I try to lay bare some of the conceptual space in which one may be a Social Trinitarian. I organize the paper around answers to five questions. These are: (1) How do the three Persons of the Trinity relate to the Godhead? (2) How many divine beings or gods are there? (3) How many distinct centers of consciousness are there in the Godhead? (4) How many omnicompetent beings are there? (5) How are the Persons of the Trinity individuated? I try (...) to make clear costs and benefits of various answers to these questions. (shrink)

Those who accept the necessity of mereological universalism face what has come to be known as the ‘junk argument’ due to Bohn [2009], which proceeds from the incompatibility of junk with universalism and the possibility of junk, to conclude that mereological universalism isn't metaphysically necessary. Most attention has focused on ; however, recent authors have cast doubt on . This paper undertakes a defence of premise against three main objections. The first is a new objection to the effect that Bohn's (...) defence of that premise presupposes far too much. I show that one can defend premise from a much weaker set of assumptions. The second objection, due to Contessa [2012], is that those who accept unrestricted composition should only accept the existence of binary sums rather than infinitary fusions. I argue that this conception of unrestricted composition is problematic: it is in conflict with an intuitive remainder principle. The final objection is .. (shrink)

The dominant theory of parts and wholes – classical extensional mereology – has faced a number of challenges in the recent literature. This article gives a sampling of some of the alleged counterexamples to some of the more controversial principles involving the connections between parthood and identity. Along the way, some of the main revisionary approaches are reviewed. First, counterexamples to extensionality are reviewed. The ‘supplementation’ axioms that generate extensionality are examined more carefully, and a suggested revision is considered. Second, (...) the paper considers an alternative approach that focuses the blame on antisymmetry but allows us to keep natural supplementation axioms. Third, we look at counterexamples to the idempotency of composition and the associated ‘parts just once’ principle. We explore options for developing weaker mereologies that avoid such commitments. (shrink)

Perichoresis, or “mutual indwelling,” is a crucial concept in Trinitarian theology. But the philosophical underpinnings of the concept are puzzling. According to ordinary conceptions of “indwelling” or “being in,” it is incoherent to think that two entities could be in each other. In this paper, I propose a mereological way of understanding “being in,” by analogy with standard examples in contemporary metaphysics. I argue that this proposal does not conflict with the doctrine of divine simplicity, but instead affirms it. I (...) conclude by discussing how mutual indwelling relates to the concepts of unity and identity. (shrink)

This paper is a systematic exploration of non-wellfounded mereology. Motivations and applications suggested in the literature are considered. Some are exotic like Borges’ Aleph, and the Trinity; other examples are less so, like time traveling bricks, and even Geach’s Tibbles the Cat. The authors point out that the transitivity of non-wellfounded parthood is inconsistent with extensionality. A non-wellfounded mereology is developed with careful consideration paid to rival notions of supplementation and fusion. Two equivalent axiomatizations are given, and are compared to (...) classical mereology. We provide a class of models with respect to which the non-wellfounded mereology is sound and complete. (shrink)

Mereological principles are often controversial; perhaps the most stark contrast is between those who claim that Weak Supplementation is analytic—constitutive of our notion of proper parthood—and those who argue that the principle is simply false, and subject to many counterexamples. The aim of this paper is to diagnose the source of this dispute. I’ll suggest that the dispute has arisen by participants failing to be sensitive to two different conceptions of proper parthood: the outstripping conception and the non-identity conception. I’ll (...) argue that the outstripping conception, can deliver the analyticity of Weak Supplementation on at least one sense of ‘analyticity’. I’ll also suggest that the non-identity conception cannot do so independently of considerations to do with mereological extensionality. (shrink)

Mereological principles are often controversial; perhaps the most stark contrast is between those who claim that Weak Supplementation is analytic—constitutive of our notion of proper parthood—and those who argue that the principle is simply false, and subject to many counterexamples. The aim of this paper is to diagnose the source of this dispute. I’ll suggest that the dispute has arisen by participants failing to be sensitive to two different conceptions of proper parthood: the outstripping conception and the non-identity conception. I’ll (...) argue that the outstripping conception (together with a specific set of definitions for other mereological notions), can deliver the analyticity of Weak Supplementation on at least one sense of ‘analyticity’. I’ll also suggest that the non-identity conception cannot do so independently of considerations to do with mereological extensionality. (shrink)

Does a commitment to mereological universalism automatically bring along a commitment to the controversial doctrine of mereological extensionalism—the view that objects with the same proper parts are identical? A recent argument suggests the answer is ‘yes’. This paper attempts a systematic response to the argument, considering nearly every available line of reply. It argues that only one approach—the mutual parts view—can yield a viable mereology where universalism does not entail extensionalism.

