Monism

1. Monisms

1.1 Many monisms

There are many monisms. What they share is that they attribute oneness. Where they differ is in what they attribute oneness to (the target), and how they count (the unit). So strictly speaking there is only monism relative to a target and unit, where monism for target \(t\) counted by unit \(u\) is the view that \(t\) counted by \(u\) is one.

Monisms are correlative with pluralisms and nihilisms. Where the monist for target \(t\) counted by unit \(u\) holds that \(t\) counted by \(u\) is one, her pluralist counterpart holds that \(t\) counted by \(u\) is many, and her nihilist counterpart holds that \(t\) counted by \(u\) is none. Among pluralists it is sometimes useful to single out the dualist: the dualist for \(t\) and \(u\) holds that \(t\) counted by \(u\) is two

To illustrate these various doctrines for various targets and units, let the target \(t_1 =\) concrete objects, and let the unit \(u_1 =\) highest type. To be a monist for \(t_1\) counted by \(u_1\) is to hold that concrete objects fall under one highest type. The materialist, idealist, and neutral monist are all monists of this sort (substance monism). They all agree that concrete objects fall under one highest type, disagreeing only over whether the one highest type is material, mental, or something deeper.

To be a pluralist for \(t_1\) counted by \(u_1\) is to hold that concrete objects fall under more than one highest type. The Cartesian dualist is a pluralist of this sort (substance dualism). She holds that concrete objects fall under two highest types: the material (with the primary attribute of extension), and the mental (with the primary attribute of thought).

To be a nihilist for \(t_1\) counted by \(u_1\) is to hold that concrete objects fall under no highest type. The bundle theorist who is an eliminativist about concrete objects is a nihilist of this sort (substance nihilism). She rejects the target: she thinks that there are no concrete objects to count.[1] One who accepts concrete objects but rejects the relevant notion of “highest” type would also be a nihilist for \(t_1\) counted by \(u_1\). She rejects the unit: she thinks that this is no way to count.

As a second illustration, let the target \(t_2 =\) properties. The monist for \(t_1\) counted by \(u_1\) (the substance monist, e.g., the materialist) might still be a pluralist for \(t_2\) counted by \(u_1\) (for properties counted by highest type). For instance, she might hold that there are two highest types of property, physical and mental, inhering in one and the same type of substance (property dualism). Or she might be a nihilist for \(t_2\) counted by \(u_1\), by being an eliminative nominalist about properties and thereby rejecting the target. (These examples show the need to relativize monism to a target.)

As a third illustration, let the unit \(u_2 =\) individual token. The monist for \(t_1\) counted by \(u_1\) (the substance monist, e.g., the materialist) might still be a pluralist for \(t_1\) counted by \(u_2\) (for concrete objects counted by tokens). For instance, she might hold that there exist many concrete object tokens (existence pluralism), while maintaining that these are all material objects. Likewise the pluralist for \(t_1\) counted by \(u_1\) might be a monist for \(t_1\) counted by \(u_2\). For instance, she might hold that there is only the one “world-person” with two highest types of property, physical and mental. (These examples show the need to relativize monism to a unit.)

Monism, along with pluralism and nihilism, must therefore be relativized to both a target and a unit. The underlying reason for this double relativity is that these are theses of numerical predication (‘…is one/many/none’), and all numerical predication is doubly relative in this way: for a target (what is to be counted), and by a unit (how it is to be counted). This is one way to understand the moral of Frege’s (1884: 59) insight:

While looking at one and the same external phenomenon, I can say with equal truth both ‘It is a copse’ and ‘It is five trees,’ or both ‘Here are four companies’ and ‘Here are 500 men.’

The “external phenomenon” is the target, and “copse” and “tree” (or “companies” and “men”) serve as potential units.[2]

1.2 Important examples

I now mention some of the more interesting target-unit pairs, leading to a list of some of the more interesting monisms. To begin with, on perhaps the most general level, one may target the categories themselves, and consider whether the schedule of categories has various sorts of unity. There are at least two interesting sorts of unity to consider: (i) the number of categories (including subcategories), and (ii) the number of highest categories (excluding subcategories).

As to the first sort of unity concerning the number of categories, some posit a categorical distinction between object and property, thereby recognizing a pluralism of at least two categories. But others would prefer the elegant monistic picture of a “one category ontology”: for instance, some trope theorists and property-only theorists claim a property-only schedule, or a schedule that effaces the object/property distinction (Williams 1953; Campbell 1990; Paul 2013); and eliminative nominalists claim an object-only schedule (Rodriguez-Pereyra 2002).

