Metaphysical Constraints, Primitivism, and

Reduction

Michael Bertrand

Draft: 3/29/17

1 Introduction

In a range of familiar philosophical debates, participants aim to explainwhat it is to be some x by providing a reductive analysis of x.1 This is the aimof reductionism about e.g., causation, modality, goodness, knowledge, andpersonal identity. Reductionism about some x is attractive because it showsx to be nothing over and above some more basic set of entities, unifying andthereby reducing the number of independently existing things that must becountenanced and independent explanations that must be provided. Whena reductive analysis of x cannot be given, that counts in favor of primitivismabout x: the view that x is a primitive entity.2

Debates that proceed this way instantiate a familiar pattern: they em-ploy the Argument from Absence of Analysis (hereafter the AAA).3 Myaim, in what follows, is to show that the AAA fails to secure its intendedprimitivist conclusion. Demonstrating this conclusion requires demonstrat-ing two claims at once: a metaphysical claim concerning the impossibility of

1[Acknowledgements omitted for blind review]2More precisely, primitivism is supposed to follow from the failure of reduction together

with the repugnance of eliminativism. However, I take eliminativism to be a position oflast resort. Because primitivism is a live option in the cases I consider, eliminativism isnot attractive and can safely be ignored. For a similar point, see Schaffer 2015.

3To my knowledge, this argument pattern was first explicitly named in Chalmers 1996.Alexander Skiles 2014 discusses the same argument pattern, calling them arguments thatappeal to past track records of failure.

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reduction and and an explanatory claim concerning the impossibility of ex-planatorily deep characterization.4 In order to secure its explanatory claim,the AAA must wrongly suppose that reduction and primitivism exhastivelypartition our options for explanatory characterization. Because the Argu-ment from Absence of Analysis fails to demonstrate this claim, it fails todemonstrate its intended primitivist conclusion.

In order to show this, I offer a third option that is distinct from reduc-tion and primitivism. Unlike reductive and primitivist views, constraintistviews characterize their objects by identifying properly construed metaphys-ical constraints. Constraintist views provide explanatorily deep characteri-zations of their objects, accounts of what it is to be them, and so do whatprimitivists say cannot be done. However, explanatory characterizations un-derwritten by metaphysical constraints are distinct from those provided byreductive analysis and are available independently of the success of the re-ductive project. Constraintist views provide a distinct third route by whichexplanatory characterizations can be provided.

My argument has an interesting implication. Because they are distinctfrom reductive and primitivist ones, constraintist views occupy previouslyhidden space in a range of philosophical debates. I conclude by consideringa case study drawn from the debate about personal identity in order to showhow this space might be occupied. This case illustrates the particular valuehad by constraintist views in debates where neither reduction nor primitivismis appealing.

2 The Argument from Absence of Analysis

The AAA is a familiar way of motivating primitivism about some bit ofour ontology. It is generally employed in debates where there is an initialpresumption in favor of reduction that has led to various unsuccessful at-tempts at reductive analysis. The idea, then, is that our persistent actualfailure to provide a reductive analysis of some x, or our in principle failure to

4I’ll soon complicate this by allowing that a very modest sort of primitivism mightbe endorsed without making any explanatory claim. However, I don’t think this is theindended conclusions of the AAA or what is typically defended by primitivists. For moreon this, see section 3.2.

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do so, provides strong evidence for the claim that x is primitive. This mightbe an inductive argument from our past failure to reduce x to our continuedfuture failure to do so. Alternatively, it might be understood as an abductiveargument concluding that the best explanation for our persistent failure isthat x is primitive.

David Chalmers 1996 employs the AAA as one of several arguments ad-vanced in support of his primitivism about conscious experience. Chalmersclaims that, in order to reductively analyze consciousness, friends of reduc-tion must give a story about how consciousness might possibly be entailed byphysical facts. However, it is hard to see how any entailment from physicalfacts to consciousness could get off the ground and so it is hard to see even inprinciple how reductive analysis is possible. Because no reductive analysis ispossible, conscious experience is likely “something of a primitive” (Chalmers1996, 23). Fundamental phenomenal or protophenomenal properties willneed to be taken as basic or primitive, much as fundamental physical fea-tures of the world cannot be explained in more basic terms (Chalmers 1996,112).

Similarly, Ned Markosian 1998 employs the AAA in favor of primitivismabout composition, otherwise called brutal composition. On Markosian’sview, mereological concepts form a closed circle that cannot be understood inindependent terms. The best reason for accepting this Doctrine of Mereolog-ical Circle “is that no non-mereological analysis of any mereological concept,including composition, seems to be forthcoming. . . no writer on mereologyhas ever proposed a non-mereological analysis of any mereological concept”(Markosian 1998, 217). Mereological facts are brute in the sense that theydo not obtain in virtue of other facts (Markosian 1998, 215).

In much the same way, Martin Lipman Forthcoming argues for primitivetemporal passage in part by arguing that existing reductive accounts fail tocapture temporal passage and that it isn’t clear how these accounts might beimproved. Though Lipman doesn’t take this to be decisive, he claims thatthe absence of reductive analysis clears the way for primitivism and showsthat it deserves serious consideration.

The AAA sees pervasive use in the causal literature, where one of the

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main arguments for causal primitivism comes from our persistent failure toanalyze causal connections in non-causal terms (cf. Schaffer 2007, 2016a).It also appears in the literature on intrinsicality and is discussed in detail byAlexander Skiles 2014.

Finally, the AAA is not restricted to metaphysics. G.E. Moore’s famousopen question argument against ethical naturalism is perhaps an instance ofthe argument drawn from ethics. The open question argument purports toshow that any apparent reduction of goodness to some non-moral base leavesopen whether x is good given that x has the non-moral features present inthis reductive base. Because purported reductions must fail in this way,Moore claims that moral goodness is primitive (Moore 1993, 62 - 69).