I propose a theory of space with infinitesimal regions called smooth infinitesimal geometry based on certain algebraic objects, which regiments a mode of reasoning heuristically used by geometricists and physicists. I argue that SIG has the following utilities. It provides a simple metaphysics of vector fields and tangent space that are otherwise perplexing. A tangent space can be considered an infinitesimal region of space. It generalizes a standard implementation of spacetime algebraicism called Einstein algebras. It solves the long-standing problem of (...) interpreting smooth infinitesimal analysis realistically, an alternative foundation of spacetime theories to real analysis, 277–392, 1980). SIA is formulated in intuitionistic logic and is thought to have no classical reformulations. Against this, I argue that SIG is such a reformulation. But SIG has an unorthodox mereology, in which the principle of supplementation fails. (shrink)

Van Inwagen's General Composition Question (GCQ) asks what conditions on an object and its constituents make the object a whole that these constituents compose, as opposed to an object linked to the constituents by a relation other than composition. The answer is traditionally expected to cite no mereological terms, to hold of metaphysical necessity and to be such that no defeating scenarios can be conceived (e.g., a scenario in which the conditions are met but the constituents fail to genuinely compose (...) the object). While not all writers agree on setting these high expectations on the principles that constitute answers to the GCQ (Hawley 2006), there is a yet unsettled issue concerning the principles’ naturalistic accreditation: Could putative principles be constrained and informed by advanced physical knowledge? Arguing positively, we outline two styles of principles worthy of naturalistic authority. In an explorative spirit, we notice that each style incurs certain costs. First, the principle in question may fail some of the above expectations set in an aprioristic context. Second, it may require a specific meta-theoretic understanding of what it takes to achieve naturalistic accreditation. Finally, it may address the GCQ “piecemeal” and fail to generalize to objects of all physical sorts.1. (shrink)

In “Tropes and Ordinary Physical Objects”, Kris McDaniel argues that ordinary physical objects are fusions of monadic and polyadic tropes. McDaniel calls his view “TOPO”—for “Theory of Ordinary Physical Objects”. He argues that we should accept TOPO because of the philosophical work that it allows us to do. Among other things, TOPO is supposed to allow endurantists to reply to Mark Heller’s argument for perdurantism. But, we argue in this paper, TOPO does not help endurantists do that; indeed, we argue (...) that anyone who accepts TOPO should reject endurantism. (shrink)

In this paper, we present an extensional system of mereology suitable to account for the intuitive distinction between heaplike and non-heaplike entities. Since the need to capture this distinction has been a key motivation for non-extensional mereologies, we first assess the main non-extensional systems advanced in the last years and highlight some mereological and metaphysical difficulties they involve. We then advance a novel program, according to which the distinction between heaplike and non-heaplike entities can be accounted for by bringing together (...) the parthood relation characterized by classical extensional mereology and an Aristotelian extensional notion of potential parthood. Thus, while rejecting the thesis of mereological monism, our proposal is consistent with the thesis of mereological extensionalism. We show that within this framework it is possible to characterize the above-mentioned distinction, to define the relation of material constitution, and to capture three fundamental standpoints in metaphysics. (shrink)

It is argued that those who accept the psychological criterion of personal identity, such as Parfit and Shoemaker, should accept what I call the ‘series’ view of a person, according to which a person is a unified aggregate of mental events and states. As well as defending this view against objections, I argue that it allows the psychological theorist to avoid the two lives objection which the ‘animalist’ theorists have raised against it, an objection which causes great difficulties for the (...) conception of a person that most psychological theorists favour, the constitution view. It is also argued that the series view allows that people can body swap and teleport, which the constitution view–which takes a person to be a physical object (but a distinct physical object from the human being)–has great trouble with. (shrink)