As to the second sort of unity concerning the number of highest categories, those who are pluralists about the number of categories still may (or may not) posit one highest category—a summum genus, such as entity or being—under which all the entities in the lower categories fall. Spinoza (Ethics IV pref., II: 207), for instance, is a pluralist about the categories but a monist about the highest categories, positing a categorical divide between substance and mode but unifying both under being:

We are accustomed to refer all individuals in nature to one genus which is called the most general, that is, to the notion of Being, which embraces absolutely all the individuals in nature.

While Aristotle is a pluralist about both the categories and the highest categories, denying that there is any higher category above his substance, quantity, quality, etc.[3]

Moving down from the level of the categories themselves, one may target a particular type of entity, and consider whether that type has various sorts of unity. Of special interest to the discussion to come is the concrete material realm as a target. For this target there are at least four interesting sorts of unity to consider: (i) the number of types (including subtypes), (ii) the number of highest types (excluding subtypes), (iii) the number of tokens (including derivative tokens), and (iv) the number of basic tokens (excluding derivative tokens). The neutral monist (as per above) is a pluralist about the number of types, but a monist about the number of highest types. On her view there are material and mental types, but both fall under a higher neutral type from which the material and the mental are derivative. The priority monist (as per above) may well be a pluralist about the number of tokens, but is a monist about the number of basic tokens. On this view there are many concrete objects other than the one fundamental whole, but these other objects are all “shards”: derivative fragments of the One.

The abstract realm is another interesting target. For this target it is not obvious that there is a sensible type/token distinction.[4] So only two of the four natural count policies for concrete objects seem applicable: (i) the number of abstract objects (including derivative ones), and (ii) the number of basic abstract objects (excluding derivative ones). So consider the hierarchy of pure set theoretic objects. One might very naturally be a pluralist about the number of pure set-theoretic abstracta that exist, but a monist about the number of basic set-theoretic abstracta, insofar as one holds that the entire transfinite hierarchy is founded upon a single element: the empty set. Those who reject abstract objects altogether will obviously be nihilists on either count policy (c.f. Goodman and Quine 1947).

In general, for any target that supports a type/token distinction—perhaps for any concrete target—it seems that there will be at least the four natural count policies as seen with concrete objects. While for any target that does not support a type/token distinction—perhaps for any abstract target—it seems that there will only be the two natural count policies as seen with abstract objects. To further illustrate these patterns: with concrete events, one might count by types, highest types, tokens, or basic tokens. While with abstract Platonic universals, one might count the number of forms, or the number of basic forms. For example, Plato is a pluralist about the number of forms, but a monist about the number of basic forms, maintaining that they are all sustained by the form of the good.[5]

Moving down from targets that concern a particular type of entity, one might also target a particular token entity, and consider whether it has various sorts of unity. A dizzying variety of natural count policies present themselves. A particular concrete object might, for instance, be counted by (i) the number of its parts, (ii) the number of its atomic parts, (iii) the number of its maximally continuous parts, (iv) the number of its functionally integrated parts, or (v) the number of its qualitatively homogeneous parts. So if one considers a chess set, one might count it functionally as 1 (1 chess set), by its connected parts as 33 (32 pieces and 1 board), by its homogeneous parts as 96 (32 pieces plus 64 squares), by its atomic parts as bazillions of particles, and by its parts as \(2^n -1\), where \(n\) is the number of its atomic parts.[6] Obviously many other count policies are available. It is not clear that there is more to be said of a systematic nature about natural count policies for various particular entities.

There is one count policy of some metaphysical interest worth mentioning, which is to count by the number of individuals (self-identicals) present. Thus one might say, for a given target, that there are exactly three individuals involved. Restricting our domain of quantification to the target, this would be to uphold the formula:

\(\exists x\exists y\exists z(x\ne y \amp x\ne z \amp y\ne z \amp \forall v(v=x \vee v=y \vee v=z))\)

Unless one thinks that identity itself is a relative notion (Geach 1962), or that there is some other problem with this formalism, this formula represents a perfectly legitimate count policy. My point is that it is not the only legitimate count policy. It is perfectly legitimate to count the copse as one, without denying the presence of the five trees, or identifying them.

Putting this together, here is a list of some of the more interesting examples of monistic doctrines mentioned above:

This list is not intended to be exhaustive, but just to indicate a handful of the more interesting monisms, and classify them with respect to their associated target and unit.[7]

Most of these five monisms are independent, though there are the following logical relations. Pluralism about the number of basic tokens for some concrete category entails pluralism about the respective number of tokens. In the other direction, both monism and nihilism about the number of tokens for some concrete category entails a corresponding monism or nihilism about the respective number of basic tokens. Further, nihilism about the number of highest types for any concrete category entails nihilism about the number of tokens (and thus the number of basic tokens) for that category.

