Formal criteria of theoretical equivalence are mathematical mappings between specific sorts of mathematical objects, notably including those objects used in mathematical physics. Proponents of formal criteria claim that results involving these criteria have implications that extend beyond pure mathematics. For instance, they claim that formal criteria bear on the project of using our best mathematical physics as a guide to what the world is like, and also have deflationary implications for various debates in the metaphysics of physics. In this paper, (...) I investigate whether there is a defensible view according to which formal criteria have significant non-mathematical implications, of these sorts or any other, reaching a chiefly negative verdict. Along the way, I discuss various foundational issues concerning how we use mathematical objects to describe the world when doing physics, and how this practice should inform metaphysics. I diagnose the prominence of formal criteria as stemming from contentious views on these foundational issues, and endeavor to motivate some alternative views in their stead. (shrink)

It is, I think, possible to generate a variation of McTaggart’s (Mind 17:457–474, 1908 ) paradox that infects all extant versions of presentism. This is not to say that presentism is doomed to failure. There may be ways to modify presentism and I can’t anticipate all such modifications, here. For the purposes of the paper I’ll understand ‘presentism’ to be the view that for all x , x is present (cf. Crisp ( 2004 : 18)). It seems only right that, (...) at a conference devoted to McTaggart’s work on time, we continue to pursue new ways in which his now infamous arguments remain relevant to us today. (shrink)

Reply in Book Symposium on James Ladyman, Don Ross: 'Everything must go: metaphysics naturalized', Oxford: Oxford University Press, 2007.

In this paper, I argue that the spatiotemporalist approach way of modeling the fundamental constituents, structure, and composition of the world has taken a wrong turn. Spatiotemporalist approaches to fundamental structure take the fundamental nature of the world to be spatiotemporal: they take the category of spatiotemporal to be fundamental. I argue that the debates over the nature of the fundamental space in the physics show us that (i) the fact that it is conceivable that the manifest world could be (...) exactly as it appears to us, even though spatiotemporal entities are not fundamental, means that a central premise of spatiotemporalism, that we may assume, given ordinary experience, that the world is fundamentally spatiotemporal, is false. (ii) Spatiotemporalism must be seen as a contingent, a posteriori physical truth. Finally, (iii) I argue that a metaphysically deeper conclusion follows from the debate over the nature of the fundamental space. The debate in physics over which sort of space is the fundamental space suggests that physicists have discovered that, even if a spacetime is an actual constituent of the world-space category, there is a world-space category that is more fundamental than the category of spacetime. (shrink)

This paper investigates the use of theories of mechanics to provide answers to questions in the metaphysics of spatial location and persistence. Investigating spatial location, I find that in classical physics bodies pertend the region of space at which they are exactly located, while a quantum system spans a region at which it is exactly located. Following this analysis, I present a ‘no-go’ result which shows that quantum mechanics restricts the available options for locational persistence theories in an interesting way: (...) it demonstrates that the spatiotemporal path of a persisting thing is discrete in time. This leads to unpalatable consequences for both perdurantists and endurantists. In particular, I argue that Butterfield's ‘anti-pointilliste’ perdurantism is ruled out, and show that endurantists relying on immanent causation run into trouble. I conclude by suggesting the revival of Whitehead's alternative mode of persistence called ‘reiteration.’. (shrink)

This paper argues that all of the standard theories about the divisions of space and time can benefit from, and may need to rely on, parsimony considerations. More specifically, whether spacetime is discrete, gunky or pointy, there are wildly unparsimonious rivals to standard accounts that need to be resisted by proponents of those accounts, and only parsimony considerations offer a natural way of doing that resisting. Furthermore, quantitative parsimony considerations appear to be needed in many of these cases.

