that for the universalist or tropist explanation of attribute agreement to succeed, one must accept something like a law to account for the connection between the repeatability and duplicability of properties. But supporters of amphibians are free to reject both accounts and provide their own explanation. Indeed, this seems to be what they ought to do, as they do not posit universals or tropes from the beginning. What would such an explanation look like? Presumably something like this: distinct objects $o_1,o_2,o_3,\dots ,o_n$ have the same quality $Q$ because either all of them instantiate the same $Q$-conferring amphibian, or each of them instantiates its own $Q$-conferring amphibian, or some of them instantiate the same $Q$-conferring amphibian while others instantiate other $Q$-conferring amphibians.¹⁴ Nothing in this explanation requires us to accept that repeatability follows from non-duplicability or that duplicability follows from unrepeatability.

Finally, as I will explain in the next section, the conception of the particular-universal distinction that I prefer can preserve the advantages of postulating the alleged law without ruling out a priori the possibility of amphibians. Therefore, I conclude that this second response to the problem of amphibians should be given up as well.

3. Deriving the Particular-Universal Distinction

3.1. Interlude: Radical Approaches

We are now on the way to seeing the plausibility of the third response, which regards amphibians as belonging to a sui generis sort of property that is neither particular nor universal. But before I spell out the details, let us consider two radical yet insightful alternatives to the reductionist approaches to the particular-universal distinction discussed so far.

First, primitivism says that the particularity of tropes and the universality of universals are primitive, basic, or fundamental. Defenders of this view might agree that a universal is both repeatable and non-duplicable and a trope is both duplicable and unrepeatable, but nonetheless deny that these features account for what it is to be a universal or a trope. Instead, these features, according to them, are derived from the particularity of tropes and the universality of universals. Maurin (2002), for instance, adopts this view about tropes. When discussing why the duplicability conception fails, she says that the duplicability of a trope ‘does not really tell us anything about the particularity of the trope’ (2002: 17) but ‘will follow given that the trope is not only qualitative (abstract) but also particular’ (2002: 17). Similarly, she rejects the repeatability conception because ‘even if it is true that one and the same trope cannot exist but in one unique region in space and time, we may still ask why … [it] cannot exist but at one place at one time’ (2002: 20). And the answer, according to her, is that it is true ‘because tropes are particulars’ (2002: 20). I do not know any universalist that explicitly adopts primitivism, but it seems to be a coherent position as well. Indeed, since primitivism in the current form can preserve what we thought of as the typical features of universals and tropes and is compatible with the possibility of amphibians, adopting it seems to be a better response to the problem of amphibians than biting the bullet or postulating a law.

I take primitivism to be a viable option, but only as our last resort. The reason is that particularity and universality under such a view seem to be mysterious and redundant. Explaining particularity and universality in terms of simple facts about properties’ capacities to repeat or duplicate might be unsatisfactory, but refusing to answer what they are doesn’t seem to make the situation better—it only makes them mysterious. More importantly, primitive particularity and universality seem to be redundant since the account that I defend below can reduce particularity and universality while preserving all the alleged advantages of primitivism.

Turning to the other radical view, scepticism denies that there is a fundamental distinction between particulars and universals.¹⁵ Indeed, why insist that there is a particular-universal distinction in the first place when the two popular approaches fail to explain adequately what it is to be a trope and a universal?

My main reason for rejecting scepticism, again, is that I believe that there is a way to characterize the particular-universal distinction unbiasedly and that if possible, accepting that there is a genuine particular-universal distinction seems to be a better stance than saying that there is none. This is because the distinction is so central to contemporary metaphysics that discarding it will imply that various theories based on it have no intellectual substance. And this seems to be a consequence we’d better avoid. Still, I believe that the sceptic tendency reveals something important about what is wrong with popular reductionist conceptions. Traditionally, the particular-universal distinction is often assumed to have cut across reality in such a way that every possibly existing entity either belongs to the category of particular or universal, but not both. But this requirement might, to use MacBride’s words, ‘impose too high a threshold’ (2005: 609) as it makes it impossible to accept both the intuitions behind the repeatability conception and the duplicability conception while admitting the possibility of amphibians. The view that I prefer rejects precisely this assumption and attempts to combine these two conceptions in a satisfying manner.

