In this paper, I advance an original view of the structure of space called Infinitesimal Gunk. This view says that every region of space can be further divided and some regions have infinitesimal size, where infinitesimals are understood in the framework of Robinson’s nonstandard analysis. This view, I argue, provides a novel reply to the inconsistency arguments proposed by Arntzenius and Russell, which have troubled a more familiar gunky approach. Moreover, it has important advantages over the alternative views these (...) authors suggested. Unlike Arntzenius’s proposal, it does not introduce regions with no interior. It also has a much richer measure theory than Russell’s proposal and does not retreat to mere finite additivity. (shrink)

The surviving sources on the Stoic theory of division reveal that the Stoics, particularly Chrysippus, believed that bodies, places and times were such that all of their parts themselves had proper parts. That is, bodies, places and times were composed of gunk. This realisation helps solve some long-standing puzzles about the Stoic theory of mixture and the Stoic attitude to the present.

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)

I argue that it may well be the case that space and time do not consist of points, indeed that they have no smallest parts. I examine two different approaches to such pointless spaces : a topological approach and a measure theoretic approach. I argue in favor of the measure theoretic approach.

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)

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)

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)

Let us say that a thing is gunky just in case every part of that thing has proper parts. The idea that all physical objects are gunky seems sufficiently sweeping, interesting, and plausible that it is worth examining. However, there is a difficulty. The features of an extended object can surely vary continuously. If an object is gunky then it cannot have point-sized parts which have no further parts. But how can one conceive of a continuous variation in features other (...) than as the obtaining of different features at different point sized locations? (shrink)

All parts of mereologically ‘gunky’ entities have proper parts. All parts relevant to mereologically ‘junky’ entities *are* proper parts. This essay explores the application of gunk and junk beyond the standard category of material object. One such application yields what is here dubbed ‘deep’ gunk and junk: a material entity x all of whose intrinsic elements from any fundamental ontological category C either have proper parts from C that also are intrinsic elements of x, or are proper parts (...) of entities from C that also are intrinsic elements of x. In addition to being independently interesting, these mereological structures pose a challenge to the bare particular ontology of substance. For bare particulars standardly are assumed to be mereologically simple, yet a deep gunky or junky entity requires any associated bare particulars to be complex. The essay closes by examining the bare particular theorist’s prospects for answering this challenge. (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.

It is customary practice to define ‘x is composed of the ys’ as ‘x is a sum of the ys and the ys are pairwise disjoint ’. This predicate has played a central role in the debate on the special composition question and on related metaphysical issues concerning the mereological structure of objects. In this note we show that the customary characterization is nonetheless inadequate. We do so by constructing a mereological model where everything qualifies as composed of atoms even (...) though some elements in the domain are gunky, i.e., can be divided indefinitely into smaller and smaller proper parts. (shrink)

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)

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)

Are there atoms in the constitution of things? Or is everything made of atomless ‘gunk’ whose proper parts have proper parts? Anaxagoras is the first gunk lover in the history of metaphysics. For him gunk is not only a theoretical possibility that cannot be ruled out in principle. Rather, it is a view that follows cogently from his metaphysical analysis of the physical world of our experience. What is distinctive about Anaxagoras’s take on gunk is not (...) only what motives the view, but also the particular type of gunk that he develops. It is qualitative gunk, rather than material gunk. Anaxagoras’s ontology was developed before matter was ‘invented’. It includes quality tropes only; they are gunky. The resulting metaphysical view – a world of qualitative gunk – is new, in the sense of being hitherto unexplored; and yet, it is derived from Anaxagoras’s writings. Drawing on Anaxagoras’s insights, this paper offers a sketch of what qualitative gunk ontology l.. (shrink)

This paper concerns the structure of any spatially extended things, including regions of space or spacetime. I shall use intuitions about the quantity of extended things to argue for a dichotomy: either a given finite extended thing is point-free gunk, that is, it has no points as parts, or it is made of grit, that is there are only finitely many points.

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)

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)

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.

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)

ABSTRACTA structure is temporally gunky just in case all of its temporal parts have proper temporal parts. Joshua Stuchlik [2003] objects to the stage theory of persistence from temporal gunk by ar...

