Philosophy Mereology
by
Paul R. Daniels
  • LAST REVIEWED: 22 November 2022
  • LAST MODIFIED: 27 July 2016
  • DOI: 10.1093/obo/9780195396577-0313

Introduction

Mereology concerns part-whole relations, which is to say that mereological discussions focus on (1) the relation between the parts of a whole and the whole of which they’re a part, and (2) the relations between the parts within a whole. But mereological discussions extend beyond mere articulation of mereological axioms. Mereologies—or part-whole theories—play a central role in many aspects of metaphysics. While this has been the case since the time of the Stoics, there has recently been a noteworthy revival of interest in mereology. Some are interested in mereology out of a genuine interest in the field itself, whereas others turn to it to find a toolkit to help them tackle problems that arise in other discussions, as many problems, it turns out, feature a mereological component. Mereology has, for instance, played a key role in motivating a variety of views. Do, for instance, any two objects “mereologically fuse” to form a further object? Some cases seem clear, like the molecules in my body and me; other more gerrymandered cases, like your nose and the Eiffel Tower, seem less clear. Our mereological views here—whether we want to be mereological nihilists, universalists, or restricted composition theorists—will, at a minimum, play a crucial role in forming our ontological commitments. Also notice that while mereological discussion typically focuses on material entities, sometimes our interests gravitate toward the mereological structure of space-time regions, or to the relations that hold between regions and the objects that occupy them, or to the mereology of such entities as events. Mereology has its fingers in many pies. But no matter how we might want to answer mereological concerns, we might further wonder if this is putting the cart before the horse. That is, should mereology take priority? Or should we work out which metaphysical theses we want to defend, and then determine which mereological principles best serve our ends? Different authors take different position here. This article highlights many of the key mereological concepts and principles, but it also outlines some of the fundamental problems that confront philosophers who think about mereology. The article also focuses on philosophical issues, rather than formal ones. For the sake of accessibility, this article avoids technical presentations of, for instance, mereological axioms. It’s also noteworthy that there is a nontrivial contribution to mereology from non-English writers, especially from Eastern Europe.

General Overviews

While there are no introductory textbooks on mereology, there are a number of good introductions, surveys, and general overviews of the field. Varzi 2016 stands out in this regard, as it is detailed, up-to-date, extensive, and clearly written. Simons 1987 assumes little on the part of the reader, and is worth reading in its entirety given the central place it holds in contemporary discussions of mereology. In addition, the introductory chapters of the anthologies on mereology can play the right role for readers interested in particular topics; for example, those unfamiliar with mereology who have a particular interest in locative relations would find the introduction to Kleinschmidt 2014 (cited under Anthologies) a good place to start.

  • Simons, Peter. Parts: A Study in Ontology. Oxford: Oxford University Press, 1987.

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    The first three chapters of this contemporary locus classicus on parthood act as an excellent introduction to mereology.

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  • Varzi, Achille. “Appendix: Formal Theories of Parthood.” In Mereology and the Sciences. Edited by Claudio Calosi and Pierluigi Graziani, 259–370. Berlin: Springer, 2014.

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    This is a succinct technical overview of many mereological principles and the ways in which they’re connected. A valuable reference to have on hand.

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  • Varzi, Achille. “Mereology.” In The Stanford Encyclopedia of Philosophy. Edited by Edward Zalta. Stanford, CA: Stanford University, 2016.

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    Surveys the range of standard mereological principles, with an emphasis on the contemporary, and gradually introduces formal presentations. Varzi also highlights the controversies and problems in the process. A comprehensive introduction, with an extensive bibliography.

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Anthologies

There are a few noteworthy anthologies that focus on mereology and related philosophical concerns. As one might expect, the entries tend to be high quality, and they tend to gravitate toward a common theme. For instance, the papers in Calosi and Graziani 2014 focus on the application of mereology to contemporary science, mathematics, and engineering; Kleinschmidt 2014 concerns mereology, locative relations, and how these discussions interact with other topics; and Cotnoir and Baxter 2014 is devoted to Composition as Identity. A few prominent journals have also had special issues dedicated to mereology—in particular, Hudson 2004 (The Monist), Mann and Varzi 2006 (the Journal of Philosophy), and Albertazzi and Libardi 1994 (Axiomathes).

  • Albertazzi, Liliana, and Massimo Libardi, eds. Special Issue: Mereology. Axiomathes 5.1 (1994).

