Typical structural universals are not just the mereological sum of their constituents. Hence, there is the Structure Problem of explaining this non-mereological structure. The Instantiation Problem is that the predicate "U is instantiated by x, y, etc., in that order" is ill-suited to be a primitive, unanalyzed predicate. The proposed solution to these problems is based on the observation that if universal U is said to supervene upon universals V, W, etc., then it is the instantiation of U that supervenes (...) on the instantiation of V, W, etc. Assuming there are few subvenient universals, which is admittedly a speculation, their instantiation may be explained in ways that would be uneconomic if there were too many. (shrink)

In the early twentieth century, many philosophers in America thought that time should be taken seriously in one way or another. George P. Adams (1882-1961) argued that the past, present and future are all real but only the present is actual. I call this theory ‘actualist eternalism’. In this paper, I articulate his novel brand of eternalism as one piece of his metaphysical system and I explain how he argued for the view in light of the best explanations of temporal (...) experience and the present. I argue that his exploitation of analogies between time and modality offer some lessons for current debates about time such as the importance of providing a temporal epistemology. I also extract what I call the temporal boundary problem and argue that it gives rise to an unaddressed challenge for presentists and growing block theorists. (shrink)

Structural universals are a kind of complex universal. They have been put to work in a variety of philosophical theories but are plagued with problems concerning their compositional nature. In this article, we will discuss the following questions. What are structural universals? Why believe in them? Can we give a consistent account of their compositional nature? What are the costs of doing so?

David Lewis objected to theories that posit necessary connections between distinct entities and to theories that involve a magical grasping of their primitives. In On the Plurality of Worlds, Lewis objected to nondescript ersatzism on these grounds. The literature contains several reconstructions of Lewis’ critique of nondescript ersatzism but none of these interpretations adequately address his main argument because they fail to see that Lewis’ critique is based on broader methodological considerations. I argue that a closer look at his methodology (...) reveals the broader objection he presented against nondescript ersatzism. This objection, I further argue, remains a challenge for the ersatzer who posits structure-less entities as possible worlds. (shrink)

In the ontology of music the Aristotelian theory of musical works is the view that musical works are immanent universals. The Aristotelian theory (hereafter Musical Aristotelianism) is an attractive and serviceable hypothesis. However, it is overlooked as a genuine competitor to the more well-known theories of Musical Platonism and nominalism. Worse still, there is no detailed account in the literature of the nature of the universals that the Aristotelian identifies musical works with. In this paper, I argue that the best (...) version of Musical Aristotelianism identifies musical works with structural universals. I first motivate the view by outlining its explanatory benefits. I then argue that Musical Aristotelianism is preferable to Musical Platonism and present a novel account of musical works as structural universals by developing D. M. Armstrong’s theory of structural universals. I discuss the consequences of Musical Aristotelianism with respect to on-going issues in debates about musical works and defend the view against an influential objection, concluding that Musical Aristotelianism is a genuine competitor in debates about the nature of musical works. (shrink)

Trenton Merricks argues for and defends a novel version of primitivism about truth : being true is a primitive monadic but non-intrinsic property. This examination consists of the following triad: a critical discussion of Merricks’ argument for his view, a rejection of his objection against Paul Horwich’s minimalist theory of truth, and a direct objection against his view on the grounds that it entails being true is a mysterious and suspicious property. The conclusion is that Merricks’ primitivism should be rejected.

Theories that posit metaphysical structure are able to do much work in philosophy. Some, however, find the notion of ‘metaphysical structure’ unintelligible. In this paper, I argue that their charge of unintelligibility fails. There is nothing distinctively problematic about the notion. At best, their charge of unintelligibility is a mere reiteration of previous complaints made toward similar notions. In developing their charge, I clarify several important concepts, including primitiveness, intelligibility, and the Armstrong-inspired “ontologism” view of the world. I argue that, (...) ultimately, their charge is best understood as an objection whose central premise is that the notion of ‘structure’ runs contrary to an important presupposition of contemporary metaphysics. But that central premise is, on closer inspection, implausible. I respond to the objection by identifying three popular metaphysical theories that violate the alleged presupposition but are still generally regarded as intelligible. The objection thus fails to show that a theory that posits metaphysical structure is unintelligible. (shrink)