According to one of the more popular endurantist packages on the market, a package I will call multilocational endurantism, enduring objects are exactly located at multiple instantaneous regions of spacetime. However, for all we know, the world might turn out to be spatiotemporally gunky and spatiotemporal gunk entails that this package is false. The goal of this paper is to sketch a view which retains the spirit of multilocational endurantism while also recognizing the possibility of certain types of objects which (...) endure through gunk. (shrink)

Some tools introduced by Linnebo to show that mathematical entities are thin objects can also be applied to non-mathematical entities, which have been thought to be thin as well for a variety of reasons. In this paper, I discuss some difficulties and opportunities concerning the application of abstraction and interpretational modalities to mereological sums. In particular, I show that on one hand some prima facie attractive candidates for the role of an explanatory plural abstraction principle for mereological sums (in terms (...) of pluralities of summed entities) are not really explanatory; on the other hand, singular abstraction principles (in terms of single summed entities) are materially inadequate. Nonetheless, explanatory criteria of identity and conditions of existence for mereological sums are provided by classical extensional mereology independent of abstraction principles. Thus, given classical extensional mereology, the reasons why, according to Linnebo, mathematical abstracted entities are thin also hold for mereological sums. Finally, I contend that interpretational modalities can be used to characterise the process by which a subject adds sums of previously admitted entities to the domain of quantification. (shrink)

Say that space is ‘gunky’ if every part of space has a proper part. Traditional theories of gunk, dating back to the work of Whitehead in the early part of last century, modeled space in the Boolean algebra of regular closed subsets of Euclidean space. More recently a complaint was brought against that tradition in Arntzenius and Russell : Lebesgue measure is not even finitely additive over the algebra, and there is no countably additive measure on the algebra. Arntzenius advocated (...) modeling gunk in measure algebras instead—in particular, in the algebra of Borel subsets of Euclidean space, modulo sets of Lebesgue measure zero. But while this algebra carries a natural, countably additive measure, it has some unattractive topological features. In this paper, we show how to construct a model of gunk that has both nice rudimentary measure-theoretic and topological properties. We then show that in modeling gunk in this way we can distinguish between finite dimensions, and that nothing in lost in terms of our ability to identify points as locations in space. (shrink)

Are there any non‐composite objects? Are there any objects every part of which is composite? Are items of either kind even possible? What would they be like? Of what significance would they be? How best can we come to have reasonable beliefs about the answers to these inquiries? Such questions – about the actuality and possibility, the analysis and significance, the methodology and epistemology of simples and pieces of gunk – have been center stage in recent contemporary analytic metaphysics. The (...) following article provides a general overview of some of the current debates on their proper answers as well as a pair of slightly more detailed investigations into two issues of special interest in the recent literature devoted to these topics. (shrink)

The ancient puzzle of Dion and Theon has given rise to a surprising array of apparently implausible views. For example, in order to solve the puzzle, several philosophers have been led to deny the existence of their own feet, others have denied that objects can gain and lose parts, and large numbers of philosophers have embraced the thesis that distinct objects can occupy the same space, having all their material parts in common. In this paper, I argue for an alternative (...) approach: I claim that human beings have ordinary parts—hands, heads, feet, and so on—but no extraordinary parts, such as ‘foot-complements’, the existence of which is essential to the puzzle. I rebut three objections to this approach: an objection that it is unacceptably metaphysically arbitrary, an objection that the view is incompatible with versions of the puzzle involving decapitation, and an objection concerning masses of matter. If we can believe that there are such things as hands and feet without involving ourselves in paradox, and without accepting large numbers of co-located material objects that share all their material parts, then that is what we should do. My view is the only known alternative which allows this. (shrink)

This paper forms part of a wider campaign: to deny pointillisme. That is the doctrine that a physical theory's fundamental quantities are defined at points of space or of spacetime, and represent intrinsic properties of such points or point-sized objects located there; so that properties of spatial or spatiotemporal regions and their material contents are determined by the point-by-point facts. More specifically, this paper argues against pointillisme about the structure of space and-or spacetime itself, especially a paper by Bricker (1993). (...) A companion paper argues against pointillisme in mechanics, especially about velocity; it focusses on Tooley, Robinson and Lewis. To avoid technicalities, I conduct the argument almost entirely in the context of ``Newtonian'' ideas about space and time. But both the debate and my arguments carry over to relativistic, and even quantum, physics. (shrink)