3 What are Reductionism and Primitivism Any-way?

As these examples help to show, the AAA figures in a wide range of philo-sophical debates. However, instances of the argument also show that greatcare is required. In part, this is because the argument and its instances oftenmake free use of the terms ‘reductive analysis’ and ‘primitive.’ Though thesefamiliar terms of art often go unanalyzed, this hides considerable disagree-ment and, I think, confusion about what reduction and primitivism involve.I won’t attempt to resolves these disagreements (though this is needed). In-stead, I’ll try to be clear about what commitments I take each kind of viewto make. In doing this, some controversy is unavoidable. However, it is moreimportant that the views I describe are recognizable and distinct and lessimportant what we choose to call them.

In addition to avoiding confusion, clarity is necessary for two furtherreasons. First, because ‘primitive’ and ‘reductive analysis’ are not used uni-vocally, I’ll soon be arguing that not every way of understanding primitivismis equally well supported by the AAA. It is further unclear what commit-ments the argument is providing evidence for when it is providing evidencefor primitivism. Second, my goal is to show that there is a distinct alternativeto reduction and primitivism available. To do this, we need to understand

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what they involve.Before discussing particular commitments, a clarification is needed. I’ll

be restricting my attention to ontological reduction and primitivism here.Ontological reduction is distinct from conceptual reduction, where one con-cept reduces to others if it can be analyzed or defined in terms of them (Lewis1970, Jackson 1998, Chalmers and Jackson 2001, Schaffer 2008). It is alsodistinct from theoretical reduction, as when one theory can be reduced toanother iff the terms of the first can be defined or translated into the termsof the second (Nagel 1979, Kim 1998, Schaffer 2008).

Unlike these other kinds, the primary aim of ontological reduction is totell us what there is in the world: ontological reduction is a thesis aboutthe world independently of our conceptual or theoretical representations ofit. In the same way, ontological primitives are primitive entities rather thanprimitive concepts or fundamental theories.5 Different kinds, particularlyontological and conceptual reduction, are often run together and this sug-gests an important link between them. However, ontological and conceptualreduction strike me as very different projects and I will restrict my attentionto ontological reduction and primitivism here.6

3.1 Reduction

Reductionism about some entity x is the view that x can be reducedto some more basic and independent y or y’s. I will not offer an accountof successful reduction or reductive explanation here. In addition to be-ing extremely difficult, I suspect any such account will be artificial giventhe diversity of usage in the literature. Instead, I’ll adopt J.C.C. Smart’sinfluential necessary condition on reduction as a minimal commitment.

5I use the term ‘entity’ for lack of a better alternative to refer to parts of our ontologyregardless of the ontological category to which they belong.

6It is sometimes claimed that primitivism is theory relative so that some x mightcount as a primitive relative to one theory and as a derivative entity relative to another.Jennifer Wang’s 2013 modal primitivism is an example. However, I am skeptical thatrobust ontological primitivism can be theory relative in this way. I will assume that beingprimitive is an absolute state.

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Minimal Reductive Commitment: “An entity x reduces to anentity y only if x does not exist over and above y” (Smart 1959,143).

Minimal Reductive Commitment is animated by the broadly Humean thoughtthat reduced entities arise from and depend on patterns of the fundamentalentities. They are nothing over and above their fundamental bases in roughlythe way that a movie is nothing over and above its frames (Lewis 1994, ?).

In addition to the minimal commitment, reductions are asymmetric. If xcan be reduced to some reductive base, then its base is in some sense priorito, more basic then, or more fundamental than x. Skiles 2014 argues thatthis relative fundamentality requirement is a necessary condition on reductionand it is also reflected in Jeffery King’s 1998 compositional view of reduc-tion. The relative fundamentality requirement underwrites the connectionbetween reduction and parsimony, the idea being that reduced entities arenot ontologically rock bottom but that their ultimate reductive bases mightbe. Finally, asymmetry is required if reductions are to back explanation.

On the traditional view, ontological reductions are secured by identitiesbetween reduced entities and their bases, as when the identity theory of mindreduces (type or token) mental states to (type or token) brain states. Justas water is nothing over and above H2O, Hesperus and lightning is nothingover and above electrical discharge, “sensations are nothing over and abovebrain processes” because they are strictly identical to them (Smart 1959, 145and Kripke 1980. See also Schroder 2005, Skiles 2014).

However, reduction might also be secured by properly understood rela-tions of ontological dependence or determination. On this view, derivativeentities are nothing over and above the more fundamental entities on whichthey depend and so can be reduced to these more fundamental entities.Gideon Rosen gives voice to this view with his Grounding-Reduction Link:“If [worldly fact] p’s being the case consists in [worldly fact] q’s being thecase, then p is true in virtue of the fact that q” (2010, 123). The connec-tion between dependence and reduction is also discussed by Skiles 2014 andis reflected in Occam’s Laser, which forbids the unnecessary proliferation

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of fundamental entities while allowing the proliferation of derivative ones(Schaffer 2015). The idea here is that derivative entities are an “ontologicalfree lunch:” because they are grounded in the fundamental, they requireno additional ontological commitment (Schaffer 2015, 648. See also Lipman2016).

Another common strategy involves reducing some x by providing neces-sary and sufficient conditions for it. I think that this strategy is more athome in cases of conceptual, rather than ontological, reduction. However, itmight be used to reduce one worldly fact to another in the following way.Let the ys be a collection of worldly facts. If the fact that the ys obtain isnecessary and sufficient for x to obtain, then x’s obtaining is nothing overand above the the fact that the ys obtain. Insofar as reductively analyzingwhat it is for x to obtain is the same as reductively analyzing what it is tobe x, a reductive analysis of x is produced.7

Finally, necessary covariation claims may well count as reductive pro-vided that they can be understood asymmetrically. Though supervenienceis weaker than dependence and reductive identity and does not entail either,it does support the claim that supervening entities are in some sense noth-ing over and above their bases. I discuss supervenience-based views in moredetail in section 3.3.

3.2 Primitivism

Primitivism about some x is the view that x is an ontological primitive.Yet like reduction, ‘ontological primitive’ does not enjoy univocal use. Iagain refrain from providing an account and identify a minimal commitmentcharacteristic of primitivism instead.