It is argued that those who accept the psychological criterion of personal identity, such as Parfit and Shoemaker, should accept what I call the 'series' view of a person, according to which a person is a unified aggregate of mental events and states. As well as defending this view against objections, I argue that it allows the psychological theorist to avoid the two lives objection which the 'animalist' theorists have raised against it, an objection which causes great difficulties for the (...) conception of a person that most psychological theorists favour, the constitution view. It is also argued that the series view allows that people can body swap and teleport, which the constitution view—which takes a person to be a physical object (but a distinct physical object from the human being)—has great trouble with. (shrink)

In the current debate on how ordinary objects persist through time, more than one philosopher has endorsed the following two theses: stage theory and diachronic universalism. In this paper, I would like to offer a solution to the problem that Balashov poses to the joint acceptance of these theses. I will also offer a number of reasons why, even if it is not necessary to undermine Balashov’s counterexamples, stage theorists can, without making their theory less appealing, reject Balashov’s understanding of (...) sorts, which plays a crucial role in his criticisms of stage universalism. (shrink)

This paper aims to better motivate the naturalization of metaphysics by identifying and criticizing a class of theories I call ’free range metaphysics’. I argue that free range metaphysics is epistemically inadequate because the constraints on its content—consistency, simplicity, intuitive plausibility, and explanatory power—are insufficiently robust and justificatory. However, since free range metaphysics yields clarity-conducive techniques, incubates science, and produces conceptual and formal tools useful for scientifically engaged philosophy, I do not recommend its discontinuation. I do recommend, however, ending the (...) discipline’s bad faith. That is, I urge that free range metaphysics not be taken to have fully satisfactory epistemic credentials over and above its pragmatic ones. (shrink)

Mereological nihilists hold that composition never occurs, so that nothing is ever a proper part of anything else. Substance dualists generally hold that we are each identical with an immaterial soul. In this paper, I argue that every popular objection to substance dualism has a parallel objection to composition. This thesis has some interesting implications. First, many of those who reject composition, but accept substance dualism, or who reject substance dualism and accept composition, have some explaining to do. Secondly, one (...) popular objection to mereological nihilism, one which contends that mereological nihilism is objectionable insofar as it is incompatible with the existence of people, is untenable. (shrink)

Mereological nihilism is the thesis that composition never occurs. Sider has defended nihilism on the basis of its relative ideological simplicity. In this paper I develop the argument from ideological simplicity, and defend it from some recent objections. Along the way I discuss the best way to formulate nihilism, what it means for a theory to exhibit lesser or greater degrees of ideological simplicity, the relationship between the parthood relation and the identity relation, and the notion that we should judge (...) the ideological simplicity of competing theories on the basis of the kinds of ideological commitments required by those theories. (shrink)

I agree with a great deal in Helen Steward's paper. I am especially sympathetic to her suggestion that we gain metaphysical illumination by considering various ways in which we arrive at ideas of certain kinds of individuals by abstraction from those of more basic kinds. My aim is to pursue that suggestion by exploring the proposal that a grounding node in this form of abstraction may be characterized by Exclusivity in spatial location. Steward claims that we arrive at our ideas (...) of specific events and processes by different modes of abstraction in cases where a more basic persisting individual undergoes some kind of change. I argue that the most basic individuals in this hierarchy of abstraction are enduring substances that occupy their spatial location exclusively at all times: no two such substances are ever precisely collocated. (shrink)

If two self-connected individuals are connected, it follows in classical extensional mereotopology that the sum of those individuals is self-connected too. Since mainland Europe and mainland Asia, for example, are both self-connected and connected to each other, mainland Eurasia is also self-connected. In contrast, in non-extensional mereotopologies, two individuals may have more than one sum, in which case it does not follow from their being self-connected and connected that the sum of those individuals is self-connected too. Nevertheless, one would still (...) expect it to follow that a sum of connected self-connected individuals is self-connected too. In this paper, we present some surprising countermodels which show that this conjecture is incorrect. (shrink)

