Ted Sider argues that nihilism about objects is incompatible with the metaphysical possibility of gunk and takes this point to show that nihilism is flawed. I shall describe one kind of nihilism able to answer this objection. I believe that most of the things we usually encounter do not exist. That is, I take talk of macroscopic objects and macroscopic properties to refer to sets of fundamental properties, which are invoked as a matter of linguistic convention. This view is (...) a kind of nihilism : it rules out the existence of objects; that is, from an ontological point of view, there are no objects. But unlike the moderate nihilism of Mark Heller, Peter van Inwagen and Trenton Merricks that claims that most objects do not exist, I endorse a radical nihilism according to which there are no objects in the world, but only properties instantiated in spacetime. As I will show, radical nihilism is perfectly compatible with the metaphysical possibility of gunk. It is also compatible with the epistemic possibility that we actually live in a gunk world. The objection raised by Ted Sider only applies to moderate nihilism that admits some objects in its ontology. (shrink)

This note points out a conflict between some common intuitions about metaphysical possibility. On the one hand, it is appealing to deny that there are robust counterfactuals about how various physically impossible substances would interact with the matter that exists at our world. On the other hand, our intuitions about how concepts like MOUNTAIN apply at other metaphysically possible worlds seem to presuppose facts about ‘solidity’ which cash out in terms of these counterfactuals. I consider several simple attempts to resolve (...) this conflict and note they all fall short. (shrink)

Hud Hudson has argued that if MaxCon, Ned Markosian's favored answer to the Simple Question, is true, then there couldn't be gunky objects. If Hudson's argument succeeds, then those who believe that gunky objects are possible have a good reason to reject MaxCon. However, I show that Hudson's argument relies on substantive metaphysical claims that a proponent of MaxCon need not accept. Thus, one who endorses MaxCon need not reject the possibility of gunky objects and those who believe that gunky (...) objects are possible need not reject MaxCon. (shrink)

Worlds where things divide forever ("gunk" worlds) are apparently conceivable. The conceivability of such scenarios has been used as an argument against "nihilist" or "near-nihilist" answers to the special composition question. I argue that the mereological nihilist has the resources to explain away the illusion that gunk is possible.

The third deduction in Plato’s Parmenides is often given a constructive reading on which Plato’s Parmenides, or even Plato himself, presents us with a positive account of the relation between parts and wholes. However, I argue that there is a hitch in the third deduction which threatens to undermine the mereology of the third deduction by the lights of the dialogue. Roughly, even if the Others partake of the One, the account of the third deduction leads to an ontology of (...) gunk, that is, an ontology on which there are no mereological atoms (except for the One). Hence, it is unclear whether the participation relation between the Others and the One is sufficient to impose the sort of structure on the Others which, in the context of this deduction, Parmenides (or Plato) seems to hope for. Instead of the constructive reading of the third deduction, I therefore offer an aporetic reading on which the third deduction raises further difficulties for the participation relation at the heart of young Socrates’ theory of Forms. (shrink)

The rational explanation of the Eucharist is at the centre of a revived debate in philosophical theology. After describing gunk-relational ontology, I show how it allows us to understand transubstantiation differently than other traditional and contemporary accounts, from which it draws a few points but combining them in a new way. In gunk-relational ontology every substance is its own relations, which constitute a gunky fundamental reality. The liturgical celebration of the Last Supper therefore creates a new relational situation (...) for the bread: the substance of the bread (its relations) profoundly changes its nature. (shrink)

-/- Abstract . In an earlier paper ‘The Topos of Emergence’ (‘TheTopos of Emrgence’, in: Boundaries - The Scientifc Aspects of ANPA 24, (ed. Keith G. Bowden), London 2003, pp 236 –250; cf.also:http://www.academia.edu/1549400/The_Topos_of_Emergence) I introduced a mathematical structure called the topos PrePhys consisting of an ever propagating emergent hierarchy made of a strict n-categorical unfolding of automorphic objects obAM .Later I came to the conclusion that this topos PrePhys perfectly matchs the concept of Gunk introduced under this name by (...) DavidLewis. (cf. D.Lewis, Parts of Classes, Oxford, Cambridge (Mass.)1991, pp 19 –21. (shrink)

Philosophers disagree whether composition as identity entails mereological universalism. Bricker :264–294, 2016) has recently considered an argument which concludes that composition as identity supports universalism. The key step in this argument is the thesis that any objects are identical to some object, which Bricker justifies with the principle of the universality of identity. I will spell out this principle in more detail and argue that it has an unexpected consequence. If the universality of identity holds, then composition as identity not (...) only leads us to universalism, but also leads to the view that there are no mereological atoms. (shrink)

We show that someone who believes in both gunk and the possibility of supertasks has to give up either a plausible principle about where gunk can be located, or plausible conservation principles.