7There are some substantial difficulties for defining what necessary and sufficient con-ditions are (see Brennan 2012 and the references therein). Furthermore, for necessary andsufficient conditions to be useful here they need to do more than define concepts, theyneed to provide criteria for entities.

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Minimal Primitivist Commitment: if x is a primitive then xcannot be reductively analyzed

Primitive entities cannot be comprehensively and non-circularly character-ized in fundamentally different terms. In this spirit, Markosian 1998 justi-fies primitivism about composition by arguing that there are no non-trivialand necessarily true principles linking non-mereological concepts or relations.Chalmers 1996 denies that consciousness ‘logically supervenes’ on the phys-ical, and Skiles claims that intrinsicness cannot be “comprehensively, com-pactly, and non-circularly characterized in more fundamental terms” (Skiles2014, 221). Because primitive entities cannot be reduced, they are some-thing over and above the rest. There is no reductive base in addition towhich they are an ontological free lunch.

The Minimal Primitivist Commitment sometimes exhausts explicit char-acterizations of primitivism in the literature. However, the Minimal Prim-itivist Commitment is much too weak to capture the position most oftendefended by actual primitivists. Minimal primitivism is a purely negativeview that leaves open what primitive entities are like. As a result, it runstogether a range of very different non-reductive views that are best keptseparate. For example, non-reductive physicalism and Cartesian substancedualism seem to belong to different kinds despite their shared endorsementof minimal primitivism. On substance dualism, mental substances are suigeneris and are only causally related to physical ones, while non-reductivephysicalists claim that the mental is not sui generis and instead superveneson or is realized by the physical. Though supervenience perhaps falls short ofreduction, it is sufficiently tight so as to preserve the primacy of the physicalin a way that substance dualism does not.

As a result, the Minimal Primitivist Commitment is often supplementedby other commitments and so made stronger by its proponents. Primitiveentities are widely thought to be the atoms of our ontology and so to providethe foundation for reductive analysis. Reflecting this, Kit Fine claims that“intuitively, one proposition will reduce to others if they bring us closer towhat is real” (2002, 26). On Fine’s view, reality is primitive and, because

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it is not itself reducible, it is the foundation to which successive reductionsdraw near.

It is often claimed that primitive entities are sui generis or form closedcircles of interrelated entities so that there is very little that can be doneeven in principle to characterize them. Lipman, for example, claims thatany description of primitive temporal passage in independent terms is boundto be metaphorical, while David Barnet 2009 claims that he is incapable ofexplaining what vagueness is in a non-circular and independent way. It isbecause they are inexplicable in independent terms that primitives are oftenintroduced by example. In addition to resisting analysis, primitive entitiesare supposed to be sui generis, fundamental constituents of our ontology.

As I’ve presented them, there are no cognitive or epistemic restrictionsconstitutive of reduction or primitivism.8 However, both reduction and prim-itivism are taken to have implications for explanation. Reductions (or theirunderwriting relations) are taken to back explanation so that reductive basesexplain what they reduce.9 Reductions make the theories that contain themmore parsimonious by reducing the number of independent ontological com-mitments that must be made. They also reduce the number of independentexplanations that must be provided, by the lights of the theory, in order tocompletely characterize the world.

Though difficult to characterize, the tie between explanation and reduc-tion is widely endorsed. Providing a reduction of x is offering an accountof what it is to be x or for x to obtain. In this way, reductive analyses ofcausation, modality, and temporal passage are all taken to explain what it isto be their objects. Requests for explanation and requests for reduction areoften conflated so that requests for reductive analysis are often paraphrasedas request for explanatory characterization (see eg. Markosian 1998, 213).In fact, reduction seems to be the primary way that philosophical theories

8For example, reduction need not be a priori or appeal to conceptual truth. This is notthe case on other accounts of reduction that are more closely allied to conceptual analysis.For an example, see Chalmers and Jackson 2001.

9Despite this connection, ontological reductions are distinct from what might be calledepistemic reductions, where some fact or entity is reducible to others if that fact or entitycan be completely explained in terms of them c.f. Nagel 1979.

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try to explain.In contrast, a common complaint against primitivism is that it does not

explain and so “fails to do what any viable philosophical account is supposedto do” (Skiles 2014, 20). Because primitives are sui generis and fundamental,they cannot be explanatorily characterized by hypothesis. While we canstill uncover interesting facts about primitive entities and their distribution,there is a sense in which primitive entities are epistemically inaccessible inprinciple: they can’t be explained in independent, non-circular terms sothat we are often reduced to metaphor or example. By adopting primitivismabout some x, we’re giving up the project of providing a deep and informativeexplanatory characterization of x.

3.3 What about Non-Reductive Views?

Recall that the AAA infers primitivism about some x from our persistentor in principle failure to provide a reductive analysis of x. In light of the dis-cussion so far, it might be worried that the inference made by AAA ignores arange of salient views that are neither reductive nor primitivist. I’m sympa-thetic to this worry. However, I don’t think that existing non-reductive viewsare sufficient to make the case: it isn’t clear that these views genuinely fallbetween reduction and primitivism. In spite of this, there is an importantinsight here: there may be space between reductive and primitivist views. Iwill argue in section §4 that properly understood metaphysical constraintsmake good on this insight.

First, there is a general argument available to the friend of the AAA.Supposing for the moment that primitivism is exhausted by the MinimalPrimitivist Commitment, primitivism and reduction cleanly partition thespace of logically possible views. It is plausible that true reductions arenecessarily true. So, if it is not the case that there is some y or y’s suchthat x is reducible to them, then no reduction of x is possible. Yet, this isprecisely what is claimed by the Minimal Primitivist Commitment.

Second, it is unclear that existing non-reductive views fall between primi-tivism and reduction when primitivism is enriched beyond the Minimal Prim-

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itivist Commitment. Many existing non-reductive views appear unstable andso threaten to collapse either into primitivism or reduction when further ex-amined. Many of these views were never meant to be stable in the way Irequire here: they were never intended to avoid reductions not forged byreductive identity.