A belief is valuable when it “gets it right”. This “getting it right” is often understood solely as a matter of truth. But there is a second sense of “getting it right” worth exploring. According to this second sense, a belief “gets it right” when its concepts accurately match the way the world is objectively organized – that is, when its concepts are joint-carving, or have fidelity. In this paper, I explore the relationship between fidelity and epistemic value. While many (...) philosophers (especially metaphysicians) acknowledge fidelity's value, they overlook just how much it might disrupt our understanding of epistemic value. To tease out this disruption, I draw on the Jamesian balance between seeking the truth and avoiding the false. A similar balance must be struck both within the pursuit of fidelity itself (“seeking the joints” and “avoiding the gruesome”) as well as between the pursuit of fidelity and the pursuit of truth. I then give an argument against the claim that truth is the higher epistemic good. (shrink)

Metaphysicians now typically distinguish between a theory’s ontology and its ideology. But besides a few cursory efforts, no one has explained the role of ideology in theory choice. In this paper I develop a framework for discussing how differing approaches to ideology impact metaphysical disputes. I first provide an initial characterization of ideology and develop two contrasting types of criteria used to evaluate its quality. In using externalist criteria, we judge the quality of a theory’s ideology by its relation to (...) external features of the world. In contrast, in using internalist criteria, we judge the quality of a theory’s ideology by features internal to the theory and the theorizer, e.g. the intelligibility of the terminology employed. I then argue for an unrestricted application of externalist criteria, what I call maximal realism. According to maximal realism, we ought to apply externalist criteria to the entirety of a theory’s ideology—to not only predicates but also to quantifiers and logical operators. I defend maximal realism from what I take to be the best objection to it: that the view leads to bad questions. As part of my defense, I argue that those who would restrict their application of externalist criteria either adopt an unjustified partition of ideology or reject seemingly benign questions. Finally, I apply my discussion of ideology to two extant metaphysical disputes. (shrink)

Many metaphysicians utilize the virtue‐driven methodology. According to this methodology, one theory is more worthy of endorsement than another insofar as it is more virtuous. In this paper, I show how a theory's overall virtue is shaped by its ideological parsimony – parsimony with respect to the terminology employed in stating the theory. I distinguish between a theory's truth and its fidelity (‘joint‐carvingness’) and the corresponding epistemic and fidelic virtues. I argue that ideological parsimony is not an epistemic virtue but (...) is a fidelic virtue. Insofar as metaphysicians value fidelity, then, ideological parsimony has an important role in theory choice. (shrink)

How can a metaphysics of abstract entities be built upon a metaphysics of time? In this paper, I address the question of how to accommodate abstract entities in a presentist world. I consider both the traditional metaontological approach of unrestricted fundamental quantification and then ontological pluralism. I argue that under the former we need to impose two constraints in the characterization of presentism in order to avoid undesired commitments to abstract entities: we have to characterize presentism as a thesis only (...) about the concrete, and we also need to avoid the widely held distinction between tensed and tenseless senses of existence. Under ontological pluralism, instead, I argue that we can naturally accommodate any view of abstract objects in a presentist world. (shrink)

Special science generalizations admit of exceptions. Among the class of non-exceptionless special science generalizations, I distinguish minutis rectis generalizations from the more familiar category of ceteris paribus generalizations. I argue that the challenges involved in showing that mr generalizations can play the law role are underappreciated, and quite different from those involved in showing that cp generalizations can do so. I outline a strategy for meeting the challenges posed by mr generalizations.

Inspired by the supervenience-determined consequence relation and the semantics of agreement operator, we introduce a modal logic of supervenience, which has a dyadic operator of supervenience as a sole modality. The semantics of supervenience modality very naturally correspond to the supervenience-determined consequence relation, in a quite similar way that the strict implication corresponds to the inference-determined consequence relation. We show that this new logic is more expressive than the modal logic of agreement, by proposing a notion of bisimulation for the (...) latter. We provide a sound proof system for the new logic. We lift onto more general logics of supervenience. Related to this, we address an interesting open research direction listed in the literature, by comparing propositional logic of determinacy and noncontingency logic in expressive powers and axiomatizing propositional logic of determinacy over various classes of frames. We also obtain an alternative axiomatization for propositional logic of determinacy over universal models. (shrink)