An object is a simple if and only if it has no proper parts. An object is gunk if and only if every proper part of that object itself has a proper part. In my dissertation, I address the following questions. The concepts of simples and gunk presuppose the concept of parthood. What is the status of this concept? his question itself divides into the following: does the concept of parthood have universal applicability, so that, just as every (...) object is self-identical, every object has parts? Finally, is the concept of parthood univocal, or are there different notions of parthood, each of which is defined on distinct ontological categories? I argue that the concept of parthood has univocal. I also argue that there is some evidence that the concept of parthood has universal applicability. I address the Simple Question, which is “under what circumstances is it true of some object that it has no proper parts?” I argue against several popular answers to the Simple Question, such as the view that simples are all and only point-sized objects, and the view that simples are maximally continuous material objects. I defend the Brutal View, which holds that there is no true, finitely expressible, and informative answer to the Simple Question. In short, there is no criterion for being a simple. Along the way, I address the question of whether extended simples, i.e., simples that are extended in space, are possible. I argue that one popular argument against the possibility of extended simples is unsound. I address the question of whether both simples and gunk are possible. I argue that it is metaphysically possible that material objects be composed of gunk. (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.

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)

Let us say that an extended object is “composed wholly of simples” just in case it is an aggregate of absolutely unextended parts spread throughout an extended region—that is, just in case there is a set S such that: every member is a point-sized part of the object, and for every x, x is part of the object if and only if it has a part in common with some member of S. Could a truly extended substance be composed entirely (...) of unextended parts? Reflection upon the fact that it must be at least possible for extended objects to touch one another suggests that the answer to this question is: No. (shrink)

Atomism, the view that indivisible atoms are the basic building blocks of physical reality, has a distinguished history. But it might not be true. The history of physical science certainly gives many of us pause. Every time some class of objects appeared to be the entities that Newton had described as “solid, massy, hard, impenetrable, movable Particles” out of which “God in the Beginning formed Matter,” further research revealed that these objects were divisible after all. One might be tempted to (...) see that history as confirming Leibniz’s dismissal of atomism as a “youthful prejudice.” Perhaps material objects and their parts are always divisible. There are no extended atoms; nor are there point particles which compose material beings. (shrink)

Recently, Jonathan Tallant has argued that we should reject priority views, which hold that some objects are fundamental and others are dependent. Tallant’s argument relies on two proposed mereological possibilities: a gunky world, where everything has a proper part, and a junky world, where everything is a proper part. In this paper, I criticise Tallant’s argument and argue that neither of these possibilities threaten priority views per se; at most, they threaten only particular forms of priority views that contain a (...) certain independently controversial assumption. First, I defend priority pluralism against the gunk argument: the genuine conceivability of gunk can be plausibly doubted on the basis of a certain principle concerning metaphysical possibility, and even if this principle is false, the possibility of a gunky world poses no devastative problem for pluralism per se because it can be considered to be consistent with nonatomism. Second, I defend priority monism against the junk argument: the possibility of a junky world poses no devastative problem for monism per se because it can be considered to be consistent with nonholism in a twofold sense. Finally, I show that even monism as defined as genuinely holistic can be plausibly defended against the junk argument once the claim of the possible nonexistence of the maximal whole is reinterpreted based on the priority-based conception of existence. (shrink)

We often speak of an object being composed of various other objects. We say that the deck is composed of the cards, that a road is the sum total of its sections, that a house is composed of its walls, ceilings, floors, doors, etc. Suppose we have some material objects. Here is a philosophical question: what conditions must obtain for those objects to compose something? In his recent book Material Beings, Peter van Inwagen addresses this question, which he calls the (...) ‘special composition question’; his answer is:1 (1) For any material objects X , the X s compose something iff the activity of the X s constitutes a life, or there is only one of the Xs. Additionally, he accepts a simpler thesis that follows from (1):2 (2) Every material object is either a mereological atom or a living thing, where a mereological atom is an object lacking proper parts. (2) may seem radical. If it is true then there are no tables, chairs, planets, protons, galaxies, gas stations, etc. But van Inwagen does not hold it lightly— there are serious difficulties with alternate views. Moreover, he claims that.. (shrink)

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)