For an example of this instability, consider the case of non-reductivephysicalism in the metaphysics of mind. While precise statements are con-troversial, physicalism is, roughly, the claim that the world is at bottomphysical: there is, in some sense, nothing over and above the physical phe-nomena (c.f. Melnyk 2008, Ney 2008). While reductive physicalism aims toreduce the mental to the physical by identifying mental and physical phenom-ena, non-reductive physicalism is distinguished by its rejection of reductiveidentities.

Instead, the view involves, at minimum, the supervenience of the mentalon the physical. The idea here is that though not identical, the mentalis nonetheless nothing over and above the physical: there can be no mentalchange or difference without a corresponding physical change or difference. Avariety of supervenience theses are available that differ in scope and strength.However, each involves necessary covariation and so is weaker than reductiveidentity and insufficient for it.

Though non-reductive physicalism is supposed to resist the reduction ofthe mental to the physical, I’m not sure it does. Consider that physicalism ofany sort seems to require that there is nothing over and above the physical.Yet, this is just what the Minimal Reductive Commitment requires. Non-reductive physicalism involves the claim that the mental supervenes on thephysical, yet supervenience is claimed to be sufficient for reduction in othercontexts, as in the debate about causal primitivism (c.f. Schaffer 2008).

If non-reductive physicalism is genuinely non-reductive then, as AndrewMelnyk 2008 argues, it is plausibly too weak to count as physicalism: it failsto secure the claim that the mental is nothing over and above the physical.While proper physicalism rules out primitivism about the mental, super-venience based non-reductive physicalism is consistent with it. It requiresnecessary covariation between the physical and the mental. However, it does

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not offer or even require that there be any explanation for this covariation.As a result, supervenience based non-reductive physicalism is consistent witha state of affairs in which supervenience is a brute modal relationship be-tween entirely distinct primitive kinds (Melnyk 2008 as well as Kim 2013,Horgan 1993).

As this case illustrates, existing non-reductive views don’t straightfor-wardly reveal space between reduction and primitivism and do not clearlymake the case against the AAA.10 However, these views do suggest thatspace might exist. In the following section, I’ll argue that metaphysical con-straints make good on this insight by underwriting metaphysical theoriesthat are neither reductive nor primitivist. While it may not fall to familiarones, constraintist views suffice to show that the AAA fails to secure itsintended conclusion.

4 Metaphysical Constraints and the Argument fromAbsence of Analysis

A tension has emerged between the AAA and its intended conclusion.The argument concludes, on the basis of our persistent or in principle failureto reductively analyze some x, that x is a primitive entity. In so far as ourfailure to reductively analyze x licenses the inference that no reductive anal-ysis of x is possible, the AAA secures the Minimal Primitivist Commitmentconcerning x: x cannot be reduced. However, we have seen that primitivismas it is actually defended is more robust. This metaphysical claim about theimpossibility of reduction is nearly always accompanied by the claim that xis fundamental, sui generis, or in some sense inexplicable: no explanatorycharacterization concerning what it is to be x can be had. The absence ofreductive analysis seems not to be a good reason to endorse this further ex-

10Of course, there are a variety of non-reductive views available and I have only dis-cussed one kind. I do, however, expect that the issues raised for supervenience basednon-reductive views will generalize to other non-reductive ones, particularly those backedby realization. Ultimately, though, I don’t think much hangs on this. I’m willing to al-low that the failure of the AAA might be overdetermined. What is significant, for mypurposes, is that its failure isn’t obvious given the existence of purportedly non-reductiveviews.

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planatory claim. We must also assume that, if x cannot be reduced then x isinexplicable. In this and the following section, I show that this assumptionis false by offering a way of providing explanatory characterizations, backedby metaphysical constraints, that is neither primitivist nor reductive.

By showing that the AAA is faulty, we deprive primitivism of an impor-tant avenue of support (though there remain good reasons for thinking thatsome things are primitive). However, the constraintist theories I develop herealso promise to open new space in debates where participants have restrictedthemselves either to primitivism or reductive analysis. Theories that makeuse of constraints in order to characterize their targets deserve philosophicaldevelopment. By providing new explanatory resources that are more widelyavailable than those furnished by reduction, metaphysical constraints licenseilluminating characterizations of their objects.4.1 Metaphysical Constraints

To show that metaphysical constraints underwrite explanatory characteriza-tions of their targets, that these promise to open new dialectical space, andthat the existence of this space undercuts the AAA, I need to say a bit aboutwhat metaphysical constraints are.

On my view, a metaphysical constraint on some entity, x, is identical toa constitutive part of the nature of x.11 Intuitively, the constraints on x arejust parts of what it is to be x. Because x has its nature in every world inwhich it exists, metaphysical constraints place limits on the ways that theirobjects can be across possible worlds. In this way, they earn their names.

Because metaphysical constraints are constitutive parts of natures, theyrequire no additional ontological commitment: they are no additions of beingover and above natures. However, this does not mean that the notion ofconstraint contributes nothing to what was already provided by natures.Rather, it is my claim here and elsewhere that metaphysical constraints

11For the purposes of this paper I will refrain from appealing to any particular accountof essence or nature. The reader is free to fill in their favorite account here provided thatnature is not understood to be reducible in some way to metaphysical modality ( See e.g.Fine 1994). By discovering the nature of x, we’re discovering what it is to be x and sogiving an account of what x is.

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ought to be adopted as a new piece of the ideology of our best theory ofthe world [References Omitted for Blind Review]. My aim in this paper isto show that metaphysical constraints underwrite constraintist theories thatcan offer explanatory characterizations when other theories cannot.

Metaphysical constraints are constitutive parts of natures and ought notbe confused with distinct but related notions found nearby. Constraints oftenhave conceptual or linguistic shadows, for example, so it might be temptingto conflate them with conceptual truths or platitudes. However, constraintsare not conceptual or linguistic. Discovering the metaphysical constraintson x, and so uncovering constitutive parts of its nature, is a substantivemetaphysical task. In contrast, uncovering platitudes or conceptual truthsabout x is not substantive in this way. Whatever work is required to grasp themeaning of our x-concept need not be sufficient to discover the metaphysicalconstraints on x (see e.g. Boghossian 1996). Intelligible debates about whatcounts as a conceptual truth or platitude about some x are supposed to berare or at least easy to settle: they fall out of the meanings of our termsor are otherwise bound up with conceptual competency. In contrast, livelydebates about metaphysical constraints are widespread and are not so easilyresolved.