This article investigates the causal efficacy of social properties, which faces the following puzzle. First, for both intuitive and scientific reasons, it seems social properties have causal import. But, second, social properties are also characteristically extrinsic: to have some social property depends, in typical cases, on what one’s society is like around them. And, third, there is good reason to doubt that extrinsic properties make a genuine causal contribution. After elaborating on these three claims, I defend the following resolution to (...) the puzzle: social causation occurs at the level at which social properties are intrinsic. (shrink)

I defend an account of God’s ineffability that depends on the distinction between fundamental and non-fundamental truths. I argue that although there are fundamentally true propositions about God, no creature can have them as the object of a propositional attitude, and no sentence can perfectly carve out their structures. Why? Because these propositions have non-enumerable structures. In principle, no creature can fully grasp God’s intrinsic nature, nor can they develop a language that fully describes it. On this account, the ineffability (...) of God is explained in terms of the inability of our language and mental capacities to grasp God as he really is. I will motivate my account by distinguishing it from a rival proposal. According to this rival, there are no fundamentally true propositions about God’s intrinsic nature. I argue that this rival proposal faces problems that my account does not face. And unlike this rival and other accounts of ineffability, my account provides a fitting explanation of why God is ineffable. God is ineffable because the structure of his intrinsic nature is infinite. (shrink)

Philosophy and Phenomenological Research, EarlyView.

Cet article se propose de reprendre les discussions autour du principe d’identité des indiscernables (PIdI) en précisant le type d’entités qui pourraient y déroger. J’y défends l’idée que le rejet du PIdI ressortit à la possibilité de trois types de doubles : les répliques pures, ou reproductions parfaites, les doubles purs, doubles qui ne peuvent pas même être distingués par des relations spatio-temporelles, et enfin les coïncidents purs qui sont des doubles « superposés ». La thèse que je défends consiste (...) à montrer que l’existence de telles entités est non seulement concevable, mais même, pour les deux premières sortes, physiquement possible. Pour ce qui concerne la possibilité des coïncidents purs, le rejet de telles entités peut être appuyé indépendamment du PIdI sur un principe de parcimonie ontologique basé sur une indifférence causale. (shrink)

Four-dimensionalism, the stage theory version in particular, has been defended as the best solution for avoiding vagueness in regards to composition, persistence and identity. Stage theory is highly problematic by itself, and the two views usually packed with it, unrestricted composition and counterpart theory, are a heavy burden. However, dispensing with these two views, four-dimensionalism could avoid vague persistence by issuing a criterion that would establish sharp temporal boundaries for the existence of genuine entities (simples, molecules and living organisms). This (...) would avoid vague existence and vague identity, but in a way that is still compatible with endurantism. Nevertheless, a minimal (substantialist) four-dimensionalism, a worm perdurantist ontology, would fit better with the unique way in which organisms persist: by retaining both identity and intrinsic change. (shrink)

The aim of this editorial introduction is twofold. First, Sects. 1–8 offer a critical introduction to the metaphysical character of physicalism. In those sections, I present and evaluate different ways in which proponents of physicalism have made explicit the metaphysical dependence that is said to hold between the non-physical and the physical. Some of these accounts are found to be problematic; others are shown to be somewhat more promising. In the end, some important lessons are drawn and different options for (...) physicalists are presented. Second, in Sect.9, the six papers that comprise the special issue are introduced and summarized. (shrink)

This paper provides an exposition and defence of Lewis' theory of radical interpretation. The first part explains what Lewis' theory was; the second part explains what it wasn't, and in so doing addresses a number of common objections that arise as a result of widespread myths and misunderstandings about how Lewis' theory is supposed to work.

According to the preference-centric approach to understanding partial belief, the connection between partial beliefs and preferences is key to understanding what partial beliefs are and how they’re measured. As Ramsey put it, the ‘degree of a belief is a causal property of it, which we can express vaguely as the extent to which we are prepared to act on it’ The Foundations of Mathematics and Other Logical Essays, Routledge, Oxon, pp 156–198, 1931). But this idea is not as popular as (...) it once was. Nowadays, the preference-centric approach is frequently dismissed out-of-hand as behaviouristic, unpalatably anti-realist, and/or prone to devastating counterexamples. Cases like Eriksson and Hájek’s :183–213, 2007) preferenceless Zen monk and Christensen’s :356–376, 2001) other roles argument have suggested to many that any account of partial belief that ties them too closely to preferences is irretrievably flawed. In this paper I provide a defence of preference-centric accounts of partial belief. (shrink)