3.2. Strong Concepts of Properties

To achieve the alleged new account, we must adopt a new methodology. Traditional reductionist approaches have typically assumed that the particular-universal distinction can be formulated as a distinction between the $F$s and the non-$F$s, where $F$ is some capacity that particulars and universals might have or lack. Thus, we have the distinction between the repeatables and the unrepeatables, or the distinction between the duplicables and the non-duplicables. Such a view, however, might lead one into thinking that we must focus on one particular capacity $F$ and identify universals with the $F$s and tropes with the non-$F$s, or vice versa. However, as I have demonstrated, no one feature alone genuinely respects all our intuitions on the matter. To unbiasedly account for the distinction, at least both repeatability and duplicability must be considered.

My suggestion, then, is to reverse this tradition, that is, to start with our preferred concepts of properties and derive from them the corresponding conception of the particular-universal distinction. The distinction will not, in principle, be restricted to a distinction between the $F$s and the non-$F$s, but will be a distinction between two fundamental categories, each of which has a distinctive metaphysical role determined by a series of capacities played exclusively by its members. More specifically, focusing on the two capacities discussed, we can draw a table representing a more fine-grained theory of different concepts of properties (see Table 1).

Table 1 gives us four sui generis sorts of property, according to which amphibians (Box-2 properties) are distinct from what I call ‘strong universals’ (Box-1 properties) and ‘strong tropes’ (Box-4 properties). We can then derive from them a novel account of the trope-universal distinction:

Trope-Universal Distinction For any property $F$, $F$is a trope iff $F$ is both duplicable and unrepeatable, and $F$ is a universal iff $F$ is both repeatable and non-duplicable.

Table 1: Novel account of property categorization

Property	Repeatable	Unrepeatable
Non-duplicable	1. Strong Universals	3. (See footnote 16)
Duplicable	2. Amphibians	4. Strong Tropes

Generalizing to include both objects and properties, we get:

Particular-Universal Distinction For any entity $x$, $x$ is a particular iff $x$ is both duplicable and unrepeatable, and $x$ is a universal iff $x$ is both repeatable and non-duplicable.

This novel conception has certain merits. First, this view, while accepting the possibility of amphibians, respects the intuitions behind both the repeatability conception and the duplicability conception. Therefore, it is a better response to the problem of amphibians than biting the bullet or postulating a law. Second, the view avoids primitive particularity and universality by reducing them to combinations of two capacities of properties: universals are universal in the sense that they are repeatable and non-duplicable and tropes are particular in the sense that they are duplicable and unrepeatable. Finally, it accepts a genuine particular-universal distinction, thus making theories based on it have sufficient resources to explain their views adequately. Therefore, it is also preferable to scepticism.¹⁶

An implication of this account, as adumbrated, is that particulars and universals are not jointly exhaustive. Here one might worry that this makes the account unmotivated, given that exhaustiveness is a longstanding and widely accepted feature associated with the particular-universal distinction.¹⁷ In reply, I agree that the proposed novel conception is, to some extent, revisionary. But it is not revisionary in any way that distorts the notion of the particular-universal distinction. Instead, as I’ve argued, it fully respects what many take to be distinctive features of particulars and universals—in an unbiased way that even the dominant conceptions, such as the repeatability conception and the duplicability conception, cannot. And it is due to the abandonment of exhaustiveness that the novel account has such merits. Therefore, the novel account is not unmotivated.

But then one might wonder why the exhaustiveness requirement is so deeply ingrained. The reason, I believe, is that traditional conceptions are mainly proposed to accommodate paradigm cases of universals and particulars. Such cases are perfectly distinguished in the way we want by traditional conceptions—which typically reduce the particular-universal distinction to the distinction between the $F$s and the non-$F$s. And since this view conforms naturally with the exhaustiveness requirement, the latter is rendered unproblematic. However, as argued above, focusing on one feature of properties, such as their repeatability or duplicability, is problematic when we take more seriously the possibility of Box-2 (and Box-3) properties. Therefore, even though we are used to taking for granted the exhaustiveness requirement, some modification might be required.