We might also be tempted to conflate the metaphysical constraints onx with (mere) metaphysically necessary truths involving x. However, thiswould also be a mistake. While every constraint on x is metaphysically nec-essary, not every metaphysically necessary truth involving x is a constrainton x. It is metaphysically necessary, for example, that x is worldmates withthe fact that 1+1 = 2. However this is not a metaphysical constraint on x:it has nothing at all to do with the nature of x and everything to do with thefact that ‘1+1=2’ obtains in every possible world and so obtains in everyworld in which x exists.

For an example of a plausible metaphysical constraint, consider the in-tuitively close relationship between free will and the power to do otherwise.This relationship is often enshrined in the Principle of Alternate Possibilities(AP), which states that a person acted freely, and so is morally responsiblefor an action, only if she could have done otherwise. A plausible way of

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understanding the tight relationship enshrined in AP is to understand it asa metaphysical constraint on free will and so as a constitutive part of itsnature. If this is the case, then there is a necessary connection between freewill and the power to do otherwise: in every possible world in which agentsact freely, these agents have the power to do otherwise.

For a very different example, consider the uniqueness of composition,which is (if true) a plausible metaphysical constraint on the compositionrelation. Composition is unique if and only if it is the case that for anycomposite objects x and y with exactly the same proper parts, x is identicalto y (Simons 1987, Lewis 1991, Sider 2007, Varzi 2008 ). That compositionis unique is plausibly a constitutive part of the nature of the compositionrelation because uniqueness partially constitutes the distinctive relationshipbetween parts and wholes. It identifies the conditions under which compositeobjects are identical: they are identical iff they share exactly the same properparts. Uniqueness is also responsible for the extensionality of parthood andthe purported innocence of mereology: the idea that wholes are so closelyrelated to the plurality of their parts that they are, in some sense, nothingover and above them.

As each case illustrates, metaphysical constraints underwrite explanato-rily deep characterizations of their objects. By uncovering that having thepower to do otherwise is a part of the nature of free will, and so capturinga metaphysical constraint, a theory of free will partially explains what it isfor a will to be free. Similarly, by uncovering that composition is unique,a theory of composition captures a constitutive part of its nature and soprovides a partial characterization of the composition relation.

This suggest a generalizable picture of the way metaphysical constraintsunderwrite explanatorily deep characterizations of the kind offered by meta-physical theories. Namely, one way of providing an explanatorily deep char-acterization of some x is to capture a metaphysical constraint on x. Becausemetaphysical constraints are identical to constitutive parts of natures, infor-mation about them constitutes correct, necessary, and informative answersto questions of the form ’what is it to be x.’ Parts of natures are, after all,just constitutive parts of what it is to be their objects. By identifying and

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precisely grasping the metaphysical constraints on e.g. composition and freewill, we better understand what it is for a will to be free and what it is forcomposition to obtain.

4.2 Constraints Needn’t Reduce

Like reductions, metaphysical constraints underwrite explanatorily deepcharacterizations of their objects. However unlike reduction, metaphysicalconstraints don’t need to support or entail reductive analysis in order to ex-plain. Instead, metaphysical constraints underwrite a way of characterizingentities that is fully independent of reduction and so is available even whenreductive analysis is not.

Recall the Minimal Reductive Commitment from section 3.1: “An entityx reduces to an entity y only if x does not exist over and above y” (Smart1959, 143). In order to count as reductive by the lights of the MinimalReductive Commitment, metaphysical constraints would need to serve asparts of the reductive base of their targets so that targets are nothing overand above the constraints on them. We ought to reject this: things do seemto exist over and above their constraints.

To see that constraints need not serve as reductive bases, consider thatmetaphysical constraints sometimes take their objects as constitutive parts.This would not be possible were entities nothing in addition to their con-straints. The alternate possibilities constraint on free will illustrates this.AP claims that a person acted freely only if they could have done otherwise.It sets out a necessary relationship between free will and the power to do oth-erwise such that standing in this relationship is a constitutive part of what itis for a will to be free. However, [that free will and the power to do otherwiseare so related] is itself a state of affairs that is composed of the propertiesand objects that are its parts.12 As a result, the AP constraint on free willhas free will as a proper part. Something analogous is true for the unique-ness of composition. In settling the individuation conditions for composite

12I am here assuming the standard view on which worldly facts are grounding in theobjects and properties that compose them.

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objects, uniqueness makes free use of the composition relation. Compositeobjects are just those objects that are composed of other objects.13 In eachof these examples, the metaphysical constraints on x themselves involve x.As a result, any reductive analysis of x based on these constraints is doomedto include the target of analysis in the analysans.

For the same reason, metaphysical constraints sometimes violate the rel-ative fundamentality requirement on reduction: the idea that if x can bereduced to some ys then the ys are in some sense prior to, more basic than,or more fundamental than x. Unlike reductive bases, metaphysical con-straints need not be any of these things. Instead, it is often the case thatconstraints and their objects stand as parts of a closed circle of interrelatedentities like those plausibly formed by mereological, modal, and moral prop-erties. Because of this, constraints need not be wholly independent of theirobjects: nothing seems to prevent e.g. mereological relations from havingmereological natures. Reductions, by contrast, must be wholly independentof their objects if they hope to avoid triviality or vicious circularity.14

In addition to these general considerations, metaphysical constraints arenot plausibly related to their objects via reductive relations. This is an addi-tional reason to think that entities are genuinely something over and abovetheir constraints. One of these relations is reductive identity such that somex is reduced to its constraints if x is identical to these constraints. However,that’s not plausible. As we’ve seen, entities need not even belong to thesame ontological category as their constraints. While composition is a re-lation among concrete objects, the metaphysical constraints on compositionare not. They are worldly facts, like the fact that composition is unique.

