This chapter argues that from a particularly weak recombination principle and plausible assumptions about the nature of parthood and location, it follows that it is possible that the mereological structure of the material world and that of space-time fail to correspond to one another in very radical ways. The chapter suggests, moreover, that rejecting the possibility of such failures of correspondence leaves us with a choice of no less unappealing alternatives. It also discusses a few ways in which their (...) possibility is relevant to various important debates in metaphysics. (shrink)

Mereological nihilism says that there do not exist (in the fundamental sense) any objects with proper parts. A reason to accept it is that we can thereby eliminate 'part' from fundamental ideology. Many purported reasons to reject it - based on common sense, perception, and the possibility of gunk, for example - are weak. A more powerful reason is that composite objects seem needed for spacetime physics; but sets suffice instead.

Elselijn Kingma argues that, in cases of mammalian placental pregnancy, the foster (roughly, the post-implantation embryo/foetus) is part of the gravida (the pregnant organism). But she does not consider the possibility of proper overlap. I show that this generates a number of serious problems for her argument and trace the oversight to a quite general issue within the literature on biological individuality. Doing so provides an opportunity to pull apart and clarify the relations between some importantly distinct questions concerning organismality (...) and organismic parthood, and to identify the implications that this has for those who want to draw on this literature when making metaphysical or mereological arguments. (shrink)

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

There will be a few themes. One to get us going: expansion versus contraction. About an object, o, and the region, R, of space(time) in which o is exactly located,1 we may ask: i) must there exist expansions of o: objects in filled superregions2 of R? ii) must there exist contractions of o: objects in filled subregions of..

I argue that from a very weak recombination principle and plausible assumptions about the nature of parthood and location it follows that it's possible that the mereological structure of the material world and that of spacetime fail to correspond to one another in very radical ways. I defend, moreover, that rejecting the possibility of such failures of correspondence leaves us with a choice of equally radical alternatives. I also discuss a few ways in which their possibility is relevant to (...) various debates in metaphysics. (shrink)

This paper offers an argument in favour of a Lewisian version of concretism that maintains both the principle of material inheritance (according to which, if all the parts of an object x are material, then x is material) and the materiality-modality link (that is, the principle that, for every x, if x is material, then x is possible).

According to a well known, yet controversial metaphysical thesis, Composition is Identity. Recently, Kris McDaniel has articulated and defended a related—and arguably more controversial—thesis, one he calls Parthood is Identity (PI). Roughly the view has it that a whole is, strictly and literally, identical to each of its parts considered individually. At first sight, the view seems rather implausible. However, McDaniel’s formulation and defense are worthy of a serious discussion. In this paper I put forth such a discussion. The (...) result is what we should have expected all along: PI is not only implausible, but arguably false. (shrink)

It is plausible that the universe exists: a thing such that absolutely everything is a part of it. It is also plausible that singular, structured propositions exist: propositions that literally have individuals as parts. Furthermore, it is plausible that for each thing, there is a singular, structured proposition that has it as a part. Finally, it is plausible that parthood is a partial ordering: reflexive, transitive, and anti-symmetric. These plausible claims cannot all be correct. We canvass some costs of (...) denying each claim and conclude that parthood is not a partial ordering. Provided that the relevant entities exist, parthood is not anti-symmetric and proper parthood is neither asymmetric nor transitive. (shrink)

In the following work we propose to incorporate the main feature of quantum mechanics, i.e., the concept of indiscernibility. To achieve this goal, first we present two models of set theories: a quasi-set theory and a non-antisymmetric mereology. Next, we show how specific objects of QST—m-atoms—can be defined within NAM. Finally, we introduce a concept of a parthood of indiscernibles and discuss its features in respect to standard notions of indiscernibles and within NAM.

In “Extensionality of Parthood and Composition,”1 Achille Varzi mounts a spirited defense of the extensionality of parthood, or ‘EP’. According to EP, if x and y are composite objects with all the same proper parts then x = y.2 A number of philosophers, he notes, have objected that EP is false on the grounds that, for example, a statue and lump of clay (or a tinkertoy house and the wood from which it is made, in Varzi’s example) are (...) distinct yet share all their proper parts. A number of considerations — for example, that a statue and lump of clay have different persistence conditions — are commonly raised to support this non-extensionalist conclusion. Varzi maintains, on the other hand, that this case and others like it do not support non-extensionalism. However, there are reasons to doubt the cogency of his argument. In outline, Varzi’s argument runs as follows. Suppose that (i) α and β are (say) a statue and a lump, respectively,3 and also suppose that (ii) α = β. ∗This is a draft and so unsuitable for citation in any form. Any comments or suggestions are welcome and can be emailed to me at [email protected]. Check back periodically for newer versions. 1Varzi 2008 2Varzi 2008, p. 108. 3To avoid complications, let’s assume throughout that they have the same lifespan. Naturally, we should suppose they are co-located. (shrink)