4. Objections and Replies

4.1. Arbitrariness

Let us now turn to possible objections directed at my new account. The first objection is that, given the novel account of property categorization, it seems arbitrary that I define universals exclusively as Box-1 properties and tropes exclusively as Box-4 properties. Indeed, why not define them differently and thus derive other conceptions of the particular-universal distinction?

I believe that strong universals and strong tropes are better candidates for ‘universals’ and ‘tropes’ than their rivals. To see this, consider what I call the ‘weak’ concepts of universals and tropes: a weak universal is a property that is repeatable, regardless of whether it is duplicable while a weak trope is a property that is duplicable, regardless of whether it is repeatable. In other words, both Box-1 and Box-2 properties count as weak universals and both Box-4 and Box-2 properties count as weak tropes. Now consider the internal unification of weak and strong universals respectively. Whereas strong universals are both repeatable and non-duplicable, thus having a higher degree of similarity; weak universals are those that resemble each other in being repeatable only, thus having a lower degree of similarity. This constitutes a reason to believe that strong universals are better candidates for what Lewis (1983) calls ‘natural properties’ which carve nature at its joints. And similarly for tropes.

Another reason to prefer strong universals and tropes is that they fit better with the universalist and tropist picture concerning attribute agreement. Take, for instance, two objects, $a$ and $b$, that both have some quality $Q$. The universalists’ typical explanation is that it is in virtue of $a$ and $b$’s instantiating the same universal $U$ that they both have $Q$. But a weak concept of universals does not guarantee this. For all it guarantees is that $U$is repeatable. It is compatible with this, as pointed out by Rodriguez-Pereyra (2017), that $a$ and $b$ both have $Q$ because they instantiate distinct, indiscernible (weak) universals. To guarantee that $a$ and $b$ instantiate numerically the same universal $U$, it must be further agreed that $U$ is the only $Q$-conferring property, that is, it is not duplicable. And the most straightforward way is to adopt the strong concept which says that to be a universal just is to be a property that is both repeatable and non-duplicable. Similarly, the tropists’ typical explanation is that it is in virtue $a$ and $b$’s instantiating their respective $Q$-conferring tropes, say $T$ and $T^{\ast }$, that they both have $Q$. However, a weak concept of tropes does not guarantee this. For all it guarantees is that a trope is duplicable. Nothing in this precludes the possibility that $a$ and $b$ both have $Q$ because they instantiate the same scattered trope. To guarantee that $a$ and $b$ instantiate distinct tropes, it must be conceded further that every trope can only be had once, that is, it is unrepeatable. But then we are turning to the strong concept. Therefore, I take strong universals and tropes to be better candidates for ‘universals’ and ‘tropes’.

4.2. Putative Counterexamples

I anticipate that the most common objection to my novel account is that it incorrectly classifies entities in one category as entities in another. Indeed, given that it combines the dominant features of both the repeatability conception and the duplicability conception, it might be objected that some putative counterexamples to these accounts are also counterexamples to my new account.

The first sort of counterexamples is repeatable particulars such as spatially extended simple particulars (Ehring 2011: 25–27) and enduring time-travelling particulars (MacBride 1998b: 222–23; Ehring 2011: 27–28). It is argued that such entities, if genuinely possible, constitute counterexamples to the repeatability conception since they are incorrectly classified as universals. Similarly, it might be objected that such entities constitute counterexamples to my account since they are incorrectly classified as amphibians.

I’ve always been bugged by this argument based upon the alleged possibility of repeatable particulars, not because I find their possible existence to be dubious, but because regarding such entities as what they are said to be according to the objectors seems to me to be begging the question. Let me ask: on what ground are they appropriately called ‘particulars’ in the first place? It is no good to say that they are particulars because they are duplicable, for that seems to have implicitly assumed something like the duplicability conception. But then why say that they are particulars? It is not as if when one calls them ‘particulars’ that they immediately count as a genuine sort of particulars. The objectors owe us a reason for seeing such entities as particulars. (Note that this does not mean that such entities constitute no difficulty for the repeatability conception. As argued in section 2, given that there could be repeatable yet duplicable entities, the repeatability conception is biased in that it cannot account for the intuition that universals are non-duplicable. But that argument does not rely on the assumption that such entities are regarded as amphibians in the first place.)¹⁸