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    A special issue devoted to mereology. Topics discussed include, but are not limited to, the limits of mereology, Brentano’s mereology, and mereological essentialism.

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  • Calosi, Claudio, and Pierluigi Graziani, eds. Mereology and the Sciences. Berlin: Springer, 2014.

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    Foundational issues in mereology are explored, with an eye on the sciences, as are issues in mereotopology, gunk, and persistence. The ways in which mereology engages with the sciences is discussed here as well; specifically physics (including relativistic parts, and composition in quantum mechanics), mathematics, biology, chemistry, computer science, and engineering.

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  • Cotnoir, Aaron, and Donald Baxter, eds. Composition as Identity. Oxford: Oxford University Press, 2014.

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    A volume dedicated to the view known as Composition as Identity. While composition is the relation between a whole and its parts, according to the Composition as Identity thesis, a whole just is identical to its parts. The contributing authors here weigh in on the debate about Composition as Identity and discuss its different commitments. The first two chapters do an excellent job of framing this debate and detailing its history.

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  • Hudson, Hud, ed. Special Issue: Simples. The Monist 87.3 (2004).

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    A special issue devoted to mereological simples and gunk.

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  • Kleinschmidt, Shieva, ed. Mereology and Location. Oxford: Oxford University Press, 2014.

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    This excellent volume concerns mereology, locative relations, and the ways in which they’re connected. The featured papers are divided between those that focus principally on mereology (e.g., the primitives of mereology), those that focus on locative concerns (e.g., occupants and modes of occupation), and those that engage with related other topics (e.g., the parts of propositions). The included bibliography provides a superb guide to the salient literature.

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  • Mann, Wolfgang, and Achille Varzi, eds. Special Issue: Parts and Wholes. Journal of Philosophy 103.12 (2006).

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    A special issue devoted to mereology, covering a range of topics, with contributions from leading philosophers. Topics discussed include, but are not limited to, mereological sums, composition, hylomorphism, and Aristotelean mereology.

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Historical Background

Mereology has featured in western philosophy for thousands of years. The introduction to Albertazzi and Libardi 1994 (cited under Anthologies) provides a nice summary of the 20th-century revival of mereology, while Mann and Varzi 2006 (also under Anthologies) provides more of an overarching synopsis with an eye on key problems mereologists seek to tackle. The following two entries succinctly summarize the longer history of mereology:

  • Burkhardt, Hans, and C. A. Dufour. “Part/Whole I: History.” In Handbook of Metaphysics and Ontology. Edited by Hans Burkhardt and Barry Smith, 663–673. Munich: Philosophia, 1991.

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    Includes brief passages on Atomism, Plato, Aristotle, Boethius, Leibniz, and Kant.

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  • Simons, Peter. “Part/Whole II: Mereology since 1900.” In Handbook of Metaphysics and Ontology. Edited by Hans Burkhardt and Barry Smith, 673–675. Munich: Philosophia, 1991.

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    Includes brief passages on principles of tenseless mereology, tensed mereology, and modal mereology.

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Ancient

The ancient philosophers discussed many of the same topics that still garner attention today—from mereological simples and gunk to the nature of composition; see, for instance, Nolan 2006 on the former, and Harte 2002 on the latter. By contemporary light, we might think the Stoics had odd views when it comes to mereology. Parmenides, it seems, denied the possibility of parts. Zeno, in contrast, relied upon the assumption that there are parts. Neo-Aristotelian views have recently been advocated by, for instance, Koslicki 2008. Neoplatonists also commented on part-whole relations, as Baltzly 2008 discusses.

Medieval

Discussions of mereology continued in medieval philosophy. Boethius was, in many ways, the principal contributor to medieval discussions of mereology. However, others—such as Abelard and Aquinas—made noteworthy contributions here as well. Arlig 2015 and Henry 1991 highlight the key contributions.

Modern

Leśniewski 1992, along with Leonard and Goodman 1940, kick-started contemporary discussions of mereology by defining mereology as it’s generally understood today. The work of Husserl (discussed in Simons 1982) also played a foundational role. Interest in mereology has continued to grow in the 21st century, and its philosophical discussions have gained increasing attention over the last few decades.

  • Leonard, Henry, and Nelson Goodman. “The Calculus of Individuals and Its Uses.” Journal of Symbolic Logic 5.2 (1940): 45–55.