Inspired by Cantor's Theorem (CT), orthodoxy takes infinities to come in different sizes. The orthodox view has had enormous influence in mathematics, philosophy, and science. We will defend the contrary view---Countablism---according to which, necessarily, every infinite collection (set or plurality) is countable. We first argue that the potentialist or modal strategy for treating Russell's Paradox, first proposed by Parsons (2000) and developed by Linnebo (2010, 2013) and Linnebo and Shapiro (2019), should also be applied to CT, in a way that (...) vindicates Countabilism. Our discussion dovetails with recent independently developed treatments of CT in Meadows (2015), Pruss (2020), and Scambler (2021), aimed at establishing the mathematical viability, and therefore epistemic possibility, of Countabilism. Unlike these authors, our goal isn't to vindicate the mathematical underpinnings of Countabilism. Rather, we aim to argue that, given that Countabilism is mathematically viable, Countabilism should moreover be regarded as true. After clarifying the modal content of Countabilism, we canvas some of Countabilism's many positive implications, including that Countabilism provides the best account of the pervasive independence phenomena in set theory, and that Countabilism has the power to defuse several persistent puzzles and paradoxes found in physics and metaphysics. We conclude that in light of its theoretical and explanatory advantages, Countabilism is more likely true than not. (shrink)

Most of our best scientific descriptions of the world employ rates of change of some continuous quantity with respect to some other continuous quantity. For instance, in classical physics we arrive at a particle’s velocity by taking the time-derivative of its position, and we arrive at a particle’s acceleration by taking the time-derivative of its velocity. Because rates of change are defined in terms of other continuous quantities, most think that facts about some rate of change obtain in virtue of (...) facts about those other continuous quantities. For example, on this view facts about a particle’s velocity at a time obtain in virtue of facts about how that particle’s position is changing at that time. In this paper we raise a puzzle for this orthodox reductionist account of rate of change quantities and evaluate some possible replies. We don’t decisively come down in favour of one reply over the others, though we say some things to support taking our puzzle to cast doubt on the standard view that spacetime is continuous. (shrink)

I first explore the notion of the world's being such that everything in it is a proper part. I then explore the notion of the world's being such that everything in it both is and has a proper part. Given two well recognized assumptions, I argue that both notions represent genuine metaphysical possibilities. Finally I consider, but dismiss, some possible objections.

Almost all philosophers interested in parthood and composition think that a composite object is a further thing, numerically distinct from the objects that compose it. Call this the orthodox view. I argue that the orthodox view is false, and that a composite object is identical to the objects that compose it (collectively). This view is known as composition as identity. -/- I argue that, despite its unpopularity, there are many reasons to favour com- position as identity over the orthodox view. (...) First, defenders of the orthodox view have not offered complete theories of composition. For instance, they have not given adequate accounts of heterogeneous properties like being black and white in composite objects. Nor have they given satisfactory explanations for the necessary connections that hold between composite objects and their proper parts. -/- Second, there appears to be no good way for defenders of the orthodox view to remedy this. Any account of the heterogeneous properties of composite objects which is compatible with the orthodox view faces serious problems, as does any account of the necessary connections between an object and its proper parts. Composition as identity, on the other hand, is compatible with intuitive responses to both of these challenges. -/- Third, there are a number of strong arguments in favour of composition as identity. For example, composition as identity fits our evidence about the way the world is better than the orthodox view does. It also allows us to easily maintain that composition sometimes occurs and sometimes does not—i.e., it allows us to easily maintain that composition is restricted. The orthodox view does not. The theories of composition put forward by most philosophers are at best incomplete or in need of improvement. At worst, they are false and composition as identity is true. (shrink)

What are the properties of composite objects, and how do the properties of composite objects and the properties of their proper parts relate to one another? The answers to these questions depend upon which view of composition one adopts. One view, which I call the orthodox view, is that composite objects are numerically distinct from their proper parts, individually and collectively. Another view, known as composition as identity, is that composite objects are numerically identical to their proper parts, taken together. (...) I argue that the orthodox view entails that the intuitive picture of composite objects and their properties that most accept is false. Not so for composition as identity. I also show that all of the available alternatives face serious difficulties. This puts composition as identity at an advantage over the orthodox view, at least when it comes to accounting for the properties of composite objects. (shrink)