The case can be made even more vivid if we consider another putative sort of counterexamples, namely properties such as being the funniest man or being the highest charged point particle in the universe. Suppose, for the sake of argument, that such properties are genuinely possible. It is striking to see that such properties can be regarded as counterexamples to the repeatability conception and the duplicability conception at the same time just by changing titles. On the one hand, they are regarded as possible candidates of necessarily singly located universals and thus constitute potential counterexamples to the repeatability conception (MacBride 1998b: 218; Ehring 2011: 42). On the other hand, they are regarded as possible candidates of necessarily non-duplicable tropes and thus constitute potential counterexamples to the duplicability conception (Ehring 2011: 42–43). But why should we interpret them as instances of universals or as instances of tropes in the first place? It is no good to say that they are universals rather than tropes because they are non-duplicable, for that seems to have implicitly assumed something like the duplicability conception. Similarly, one should not regard them as tropes simply because they are unrepeatable. Are there other reasons to regard them as universals or tropes? It is hard to see. Indeed, reflecting on the fact that they are both non-duplicable and unrepeatable, and thus have and lack some typical capacities associated with both universals and particulars, one might have reasons to regard them as neither universals nor tropes. And that is what is to be expected according to my account: they are Box-3 properties.¹⁹

In sum, the alleged counterexamples to my account do not work since they are problematic only if I adopt other conceptions of the particular-universal distinction in the first place. The lesson to be learnt here seems to be that we have no conception-free intuition about which property belongs to which category. A property can plausibly be regarded as belonging to a category only when it has certain capacities typically associated with that category.

In closing, I would like to draw attention to a point made by MacBride (1998b). It is mandatory that the particular-universal distinction should ‘guarantee that, by and large, paradigm examples of particulars are classified as particulars and that paradigm examples of universals are classified as universals’ (1998b: 226). However, extensional adequacy alone is not all there is in determining an adequate conception of the particular-universal distinction, as there may be intensional or ideological aspects one must also take into account (1998b: 206). In fact, I believe that extensional adequacy should only be seen as our starting point. Once the paradigm examples are given and several initially plausible accounts are proposed, we are in a position to see what features or capacities are relevant in our thoughts about what it is to be a particular and a universal. In the current case, it is shown by the two popular conceptions that at least repeatability and duplicability are relevant in characterizing a satisfactory conception. At this stage, the most important task becomes adopting a theory that combines all the relevant capacities unbiasedly. It is even negotiable that some of the eccentric cases do not turn out to belong to the categories that we initially suppose them to be in. And this is exactly what I attempt to do when developing the novel account.

Acknowledgements

I would like to thank Lok-Chi Chan, Duen-Min Deng, Hsuan-Chih Lin, Yi-Cheng Lin, Tien-Chun Lo, Gonzalo Rodriguez-Pereyra, Barbara Vetter, and two anonymous AJP referees for their helpful comments on drafts of this paper.

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Notes

1 For various criticisms of this view, see MacBride 1998a; b, 1999, 2004a, 2005, 2009.

2 Of course, the two conceptions discussed in this paper do not cover all conceptions in the literature, a fortiori all logically possible conceptions. For instance, there are conceptions attempting to define the particular-universal distinction in terms of instantiation, such as the conception favoured by Lowe (1998, 2004, 2006). (For discussion of related accounts, see MacBride 2004b, 2005 and Ehring 2011.) There may also be modified versions of these conceptions. My goal is not to rebut all possible conceptions and argue that my own account is the only viable one. Instead, what I wish to do is simply to show that through some considerations about amphibians, a more flexible approach which abandons an assumption often associated with traditional accounts should at least be seen as a serious contender.

3 I use the term ‘instantiation’ here in a theory-neutral sense, referring to the relation between properties and objects that have or possess them without assuming any specific account of properties or objects.

4 Rodriguez-Pereyra (2017: 606) also mentions the connection to Lewis (1986a).

5 This explains why I choose the term ‘amphibians’ as opposed to ‘indiscernible universals’. Rodriguez-Pereyra regards amphibians as a sort of universals since he adopts the repeatability conception, taking anything repeatable to be a universal. But I disagree and do not see amphibians as a sort of universals. Thanks to a referee for forcing me to be clear on this.