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    Articulates a calculus of individuals and demonstrates the work it can do. Further develops the work undertaken in Leśniewski 1992. This article plays a foundational role in contemporary mereology.

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  • Leśniewski, Stanisław. Collected Works. 2 vols. Edited by Stanisław J. Surma, Jan T. Srzednicki, and D. I. Barnett. Dordrecht, The Netherlands: Kluwer, 1992.

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    Lešniewski introduced what would become classical extensional mereology. Originally published in 1916, in Polish, this work is noteworthy as it plays a foundational role in contemporary mereology. Lešniewski is credited with coining the term mereology as it’s used today.

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  • Simons, Peter. “The Formalisation of Husserl’s Theory of Wholes and Parts.” In Parts and Moments: Studies in Logic and Formal Ontology. Edited by Barry Smith, 113–159. Munich: Philosophia, 1982.

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    In his third Logical Investigation, originally published in 1901, Husserl presented a formal theory of mereology and highlighted connections with other ontological concepts. Here Simons clarifies and interprets Husserl’s work, and argues that it has an important role to play in ontology.

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Mereological Systems

The nature of a mereology, and which principles it espouses, is a core issue within mereology. Today, classical extensional mereology is widely regarded as the standard mereology. Extensional mereologies feature an extensionality principle where the sameness of proper parts across, say, x and y is necessary and sufficient for sameness with no further qualification. Classical extensional mereology is, as the name suggests, one such mereology; it features the following principles: Extensionality: if x and y have the same proper parts, then they are identical. Asymmetry: if x is a proper part of y, then y is not a proper part of x. Transitivity: if x is a proper part of y, and y a proper part of z, then x is a proper part of z. Weak Supplementation: if x is a proper part of y, then y has a part disjoint from x. Summation: for any disjoint x and y, there is a unique mereological fusion which features all and only x and y. The key terms here are defined in the common way: x is a proper part of y if and only if x is a part of y, but x is not identical to y; x overlaps y if and only if x and y have a common proper part; x is disjoint from y if and only if x and y do not overlap. While classical extensional mereology is commonly regarded as the standard mereology, reservations about it have been raised; classical extensional mereology is not uncontroversial. As Cotnoir 2013 explains, we might wonder if we should accept all and only the above principles? Which plausible principles does classical extensional mereology lack? Which of its principles are implausible? Whichever principles we want to endorse, do they depend on the sorts of entities under consideration? Some reject the extensionality principle because they think, for instance, that a lump of clay and a statue made out of it have all the same proper parts—yet the statue and the clay are not identical as they have different properties (e.g., the clay can survive an episode of being squished, while the statute cannot). As such, for example, discussions here sometimes overlap with discussions of Composition as Identity.

  • Cotnoir, Aaron. “Strange Parts: The Metaphysics of Non‐classical Mereologies.” Philosophy Compass 8.9 (2013): 834–845.

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    An excellent and clearly written starting point for those interested in the debate surrounding classical extensional mereology itself. Cotnoir discusses some of the key problems and counterexamples that the core principles of classical extensional mereology face.

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Classical Extensional Mereology and its Challenges

Hovda 2009 nicely clarifies key aspects of classical extensional mereology. Those who reject it are typically driven to either non-extensional or non-classical mereologies. Cotnoir 2010 highlights some virtues of a non-extensional mereology. It’s important to note that non-classical mereologies are not based in non-classical logic—though there are such mereologies discussed in the literature—instead, non-classical mereologies are so-called because they are weaker than classical extensional mereology. Cotnoir and Bacon 2012 discuss a division between well-founded and non-well-founded mereology that also arises in the literature. Well-founded mereologies rule out gunk and parthood loops—e.g., cases where x is a proper part of y, while y is also a proper part of x. But a mereology need not be well-founded; certain problematic cases (e.g., from time travel) provide motivation for a non-well-founded mereology.

  • Cotnoir, Aaron. “Anti‐Symmetry and Non‐Extensional Mereology.” Philosophical Quarterly 60.239 (2010): 396–405.

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    Cotnoir develops a non-extensional mereology that rejects the anti-symmetry of parthood, giving the anti-extensionalist the resources to handle some objections that have been previously levied.

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  • Cotnoir, Aaron, and Andrew Bacon. “Non-Wellfounded Mereology.” The Review of Symbolic Logic 5.2 (2012): 187–204.