13Because mereological notions are inter-definable, we are not obligated to understanduniqueness in terms of composition: it could just as well be understood in terms of overlapor proper parthood, for example. What is important for our purposes, is that understand-ing uniqueness and composite object in terms of composition doesn’t seem to involve amistake even though uniqueness is, if true, a constraint on composition. Finally, though wehave some choices about our primitive mereological notions, we cannot formulate unique-ness in non-mereological terms. For more on this see Simons 1987, Lewis 1991, Varzi2008.

14Constraints are not independent enough from their objects to serve as reductive bases.However, it seems to me that they are independent enough to serve as parts of a satisfyingexplanation.

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For the same reason, entities are not identical to the complete set of theirconstraints: their complete natures. A complete set of constraints is a set ofworldly facts or a single complex one.

Alternatively, some x might be reduced to its constraints by being (whollyor partly) grounded in them. This isn’t plausible either. Because metaphys-ical constraints need not be, and often aren’t, independent of what theyconstrain, attempts to ground objects in their constraints invite violationsof the irreflexivity of grounding by inviting cases in which objects wholly orpartly ground themselves. Perhaps AP and Uniqueness are cases like this.As a result, it isn’t clear that the grounding claims required by this strategycan even satisfy the formal requirements typically placed on grounding.15 Inaddition, grounding is a generative relation often taken to serve as a kindof metaphysical analog of causation. “Roughly speaking, just as causationlinks the world across time, grounding links the world across levels. Ground-ing connects the more fundamental to the less fundamental” (Schaffer 2012,122. See also Sider 2001, Bennett 2011, Wilson 2014, Schaffer 2016b, Wil-son 2016, 2017. In contrast, Koslicki 2016, Bernstein 2016 argues that thereare important differences between grounding and causing that ought to berespected.). Less fundamental entities exist and have the features they do invirtue of the more fundamental entities that ground them. But metaphysicalconstraints and their objects need not stand in generative relations to oneanother: entities seem not to be generated from what it is to be them.16

Conforming to a constraint on x is a necessary condition on x and per-haps conforming to all the constraints is sufficient for being x. So, it mightbe thought that constraints reduce by furnishing necessary and sufficientconditions. The problem, again, is that we require necessary and sufficientconditions to be independent of their analysanda. As we’ve seen, metaphys-ical constraints need not be independent of what they constrain. It is alsoworth emphasizing that while they are necessary conditions, constraints are

15Though typical, these requirements are not universally endorsed. For discussion, seeJenkins 2011

16Grounding and metaphysical constraints also function differently in explanatory con-texts and plausibly back different sorts of explanation. For an argument to this effect, see[Omitted for Blind Review].

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not merely necessary. They are necessary because they are constitutive partsof the nature of the thing at issue. In general, necessary conditions are easyto come by: that 2+2 = 4 is a necessary condition on the existence of x, what-ever x may be. So, we are in fact interested in some special sort of necessarycondition. Perhaps there are other ways of characterizing the specialnessat issue here but one way it can be done is in terms of constraints: whensearching for a criterion, we’re interested not merely in necessary conditionsbut in necessary conditions that capture constraints.

In light of this discussion, I don’t think it’s plausible that constraintsserve as the basis for reductive analysis. The constraints on some x aredistinct from any base to which it might be reduced. Because metaphysi-cal constraints are independent of reduction in this way, they are availableeven in cases in which no reductive analysis is possible. It may be true inprinciple, for example, that no reductive analysis of composition is possible.However, the uniqueness of composition is nonetheless a plausible constrainton composition (again, if it is true at all) and so is nonetheless a constitutivepart of what it is to be the composition relation.

I’ve argued that metaphysical constraints can be used to underwrite ex-planatorily rich characterizations of their targets so that constraintist theo-ries share many of the explanatory virtues enjoyed by reductive ones. How-ever, because constraintist theories are independent of reductive analysis,they, unlike their reductive counterparts, are not hostage to the availabilityof reductive analysis and so are available even when the reductive projectfails. This tells us something important: that the explanatory question con-cerning whether it is possible to explain what it is to be some x is separablefrom the ontological question concerning whether x can be reduced. We’veseen that it is possible to give a negative answer to the ontological questiontogether with an affirmative answer to the explanatory one.4.3 Constraintism is not Primitivism

Constraintist accounts do not reduce their targets. In the spirit of theArgument from Absence of Analysis, it might be thought that constraintistaccounts are committed to primitivism about their objects instead. How-

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ever, I will argue that this is not the case either. Metaphysical constraintsunderwrite a way of providing explanatory characterizations that is distinctboth from reduction and primitivism and so provides a way of answeringthe explanatory question while ignoring or remaining agnostic concerningthe possibility of reduction. In doing so, it witnesses my central claim: thatthere is no implication from the failure of reduction to the impossibility ofexplanatory characterization. If it is to secure the robust primitivism oftenfound in the literature, then the AAA requires this implication. So the AAAfails to secure its intended conclusion.

Recall the Minimal Primitivist Commitment from section 3.2: if x isa primitive then x cannot be reductively analyzed. Though constraintistaccounts are compatible with the truth of the Minimal Primitivist Commit-ment, they are also compatible with its falsity. Again, the availability of ex-planatorily deep characterizations underwritten by metaphysical constraintsis orthogonal to the success or failure of reduction. Because genuinely prim-itivist theories must not be indifferent to the truth or falsity of the MinimalPrimitivist Commitment, constraintist theories are not primitivist theorieseither. This is compatible with the claim that reduction and minimal primi-tivism partition the space of logically possible views about what can be reducedto what. The availability of constraintist views shows that the question ofwhether an explanatory characterization of some x can be given outruns thequestion of whether an ontological reduction of x can be provided.

Primitivism as it is usually defended is not exhausted by the MinimalPrimitivist Commitment, it is often supplemented with stronger clams. Con-straintist theories ought to reject these stronger claims and so are not com-mitted to primitivism in the way that Chalmers 1996is committed to primi-tivism about the mental, Lipman Forthcoming entertains primitivism aboutpassage, or Moore 1993 is committed to primitivism about the moral.