Eliminativism about macroscopic material objects claims that we do not need to include tables in our ontology, and that any job – practical or theoretical – they have to do can be done by 'atoms arranged tablewise'. This way of introducing eliminativism faces the worry that if there are no 'atoms', that is, if there are no simples and the world is 'gunky', there are no suitable entities to be 'arranged tablewise'. In this article, I discuss various strategies the eliminativist (...) can have to face this objection, and I conclude by showing that the objection is actually misdirected and does not threaten eliminativism at all. (shrink)

Mereological realism holds that the world has a mereological structure – i.e. a distribution of mereological properties and relations. In this article, I defend Eleaticism about properties, according to which there are no causally inert non-logical properties. I then present an Eleatic argument for mereological anti-realism, which denies the existence of both mereological composites and mereological simples. After defending Eleaticism and mereological anti-realism, I argue that mereological anti-realism is preferable to mereological nihilism. I then conclude by examining the thesis that (...) composition is identity and noting its consequences for the question of mereological structure. (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.

The book aims to examine how a Trinitarian Theism can be formulated through the elaboration of a Relational Ontology and a Trinitarian Metaphysics, in the context of a hyperphatic epistemology. This metaphysics has been proposed by some supporters of the so-called Open Theism as a solution to the numerous dilemmas of Classical Theism. The hypothesis they support is that the Trinitarian nature of God, reflected in a world of multiplicity, relationality, substance and relations, demands that we think of God as (...) dynamic, internally multiple and relational. However, if the expression «God is love» – understood as the formula of the Trinity – is the key to a new theism, it leaves a problem open: how can it be translated philosophically? The research develops on two different levels: first, it assesses whether the expression should be translated into the Trinitarian paradigm, and the aporias it generates; secondly, it tries to assess whether this paradigm (eminently relational) has a correspondence in ontology: is there a satisfactory Relational Metaphysics already available? The suspicion is that such Trinitarian-Relational Ontology, invoked by many as a solution to the incongruities of classical theism, has yet to be formulated in a satisfactorily manner, despite the existence of various attempts to formulate Relational Ontologies. In order to provide an evaluation of all these attempts and to outline some possible new perspectives, the thesis consists of five chapters. It is the aim of the present dissertation to evaluate such attempts, and to outline some possible new solutions. In the chapters some points have been established: 1. there must be at least one irreducible real relation (non-reductionist realism); 2. the relation must be equally fundamental to the substance: this means that it is both external and internal; 3. this relation must be able to account for contingent causality; 4. holism is a plausible position; 5. the Trinity is a good theistic model of the divine, apophatic but rational. The last chapter then returns to ontological questions: several Relational Ontologies are examined – including ontic structural realism and process (or eventist) ontology – together with their applications in philosophy of religion (e.g.: the Relational God, Process Trinitarianism, the Entangled God). This assessment shows how all these ontologies postulate real transcendental relations (subsistent relations), inside the substances or inside the powers, inside the tropes or the structures, describing them as monads or processes (or actual occasions). These relations are the same we need to describe the Trinity. Therefore, they are either possible for both domains – ontology and theology – or they are both impossible. It has been opted for the second conclusion. But they are both impossible and inevitable: the fundamental entities of the world and their interactions (causation) must be described as real transcendental relations because each ontology transforms entities or relations into real transcendental relationships at some point. Thus, neither relationalism nor substantialism are convincing: from the fall of these two dogmas (or, rather, from the fall of their naive interpretations) we can realise that the fundamental reality is something that lies between processism (relationalism) and substantialism. It is impossible to completely substitute the notion of substance with the notion of event, process, structure or relation, both in speaking of God and in speaking about the entities of fundamental ontology. Neither monism nor pluralism can be affirmed in their pure forms. The hypothesis proposed, then, is that the notion of gunk-junk is the only one that can translate the relationality hitherto sought in an ontological model. The central part of the chapter describes the merits and defects of an eventist-infinitive ontology (EIO) based on the concept of gunk, and its potentiality to generate new theistic accounts. Through the notion of infinityings it seems to be possible to find some solutions for the questions left open by the causal relation, and therefore to defend at least the existence of one relation (external and internal). Each fundamental entity is described, in this ontology, through four transcendentals: ‘entity’, ‘relation’, ‘unity’ and ‘multiplicity’. The co-primarity between substance and relations (borrowed from the notion of relatio subsistens) differentiates EIO from the process philosophies precisely because it does not pretend to eliminate the substantial principle, or the category of substance, but wants to think of it with the transcendental of relationality. Of course, EIO poses a challenge to the role, the method and the explicative capacity of metaphysics, because what we can state of the fundamental reality is antinomic. EIO tries to assume the antinomy as a result, to make it the basis of a kind of apophatic ontology. If our best ontology is gunky, then it is possible to confirm what has been said in chap. 4: the ‘how’ of individual substances is unknown to us at least as much as the ‘how’ of God. Even in the world we have the mystery of a distinction that is not division. However, the convergence of these antinomies can find an ultimate explanation in a theistic metaphysics (EIM): God creates inside of Himself and his Trinitarian substance is “contracted” into the worldly entities. They are made contingent and ontologically different by this self-limitation, but it is still the infinity of God that makes space in Himself for something new, even though He is totally present in every entity. It is not absurd to think that the substances of the world keep track of the divine nature, even in His “contraction”. Among the characteristics of the divine nature that each created entity maintains we have the subsistent relationality, the pericoretic indwelling (the infinite gunk-junk), the fact of being always one-and-many. If EIO and EIM are accepted as a good compromise between relationalism and substantialism, even in their apophaticity, then, on this basis, a Trinitarian Philosophy is possible. The picture of reality that emerges represents the world as multiple, substantial, contingent and intrinsically relational, forcing us to postulate the transcendental of relationality and multiplicity. Such transcendental leads us to think of the world and God (and their relations) in a Trinitarian way – With the necessary acknowledgement that this is a reasonable but apophatic discourse. (shrink)