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    A study of non-well-founded mereology. In particular, the authors highlight the appeal of non-well-founded mereology, survey some applications for non-well-founded mereology, and discuss extensionality and supplementation principles with non-well-founded mereology in mind.

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  • Hovda, Paul. “What Is Classical Mereology?” Journal of Philosophical Logic 38.1 (2009): 55–82.

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    Hovda doesn’t take a stake here on whether or not classical mereology is plausible, but rather examines the common definitions of a mereological fusion and clarifies the salient concepts.

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  • Johnston, Mark. “Parts and Principles: False Axioms in Mereology.” Philosophical Topics 30.1 (2002): 129–166.

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    Johnston discusses how mereology is to be best understood, with regard to mereological sums and constitution. He ultimately argues that mereology should be reconceived in key ways. Clearly written and quite accessible.

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Mereology and Set Theory

David Lewis, in Lewis 1991, famously sought to bridge the gap between mereology and set theory. Yi 1999 argues that the Lewisian proposal is problematic, while Forrest 2002 builds on the foundation laid by Lewis. But even without Lewis’s efforts, there are many parallels between mereology and set theory. For instance, set theory features a similar extensionality principle (where two sets are identical if and only if they have all and only the same members). Like many of the other topics, much is controversial here.

Parthood

The issue of parthood is in many ways the core issue in philosophical discussions of mereology. Some parthood relations are functional, such as the steering wheel as a part of the car, while others are more arbitrary—like the left half of the tree. Typically, but not always, mereologists are interested in the sort of part typified by that second example: proper parts. Crucially, a proper part is less than the whole (whereas the whole is an improper part of itself). McDaniel 2010 offers a fine introduction and overview of the issues particular to parthood. Simons 1987 plays an important role in the contemporary literature and is essential reading.

  • McDaniel. “Parts and Wholes.” Philosophy Compass 5.5 (2010): 412–425.

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    McDaniel focuses his discussions on a few key questions: “How general is parthood? Are there different kinds of parthood or ways to be a part? Can two things be composed of the same parts? When does composition occur? Can material objects gain or lose parts? What is the logical form of the parthood relation enjoyed by material objects?” (p. 412).

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  • Simons, Peter. Parts: A Study in Ontology. Oxford: Clarendon, 1987.

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    In many ways, this is the standard book on contemporary mereology. Topics covered include the logic of parthood, temporary parts, composition, essential parts, and more.

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Parts and the Part-Whole Relation

Some of the core questions that arise in relation to parthood include: Is the parthood relation a two-place relation (between a part and a whole)? The standard answer is that it is, but could it instead actually be a three- or four-place relation? Gilmore 2009 argues in favor of four-place parthood. Can an object have a part twice over? Bennett 2013 highlights the difference between being a material part and a mere parthood slot. Does quantum physics carry any consequences for the nature of parthood? Maudlin 1998 discusses this. What are the different kinds of parts? Are there, for instance, important differences between temporary parts, timeless parts, and temporal parts? Fine 1999 provides an answer that there are such differences and that they are important. Van Inwagen 1981, Parsons 2004, and van Inwagen 2006 all make insightful remarks about the parts of a whole, and how those parts relate to that particular whole; if at a loss as to where to enter this literature, these three would be a safe bet.

  • Bennett, Karen. “Having a Part Twice Over.” Australasian Journal of Philosophy 91 (2013): 83–103.

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    Bennett presents and discusses a distinction between parthood “slots,” and actual material parts that occupy such slots. For instance, the car will have four slots for tire parts and, possibly, four tires occupying those slots. She explains the ways in which such a distinction is both intuitive and useful.

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  • Cruse, Alan. “On the Transitivity of the Part-Whole Relation.” Journal of Linguistics 15.1 (1979): 29–38.

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    Cruse evaluates whether or not we should think the part-whole relation is transitive. His principle interest is in the semantics of parthood and its use in language. He diagnoses some of the peculiar ways in which we talk about parts, and discusses the implications.

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  • Fine, Kit. “Things and Their Parts.” Midwest Studies in Philosophy 23 (1999): 61–74.

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    Fine highlights a distinction between temporary parts and timeless parts, and explains how they relate to a whole in different ways. Roughly, temporary parts are parts of a whole relative to a time (e.g., this particular bottle of scotch is only part of the liquor cabinet from this time to that), whereas timeless parts are not (e.g., carbon is part of carbon monoxide).