This article presents a semantic analysis of indirect speech reports. The analysis aims to explain a combination of two phenomena. First, there are true utterances of sentences of the form α said that φ which are used to report an utterance u of a sentence wherein φ's content is not u's content. This implies that in uttering a single sentence, one can say several things. Second, when the complements of these reports (and indeed, these reports themselves) are placed in conjunctions, (...) the conjunctions are typically infelicitous. I argue that this combination of phenomena can be explained if speech reports report (perhaps contingent) parts of the contents of the sentences reported. (shrink)

What is a temporal part? Most accounts explain it in terms of timeless parthood: a thing's having a part without temporal qualification. Some find this hard to understand, and thus find the view that persisting things have temporal parts--fourdimensionalism--unintelligible. T. Sider offers to help by defining temporal parthood in terms of a thing's having a part at a time. I argue that no such account can capture the notion of a temporal part that figures in orthodox four-dimensionalism: temporal (...) parts must be timeless parts. This enables us to state four-dimensionalism more clearly. (shrink)

I focus on three mereological principles: the Extensionality of Parthood (EP), the Uniqueness of Composition (UC), and the Extensionality of Composition (EC). These principles are not equivalent. Nonetheless, they are closely related (and often equated) as they all reflect the basic nominalistic dictum, No difference without a difference maker. And each one of them—individually or collectively—has been challenged on philosophical grounds. In the first part I argue that such challenges do not quite threaten EP insofar as they are either (...) self-defeating or unsupported. In the second part I argue that they hardly undermine the tenability of EC and UC as well. (shrink)

Metaphysicians of various stripes claim that a single object can have more than one exact location in space or time – e.g. endurantists claim that an object persists by being ‘all there’ at different moments in time. Antony Eagle has developed a formal theory of location which is prima facie consistent with multi-location, but Damiano Costa and Claudio Calosi argue that the theory is unattractive to multi-location theorists on other grounds. I examine their charge that Eagle’s theory won’t allow an (...) endurantist to account for certain cases of mereological change. I argue that the charge sticks, but not for the reasons Costa and Calosi think. Along the way, I explore an issue which is underexplored in their paper, namely, how an endurantist might modify Eagle’s theory to incorporate a parthood relation which obtains, not absolutely, but only relative to times. (shrink)

Despite having faced severe criticism in the past, mereological approaches to group ontology, which argue that groups are wholes and that groups members are parts, have recently managed a comeback. Authors such as Katherine Ritchie and Paul Sheehy have applied neo-Aristotelian mereology to groups, and Katherine Hawley has defended mereological approaches against the standard objections in the literature. The present paper develops the mereological approaches to group ontology further and proposes an analysis of group membership as parthood plus further (...) restrictions. While all mereological accounts agree that group members are parts of the group, it has become clear that this analysis is insufficient. I discuss three proposals to develop the mereological analysis of group membership and then put forward a combined solution to the puzzle. According to my proposal, the members of a reading group are agents who are part of the group and have been designated to contribute to the group. (shrink)

According to some views of reality, some objects are fundamental and other objects depend for their existence upon these fundamental objects. In this article, I argue that we have reason to reject these views.

There are three families of solutions to the traditional Amputation Paradox: Eliminativism, Contingent Identity Theories, and Theories of Coincident Entities. Theories of Coincident Entities challenge our common understanding of the relation between identity and parthood, since they accept that two things can be mereologically coincident without being identical. The contemporary discussion of the Amputation Paradox tends to mention only one theory of Coincident Entities, namely the Constitution View, which violates the mereological principle of Extensionality. But in fact, there is (...) another theory, namely the Unique Part View, which violates another mereological principle. In this paper, I argue that the contemporary focus on the Constitution View is unmotivated, at least when we are confronted with the Amputation Paradox, and that a balanced comparison of the two views should favour the Unique Part View. (shrink)

Defenders of the subset view of realization have claimed that we can resolve well-known worries about mental-physical causal overdetermination by holding that mental properties are subset realized by physical properties, that instances of subset realized properties are parts of physical realizers, and that part-whole overdetermination is unproblematic. I challenge the claim that the overdetermination generated by the subset view can be legitimated by appealing to more mundane part-whole overdetermination. I conclude that the subset view does not provide a unique solution (...) to overdetermination worries. (shrink)