On the robust way in which they are often understood, primitive entitiesare sui generis and fundamental. Because of this, many facts about them arebrute so that no explanatory characterization illuminating what it is to be aprimitive entity is possible. Though it is not the case that primitive entitiesare totally mysterious (it is true that we can uncover interesting facts about

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primitive entities and their distribution) primitive entities are in a certainsense epistemically inaccessible.

Because metaphysical constraints underwrite explanatory characteriza-tions of their objects and so provide information about what it is to bethem, constraintist theories are incompatible with this robust primitivism.If something can receive an explanatorily deep characterization underwrit-ten by constraints, then it need not be ontologically fundamental and is notepistemically inaccessible in the way that primitive entities are meant to be.We are not reduced to metaphor or example when explaining what it is tobe the object of constraint because we can provide an informative account ofwhat it is to be that object by understanding the metaphysical constraintson it. While primitivist theories are often accused of failing to provide anyexplanatory understanding of their target phenomena, an account backed bymetaphysical constraints is not guilty of any such failure. In other words,constraintist theories are distinct from primitivist ones because they can dowhat primitivist theories deny is possible: provide explanatorily deep char-acterizations of their objects.

If the AAA is to be useful for securing primitivism as it is broadly en-dorsed, then it must secure an explanatory claim concerning the impossibilityof explanatory characterization in addition to a metaphysical claim aboutthe impossibility of reduction. It must do more than prove that the MinimalPrimitivist Commitment is true. However, the AAA as applied to some xfails to rule out that a constraintist account of x might be available. As aresult, it fails to secure the explanatory claim necessary for primitivism.

5 Constraints Reveal Hidden Dialectical Space

Let’s take stock. I’ve argued that, though the Argument from Absenceof Analysis is pervasive, it fails to secure the explanatory claim that primi-tivism requires. In order to show that the AAA is dubious, I offered a way ofexplaining what it is to be some x underwritten by metaphysical constraints.That these explanatory characterizations are available opens new dialecticalspace to explore. Though there are many things for which reductive analysisis so far unavailable, we may still provide explanatory characterizations of

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these things underwritten by metaphysical constraints: we need not abandonthe explanatory project to primitivism. In this section, I’ll present the de-bate concerning personal identity as a case study illustrating how the spaceopened by metaphysical constraints might be occupied.5.1 Case Study: Personal Identity

Constraintist theories are especially promising in debates in which reduc-tionist and primitivist opponents have fought to a stalemate. To see this,consider the debate about the persistence question in the metaphysics ofpersonal identity. Although care is required, the question is often asked asfollows: “under what possible circumstances is a person who exists at onetime identical with something that exists at another time” (Olson 2016, 4).The question is often paraphrased as a request for necessary and sufficientconditions (as in Olson 2016, 4). The aim here is to provide a criterion ofpersonal identity that reduces it to a set of conditions that are individu-ally necessary, jointly sufficient, and informative: they are non-trivial andindependent of personal identity. These conditions serve as a reductive basefor personal identity so that what it is for a person to persist over time isnothing over and above their satisfying them.

Attempts to provide a reductive analysis, and so to explain what it is fora person to persist over time, have come in roughly two kinds. On the first,psychological approach, proponents claim that some psychological relationis necessary and sufficient for persistence. One candidate reductive base ispsychological connection. A being at some future time is psychologicallyconnected with you at the present time if she is in the psychological statesshe is at some future time because or in large part because of the psycholog-ical states that you are in now (Lewis 1983, Shoemaker 1984, Olson 2016).Another candidate is psychological continuity. A being at some future timeis psychologically continuous with you at the present time if some of yourcurrent mental states are related to hers by way of a chain of psychologicalconnection. These are offered as a criterion of identity so that, as Lewisclaims, “what matters in survival is mental continuity and connectedness”(Lewis 1983, 56). On the second, somatic approach, identity through time

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consists in some (perhaps brute) physical relation. A being at some futuretime is identical to you iff, e.g. you share the same life, are the same animal,or have the same body or brain (Thomson 1997, Olson 1999, 2016). Whatmatters for survival on this approach is the sameness of a particular kind ofphysical object so that the problem of personal identity reduces to the moregeneral problem of identity over time.

Though otherwise very different, these approaches agree that there issomething that it takes for us to persist so that “our identity through timeconsists in or necessarily follows from something other than itself (Olson2016, 7). While there is disagreement concerning the base to which personalidentity can be reduced, there is agreement that personal identity can bereductively analyzed: a criterion of personal identity, stated in independentterms can be given.

Unfortunately, attempts at reductive analysis along these lines are uni-formly subject to devastating counterexamples targeting the sufficiency ofthe analysis. The psychological continuity view is threatened by fission casesin which more than one future person is psychologically continuous with youeven while each future person fails to be identical to the other. Becauseidentity is plausibly transitive, something more than continuity must be re-quired. In contrast, different versions of the somatic view are plagued bytransplant cases that preserve the relevant physical relations while destroy-ing the psychological features that intuitively matter.

When a reductive analysis cannot be provided, as is suggested by theapparent failure of existing analyses, that is taken as evidence in favor ofanticriterialism: the view that there is no true and informative theory ofpersonal identity so that personal identity is a primitive notion (Merricks1998). No sort of continuity is both necessary and sufficient for you tosurvive and so no informative criterion of identity is available for explainingwhy two things are identical to one another. While anticriterialism doesnot entail that persistence or existence at a time is brute, unexplainable, oruncaused, it does follow that no informative explanation of what it is fora person to survive can be given. That your future self exists is explainedcausally and there is no need to explain why you are identical to your future

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self because identity facts are primitive: they don’t require explanation (c.f.Merricks 1998).

Metaphysical explanations by constraint underwrite a third sort of ac-count distinct from the reductive and primitivist ones found in the literature.Like the anticriterialist, the constraintist can deny that persistence over timeis reductively analyzable. However, it does not follow that there can be notrue and informative explanation for what it is to persist. Though no criteriaof identity may be possible, the constraintist claims that an explanatorilydeep characterization of persistence over time is available nonetheless.