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  • Fine, Kit. “Towards a Theory of Part.” Journal of Philosophy 107.11 (2010): 559–589.

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    Sketches a very general framework of part-whole, in which mereology is merely a small branch.

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  • Gilmore, Cody. “Why Parthood Might Be a Four-Place Relation, and How It Behaves If It Is.” In Unity and Time in Metaphysics. Edited by Ludger Honnefelder, Edmund Runggaldier, and Benedikt Schick, 83–133. Berlin: de Gruyter, 2009.

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    Parthood is commonly taken to be a two-place relation, where x is a part of a whole, y. The chief rival is three-place parthood, where x is a part of a whole y at z (e.g., a space-time region). Gilmore rejects both, and argues in favor of four-place parthood, where x at w is a part of a whole y at z (e.g., w is the location of x, and z the location of y).

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  • Maudlin, Timothy. “Part and Whole in Quantum Mechanics.” In Interpreting Bodies. Edited by Elena Castellani, 46–60. Princeton, NJ: Princeton University Press, 1998.

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    Maudlin considers some of the part-whole consequences of quantum physics. Most notably, that quantum theory supports holism (the thesis that a whole is something more than the sum of its parts) over reductionism (wholes can be understood merely in terms of their parts).

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  • Parsons, Josh. “Dion, Theon, and DAUP.” Pacific Philosophical Quarterly 85.1 (2004): 85–91.

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    Parsons objects to van Inwagen 1981. He argues that van Inwagen’s argument against DAUP relies on the rejection of what Parsons calls a plausible “remainder principle.” Roughly, the idea that if P is a proper part of O, then there’s another object that is distinct from O (i.e., the remainder of O, without P).

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  • van Inwagen, Peter. “The Doctrine of Arbitrary Undetached Parts.” Pacific Philosophical Quarterly 62 (1981): 123–137.

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    Van Inwagen introduces the doctrine of arbitrary undetected parts (DAUP)—roughly, the thesis that “for every material object M, if R is the region of space occupied by M at time t, and if sub-R is any occupiable sub-region of R whatever, there exists a material object that occupies the region sub-R at t” (p. 123). While he believes DAUP is widely accepted, he argues that arbitrary undetached parts do not exist.

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  • van Inwagen, Peter. “Can Mereological Sums Change Their Parts?” Journal of Philosophy 103.12 (2006): 614–630.

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    Van Inwagen seeks to clarify the concept of a mereological sum, and he argues that mereological sums can change their parts.

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Temporal Parthood

Temporal parthood amounts to something of a special issue here. Olson 2006 nicely clarifies key concepts. We might be tempted to think views about temporal parts would be isomorphic with views about parthood tout court, but this may be too hasty. While even the eternalist (a theory of the nature of time, where all times are equally real) thinks time is very much like space, she does not think time is exactly like space. And, importantly, the ways in which they differ give rise to unique considerations about the nature of temporal parts—including whether or not anything could have such parts. Thomson 1983, for instance, comes out against temporal parts; Sider 2003, in contrast, is a proponent of temporal parts. Unsurprisingly, then, the issue here overlaps the persistence debate. Persistence concerns how objects exist over time, and the two chief rivals here are endurantism and perdurantism. According to the former, persisting objects persist by being wholly located at every time through which they persist; consequently, many regard enduring objects as at most 3D objects. In contrast, according to the latter, persisting objects persist by having temporal parts at all the times through which they persist; perduring objects are typically 4D objects with temporal parts that are analogous to their spatial parts. Endurantists deny the existence of temporal parts. Hawley 2015 provides more on the persistence debate and its connection here. Notice that we’ve introduce a locative relation here—wholly located—which is noteworthy as it highlights the role played by a theory of location in the persistence debate.

  • Hawley, Kathrine. “Temporal Parts.” In The Stanford Encyclopedia of Philosophy. Edited by Edward Zalta. Stanford, CA: Stanford University, 2015.

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    A nice starting point to special issues that pertain to temporal parthood; as is natural for discussions of temporal parthood, much of the discussion here gravitates toward theories of persistence.

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  • Olson, Eric. “Temporal Parts and Timeless Parthood.” Noûs 40.4 (2006): 738–752.