The premise of biological modularity is an ontological claim that appears to come out of practice. We understand that the biological world is modular because we can manipulate different parts of organisms in ways that would only work if there were discrete parts that were interchangeable. This is the foundation of the BioBrick assembly method widely used in synthetic biology. It is one of a number of methods that allows practitioners to construct and reconstruct biological pathways and devices using DNA (...) libraries of standardized parts with known functions. In this paper, we investigate how the practice of synthetic biology reconfigures biological understanding of the key concepts of modularity and evolvability. We illustrate how this practice approach takes engineering knowledge and uses it to try to understand biological organization by showing how the construction of functional parts and processes can be used in synthetic experimental evolution. We introduce a new approach within synthetic biology that uses the premise of a parts-based ontology together with that of organismal self-organization to optimize orthogonal metabolic pathways in E. coli. We then use this and other examples to help characterize semisynthetic categories of modularity, parthood, and evolvability within the discipline. (shrink)

The pivotal role of the relation part-of in the description of living organisms is widely acknowledged. Organisms are open systems, which means that in contradistinction to mechanical artifacts they are characterized by a continuous flow and exchange of matter. A closer analysis of the spatial relations in biological organisms reveals that the decision as to whether a given particular is part-of a second particular or whether it is only contained-in the second particular is often controversial. We here propose a rule-based (...) approach which allows us to decide on the basis of well-defined criteria which of the two relations holds between two anatomical objects, given that one spatially includes the other. We discuss the advantages and limitations of this approach, using concrete examples from human anatomy. (shrink)

A compact overview of the main formal theories of parthood and of their mutual relationships, up to Classical Extensional Mereology. Written as an Appendix to the other essays included in the volume.

Consider the things that exist—the entities—and let us suppose they are mereologically structured, that is, some are parts of others. The project of ontology within the bounds of bare mereology use this structure to say which of these entities belong to various ontological kinds, such as properties and particulars. My purpose in this paper is to defend the most radical section of the project, the mereological theory of the exemplification of universals. Along the way I help myself to several hypotheses: (...) the existence of merely possible worlds; that particulars have thisnesses; and that mereology is far from classical. Moreover, the way I characterize instantiation might be judged too complicated to be plausible. At the end of the paper, I reply to these objections based on complexity. (shrink)

Structural properties are properties something has in virtue of its mereological structure in that they are properties whose instantiation by a particular involves the parts of the particular being propertied and related in the appropriate way. Most of the literature on structural properties has focused on problems that arise from the pairing of two assumptions: (1) structural properties are universals and (2) structural properties are, in some sense, composed of the properties they involve. Chief among these difficulties is David Lewis’ (...) claim that the conjunction of (1) and (2) require non-unique composition and hence entail the denial of the extensionality of parthood: butane, as well as methane, is composed of the universals carbon, hydrogen and bonded, yet they are distinct properties. This is the extensionality problem. In this paper I discuss a different problem for the conjunction of (1) and (2) and propose a single solution to both problems. First, in section two, I introduce the idea of multiple decomposition and suggest that at least some structural properties are multiply decomposable. In section three, I introduce the “problem of multiple decompositions.” This problem arises when it seems possible for a structural property to be composed of some xs and some ys even when the xs ≠ ys. Finally, in section four I show how both problems admit of a single solution by focusing on the parthood relation that holds between structural properties and their constituents. While the solution I propose is theoretically costly, I argue that this cost should be paid to retain both (1) and (2). (shrink)

This paper contains a formal theory of functional parthood. Since the relation of functional parthood is defined here by means of the notion of design, the theory of functional parthood turns out to be a theory of design. The formal theory of design I defend here is a result of introducing a number of constraints that are to express the rational aspects of designing practice. The ontological background for the theory is provided by a conception of states (...) of affairs. The theory is accompanied with a formal model. I prove that the theory is sound and complete with respect to this model. (shrink)

David Lewis famously argued against structural universals since they allegedly required what he called a composition “sui generis” that differed from standard mereological com¬position. In this paper it is shown that, although traditional Boolean mereology does not describe parthood and composition in its full generality, a better and more comprehensive theory is provided by the foundational theory of categories. In this category-theoretical framework a theory of structural universals can be formulated that overcomes the conceptual difficulties that Lewis and his (...) followers regarded as unsurmountable. As a concrete example of structural universals groups are considered in some detail. (shrink)

That parthood is a transitive relation is among the most basic principles of classical mereology. Alas, it is also very controversial. In a recent paper, Ingvar Johansson has put forward a novel diagnosis of the problem, along with a corresponding solution. The diagnosis is on the right track, I argue, but the solution is misleading. And once the pieces are properly put together, we end up with a reinforcement of the standard defense of transitivity on behalf of classical mereology.