Noneism a is form of Meinongianism, proposed by Richard Routley and developed and improved by Graham Priest in his widely discussed book Towards Non-Being. Priest's noneism is based upon the double move of building a worlds semantics including impossible worlds, besides possible ones, and admitting a new comprehension principle for objects, differerent from the ones proposed in other kinds of neo-Meinongian theories, such as Parsons' and Zalta's. The new principle has no restrictions on the sets of properties that can deliver (...) objects, but parameterizes the having of properties by objects to worlds. Modality is therefore explicitly built in - so the approach can be conveniently labeled as "modal noneism". In this paper, I put modal noneism to work by testing it against classical issues in modal logic and semantics. It turns out that - perhaps surprisingly - the theory performs well in problems of transworld identity, which are frequently considered to be the difficult ones in the literature; faces a limitation, albeit not a severe one, when one comes to transworld individuation, which is often taken as an easy issue, if not a pseudo-problem; and may stumble upon a real trouble when dealing with what I shall call 'extensionally indiscernible entities' - particular nonexistent objects modal noneism is committed to. (shrink)

I would like to attack a certain view: The view that the concept of identity can fail to apply to some things although, for some positive integer n, we have n of them. The idea of entities without self-identity is seriously entertained in the philosophy of quantum mechanics. It is so pervasive that it has been labelled the Received View. I introduce the Received View in Section 1. In Section 2 I explain what I mean by entity, and I argue (...) that supporters of the Received View should agree with my characterization of the corresponding notion of entity. I also explain what I mean by identity, and I show that supporters of the Received View agree with my characterization of that notion. In Section 3 I argue that the concept of identity, so characterized, is one with the concept of oneness. Thus, it cannot but apply to what belongs to a collection with n elements, n being a positive integer. In Section 4 I add some considerations on the primitiveness of identity or unity and the status of the Identity of Indiscernibles. In Section 5 I address the problem of how reference to indiscernible objects with identity can be achieved. (shrink)

Meta-ontology (in van Inwagen's sense) concerns the methodology of ontology, and a controversial meta-ontological issue is to what extent ontology can rely on linguistic analysis while establishing the furniture of the world. This paper discusses an argument advanced by some ontologists (I call them unifiers) against supporters of or coincident entities (I call them multipliers) and its meta-ontological import. Multipliers resort to Leibniz's Law to establish that spatiotemporally coincident entities a and b are distinct, by pointing at a predicate F (...) () made true by a and false by b . Unifiers try to put multipliers in front of a dilemma: in attempting to introduce metaphysical differences on the basis of semantic distinctions, multipliers either (a) rest on a fallacy of verbalism, entailed by a trade-off between a de dicto and a de re reading of modal claims, or (b) beg the question against unifiers by having to assume the distinction between a and b beforehand. I shall rise a tu quoque, showing that unifiers couldn't even distinguish material objects (or events) from the spatiotemporal regions they occupy unless they also resorted to linguistic distinctions. Their methodological aim to emancipate themselves from linguistic analysis in ontological businesses is therefore problematic. (shrink)

The basic form of the exclusion problem is by now very, very familiar. 2 Start with the claim that the physical realm is causally complete: every physical thing that happens has a sufficient physical cause. Add in the claim that the mental and the physical are distinct. Toss in some claims about overdetermination, give it a stir, and voilá—suddenly it looks as though the mental never causes anything, at least nothing physical. As it is often put, the physical does all (...) the work, and there is nothing left for the mental to do. (shrink)

A lot of people believe that distinct objects can occupy precisely the same place for the entire time during which they exist. Such people have to provide an answer to the 'grounding problem' – they have to explain how such things, alike in so many ways, nonetheless manage to fall under different sortals, or have different modal properties. I argue in detail that they cannot say that there is anything in virtue of which spatio-temporally coincident things have those properties. However, (...) I also argue that this may not be as bad as it looks, and that there is a way to make sense of the claim that such properties are primitive. (shrink)