It is often said that there are two varieties of identity theory. Type-identity theorists interpret physicalism as the claim that every property is identical to a physical property, while token-identity theorists interpret it as the claim that every particular is identical to a physical particular. The aim of this paper is to undermine the distinction between the two. Drawing on recent work connecting generalized identity to truth-maker semantics, I demonstrate that these interpretations are logically equivalent. I then argue that each (...) has the resources to resolve problems facing the other. (shrink)

It is often said that there are two varieties of identity theory. Type-identity theorists interpret physicalism as the claim that every property is identical to a physical property, while token-identity theorists interpret it as the claim that every particular is identical to a physical particular. The aim of this paper is to undermine the distinction between the two. Drawing on recent work connecting generalized identity to truth-maker semantics, I demonstrate that these interpretations are logically equivalent. I then argue that each (...) has the resources to resolve problems facing the other. (shrink)

I argue that constructive nominalism is preferable to scientific realism. Rather than reflecting without distortion the way the mind-independent world is, theories refract. They provide an understanding of the world as modulated by a particular theory. Truth is defined within a theoretical framework rather than outside of it. This does not undermine objectivity, for an assertion contains a reference to the framework in terms of which its truth is claimed.

In his Ontology and the Ambitions of Metaphysics, Thomas Hofweber among other things presents a radical perspective on ontology and metaphysics. In this note, I critically discuss some of the points Hofweber makes.

The main thesis of this paper is that we sometimes are disposed to accept false and even jointly inconsistent claims by virtue of our semantic competence, and that this comes to light in the sorites and liar paradoxes. Among the subsidiary theses are that this is an important source of indeterminacy in truth conditions, that we must revise basic assumptions about semantic competence, and that classical logic and bivalence can be upheld in the face of the sorites paradox.

The article is centered on the question of how best to understand the logical pluralism/logical monism debate. A number of suggestions are brought up and rejected on the ground that they re...

In his important book The Construction of Logical Space, Agustín Rayo lays out a distinctive metametaphysical view and applies it fruitfully to disputes concerning ontology and concerning modality. In this article, I present a number of criticisms of the view developed, mostly focusing on the underlying metametaphysics and Rayo’s claims on its behalf.

The problem, or cluster of problems, of the unity of the proposition, along with the cluster of problems that tend to go under the name of Bradley’s regress, has recently again become a going concern for philosophers, after having for some time been regarded as primarily of historical interest. In this paper, I distinguish between the different problems that tend to be brought up under the heading of the unity of the proposition, and between different related regress arguments. I present (...) my favored solutions to these problems. (shrink)

This paper argues that, assuming properties exist and must be located in spacetime, the prevailing view that they are exactly located where their instances are is false. Instead a property is singularly located at just one region, namely the union of its instance's locations. This bears not just on issues in the metaphysics of properties, but also on the debate over whether multi-location is conceivable and/or possible.

Philosophy and Phenomenological Research, EarlyView.

When a study shows statistically significant correlation between an exposure and an outcome, the credence of a real connection between the two increases. Should that credence remain the same when it is discovered that further independent studies between the exposure and other independent outcomes were conducted? Matthew Kotzen argues that it should remain the same, even if the results of those further studies are discovered. However, we argue that it can differ dependent upon the results of the studies.

One of the many ways that ‘deflationary’ and ‘inflationary’ theories of truth are said to differ is in their attitude towards truth qua property. This difference used to be very easy to delineate, with deflationists denying, and inflationists asserting, that truth is a property, but more recently the debate has become a lot more complicated, owing primarily to the fact that many contemporary deflationists often do allow for truth to be considered a property. Anxious to avoid inflation, however, these deflationists (...) are at pains to point out that the truth property, on their view, is not a property of any significant interest. Correspondingly, inflationists have seen this as an opportunity to refine what kind of property they think truth is, which—according to them—moves their views beyond deflationism. The upshot of this is that there are number of different accounts in the literature of what distinguishes an inflationary truth property from a deflationary one, or—as it is sometimes put—what distinguishes a ‘substantive’ property from an ‘insubstantive’ one. This has made it hard to pin down exactly what is at issue at the metaphysical level between deflationists and inflationists, which makes it increasingly hard to see how debates between them are properly phrased. Given that these positions represent the two central attitudes towards truth in contemporary debates, this makes for a serious obstacle for the project of discerning the correct theory of truth. The aim of this paper is to discern the best way to distinguish between substantive and insubstantive properties, and thus to restore some focus to these debates. I argue that the three central distinctions in the literature fail, and offer what I take to be a more promising distinction in terms of a graded distinction between abundant and sparse properties. (shrink)