In his ‘Could Extended Objects Be Made Out of Simple Parts?: An Argument for “Atomless Gunk’’, Dean Zimmerman defends the claim that no physical object has a complete decomposition into simples but instead has among its parts a piece of ‘atomless gunk’ His argument for this claim rests in part upon a theory of the impenetrability of physical objects. In that theory, Zimmerman distinguishes ‘[t]he sort of impenetrability that is a part of the concept of’ a physical object (...) from ‘a power to resist the pressure of other objects’. He says that impenetrability is but ‘an essential inability’ of two physical objects to occupy one and the same region of space, an essential inability that is not a power of one physical object to exert repulsive forces on others in its vicinity. I argue that this theory of impenetrability is false and that Zimmerman's argument for the existence of ‘atomless gunk’ fails. (shrink)

Consider the beginningless sequence: ... being less than 0.01 grams, being less than 0.1 grams, being less than 1 gram, being less than 10 grams ... There is no super-determinate in this chain. Just as the possibility of bottomless constitution shows that there may be no fundamental layer of reality with respect to objects , the possibility of bottomless determination shows that there may be no fundamental level of reality with respect to properties . This possibility supports Stephen Yablo's proportionality (...) principle that the cause of an event is the most specific property that makes a difference. (shrink)

Mereological nihilists are faced with a difficult challenge: explaining ordinary talk about material objects. Popular paraphrase strategies involve plurals, arrangements of particles, or fictions. In this paper, a new paraphrase strategy is put forward that has distinct advantages over its rivals: it is compatible with gunk and emergent properties of macro-objects. The only assumption is a commitment to a liberal view of the nature of simples; the nihilist must be willing to accept the possibility of heterogeneous extended simples. The (...) author suggests reinterpreting the parthood and composition relations as modal. According to this paraphrase, composition is a kind of counterpart relation. The author shows that one can accept that mereological nihilism is metaphysically necessary, while endorsing all the claims of classical mereology. As a result, the nihilists are in exactly the same position as the classical mereologist when it comes to explaining talk about ordinary objects, but without the additional ontology. (shrink)

Priority pluralism, perdurantism and that temporal gunk – where some interval of time is gunky iff every interval of it has a proper subinterval – is at least metaphysically possible, are three commonly held views in contemporary metaphysics. However, there cannot be a temporally gunky world where objects perdure, and where there are mereological simples. Given that – as I will argue – pluralists should be committed to atomism, and cannot plausibly revise their view to accommodate temporal gunk (...) if they are perdurantists, pluralism is incompatible with the combination of temporal gunk and perdurantism. Therefore, priority pluralism, perdurantism and the possibility of temporal gunk are jointly incompatible, and at least one of these views must be false. Subsequently, it means that at least one of the following views must be true: priority monism or metaphysical infinitism; endurantism; and/or that time is atomistic. The triad's inconsistency, then, has some interesting metaphysical implications. (shrink)

This chapter takes a close look at the thought that mereological relations on material objects mirror, and are mirrored by, parallel mereological relations on their exact locations. This hypothesis is made more precise by means of a battery of principles from which more substantive consequences are derived. Mereological harmony turns out to entail, for example, that atomistic space is an inhospitable environment for material gunk or that Whiteheadian space is not a hospitable environment for unextended material atoms.

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 Lewis, mereology is the general and exhaustive theory of ontological composition, and every contingent feature of the world supervenes upon some fundamental properties instantiated by minimal entities. A profound analogy can be drawn between these two basic contentions of his metaphysics, namely that both can be intended as a denial of emergentism. In this essay, we study the relationships between Humean supervenience and two philosophical spin-offs of mereological monism: the possibility of gunk and the thesis of composition (...) as identity. In a gunky scenario, there are no atoms and, thus, some criteria alternative to mereological atomicity must be introduced in order to identify the bearers of fundamental properties; this introduction creates a precedent, which renders the restriction of the additional criteria to gunky scenarios arbitrary. On the other hand, composition as identity either extends the principle of indiscernibility of identicals to composition or is forced to replace indiscernibility with a surrogate; both alternatives lead to the postulation of a symmetric kind of supervenience which, in contrast to Humean supervenience, does not countenance a privileged level. Both gunk and composition as identity, thus, display a tension with Humean supervenience. (shrink)

E. J. Lowe and others argue that there can be 'uncountable' things admitting of no numerical description. This implies that there can be something without there being at least one such thing, and that things can be identical without being one or nonidentical without being two. The clearest putative example of uncountable things is portions of homogeneous stuff or 'gunk'. The paper argues that there is a number of portions of gunk if there is any gunk at (...) all, and that the possibility of uncountable things is inadequately supported. (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)