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    Olsen clarifies how we should understand temporal parts. Through this, he argues, we can gain a deeper appreciation of perdurantism as well as the nature of the disagreement between perdurantists and endurantists.

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  • Sider, Theodore. “Against Vague Existence.” Philosophical Studies 114.1 (2003): 135–146.

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    Presents an argument in defense of temporal parts from the premise that existence is never vague (this argument is prompted by an objection from Kathrin Koslicki, which was aimed at an earlier similar argument by Sider provided elsewhere).

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  • Thomson, Judith. “Parthood and Identity over Time.” Journal of Philosophy 80 (1983): 201–220.

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    A classic paper against temporal parts. The crux of Thomson’s argument is that the notion of temporal parthood is incoherent.

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Mereological Essentialism

Chisholm 1973 is typically cast as the key contemporary proponent of mereological essentialism. However, there are various theses that often bear the name “mereological essentialism,” and it’s not clear that Chisholm is ultimately interested in the most common characterization of the view. In the extreme, we find the typical characterization of mereological essentialism: the thesis that, for any proper part of an object, that proper part is a part of the object whenever it exists and in any possible world where it exists—the object has all its parts essentially. Here, then, the actual or merely possible addition, replacement, loss, or destruction of any proper part—no matter how superficial it may seem—marks the end of the object. In some discussions, the characterization is reined in—sometimes by limiting it to the modal case, and other times to the temporal case. Plantinga 1975 highlights some key counterexamples to mereological essentialism. Jubien 2001 and van Cleve 1986 provide further arguments in support of mereological essentialism.

  • Chisholm, Roderick. “Parts as Essential to Their Wholes.” Review of Metaphysics 26 (1973): 581–603.

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    Chisholm spearheaded contemporary interest in mereology essentialism (by defending it). He argues mereological essentialism is intuitive. For instance, if you have a table made of merely a board and a stump, and you swap out either the board or the stump, you clearly end up with a different table than the original.

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  • Jubien, Michael. “Thinking about Things.” Philosophical Perspectives 15 (2001): 1–15.

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    To great effect, Jubien milks the idea that if you have some arbitrary thing, T, and you take away any proper part of it, the remainder cannot be identical to T. According to Jubien, a defender of mereological essentialism, ordinary objects are merely some stuff instantiating certain properties. So if an object really is just some stuff, it cannot be the case that we have the same object (the very same stuff) without having all of it (all of its parts).

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  • Plantinga, Alvin. “On Mereological Essentialism.” Review of Metaphysics 28 (1975): 468–476.

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    Plantinga objects to Chisholm 1973: even if his bipartite table example supports mereological essentialism, we can easily find counterexamples. For instance, of that same table, imagine you chip a few molecules off of it. Surely you still have the same table. If so, mereological essentialism is false.

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  • van Cleve, James. “Mereological Essentialism, Mereological Conjunctivism, and Identity through Time.” Midwest Studies in Philosophy 11.1 (1986): 141–156.

    DOI: 10.1111/j.1475-4975.1986.tb00491.xSave Citation »Export Citation » Share Citation »

    Van Cleve argues that ordinary objects must be either mereological sums, or they must coincide with sums; the latter is not plausible, so the former must be the case.

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Simples and Gunk

When we start thinking about parthood, we might naturally wonder whether or not there can be such a thing as a smallest proper part. Or, rather, for any proper part, if it will have a further proper part. This divide captures the debate over simples and gunk. On the one hand, we have the proponent of simples: she argues that it’s at least possibly the case that, for some class of entity, it has a smallest proper part; something is mereologically simple if and only if it has no proper parts. In this way, a mereological simple corresponds to the classical notion of an atom. In ancient philosophy, mereological simples were discussed as indivisible entities; today, some argue that—despite not having any proper parts—simples may be possibly divisible. On the other hand, the proponent of mereological gunk—a term coined by Lewis 1991 (cited under Mereology and Set Theory)—argues that for anything we might point to as a proper part, it will have a further proper part. This is a very old debate, but it still very much alive today. And while the focus in discussions of these issues is often on material objects, there is an adjacent discussion that concerns space-time regions. It is an open question how linked (or separate) the object-question and the region-question should be. For instance, can a mereologically simple object be located at a gunky space-time region (or the reverse)? Or, instead, does one position on the object-question carry a corresponding commitment on the region-question? This way of characterizing simples is not uncontroversial, though. Markosian 1998 makes for a good starting place on this issue, while McDaniel 2007 provides a competing characterization. (While not discussed as frequently as simples and gunk, there is also junk. A junky world is one in which, for any mereological sum, f, there is a further mereological sum which has f as a proper part. While an endorsement of gunk and an endorsement of junk are crucially different, with different ontological consequences, there are parallels between gunk and junk; for instance, while gunk never “bottoms out,” junk never “tops out.”) Be sure to see Hudson 2004 (cited under Anthologies), a special issue of The Monist, as well as the following entries. Gilmore 2014 (cited under Location) also discusses mereological simples and provides a fine introduction to core issues.