In these replies I develop responses to the fascinating issues raised in the commentaries on my book The Metaphysics of Truth from Matti Eklund, Gila Sher, Crispin Wright, and Jeremy Wyatt. I focus on four main areas where there seemed to be a degree of convergence amongst the critics: (1) the viability and use of the sparse/abundant property distinction; (2) truth, dependence, and superassertibility; (3) correspondence, realism, and anti—realism; and (4) my ‘globalizing’ argument against deflationism.

Two grams mass, three coulombs charge, five inches long – these are examples of quantitative properties. Quantitative properties have certain structural features that other sorts of properties lack. What are the metaphysical underpinnings of quantitative structure? This paper considers several accounts of quantity and assesses the merits of each.

Is part of a perfectly natural, or fundamental, relation? Philosophers have been hesitant to take a stand on this issue. One reason for this hesitancy is the worry that, if parthood is perfectly natural, then the perfectly natural properties and relations are not suitably “independent” of one another. In this paper, I argue that parthood is a perfectly natural relation. In so doing, I argue that this “independence” worry is unfounded. I conclude by noting some consequences of the naturalness of (...) parthood. (shrink)

The Argument from Temporary Intrinsics is one of the canonical arguments against endurantism. I show that the two standard ways of presenting the argument have limited force. I then present a new version of the argument, which provides a more promising articulation of the underlying objection to endurantism. However, the premises of this argument conflict with the gauge theories of particle physics, and so this version of the argument is no more successful than its predecessors. I conclude that no version (...) of the Argument from Temporary Intrinsics gives us a compelling reason to favor one theory of persistence over another. (shrink)

The standard counterexamples to David Lewis’s account of intrinsicality involve two sorts of properties: identity properties and necessary properties. Proponents of the account have attempted to deflect these counterexamples in a number of ways. This paper argues that none of these moves are legitimate. Furthermore, this paper argues that no account along the lines of Lewis’s can succeed, for an adequate account of intrinsicality must be sensitive to hyperintensional distinctions among properties.

In Science Without Numbers (1980), Hartry Field defends a theory of quantity that, he claims, is able to provide both i) an intrinsic explanation of the structure of space, spacetime, and other quantitative properties, and ii) an intrinsic explanation of why certain numerical representations of quantities (distances, lengths, mass, temperature, etc.) are appropriate or acceptable while others are not. But several philosophers have argued otherwise. In this paper I focus on arguments from Ellis and Milne to the effect that one (...) cannot provide an account of quantity in ''purely intrinsic'' terms. I show, first, that these arguments are confused. Second, I show that Field's treatment of quantity can provide an intrinsic explanation of the structure of quantitative properties; what it cannot do is provide an intrinsic explanation of why certain numerical representations are more appropriate than others. Third, I show that one could provide an intrinsic explanation of this sort if one modified Field's account in certain ways. (shrink)

Benacerraf’s 1965 multiple-reductions argument depends on what I call ‘deferential logicism’: his necessary condition for number-set identity is most plausible against a background Quineanism that allows autonomy of the natural number concept. Steinhart’s ‘folkist’ sufficient condition on number-set identity, by contrast, puts that autonomy at the center — but fails for not taking the folk perspective seriously enough. Learning from both sides, we explore new conditions on number-set identity, elaborating a suggestion from Wright.