Thus with existence monism and priority monism (the main foci of what follows), one finds the following logical relations: existence monism entails priority monism, and priority pluralism entails existence pluralism. But otherwise the views are independent. So for instance, one might be an existence pluralist but a priority monist. This would be to maintain that many things exist (not just the world, but also persons, furniture, particles, and whatnot), but that the whole world is basic. The partialia are merely dependent fragments. It may be that this is the view that most historical monists have held, and that especially deserves serious attention.[8]

2. Existence Monism

2.1 Overview

Existence monism targets concrete objects and counts by individual token. It holds that exactly one concrete object token exists (the One). It represents an interesting and historically important form of monism, albeit one which is widely regarded as deeply implausible. Consider any two concrete individuals, such as you and I. The existence monist must either deny that at least one of us exists, or deny that at least one of us is a concrete object, or hold that we are identical. This is hard to swallow. (It is important to distinguish existence monism from priority monism, which does not have this implausible implication.)

Historically, existence monism may have been defended by Parmenides, Melissus, Spinoza, and Bradley, though in each case the claim is controversial.[9] Among contemporary philosophers, Horgan and Potrč are probably the leading, and perhaps the only, existence monists.[10] Thus Horgan and Potrč (2000: 249; c.f. 2008: 8) advance the following ontological and semantical theses:

Note that existence monism should not be confused with the formula: \(\exists x\forall y(x=y)\). That is the logician’s formula for expressing the claim that exactly one entity exists. The existence monist is making a much weaker (and slightly more plausible) claim. She can allow that many abstract entities exist, she can allow that many spatiotemporal points exist (assuming that she does not follow the supersubstantivalist in identifying objects with regions), and she can allow that many property tokens exist (assuming she does not follow the bundle theorist in identifying objects with compresent property tokens), as long as she maintains that only one concrete object token exists.[11]

In order to properly characterize existence monism, one should first introduce a predicate ‘\(C\)’ that denotes the property of being a concrete object. (The notion of being a concrete object is natural and useful, so this should be clear enough to work with.) Then one can introduce the formula:

Existence monism: \(\exists x(Cx \amp \forall y(Cy \rightarrow x=y))\)

The corresponding logical formulae for existence pluralism and nihilism then run:

Existence pluralism: \(\exists x\exists y (Cx \amp Cy \amp x\ne y)\)

Existence nihilism: \({\sim}\exists xCx\)

It is not built into the formulation of Existence monism that the one concretum has any particular nature. It might be my nose or your left foot. It might be material (realist) or mental (idealist) or neutral. Idealist and neutral forms of existence monism may or may not identify the One with some sort of divinity. Materialist and neutral forms of existence monism typically identify the One with the whole cosmos (Horgan and Potrč’s “blobject”). Using ‘\(u\)’ as a dedicated constant for the cosmos, which may be defined mereologically as the sum of all concreta, one thus reaches:

Existence monism (cosmic): \(\exists !xCx \amp Cu\)

This says that there is exactly one concretum, namely the cosmos.

2.2 Arguments

As mentioned, existence pluralism is widely embraced. This attitude came to the fore in the early analytic revolt against the neo-Hegelian monistic idealists, and has made all forms of “monism” something of a taboo until recently (cf. Schaffer 2010b: §1). This pluralistic stance is fairly explicit in Moore’s (1993: 166) declaration: “Here is one hand… and here is another,” and fully explicit in Russell’s (1918 [1985]: 36) declaration:

I share the common-sense belief that there are many separate things; I do not regard the apparent multiplicity of the world as consisting merely in phases and unreal divisions of a single indivisible Reality.

Whether due wholly to argumentative force or at least partly to historical contingencies, such declarations had the effect of ending any interest in monism (even in forms of monism such as priority monism that agree with Moorean truisms: §3), for nearly one hundred years. And so philosophical fashion swung from some form of monism in the nineteenth century, to some form of pluralism in the twentieth century.[12]

There are actually two distinct sources of evidence for existence pluralism: intuition and perception. Where Russell seems to be appealing to his “common-sense belief,” Moore seems to be appealing directly to the content of perception, as do Hoffman and Rosenkrantz (1997: 78):

Monism… is inconsistent with something that appears to be an evident datum of experience, namely, that there is a plurality of things. We shall assume that a plurality of material things exists, and hence that monism is false.

So, barring a radical skepticism about both intuition and perception, there seems to be strong prima facie evidence for existence pluralism.