  • Hudson, Hud. “Simples and Gunk.” Philosophy Compass 2.2 (2007): 291–302.

    DOI: 10.1111/j.1747-9991.2007.00068.xSave Citation »Export Citation » Share Citation »

    Excellent introduction to mereological simples, extended simples, and gunk. Hudson outlines the core concepts at play and highlights the issues around which the discussions tend to gravitate.

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  • Markosian, Ned. “Simples.” Australasian Journal of Philosophy 76 (1998): 213–226.

    DOI: 10.1080/00048409812348361Save Citation »Export Citation » Share Citation »

    This paper kicked off the contemporary interest in mereological simples. Markosian articulates what’s known as the Simple Question: “What are the necessary and jointly sufficient conditions for an object’s being a simple?” (p. 214), and defends the maximally continuous view (MaxCon) as the answer: O is a simple if and only if it’s a maximally continuous object.

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  • McDaniel, Kris. “Brutal Simples.” In Oxford Studies in Metaphysics. Vol. 3. Edited by Dean Zimmerman, 233–265. Oxford: Oxford University Press, 2007.

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    McDaniel defends a rival answer to the Simple Question, which he calls the Brutal view, according to which “there is no non-mereological criterion for being a simple” (233). In the process, McDaniel voices objections to the other answers that have been previously raised.

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Extended Simples

Typically, to say that x is mereologically simple is taken to entail that x is point-size. However, there might also be extended mereological simples: an object, or region, is an extended mereological simple if and only if it has no proper parts and it occupies a greater than point-size region. Notice that an extended mereological simple could be spatially extended, and temporally complex or instantaneous; or, an extended mereological simple could be temporally extended, and spatially point-size or spatially complex. Or, of course, an extended mereological simple could be extended in both space and time. McDaniel 2007 defends extended simples, and Parsons 2004 strengths the case. While the focus is typically on material objects, we might also ask about regions. Braddon-Mitchell and Miller 2006 focuses on the region-question and argues that spatial regions might ultimately be extended simples.

  • Braddon-Mitchell, David, and Kristie Miller. “The Physics of Extended Simples.” Analysis 66.291 (2006): 222–226.

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    Braddon-Mitchell and Miller argue that contemporary science seems to give us reason to think that spatial regions may ultimately be extended simples (i.e., that the smallest possible region of space must be greater than point-sized).

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  • McDaniel, Kris. “Extended Simples.” Philosophical Studies 133 (2007): 131–141.

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    McDaniel defends the possibility of extended simples via an argument that shape properties are extrinsic properties.

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  • McKinnon, Neil. “Vague Simples.” Pacific Philosophical Quarterly 84.4 (2003): 394–397.

    DOI: 10.1046/j.1468-0114.2003.00181.xSave Citation »Export Citation » Share Citation »

    McKinnon argues that even if there couldn’t be vague identities, nor vague composition, objects—such as extended simples—could nevertheless have vague boundaries.

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  • Parsons, Josh. “Distributional Properties.” In Lewisian Themes. Edited by Frank Jackson and Graham Priest, 173–180. Oxford: Oxford University Press, 2004.

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    Outlines and defends distributional properties. Parsons argues that a distributive properties framework can, for instance, address certain worries about heterogeneous extended simples. For instance, an extended simple that is principally white with red-dotted areas can be understood as having a non-uniform polka-dotted color distributional property (rather than, say, red parts and white parts).

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Gunk

In contrast with mereological simples, there is gunk (a term coined by Lewis 1991, cited under Mereology and Set Theory). An object, or region, is gunky if and only if every part of it has a further proper part, and all those proper parts have further proper parts themselves, and so on. Colloquially, the proper parts of gunk never “bottom out,” since they will always be made up of further proper parts. Sider 1993 and Zimmerman 1996 provide strong cases in support of gunk. McDaniel 2006 focuses on the possibility of connections between a gunky region and that which occupies it.