A first approximation of such an account can be constructed from themost attractive pieces of reductive theories while disavowing their reductiveaspirations. For example, a promising constraintist theory might adopt thepsychological approach by identifying psychological continuity as a meta-physical constraint on persistence over time rather than as part of its reduc-tive base. On this view, a constitutive part of what it is for a future personto be identical to you is for that person to be psychologically continuous withyou. Psychological continuity is necessary for persistence, on this view, butneed not be sufficient for it. As a result, such a theory is not threatened bythose challenges to sufficiency, like fission cases, that plague its reductionistcousins.17

The research project underwritten by metaphysical constraints is distinctfrom the project of reductive analysis and isn’t threatened by the fact thatpsychological continuity is insufficient for persistence. Though it need notsecure a set of necessary and sufficient conditions, the constraintist projectwill, if successful, secure an explanatorily deep characterization. By identi-fying constitutive parts of the nature of diachronic personal identity, if offersan interesting and informative answer to the question what it is for a person

17The theory of personal identity over time can be developed making use of the psycho-logical continuity constraint by exploring possible worlds via the IPA method defended in[Omitted for Blind Review]. Making use of this method requires us to identify and makesuitably precise the constraint and then to assess it by exploring possible worlds in whichthe constraint is and is not satisfied. The result, if all goes well, is a revealing test thatprovides information about how personal identity must be and in what ways it can bedifferent than it is.

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to persist over time. Constraintist views shoulder the explanatory burdenthat the anticriterialist shrugs by claiming that identity facts are primitiveand so don’t require explanations.5.2 A Revealing Objection

It might be objected that the constraintist theory of personal identity pro-vides, at best, a partial characterization of personal identity and so a partialexplanation of what it is for a person to persist through time. In contrast,had a reductive account been available, it would have fully characterizedand so fully explained identity over time. Because the constraintist accountprovides a merely partial characterization, it falls short (so the worry goes)of explaining what it is for a person to be identical to some past or futurething.

Though they might be complete in principle, I agree that constraintisttheories are often partial. Rarely if ever do we completely grasp the meta-physical constraints on entities about which we wish to theorize. Requiringthis sets the bar for theorizing much too high. I do not agree, however, thatit follows that any theory of personal identity underwritten by metaphysicalconstraints will fail to explain what it is for a person to be identical to somefuture thing: failing to provide a complete explanation is not the same asfailing to provide an explanation tout court. When a theory is underwrittenby an incomplete set of constraints, it provides a partial explanation of itstarget and such a partial explanation is a significant achievement, particu-larly in contexts in which no complete reductive explanation is forthcoming.

Importantly, the same cannot be said for incomplete reductive accounts.Reductive accounts explain what it is to be their targets by reducing them:showing them to be nothing over and above some independent y or y’s.Because incomplete reductions do not do this, they fail to discharge theexplanatory burden shouldered by reductive accounts even in part.18 Re-duction is an all or nothing affair. In contrast, constraintist theories explain

18It might be suggested that partial reductions offer partial explanations. This is im-plausible. It would require us to show that some x is partially nothing over and abovesome further y. Yet, partial nothing over and aboveness seems to me to be a contradictionin terms.

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their targets by providing information about what it is to be them. A partialcollection of this information partially discharges the explanatory burden as-sumed by constraintist accounts and constitutes an explanatory achievementas a result.

Finally, while differences in completeness might be a reason to preferreductive views to constraintist ones in debates in which both are available,I have argued that constraintist views are important precisely because this isnot often the case.19 It is not the case that reductive analysis is available, forexample, in debates in which the AAA is appropriate. Furthermore, it is notthe case that reductive analysis is readily available in those debates for whichthe new ground broken by constraints is most promising. In these debates,like the one about personal identity, there is an impasse between reductionand primitivism so that each view is subject to significant objections makingneither view attractive.

Theories underwritten by constraints contribute to debates like theseby offering explanatory characterizations that are not vulnerable to exist-ing objections, are informative, and do not require reduction. Rather thanmitigating objections to reductive or primitivist views, as friends of eitherview must, constraintist theories make their contribution by untangling on-tological questions concerning whether and how personal identity can bereduced from explanatory questions concerning what it is to be identical tosome future thing. By providing an attractive third option in debates inwhich neither reduction nor primitivism is appealing, theories underwrittenby metaphysical constraints promise to break the impasse between existingviews.

19In fact, I’m skeptical that we ought always prefer reductive views even under thesecircumstances. One reason is that I’m skeptical that reductive views really provide com-plete explanations. It is plausible, for example, that what it is for a person to persistover time is exhausted by its reductive base. However I think the resulting reductive ex-planation reveals little about the nature of personal identity in absence of an additionalexplanatorily deep characterization of its reductive base. In absence of such a characteri-zation, a reductive explanation of personal identity does nothing to characterize its targetbeyond pointing to some further thing. In contrast, metaphysical constraints are not oftencomplete but do illuminate the natures of their targets. We might have reason to preferilluminating explanations to complete ones when doing metaphysics, though there is noneed to stand on this controversial claim here.

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6 Conclusion

Despite its widespread use, the Argument from Absence of Analysis is du-bious. While the argument depends on dividing the space of possible viewsconcerning explanation between primitivism and reduction, I have arguedthat metaphysical constraints provide a middle path that secures the bene-fits of each kind of view without the costs of either. Like reductionist ones,constraintist theories offer explanations for what it is to be their objects.Like primitivist theories, constraintist theories are not hostage to the dimprospects for ontological reduction.

Metaphysical constraints underwrite a general objection to the Argu-ment from Absence of Analysis that applies uniformly to its instances. As aresult, they make unavailable an important argument for primitivism. How-ever, metaphysical constraints also reveal new dialectical space in a range ofphilosophical debates so that by discovering constraintist theories are avail-able, we uncover previously hidden space that has yet to be explored. Thisnew space is especially valuable when, as in the case of the debate aboutdiachronic personal identity, existing views are unappealing.

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