The argument may be formulated in various ways, but—for reasons that will emerge below—one of the more interesting (and very natural) formulations runs as follows:

1 makes a claim about the status of a given proposition, that there are a plurality of concrete objects. It says that this proposition is intuitively obvious and/or perceptually apparent.

2 makes an epistemic claim about propositions that enjoy the status of being intuitively obvious (/perceptually apparent). The epistemic claim is that these propositions thereby enjoy prima facie justification. The argument thus concludes:

The argument is valid and the premises seem plausible. Of course the conclusion is not existence pluralism, but rather the weaker claim that there is prima facie reason to believe in existence pluralism. But this leaves existence pluralism as the default view barring any overriding arguments otherwise. This is exactly the way Russell (1918 [1985]: 48) sees the dialectic:

The empirical person would naturally say, there are many things. The monistic philosopher attempts to show that there are not. I should propose to refute his a priori arguments.

How might the existence monist or nihilist reply? As a claim about the content of intuition (/perception), 1 seems hard to question. And as a claim about prima facie justification, 2 seems plausible as well (albeit more theoretically loaded).

There is a fairly standard existence monist and nihilist reply to arguments in the vicinity of 1–3, which involves attempts to paraphrase claims of commonsense. For instance, when one claims that there is a hand here, the existence monist might hold that what is strictly the case is that the world is handish here. The claims of commonsense could then be downgraded to being strictly false but still explicable given the truth of the paraphrase, or as true but only according to the ‘tacit fiction’ of decomposition, which is the ‘fiction’ that the world decomposes into proper parts. [13]

Other techniques besides paraphrase may be employed. For instance, Horgan and Potrč (2000: 50–51) offer an indirect correspondence theory of truth, declaring talk of a plurality of discrete objects apt for tracking “lumps” and “congealings” of the blobject, saying that “such tracking would constitute an indirect kind of language/world correspondence” which “would be a very plausible candidate for truth” (2000: 50–1). Their idea is to posit a contextually sensitive parameter in truth-evaluation, for directness of correspondence required, so that Moorean truisms can count as true in lax contexts.[14] Another option would be to offer a truthmaker theory of commitment, claiming that truths commit one just to their truthmakers, and that the truthmaker for the Moorean truism is just the world.[15]

But it is unclear, however, exactly how these various responses address the argument as formulated via 1–3. Is the idea that, contra 1, the paraphrase reveals that what is obvious and/or apparent might not be exactly what we thought? This is puzzling since the paraphrased claim appears in 1 as the content of intuition and/or perception, and it is dubious that one can freely paraphrase inside such contexts. Perhaps it in some sense “comes to the same thing” if there is a hand, or if the world is handish hereish, but it still might seem to one specifically as if the former were the case. Or is the idea that, contra 2, the paraphrase reveals that what is obvious and/or apparent is not prima facie rational to believe? This is puzzling as well, and raises concerns that the existence of paraphrases would engender a general skepticism about any intuitions and perceptions. Or is the idea that the argument goes through to 3, but that the existence of the paraphrase provides an at least partially undermining defeater to the reason to believe in a plurality of concrete objects? Again this raises worries about engendering a general skepticism, for making defeaters too easy to come by.

The existence monist and nihilist can of course just “bite the bullet” by accepting 3 but claiming overriding arguments otherwise. But this is a dialectically difficult situation for her: whatever support the premises of her arguments otherwise might have will almost certainly pale in comparison to the support that 3 provides for existence pluralism. Not for nothing are existence monism and nihilism widely dismissed as crazy views.[16]

Given the highly plausible case for existence pluralism, it seems as if the existence monist and nihilist need strong arguments for their view. For instance, if it could be proven that positing a plurality of concrete objects (or a plurality of anything, or even a single concrete object) led irrevocably to contradiction, this should turn the tide. But nothing like this has ever been proven.

Perhaps the best argument for existence monism is that it provides the simplest sufficient ontology.[17] The idea is that we can give a complete account of the phenomena in which the world is the only concrete object mentioned, so that there is no need to posit any further concreta. The argument may be formulated as follows:

Somewhat more precisely, 4 claims that the complete causal story of the world can be told in terms of the physical aspect of the world (a path in physical configuration space), together with whatever laws of nature govern temporal evolution. No pieces of the world (such as tables or particles) need be mentioned in this story. To take a toy example, consider a Newtonian world containing what the folk would describe as a rock shattering a window. The complete causal story here can be told purely in terms of the world’s occupational manner vis-á-vis Newtonian configuration space.[18] The rock and the window need not be mentioned in this story. The world bears all the causal information.