Metaphysics has enjoyed a vigorous revival in the last few decades. Even so, there has been little ontological interest in the things that we interact with everyday—trees, tables, other people.1 It is not that metaphysicians ignore ordinary things altogether. Indeed, they are happy to say that sentences like ‘The daffodils are out early this year’ or ‘My computer crashed again’ are true. But they take the truth of such sentences not to require that a full description of reality mention daffodils (...) or computers. Many metaphysicians now interpret the apparent variety of things in the world as variety only of concepts applied to things that are basically of the same sort—for example, sums of particles or of temporal parts of particles. (shrink)

Jaegwon Kim has argued that unless mental events are reducible to subvening physical events, they are at best overdeterminers of their effects. Recently, nonreductive physicalists have endorsed this consequence claiming that the relationship between mental events and their physical bases is tight enough to render any such overdetermination nonredundant, and hence benign. I focus on instances of this strategy that appeal to the notion of constitution. Ultimately, I argue that there is no way to understand the relationship between irreducible mental (...) events and their physical bases such as to both eliminate causal redundancy and preserve the efficacy of mental events. (shrink)

A material object is constituted by a sum of parts all of which are essential to the sum but some of which seem inessential to the object itself. Such object/sum of parts pairs include my body/its torso and appendages and my desk/its top, drawers, and legs. In these instances, we are dealing with objects and their components. But, fundamentally, we may also speak, as Locke does, of an object and its constitutive matter—a “mass of particles”—or even of that aggregate and (...) the sum of subatomic particles ‘making it up’. The “problem of material constitution” (henceforth, PMC) is generated by assuming inter alia that the members of any such pair are numerically identical, that is, that the constituted and the constituting are one and the same thing. (shrink)

A new puzzle about material constitution is presented and its implications are discussed. The moral of the story is that familiar intuitions supporting a neo-Aristotelian view of the material world are contradictory. To accommodate these intuitions is to embrace inconsistency. Therefore, neo-Aristotelianism is worse off for its intuitive appeal. Furthermore, the puzzle is used to argue for an account of ordinary modal thought and language that’s reconstructive, or ameliorative.

Corruptionism is the view that following physical death, the human being ceases to exist but their soul persists in the afterlife. Survivalism holds that both the human being and their soul persist in the afterlife, as distinct entities, with the soul constituting the human. Each position has its defenders, most of whom appeal both to metaphysical considerations and to the authority of St Thomas Aquinas. Corruptionists claim that survivalism violates a basic principle of any plausible mereology, while survivalists tend to (...) reject the principle, though without as much detail as one would like. In this paper I examine both the key exegetical issues and the mereological question, arguing that Aquinas cannot be shown to have supported the principle in question, and that the principle should be rejected on independent grounds. If correct, some key planks in support of survivalism are established, with others to await further examination. (shrink)

Constitution theorists have argued that due to a difference in persistence conditions, persons are not identical with the animals or the bodies that constitute them. A popular line of objection to the view that persons are not identical with the animals/bodies that constitute them is that the view commits one to undesirable overpopulation, with too many minds and too many thinkers. Constitution theorists are well aware of these overpopulation concerns and have gone a long way toward answering them. However, there (...) is one mental excess worry that remains especially problematic. It is argued here that the worry about too many thoughts, or too many instantiations of mentality in general, remains a serious threat to the constitution view of persons. What exactly the threat is and how it arises is described in detail in Section III. It is then shown that attempts to allay the concern are unsuccessful. I argue, in particular, that appealing to the distinction between derivative and non-derivative instantiation fails to solve the problem. (shrink)

Debates about material coincidence tend to start with common-sense intuitions but quickly leave them behind and lead to highly problematic conclusions. Reconciling the latter with common sense is the next stage in the process, which often requires revision of some of the initial beliefs and has been used to adjudicate many rather abstract and technical proposals in the metaphysics of composition and persistence, ranging from natural (constitutionalism) to radical (nihilism). -/- I have no disagreement with this overall strategy: theories do (...) need to turn abstract at some point, move beyond common sense, and eventually force upon us interesting, novel, and often counterintuitive revisions in our overall conceptual scheme. This applies to all theoretical areas, and contemporary metaphysics is no exception. But while the latter is widely regarded as being quite extreme in this respect, I want to argue that, in one sense, it is not extreme enough. I do it by developing a new case of material coincidence that is initially motivated not by common sense but by physical considerations, and is not susceptible to any of the standard solutions. -/- One lesson of science is its ability to expand our imagination beyond the limits of common sense. This may have importance for metaphysics too. (shrink)