The paper is the summary of a wider work, a research program. The hypothesis is that if Fundamental Ontology is apophatic – that is, if it has the same dialectical nature (relationality-substantiality) as the Trinity – we can accept that Trinity is also apophatic. The apophatic-relational explanation may sound odd, but it is the most honest one, because it does not hide the problems under the carpet. What emerges is a coherent form of Trinitarian Theism – since there is correspondence (...) between the human (un)ability to know the two levels of reality (the World and God) – that is based on an inevitable relational-apophatic paradigm. The apophaticism that we see in the Trinity (and in ontology) ensures that Trinitarian Theism can neither be proven nor disproven. (shrink)

The interpretation of Lewis‘s doctrine of natural properties is difficult and controversial, especially when it comes to the bearers of natural properties. According to the prevailing reading – the minimalist view – perfectly natural properties pertain to the micro-physical realm and are instantiated by entities without proper parts or point-like. This paper argues that there are reasons internal to a broadly Lewisian kind of metaphysics to think that the minimalist view is fundamentally flawed and that a liberal view, according to (...) which natural properties are instantiated at several or even at all levels of reality, should be preferred. Our argument proceeds by reviewing those core principles of Lewis‘s metaphysics that are most likely to constrain the size of the bearers of natural properties: the principle of Humean supervenience, the principle of recombination in modal realism, the hypothesis of gunk, and the thesis of composition as identity. (shrink)

According to Whitehead’s rectified principle, two individuals are connected just in case there is something self-connected which overlaps both of them, and every part of which overlaps one of them. Roberto Casati and Achille Varzi have offered a counterexample to the principle, consisting of an individual which has no self-connected parts. But since atoms are self-connected, Casati and Varzi’s counterexample presupposes the possibility of gunk or, in other words, things which have no atoms as parts. So one may still (...) wonder whether Whitehead’s rectified principle follows from the assumption of atomism. This paper presents an atomic countermodel to show the answer is no. (shrink)

It is commonly assumed that grounding relations are asymmetric. Here I develop and argue for a theory of metaphysical structure that takes grounding to be nonsymmetric rather than asymmetric. Even without infinite descending chains of dependence, it might be that every entity is grounded in some other entity. Having first addressed an immediate objection to the position under discussion, I introduce two examples of symmetric grounding. I give three arguments for the view that grounding is nonsymmetric (I call this view (...) ‘metaphysical interdependence’). These arguments are: (i) that metaphysical interdependence is the only theory able to reconcile competing intuitions about grounding; (ii) that it is the only theory consistent with both ‘gunk’ and ‘junk’; and (iii) that offers a satisfactory solution to the problem concerning whether or not grounding is itself grounded. (shrink)