The argument then adds that recognizing proper parts of the world is recognizing what is either explanatorily redundant or epiphenomenal:

If the world suffices to explain everything, then there is nothing left for its proper parts to explain. Its proper parts can at best explain what the world already suffices for. So if the proper parts explain anything at all they are redundant, while if they explain nothing at all they are epiphenomenal.

The argument continues with a rejection of both explanatorily redundant and epiphenomenal entities:

Such a rejection is best defended on methodological grounds. Occam’s Razor cuts against both explanatorily redundant and epiphenomenal entities, as there can be no need for positing either.[19] From which the argument concludes:

The conclusion may seem shocking, but the argument is valid, and the premises seem plausible.

How might the existence pluralist and the existence nihilist reply to such an exclusion argument? Starting with the existence pluralist, she might try to deny 4 by denying that the world exists. This might seem an unlikely reply, though there are those who endorse principles of restricted composition that entail that the world does not exist. For instance, van Inwagen 1990 holds that composition only occurs when the result is a life, and the world is (presumably) not a life—a consequence van Inwagen himself (2002: 127) later notes and embraces.[21] Lowe (2012: 93-5) is more directly skeptical about “the cosmos” that monists invoke (though see Tallant 2015 (3103-06) for a reply to Lowe, based on Schaffer’s 2009b proposed identification of the cosmos with the spacetime manifold).

So much the worse for those sorts of principles of restricted composition, the existence monist might respond. Indeed, insofar as restricted principles of composition are supposed to improve on unrestricted composition either with respect to intuitions or with respect to science, it seems that any plausible principle of restricted composition should retain the world. For the existence of the world enjoys both intuitive and empirical support. Intuitively, we folk speak of “the cosmos” and our poets write verses like “All are but parts of one stupendous whole, whose body nature is, and God the soul;” (Alexander Pope; Essay on Man, Epistle I.IX). Empirically, the cosmos is the very subject matter of physical cosmology, and quantum cosmology directly attempts to solve for the wave function of the cosmos.[22]

The existence pluralist might do better to deny 5, by maintaining that composition is identity. If the world is its proper parts, then positing the former just is positing the latter.[23] But there seem to be two main reasons for denying that composition is identity. First, the whole and its parts differ structurally. Pluralities like “the parts” have a privileged structure in terms of their individuals. Thus consider a circle (the whole) divided into two semicircles (the parts). Here the semicircles are structured into a pair of distinct semicircular shapes.[24] But (given mereological extensionality) fusions lack such privileged structure. The circle is just as much the fusion of its two semicircles, as it is the fusion of its four quadrants, and its continuum-many points. Second, the whole and its parts differ numerically. As Lewis (1991: 87) writes: “What’s true of the many is not exactly what’s true of the one. After all they are many while it is one.”[25] So, assuming that the extended many-one conception of identity retains some analogue of Leibniz’s law of the indiscernibility of identicals, the one whole cannot be identical to its many parts.

The existence pluralist might do best to deny 6. One way to deny 6 is to invoke competing methodological considerations. Perhaps Occam’s Razor cuts against both explanatorily redundant and epiphenomenal entities, but Occam’s Razor is not the only methodological consideration. There are also considerations of conservativeness, which seem to favor an ontology that includes you and I as distinct concrete objects. Though here the existence monist might reply that Occam’s Razor trumps conservativeness when the two conflict. And there are also considerations of theoretical elegance, which might still favor the pluralistic account of the world, if the monistic “world particle” story requires the use of overly complicated and disunified predicates.

Perhaps a better way for the existence pluralist to deny 6 (and the best overall way for her to reply to the exclusion argument) is to argue that Occam’s Razor should be modified to take into account the notion of basicness. For there seems little harm in multiplying entities that are derivative—what seems problematic is the multiplication of basic entities. In this vein Armstrong (1997: 12) speaks of “the ontological free lunch,” explaining:

[W]hatever supervenes, … is not something ontologically additional to the subvenient, or necessitating, entity or entities. What supervenes is no addition to being.

So the existence pluralist might suggest that the better methodological maxim is: do not multiply basic entities without necessity (but help yourself to derivative entities).[26]

Turning to the existence nihilist, she might react to the exclusion argument by claiming to beat the existence monist at her own game. The existence nihilist denies that any concrete objects exist (this is a variant way of denying that the world exists, and so a variant way of denying 4). Just as the complete causal story of the world can be told in terms of the world’s having various configurational properties, so the story can be told without mentioning any concrete object at all, and simply speaking of the instantiation of the relevant properties. This involves what Hawthorne and Cortens 1995 (following Strawson 1959) call a “feature-placing language.” Instead of saying that the world has certain properties, a feature-placing language just says that there are those properties, or (to express the same idea in a different way) instead of saying that the world is \(F\), a feature-placing language just says that it \(F\)s, where ‘it’ is understood as a semantically vacuous placeholder that is present for purely syntactic reasons. Here the existence nihilist might claim to beat the monist at her own game, by providing an even simpler sufficient ontology.