6 The possibility of scattered tropes—or at least the possibility of such properties construed as tropes—is first introduced by Schaffer, where he calls them ‘scattering individuals’ instead (2001: 249). Schaffer takes such entities to be problematic and suggests we adopt what he calls the ‘spatiotemporal individuation principle’, according to which ‘$x$ and $y$ are distinct tropes iff they are either not exactly resembling, or at distant locations $(\mathrm{Distance}(x,y)>0)$’ (2001: 249). This principle seems to have relied on something like ML-P, as the latter explains why tropes are thus individuated: it is because tropes cannot be multiply located that they are distinct when occupying different locations. This view leads us back to the repeatability conception considered above. That the duplicability conception doesn’t rule out the possibility of scattered particulars is also mentioned by Giberman (2016).

7 If my interpretations of Rodriguez-Pereyra (2017) and Ehring’s (2011) views are correct, then indiscernible universals and scattered tropes turn out to be the same thing, namely amphibians. This fact is itself interesting, showing that some contemporary universalists’ and tropists’ theories might not be that different in the end.

8 Such a view becomes even more counterintuitive if tropes are taken to be non-transferable, that is, not capable of being instantiated by objects other than those which, in fact, instantiate them (Heil 2003: 141–42). Thanks to a referee for pointing out a mistake here.

9 Thanks to two referees for raising similar worries here.

10 See Keinänen and Hakkarainen 2010, 2014 and Keinänen 2011 for their view (the strong nuclear theory).

11 Thanks to a referee for this point.

12 This conforms with my usage of the term (see footnote 3).

13 I take ‘law’ in its ontological sense. That is, I take them to be the truthmakers of law statements rather than the law statements themselves.

14 See Rodriguez-Pereyra 2017 for a defence of a similar ‘disjunctive’ account.

15 See Ramsey 1925 and MacBride 2005 for arguments in favour of scepticism. Given the limited objective of this paper, I will focus on whether admitting the possibility of amphibians leads one toward scepticism.

16 What about Box-3 properties? Nothing seems to rule out their possible existence as well. And for similar reasons as in the case of amphibians, we should treat them as belonging to a sui generis sort of property. But what are they? Has anyone postulated such entities?

On the face of it, proponents of Box-3 properties might have difficulty accounting for attribute agreement. On the one hand, since they are non-duplicable, there is at most one property that could confer the quality Q. On the other hand, since they are unrepeatable, that property could be possessed by at most one object. But then it is hard to explain how there could be multiple objects having the same quality Q.

There are, nevertheless, several ways out. First, the proponents can reject attribute agreement in a strict sense and identify the whole concrete world with an ‘enormously structured’ distributional property (Builes 2021). Such an overarching property is an example of Box-3 properties, for it is unrepeatable (in no world are there two worlds having such a property) and non-duplicable (in no world are there two overarching properties). Platonic properties can also be seen as a sort of Box-3 properties, as they lack spatiotemporal locations (which makes them unrepeatable) and are abstract like numbers (which makes them non-duplicable). Other candidates include individual essences (see footnote 19) and qualitative haecceities (Adams 1979: 9–13). The possibility of such properties constitutes further reasons for regarding the particular-universal distinction as not jointly exhaustive.

17 Thanks to a referee for raising this worry.

18 Giberman (2021) recently argues that cases like spatially extended simple particulars and enduring time-travelling particulars do not constitute genuine counterexamples to the repeatability conception because they are based on uncompelling principles. If his arguments were successful, then these cases do not constitute genuine counterexamples to my account as well.

19 Similar arguments apply to entity haecceities and individual essences. Assume they are candidates for necessarily singly located universals, and hence potential counterexamples to the repeatability conception. MacBride asks: ‘why should we grant that haecceities and individual essences are universals in the first place? Surely we lack reliable pre-theoretical intuitions concerning such outlandish entities?’ (1998b: 217). I’d add that if the reason for regarding such entities as universals is that they are non-duplicable, one is likely assuming something like the duplicability conception, which begs the question against the repeatability conception. For parallel reasons, we should not treat them as particulars just because they are unrepeatable. In fact, seeing that they are both non-duplicable and unrepeatable, we have reason to regard them as neither universals nor tropes.