For Anaxagoras, both before the beginning of the world and in the present, “all is together” and “everything is in everything.” Various modern interpretations abound regarding the identity of this “mixture.” It has been explained as an aggregation of particles or as a continuous “fusion” of different sorts of ingredients. However—even though they are not usually recognized as a distinct group—there are a number of other scholars who, without seemingly knowing each other, have offered a different interpreta- tion: Anaxagoras’ mixture (...) as an “interpenetration” of different ingredients, which are as far-extended as the whole mixture is. As a result, there are different entities occupying the same place at the same time. This explanation assigns to Anaxagoras the same model of mixture which was later used by the Stoics. A new book by Marmodoro helps us to clarify this position. (shrink)

The idea that there could be spatially extended mereological simples has recently been defended by a number of metaphysicians (Markosian 1998, 2004; Simons 2004; Parsons (2000) also takes the idea seriously). Peter Simons (2004) goes further, arguing not only that spatially extended mereological simples (henceforth just extended simples) are possible, but that it is more plausible that our world is composed of such simples, than that it is composed of either point-sized simples, or of atomless gunk. The difficulty for (...) these views lies in explaining why it is that the various sub-volumes of space occupied by such simples, are not occupied by proper parts of those simples. Intuitively at least, many of us find compelling the idea that spatially extended objects have proper parts at every sub-volume of the region they occupy. It seems that the defender of extended simples must reject a seemingly plausible claim, what Simons calls the geometric correspondence principle (GCP): that any (spatially) extended object has parts that correspond to the parts of the region that it occupies (Simons 2004: 371). We disagree. We think that GCP is a plausible principle. We also think it is plausible that our world is composed of extended simples. We reconcile these two notions by two means. On the one hand we pay closer attention to the physics of our world. On the other hand, we consider what happens when our concept of something—in this case space—contains elements not all of which are realized in anything, but instead key components are realized in different features of the world. (shrink)

I introduce the implantation argument, a new argument for the existence of God. Spatiotemporal extensions believed to exist outside of the mind, composing an external physical reality, cannot be composed of either atomlessness, or of Democritean atoms, and therefore the inner experience of an external reality containing spatiotemporal extensions believed to exist outside of the mind does not represent the external reality, the mind is a mere cinematic-like mindscreen, implanted into the mind by a creator-God. It will be shown that (...) only a creator-God can be the implanting creator of the mindscreen simulation, and other simulation theories, such as Bostrom’s famous account, that do not involve a creator-God as the mindscreen simulation creator, involve a reification fallacy. (shrink)

The thesis of Weak Unrestricted Composition says that every pair of objects has a fusion. This thesis has been argued by Contessa and Smith to be compatible with the world being junky and hence to evade an argument against the necessity of Strong Unrestricted Composition proposed by Bohn. However, neither Weak Unrestricted Composition alone nor the different variants of it that have been proposed in the literature can provide us with a satisfying answer to the special composition question, or so (...) we will argue. We will then go on to explore an alternative family of purely mereological rules in the vicinity of Weak Unrestricted Composition, Cardinal Composition: A plurality of pairwise non-overlapping objects composes an object iff the objects in the plurality are of cardinality smaller than $$\kappa $$ κ. As we will show, all the instances for infinite $$\kappa $$ κ s determine fusion and are compatible with junk, and every instance for a $$\kappa > \aleph _0$$ κ > ℵ 0 is furthermore compatible with gunk and dense chains of parthood. (shrink)

Many philosophers accept a ‘layered’ world‐view according to which the facts about the higher ontological levels supervene on the facts about the lower levels. Advocates of such views often have in mind a version of atomism, according to which there is a fundamental level of indivisible objects known as simples or atoms upon whose spatiotemporal locations and intrinsic properties everything at the higher levels supervenes.1 Some, however, accept the possibility of ‘gunk’ worlds in which there are parts ‘all the (...) way down’ such that there are no simples and insofar as composite objects exist these are composed of smaller objects which in turn are composed of smaller objects, and so on. It may nonetheless still be claimed that the facts about each ontological level supervene on the facts about the lower levels. (shrink)

In its simplest form, a Spritz is an aperitif made with (sparkling) water and (white) wine. A ‘gunky Spritz’, as I will call it, is a Spritz in which the water and the wine are mixed through and through, so that every proper part of the Spritz has a proper part containing both water and wine. In the literature on the notion of location the possibility of mixtures like a gunky Spritz has been thought of as either threatening seemingly intuitive (...) locative principles, or as requiring the position of multiple primitive locative relations. In this paper I present a new theory of location which assumes as primitive only the notion of pervasive location and show that it can account for the possibility of gunky Spritz in an intuitive and adequate way. (shrink)