In reply, the existence monist could say that property instantiations metaphysically presuppose concrete objects as the instantiators of such properties.[27] That is, the existence monist should reply that existence nihilism is impossible, for positing properties without bearers. If so then at least one concrete object is required, by the argument that properties need bearers; and at most one concrete object is required, by the argument from exclusion discussed above.

To summarize the dialectic as presented so far, the existence monist must defend both the exclusion argument and the “properties need objects” argument. The existence nihilist must defend both the exclusion argument and the possibility of properties without objects. And both the existence monist and nihilist must establish that the premises of the exclusion argument—or any alternative argument they would provide—have sufficient plausibility to override the considerations from intuition and from perception, which seem to tilt so strongly towards existence pluralism (§2.1).

Of course existence monism is not the only form of monism (§1). If considerations from intuition and from perception ultimately tell against existence monism, there is still room to combine existence pluralism with priority monism. This would yield a view on which many things exist (as is intuitively obvious and perceptually apparent), but only as dependent fragments of the one fundamental whole. This may be the view that many historical monists have held, and is a view that deserves very serious consideration.

But before turning to priority monism, it is worth mentioning in more detail the argument from ontological vagueness that motivates Horgan and Potrč 2000 and 2008. Their core idea, seen in their 2008 (§7.3), is that the ontologist has three main options. She may posit a world full of commonsense objects (“slob-jects”), but at the price of admitting ontological vagueness. Or she may posit a world of many small precise objects (“snob-jects”), which may or many not stand in composition relations. Or she may posit just one precise object, namely the world itself (“the snob-ject is the blob-ject”).

Horgan and Potrč argue that ontological vagueness is impossible since it entails a contradiction, and take this to rule out an ontology of common-sense objects. (See Lowe 2012 for a defense of the coherence of this sort of ontological vagueness, and see Schaffer 2012 for an argument that semantic conceptions of vagueness such as supervaluationism resolve the problem.)

Horgan and Potrč then take the rejection of ontological vagueness to force an ontology of precise objects (no “slob-jects” only “snob-jects”), and take the remaining issue solely to concern which inventory of precise objects the ontologist should countenance. They consider three main inventories: a nihilist inventory of many small precise objects (e.g. particles) with no composites, a universalist inventory of many small precise objects plus all composites formed therefrom, and an existence monist inventory of just one big precise object. And they conclude (2008: 183) that the existence monist inventory is to be preferred on grounds of parsimony:

[T]hese three candidates can be ordered with respect to comparative ontological parsimony. The simplest is [existence monism]; it maximizes ontological parsimony by countenancing just one real concrete object, the blobject. Less parsimonious is [nihilism], since it countenances all those point-objects… Still less parsimonious is [universalism], since it countenances not only all the same point-objects, but also a completely unrestricted mereological hierarchy of snobjective region-objects as well.

I think that there are at least three problems with this argument. The first is that the parsimony comparison between the nihilist and existence monist inventory is problematic, since the ontologies in question are disjoint. This is not a case where one ontology is a proper subset of another (rather both are disjoint proper subsets of the universalist inventory). Rather each inventory is itself minimally complete. From the perspective of each inventory, there are no elements that are superfluous.

The second problem—hinted at in §2.2.2—is that any added parsimony gains for the existence monist must be weighted against potential explanatory losses. In particular, the existence monist is going to struggle to account for linguistic phenomena such as reference, without positing any objects to serve as referents (Schaffer 2012). And she will struggle to formulate her own theory, insofar as her own theory speaks of things such as “sentences” and “posits” whose very existence it denies (Lowe 2012).

The third problem is that—given that parsimony considerations only attach to fundamental posits (§2.2.2)—there is room to combine a universalist total ontology with a monistic conception of what is fundamental, and so reclaim all of the relevant parsimony of existence monism with none of the wild rejections of obvious commonsense objects or useful linguistic referents. This is a form of the priority monist alternative.