Ethics in the tradition of Derek Parfit’s Reasons and Persons is riddled with sorites-like arguments, which lead us by what seem innocent steps to seemingly false conclusions. Take, for example, spectrum arguments for the Repugnant Conclusion that appeal to slight differences in quality of life. Several authors have taken the view that, since spectrum arguments are structurally analogous to sorites arguments, the correct response to spectrum arguments is structurally analogous to the correct response to sorites arguments. This sorites analogy is (...) here argued against. There are potential structural disanalogies between spectrum arguments and sorites arguments. But even if these arguments are relevantly structurally analogous, they differ in their content in ways that show the sorites analogy to be implausible. Two content-based disanalogies are here explored—one is inspired by Parfit’s work on reductionism, and the other involves hypersensitivity. The chapter concludes with a methodological lesson. (shrink)

The paper takes up Bell's “Everett theory” and develops it further. The resulting theory is about the system of all particles in the universe, each located in ordinary, 3-dimensional space. This many-particle system as a whole performs random jumps through 3N-dimensional configuration space – hence “Tychistic Bohmian Mechanics”. The distribution of its spontaneous localisations in configuration space is given by the Born Rule probability measure for the universal wavefunction. Contra Bell, the theory is argued to satisfy the minimal desiderata for (...) a Bohmian theory within the Primitive Ontology framework. TBM's formalism is that of ordinary Bohmian Mechanics, without the postulate of continuous particle trajectories and their deterministic dynamics. This “rump formalism” receives, however, a different interpretation. We defend TBM as an empirically adequate and coherent quantum theory. Objections voiced by Bell and Maudlin are rebutted. The “for all practical purposes”-classical, Everettian worlds exist sequentially in TBM. In a temporally coarse-grained sense, they quasi-persist. By contrast, the individual particles themselves cease to persist. (shrink)

Could space consist entirely of extended regions, without any regions shaped like points, lines, or surfaces? Peter Forrest and Frank Arntzenius have independently raised a paradox of size for space like this, drawing on a construction of Cantor’s. I present a new version of this argument and explore possible lines of response.

An object is T-gunky just in case all its parts (i) have proper parts and (ii) are of non-zero measure in every spatial dimension. I show that a recent argument due to Hud Hudson—though not intended as a threat to gunk—bears on the possibility of T-gunky material objects in non-gunky space. I then show that the friend of T-gunk can circumvent Hudson’s argument without abandoning pointy space or standard mereology. What is needed is a novel conception of the relation of (...) exact occupation of pointy regions by T-gunky objects. With the new conception in hand, the friend of material T-gunk need not look to theories of gunky spacetime in order to reconcile the possibility of material gunk with mathematical physics. (shrink)

The purpose of this thesis is to demonstrate that metaphysics is a necessary discipline -- necessary in the sense that all areas of philosophy, all areas of science, and in fact any type of rational activity at all would be impossible without a metaphysical background or metaphysical presuppositions. Because of the extremely strong nature of this claim, it is not possible to put forward a very simple argument, although I will attempt to construct one. A crucial issue here is what (...) metaphysics in fact is -- the nature of metaphysics. The conception of metaphysics which I support could be called Aristotelian, as opposed to Kantian: metaphysics is the first philosophy and the basis of all other philosophical and scientific inquiry. I will argue that this is indeed the most plausible conception of metaphysics. (shrink)

It is widely accepted that continuity is the most essential characteristic of motion; the motion of macroscopic objects is apparently continuous, and classical mechanics, which describes such motion, is also based on the assumption of continuous motion. But is motion really continuous in reality? In this paper, I will try to answer this question through a new analysis of the cause of motion. It has been argued that the standard velocity in classical mechanics cannot fulfill the causal role required for (...) explaining continuous motion in a deterministic way. However, there is a hot debate over the solution to this causal explanation problem. The existing solutions, i.e. the "at-at" theory, the impetus view and the "no instants" view, have serious drawbacks. After reviewing their drawbacks and presenting my own objections, I propose a new solution to this causal explanation problem. It is argued that the relativity of motion or the equivalence between motion and rest demands that motion has no deterministic cause, and thus no causal explanation is needed for motion. Based on this result, I further argue that the uncaused motion is not deterministic and continuous but essentially random and discontinuous. Moreover, objects have a potential that determines the probabilities of their future positions. This suggests a possible connection with quantum mechanics. Lastly, I give a brief explanation for the apparent inconsistency between the suggested potential theory of motion and the appearance of continuous motion in the macroscopic world. (shrink)