Some hold that the lesson of Russell’s paradox and its relatives is that mathematical reality does not form a ‘definite totality’ but rather is ‘indefinitely extensible’. There can always be more sets than there ever are. I argue that certain contact puzzles are analogous to Russell’s paradox this way: they similarly motivate a vision of physical reality as iteratively generated. In this picture, the divisions of the continuum into smaller parts are ‘potential’ rather than ‘actual’. Besides the intrinsic interest of (...) this metaphysical picture, it has important consequences for the debate over absolute generality. It is often thought that ‘indefinite extensibility’ arguments at best make trouble for mathematical platonists; but the contact arguments show that nominalists face the same kind of difficulty, if they recognize even the metaphysical possibility of the picture I sketch. (shrink)

In formal ontology, infinite regresses are generally considered a bad sign. One debate where such regresses come into play is the debate about fundamentality. Arguments in favour of some type of fundamentalism are many, but they generally share the idea that infinite chains of ontological dependence must be ruled out. Some motivations for this view are assessed in this article, with the conclusion that such infinite chains may not always be vicious. Indeed, there may even be room for a type (...) of fundamentalism combined with infinite descent as long as this descent is “boring,” that is, the same structure repeats ad infinitum. A start is made in the article towards a systematic account of this type of infinite descent. The philosophical prospects and scientific tenability of the account are briefly evaluated using an example from physics. (shrink)

This sketch of a perhaps future 'Elementary Theory of the Category of Mereological Sums (including Mereological Wholes and Parts)' relates to my previous papers "The Topos of Emergence" and "Intelligible Gunk". I assert that for successfully categorizing Mereology one has to start with a specific setting of gunk. In this paper we will give a sketch of a categorically version of particular mereological structures. I.e. we will follow the example of F.W.Lawvere’s “An elementary theory of the category of (...) sets” -/- where he introduced a categorised version of set theory. We refer to sirenians mainly for the reason that they are the closest living relatives of elephants. -/- But they are also rather underestimated creatures - at the first moment rather dull and clumsy, but moving gracefully and elegant in their natural habitat.And some sailors already reckognized their bewitching attraction before we did.Yet we still think this sirenia is a modest creature compared with the elephant in the room. (shrink)

In this paper I will combine ideas of Meinong's objectology with earlier ideas of ethereal or intelligible gunk. I will try to make that useful for a better understanding of 'emergence'. I also spend some remarks on mathematical theories.

A contemporary form of panpsychism says that phenomenality is prevalent because all physical ultimates instantiate phenomenal or protophenomenal properties. According to priority cosmopsychism, an alternative to panpsychism that we propose in this chapter, phenomenality is prevalent because the whole cosmos instantiates phenomenal or protophenomenal properties. It says, moreover, that the consciousness of the cosmos is ontologically prior to the consciousness of ordinary individuals like us. Since priority cosmopsychism is a highly speculative view our aim in this chapter remains modest and (...) limited. Instead of providing a full defense of priority cosmopsychism, we try to show only the theoretical advantage of the view over panpsychism. Tis, however, by no means entails that we develop the view in logical space merely for its own sake. We offer instead a blueprint for a new alternative to panpsychism and explain how such a view avoids some of the most persistent problems for panpsychism while maintaining several of its strengths. (shrink)

In this paper I argue against grounding being necessarily well-founded, and provide some reasons to think it's actually not well-founded.

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)

In this chapter, a generic definition of fundamentality as an ontological minimality thesis is sought and its applicability examined. Most discussions of fundamentality are focused on a mereological understanding of the hierarchical structure of reality, which may be combined with an atomistic, object-oriented metaphysics. But recent work in structuralism, for instance, calls for an alternative understanding and it is not immediately clear that the conception of fundamentality at work in structuralism is commensurable with the mereological conception. However, it is proposed (...) that once we understand fundamentality as an ontological minimality thesis, these two as well as further conceptions of fundamentality can all be treated on a par, including metaphysical infinitism of the ‘boring’ type, where the same structure repeats infinitely. (shrink)