3. Priority Monism

3.1 Overview

Priority monism targets concrete objects and counts by basic tokens. It holds that exactly one basic concrete object exists—there may be many other concrete objects, but these only exist derivatively. The priority monist will hold that the one basic concrete object is the world (the maximal concrete whole). To distinguish herself from the existence monist, she will allow that the world has proper parts, but hold that the whole is basic and the proper parts are derivative. In short, she will hold the classical monistic doctrine that the whole is prior to each of its (proper) parts. This doctrine presupposes that the many proper parts exist, for the whole to be prior to. Historically, priority monism may have been defended by Plato, Plotinus, Proclus, Spinoza, Hegel, Lotze, Royce, Bosanquet, and Bradley, inter alia.[28] But today, priority monism has few advocates.[29] Indeed, until the last decade, priority monism was seldom even recognized as a possible position. ‘Monism’ was typically understood as existence monism (exactly one concrete object exists), and summarily dismissed.[30]

In order to properly characterize priority monism, one should introduce a predicate ‘\(B\)’ that denotes the property of being a basic concrete object. Then one can introduce the formula:

Priority monism: \(\exists x(Bx \amp \forall y(By \rightarrow x=y))\)

The corresponding logical formulae for priority pluralism and nihilism then run:

Priority pluralism: \(\exists x\exists y(Bx \amp By \amp x\ne y)\)

Priority nihilism: \({\sim}\exists xBx\)[31]

The formulae associated with priority monism are thus the same formulae as for existence monism/pluralism/nihilism, save for the replacement of ‘\(C\)’ with ‘\(B\).’ Note that it is not built into the formulation of Priority monism that the one basic concretum has any particular nature. Priority monism, Priority pluralism, and Priority nihilism are so far characterized as strictly numerical doctrines, concerning the number of basic concreta (one, many, or none).

It is standard for priority monists and nihilists to also have views about the “size” of the basic concreta. Like the existence monist, the priority monist standardly associates her one basic concretum with the whole cosmos. Using ‘\(u\)’ as a dedicated constant for the cosmos, one thus reaches:

Priority monism (cosmic): \(\exists !xBx \amp Bu\)

This says that there is exactly one basic concretum, namely the cosmos.[32] Likewise the priority pluralist standardly associates her many basic concreta with proper parts of the cosmos:

Priority pluralism (partial): \(\exists x\exists y(Bx \amp By \amp x\ne y) \amp{\sim}Bu\)

This adds that the cosmos is not among the basic concreta.

To get from Priority monism (cosmic) to the further claim that the proper parts of the cosmos are dependent on the whole, one need only add that the cosmos has proper parts, and that nonbasic concreta depend on basic concreta. These proper parts will be nonbasic concreta by Priority monism (cosmic), and hence must depend on the one and only basic concretum. (Analogous reasoning allows one to move from Priority pluralism (partial) to the further claim that the cosmos depends on its proper parts.)

The doctrines of priority monism, pluralism, and nihilism—indeed the very idea that “basic concrete token” is a legitimate unit of counting—presuppose a notion of basicness. This notion of basicness may be understood with reference to the classical hierarchical view of reality. The basic forms the sparse structure of being, while the derivative forms the abundant superstructure. The basic is fundamental. It is the ground of all else. It is (as it were) all God would need to create, while the derivative is a mere byproduct. The derivative is dependent on, grounded in, and existent in virtue of the basic.

Such a notion of basicness—and the hierarchical picture associated with it—is intuitively natural and theoretically useful, in this context and others. It has classical roots in Aristotle’s notion of priority in nature, and has branched into the contemporary program of sparse ontology, in a way that has proven fruitful in understanding a wide range of issues. For instance, the physicalist holds that physical entities are basic, and that mental and moral entities are derivative. For the abstract objects of pure set theory, it is natural to think that the empty set is basic, and that the other pure sets are founded on it. With respect to holes, one might hold that the material host is basic and that its holes are formed by it. And with respect to objects and properties, one classical idea is that objects are basic and properties inhere in them as dependent abstractions (modes). Some are skeptical of these locutions. But for better or worse, such talk has rapidly become ubiquitous.[33]

There are many ways to make sense of these notion, but one natural approach is to take basicness as the foundation of ontological priority. That is, suppose that one begins with the notion of ontological priority, understood as an irreflexive and transitive relation between entities. Then ontological priority will induce a partial ordering over the domain of entities. Suppose one now adds the assumption that ontological priority requires foundations. These foundations will be those entities that are not posterior to any other entities. These are the basic, ungrounded entities.[34] Suppose one now adds a third assumption that there is a well-founded ontological dependency structure within the domain of concrete objects. Then one gets basic concrete objects. Being such an object is the property denoted by ‘\(B\)’.