This paper concerns an epistemological objection against mathematical platonism, due to Hartry Field.The argument poses an explanatory challenge – the challenge to explain the reliability of our mathematical beliefs – which the platonist, it’s argued, cannot meet. Is the objection compelling? Philosophers disagree, but they also disagree on (and are sometimes very unclear about) how the objection should be understood. Here I distinguish some options, and highlight some gaps that need to be filled in on the potentially most compelling version (...) of the argument. (shrink)

Friends of states of affairs and structural universals appeal to a relation, structure-making, that is allegedly a kind of composition relation: structure-making ?builds? facts out of particulars and universals, and ?builds? structural universals out of unstructured universals. D. M. Armstrong, an eminent champion of structures, endorses two interesting theses concerning composition. First, that structure-making is a composition relation. Second, that it is not the only (fundamental) composition relation: Armstrong also believes in a mode of composition that he calls mereological, and (...) which he takes to be the only kind of composition recognized by his philosophical adversaries, such as David Lewis. Armstrong, accordingly, is a kind of pluralist about compositional relations: there is more than one way to make wholes from parts. In this paper, I critically evaluate Armstrong's compositional pluralism. (shrink)

This book is in honour of Professor Anna-Sofia Maurin on her 50th birthday. It consists of eighteen essays on metaphysical issues written by Swedish and international scholars.

The phasalist solution to the puzzle of the statue and the piece of clay claims that being a statue is a phase sortal property of the piece of clay, just like being a child is a phase sortal property of a human being. Some philosophers reject this solution because it cannot account for cases where the statue seems to gain and lose parts that the piece of clay does not. I rebut this objection by arguing, contrary to the prevailing view, (...) that the piece of clay is not mereologically constant and might even be highly mereologically flexible. (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.

Are a material object, such as a statue, and its constituting matter, the clay, parts of one another? One wouldn't have thought so, and yet a number of philosophers have argued that they are. I review the arguments for this surprising claim showing how they all fail. I then consider two arguments against the view concluding that there are both pre-theoretical and theoretical considerations for denying that the statue and the clay are mutual parts.

We tend to talk about (refer to, quantify over) parts in the same way in which we talk about whole objects. Yet a part is not something to be included in an inventory of the world over and above the whole to which it belongs, and a whole is not something to be included in the inventory over and above its constituent parts. This paper is an attempt to clarify a way of dealing with this tension which may be labeled (...) the Minimalist View: An element in the field of a part-whole relation is to be included in an inventory of the world if and only if it does not overlap any distinct element that is itself included in the inventory. (shrink)

Identity is a modally inflexible relation: two objects are necessarily identical or necessarily distinct. However, identity is not alone in this respect. We will look at the relation that one object bears to some objects if and only if it is one of them. In particular, we will consider the credentials of the thesis that no matter what some objects are, an object is necessarily one of them or necessarily not one of them.

Mainstream metaphysics has been preoccupied by inquiring into the nature of major kinds of entities, like objects, properties and events, while avoiding minor entities, like shadows or holes. However, one might want to hope that dealing with such minor entities could be profitable for even solving puzzles about major entities. I propose a new ontological puzzle, the Shadow of Constitution Puzzle, incorporating the old puzzle of material constitution, with shadows in the role of the minor entity to guide our approach (...) to the issues involved. I then analyze the standard answers to the original puzzle of constitution, in their role as potential solutions to the new puzzle. Finally, I discuss three views that can solve the proposed puzzle. (shrink)

According to constitution views of persons, we are constituted by spatially coinciding human animals. Constitution views face an ‘overpopulation’ puzzle: if the animal has my brain, there is another thinker where I am. An influential solution to this problem distinguishes between derivative and non‐derivative property possession: persons non‐derivatively have their personal properties, while inheriting others from their constituters. I will show that this solution raises a new problem, by constructing a puzzle with the absurd result that we instantiate certain properties (...) incompatibly. In setting up the puzzle, I demonstrate the relevance of the bodily awareness and self‐awareness literatures to overpopulation puzzles. (shrink)