There are at least three vaguely atomistic principles that have come up in the literature, two explicitly and one implicitly. First, standard atomism is the claim that everything is composed of atoms, and is very often how atomism is characterized in the literature. Second, superatomism is the claim that parthood is well-founded, which implies that every proper parthood chain terminates, and has been discussed as a stronger alternative to standard atomism. Third, there is a principle that lies between these two (...) theses in terms of its relative strength: strong atomism, the claim that every maximal proper parthood chain terminates. Although strong atomism is equivalent to superatomism in classical extensional mereology, it is strictly weaker than it in strictly weaker systems in which parthood is a partial order. And it is strictly stronger than standard atomism in classical extensional mereology and, given the axiom of choice, in such strictly weaker systems as well. Though strong atomism has not, to my knowledge, been explicitly identified, Shiver appears to have it in mind, though it is unclear whether he recognizes that it is not equivalent to standard atomism in each of the mereologies he considers. I prove these logical relationships which hold amongst these three atomistic principles, and argue that, whether one adopts classical extensional mereology or a system strictly weaker than it in which parthood is a partial order, standard atomism is a more defensible addition to one’s mereology than either of the other two principles, and it should be regarded as the best formulation of the atomistic thesis. (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.

Extended simples are fruitfully discussed in metaphysics. They are entities which are located in a complex region of space but do not themselves have parts. In this paper, I will discuss unextended complexes: entities which are not located at a complex region of space but do themselves have parts. In particular, I focus on one type of unextended complex: pointy complexes. Four areas are indicated where pointy complexes might prove philosophically useful. Unextended complexes are therefore philosophically fruitful, in much the (...) same way as extended simples. (shrink)

Brentano’s theory of continuity is based on his account of boundaries. The core idea of the theory is that boundaries and coincidences thereof belong to the essence of continua. Brentano is confident that he developed a full-fledged, boundary-based, theory of continuity1; and scholars often concur: whether or not they accept Brentano’s take on continua they consider it a clear contender. My impression, on the contrary, is that, although it is infused with invaluable insights, several aspects of Brentano’s account of continuity (...) remain inchoate. To be clear, the theory of boundaries on which it relies, as well as the account of ontological dependence that Brentano develops alongside his theory of boundaries, constitute splendid achievements. However, the passage from the theory of boundaries to the account of continuity is rather sketchy. This paper pinpoints some chief problems raised by this transition, and proposes some solutions to them which, if not always faithful to the letter of Brentano’s account of continua, are I believe faithful to its spirit. §1 presents Brentano’s critique of the mathematical account of the continuous. §2 introduces Brentano’s positive account of continua. §3 raises three worries about Brentano’s account of continuity. §4 proposes a Neo-Brentanian approach to continua that handles these worries. (shrink)

In my dissertation, I address a variety of issues in the metaphysics of space and related areas. I begin by discussing the popular thesis that regions of space are identical to sets of points in space. I present three arguments against this thesis and conclude that we should be skeptical of it. In its place, I propose an axiomatic theory of regions of space that is consistent with both reductive accounts of their nature and with accounts that treat them as (...) sui generis entities. -/- I next explore the consequences of the aforementioned considerations. In particular, I describe five different sorts of structure each of which is such that the claim that space could have that structure is consistent with the axiomatic theory previously proposed. I claim that this fact, together with the skepticism concerning reductive accounts argued for earlier, shows that we should take seriously the claim that space could have any of these structures. -/- Having argued that we should be skeptical of the thesis that regions of space are identical to sets of points in space and suggesting that space could have different sorts of structure, I discuss how best to analyze continuity. I present an analysis of continuity inspired by remarks of Richard Cartwright in his 1975 paper ‘Scattered Objects’. I argue that this Cartwrightian analysis should be rejected because it identifies regions of space with sets of points in space, and I present a modified version of the analysis that does not do so. I note, however, that there is an intuitive notion of continuity that is not captured by this modified Cartwrightian analysis. I present and defend an analysis of continuity that better captures this intuitive notion. -/- I then turn to the issue of how to analyze what it is for a region of space to be open and what it is for a region of space to be closed. Here I argue that Cartwright’s analyses of these notions are incorrect. I then present a series of alternative analyses, revising each in response to objections. This process culminates with my proposed analyses of what it is for a region of space to be open and what it is for a region of space to be closed. -/- Finally, I discuss the Maximally Continuous Account of Simples (MaxCon), originally formulated and defended by Ned Markosian in his 1998 paper ‘Simples’. I argue that Markosian’s version of MaxCon, which identifies regions of space with sets of points in space and relies on the Cartwrightian analysis of continuity, should be rejected. I then formulate a new version of MaxCon that builds on the views defended earlier in my dissertation and defend this new version of MaxCon from objections. (shrink)

Book review of 'The Universe As We Find It' (2012, OUP). By John Heil.