In his ‘A Subjectivist’s Guide to Objective Chance’, Lewis argued that a particular kinematical model for chances follows from his principal principle. According to this model, any later chance function is equal to an earlier chance function conditional on the complete intervening history of non-modal facts. This article first investigates the conditions that any kinematical model for chance needs to satisfy to count as Lewis’s kinematics of chance. Second, it presents Lewis’s justification for his kinematics of chance and explains why (...) it is bound to be problematic. Third, it gives an alternative justification for Lewis’s kinematics of chance that does not appeal to the principal principle. Instead, this justification appeals to a well-supported requirement for chance, according to which any prior chance function must be a convex combination of the possible posterior chance functions. It is shown that under a plausible assumption, Lewis’s kinematics of chance is equivalent to this requirement. Finally, by focusing on this requirement, it is explained why the so-called self-undermining chances fail to obey Lewis’s kinematics of chance. (shrink)

Symmetry principles are a central part of contemporary physics, yet there has been surprisingly little metaphysical work done on them. This article develops the Wignerian treatment of symmetries as higher-order laws—metalaws—within a Humean framework of lawhood. Lange has raised two obstacles to Humean metalaws, and the article shows that the account has the resources available to respond to both. It is argued that this framework for Humean metalaws stands as an example of naturalistic metaphysics, able to bring Humeanism into contact (...) with the practice of actual science without giving up on the central denial of necessary connections. (shrink)

A long-standing charge of circularity against regularity accounts of laws has recently seen a surge of renewed interest. The difficulty is that we appeal to laws to explain their worldly instances, but if these laws are descriptions of regularities in the instances then they are explained by those very instances. By the transitivity of explanation, we reach an absurd conclusion: instances of the laws explain themselves. While drawing a distinction between metaphysical and scientific explanations merely modifies the challenge rather than (...) resolving it, I argue that it does point us towards an attractive solution. According to Humeanism, the most prominent form of the regularity view, laws capture information about important patterns in the phenomena. By invoking laws in scientific explanations, Humeans are showing how a given explanandum is subsumed into a more general pattern. Doing so both undermines a principle of transitivity that plays a crucial role in the circularity argument and draws out a central feature of the Humean approach to scientific explanation. (shrink)

In this paper, I discuss a specific approach to measuring and comparing the simplicity of theories that is based on Lewis’s notion of fundamental properties. In particular, I discuss the criterion of simplicity as stated by Williams. According to Williams, the best candidate for a theory is the one which has the shortest definition in terms of fundamental properties. The aim of this paper is to show that the criterion thus specified has two constraints. First, the criterion is not applicable (...) to cases in which candidates for theories that specify fundamental properties are compared. Secondly, the applicability of the criterion in social sciences seems to be unwarranted. (shrink)

The criterion of naturalness represents David Lewis’s attempt to answer some of the sceptical arguments in semantics by comparing the naturalness of meaning candidates. Recently, the criterion has been challenged by a new sceptical argument. Williams argues that the criterion cannot rule out the candidates which are not permuted versions of an intended interpretation. He presents such a candidate – the arithmetical interpretation semantics by comparing the naturalness of meaning candidates. Recently, the criterion has been challenged by a new sceptical (...) argument. Williams argues that the criterion cannot rule out the candidates which are not permuted versions of an intended interpretation. He presents such a candidate – the arithmetical interpretation, and he argues that it opens up the possibility of Pythagorean worlds, i.e. the worlds similar to ours in which the arithmetical interpretation is the best candidate for a semantic theory. The aim of this paper is a) to reconsider the general conditions for the applicability of Lewis’s criterion of naturalness and b) to show that Williams’s new sceptical challenge is based on a problematic assumption that the arithmetical interpretation is independent of fundamental properties and relations. As I show, if the criterion of naturalness is applied properly, it can respond even to the new sceptical challenge. (shrink)

Drawing on Earman’s definition of determinism and Lewis’ best systems account of laws, in What Makes Time Special? Craig Callender develops an account of time as ‘the strongest thing’. The characterisation of this account apparently assumes no action at a temporal distance, an assumption that also underlies Earman’s account of determinism. In this paper I show that there is a way to define determinism that allows worlds with action at a temporal distance to count as deterministic, that action at a (...) temporal distance is possible on a best systems account of laws, and hence that Callender need not make this assumption. (shrink)

Drawing on Earman’s definition of determinism and Lewis’ best systems account of laws, in What Makes Time Special? Craig Callender develops an account of time as ‘the strongest thing’. The characterisation of this account apparently assumes no action at a temporal distance, an assumption that also underlies Earman’s account of determinism. In this paper I show that there is a way to define determinism that allows worlds with action at a temporal distance to count as deterministic, that action at a (...) temporal distance is possible on a best systems account of laws, and hence that Callender need not make this assumption. (shrink)