This is a work in analytic metaphysics, which addresses a cluster of interrelated issues at the interface of mereology and persistence over time. In particular, it outlines a defence of a version of Endurance Theory according to which every enduring object is either a mereological simple or a mere sum of mereological simples. It includes, among other things, a proposal of a new way of framing the debate between Endurance Theory and Four-Dimensionalism, a defence of Endurance Theory over Four-Dimensionalism, arguments (...) against the existence of compound substances, and a defence of a traditional metaphysical atomism according to which all objects are ultimately made up of microscopic simples. (shrink)

In this article, I discuss parthood status in mereologi- cally interpreted Daoist metaphysics, based on the Daodejing. I depart from the dao and you interrela- tion, which mereologically overlap by sharing parts. I consider the case of a complete overlap, which (a) challenges proper parthood, according to which a part cannot be identical with the whole that it com- poses, and (b) entails the question of identity that, while complying with classical mereology, cannot be consis- tent with Daoist (...) metaphysics. The discussion leads to abandoning proper parthood and antisymmetry axiom from classical axiomatics. It also shows a plausible fur- ther direction for mereological reconstruction. (shrink)

This paper presents three claims concerning boundaries, dependence and parthood. The claims are intuitively plausible, but cannot, at face value, all be true on pain of contradiction. Each of the three claims is shown to be more plausible than its converse and some solutions to the puzzle are presented.

This dissertation investigates the metaphysics of human body parts; particularly, the epistemic conditions under which something can be said to be a “body part of” some particular human being. In this dissertation I draw on the hylomorphism of Aristotle and John Duns Scotus to argue that a necessary and sufficient condition on human bodily parthood is an object’s functioning for the sake of the whole human being and the maintenance of her biological life. I argue that, on this view (...) of bodily parthood, at least some prostheses or artificial organs are truly body parts of the human beings in whom they operate. I defend this view in reference to both Aristotelian and Scotistic hylomorphism, as well as answering objections raised by some contemporary views of bodily parthood as merely conventional. I argue that this has important implications for medical ethics, including potentially restricting medical interventions in end-of-life care and heightening the legal ramification of damage done to prostheses. I argue that investigation into the metaphysical questions surrounding body parts and their composition can illuminate hitherto underappreciated dimensions of ethical questions in medicine. (shrink)

In fields such as medicine, geography, and mechanics, spatial reasoning involves reasoning about entities that may coincide without overlapping. Some examples are: cavities and invading particles, passageways and valves, geographic regions and tropical storms. The purpose of this paper is to develop a formal theory of spatial relations for domains that include coincident entities. The core of the theory is a clear distinction between mereotopological relations, such as parthood and connection, and relative location relations, such as coincidence. To guide (...) the development of the formal theory, I construct mathematical models in which nontrivial relative location relations are defined. (shrink)

In this paper, I defend an unconventional mereological framework involving the doctrine of divine simplicity, to surmount a significant yet neglected dilemma resulting from that long-standing view of God as absolutely, and uniquely, simple. This framework establishes God as literally a part of everything—an “omni-part.” Although consequential for the many prominent religious traditions featuring divine simplicity, my analysis focuses on potential implications for an important formative issue in medieval Islamic philosophy. This problem of principality, with regards to metaphysical primacy and (...) importance, derives from Ibn Sīnā’s celebrated distinction between essence and existence, and involves determining which is genuinely, objectively, real. Instead of supporting the historically dominant opposing viewpoints advancing either the principality of existence or of essence (aṣālat al-wujūd/al-māhiyya), I claim that God as omni-part aids renewed defence of the majority rejected view which upholds the combined principality of existence and essence together. Additionally, my proposal reinforces various theological desiderata including divine omnipresence and God’s necessity across possible worlds, while also supporting new perspectives on Ibn ‘Arabi’s influential notion of waḥdat al-wūjūd, understood as the absolute unity of being. (shrink)

A.J. Cotnoir has argued that we should distinguish between two notions of proper parthood: outstripped part and non-identical part. Outstripped parthood is an asymmetric relation, but non-identical parthood is not. We argue, first, that the intuitions Cotnoir uses to motivate these notions do not always give the right verdict; and, second, that systematic reasons for distinguishing these two notions of parthood have further counter-intuitive consequences. This means the distinction between two notions of proper parthood currently (...) lacks adequate motivation. (shrink)

This article explores process mereology, the theory of part-whole relations. I compare and contrast the mereology of Theodore Sider with that of Alfred North Whitehead, broadly favoring the latter’s approach for allowing us to take seriously an evolutionary structure in metaphysics.

Late Lowe’s metaphysics of material objects is an interesting multi-thingist theory that still attracts interest from various authors. The core idea is that ifxmaterially constitutesy, thexis a proper part ofy. I discuss some mereological issues that arise from the approach and propose a revision of the mereology associated. Particularly, I examine the tenability of a number of supplementation principles and conclude that just one may serve the theory adequately. Still, the endorsement of such a principle does not come for free. (...) Successively, I address the derivability of an important extensionality theorem and conclude that the theorem must be taken as an axiom in the mereology at stake. Lastly, I discuss two notable definitions of mereological fusions to assess which one best suits the present theory. The result is that authors sharing Lowe’s multi-thingist conception of material objects can still enjoy a moderately strong mereology. (shrink)