Formally speaking, this natural approach begins with an irreflexive and transitive ontological priority relation \(P\). A foundational entity may then be defined as an entity that has nothing prior to it:

Foundational entity: \(Fx =_{df} {\sim}\exists yPyx\)

Ontological foundationalism may then be formulated as the following thesis:

Ontological foundationalism: \(\forall x(Fx \vee \exists y(Fy \amp Pyx))\)

In words, ontological foundationalism holds that every entity is either basic or posterior to something basic. In content, what ontological foundationalism excludes is the prospect of something being neither itself foundational nor founded on something else that is foundational.[35]

Within the domain of concrete objects, a basic object is then a concrete object that has no concrete object prior to it:

Basic concreta: \(Bx =_{df} Cx \amp{\sim}\exists y(Cy \amp Pyx)\)

Here ‘\(C\)’ continues to denote the property of being a concrete object (as per the formulation of existence monism: §2), and ‘\(P\)’ the priority relation. This defines the predicate ‘\(B\)’ used in the formulations of priority monism, pluralism, and nihilism above. Object foundationalism may then be defined as the following thesis:

Concreta foundationalism: \(\forall x(Cx \rightarrow(Bx \vee \exists y(By \amp Pyx)))\)

In words, concreta foundationalism holds that every concrete object is either basic-among-the-concreta or posterior to something basic-among-the-concreta.

Given these assumptions, the debate between the priority monist and the priority pluralist may be described as a debate over what is at the foundation of the priority relation on concrete objects. The priority monist holds that whole is prior to (proper) part, and that the maximal whole is ultimately prior. The priority pluralist holds that (proper) part is prior to whole, and typically holds that the minimal parts are ultimately prior. This is not a debate over what exists. Both sides may accept the same roster of existent beings (including the world, you and I, planets and particles, etc.) This is a debate over what is basic.

Under a certain natural picture about basic objects, Priority monism and Priority pluralism are exhaustive and exclusive doctrines. The picture is that the basic objects tile the cosmos, in the sense that they cover every portion of reality without overlap. More precisely, the tiling constraint (c.f. Schaffer 2010a: §1.3) may be thought of as the conjunction of two conditions:

No gaps: Sum:\(x(Bx)=u\),

(Sum:\(x(Bx)\) is the mereological sum of all things that are such that \(Bx\).)

No overlaps: \(\forall x\forall y((Bx \amp By \amp x\ne y) \rightarrow{\sim}\exists z(\text{PART}zx \amp \text{PART}zy))\)

No gaps expresses the requirement that the sum of all the basic entities is the cosmos as a whole. No portion of the cosmos is left uncovered. No overlaps expresses the requirement that the basic entities be mereologically disjoint, having no common parts.

The picture given by No gaps and No overlaps is one on which the basic concreta partition the cosmos. The question of which concreta are basic becomes the question of how to carve nature at the joints. Or to invoke Lewis’s (1986) memorable picture of the cosmos as a vast mosaic, the question becomes what are the tiles from which the cosmic mosaic is inlaid?[36]

No gaps rules out Priority nihilism. For if nothing is basic, then the sum of the basic concreta cannot be the cosmos. This makes Priority monism and Priority pluralism exhaustive doctrines.

No gaps also renders Priority monism equivalent to Priority monism (cosmic). For if only one concretum is basic, and it must sum to the cosmos, then it must be the cosmos. Likewise No overlaps renders Priority pluralism equivalent to Priority pluralism (partial). For if many concreta are basic, then the cosmos cannot be among the basic concreta or it will overlap the others.

Given No gaps plus No overlaps, further equivalences follow. On the monistic side, the two conjuncts of Priority monism (cosmic)—\(\exists !xBx\) and \(Bu\)—turn out to be mutually entailing. And likewise on the pluralistic side, the two conjuncts of Priority pluralism (partial)—\(\exists x\exists y(Bx \amp By \amp x\ne y)\) and \({\sim}Bu\)—turn out to be mutually entailing. That is to say that, given the tiling constraint, the numerical thesis that the number of basic concreta is one turns out equivalent to the holistic thesis that the basic concretum is mereologically maximal.

Since Priority monism turns out equivalent to Priority monism (cosmic) which turns out equivalent to \(Bu\), and Priority pluralism turns out equivalent to Priority pluralism (partial) and so equivalent to \({\sim}Bu\), Priority monism and Priority pluralism turn out to be contradictories. They are exhaustive and exclusive conceptions of the basic concreta. Given the tiling constraint, Priority monism and Priority pluralism turn out to be exhaustive and exclusive conceptions of how to carve nature at the joints.