The Special Composition Question

Van Inwagen 1990 introduced the Special Composition Question: when do some things compose another thing? A substantial literature has emerged in response to it, and the full range of possible answers have their proponents: some say always (mereological universalists), some say never (mereological nihilists), while others say sometimes (restricted composition theorists).

  • van Inwagen, Peter. Material Beings. Ithaca, NY: Cornell University Press, 1990.

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    Here van Inwagen introduced the Special Composition Question. His own answer is that composition only occurs when the whole is alive. Thus the world is populated only by mereological simples and living organism (strictly speaking, there are no tables or chairs).

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Mereological Nihilism

According to the mereological nihilist, all objects are mereologically simple; no objects mereologically fuse to form a further object in our ontology. Williams 2006 defends the mereological nihilist, while Schaffer 2007 highlights some of the commitments had by the nihilist. Much like mereological essentialism, most think mereological nihilism is radical and counterintuitive—for instance, surely I am a mereological fusion.

  • Schaffer, Jonathan. “From Nihilism to Monism.” Australasian Journal of Philosophy 85.2 (2007): 175–191.

    DOI: 10.1080/00048400701343150Save Citation »Export Citation » Share Citation »

    Schaffer argues that from mereological nihilism, we get existence monism. Existence monism is the thesis that the only object that exists is the world (in its entirety), and that this object is mereologically simple.

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  • Williams, J. R. G. “Illusions of Gunk.” Philosophical Perspectives 20.1 (2006): 493–513.

    DOI: 10.1111/j.1520-8583.2006.00117.xSave Citation »Export Citation » Share Citation »

    Just as the mereological nihilist is committed to the view that mereological simples exist, the possibility of gunk seems to provide an argument against nihilism. Williams presents two responses to such an objection on behalf of the nihilist.

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Mereological Universalism

Mereological universalism, also known as unrestricted mereological composition, maintains that for any two objects, the objects mereological fuse (or sum) to form a further object. Consider, for instance, an atom in one of your fingernails and some particular speck of space dust near Pluto. According to the mereological universalist, they form an object that has the same ontological status as you. Surely, this view is no more intuitively appealing than mereological nihilism (some folks might say). While Daniel Korman is ultimately a restricted composition theorist, in Korman 2008 he gives strategic advice to the universalist. Rea 1998 defends universalism, while Varzi 2009 and Cameron 2007 discuss what might follow from universalism.

  • Cameron, Ross. “The Contingency of Composition.” Philosophical Studies 136.1 (2007): 99–121.

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    Do the facts that concern when composition occurs hold necessarily? Cameron argues that Composition as Identity, or at least the version of it that entails mereological universalism, is unfounded. He also objects to other arguments in favor of universalism.

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  • Korman, Daniel. “Unrestricted Composition and Restricted Quantification.” Philosophical Studies 140.3 (2008): 319–334.

    DOI: 10.1007/s11098-007-9147-3Save Citation »Export Citation » Share Citation »

    Mereological universalism is at odds with common sense. Sometimes, proponents explain this away by saying we colloquially engage in a kind of restrictivism, where we exclude strange fusions for the things we quantify over. Korman argues that this is a mistake. Instead, universalists should tackle this problem head-on.

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  • Rea, Michael. “In Defense of Mereological Universalism.” Philosophy and Phenomenological Research 58.2 (1998): 347–360.

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    Rea responses to a particular argument against mereological universalism, and then offers a novel argument in favor of universalism. Crucially, Rea argues, belief in artifacts commits one to accept universalism.

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  • Varzi, Achille. “Universalism Entails Extensionalism.” Analysis 69.4 (2009): 599–604.

    DOI: 10.1093/analys/anp102Save Citation »Export Citation » Share Citation »

    Varzi argues that mereological universalism entails extensionalism—the idea that “no two things have exactly the same proper parts” (p. 599)

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Restricted Composition

Restricted composition might seem intuitive, but the intuitive force it has tends to evaporate when we try to work out the details about where we want to draw the line. At the end of the day, though, many think it’s not clear what role intuitions should play in discussions about the Special Composition Question. Markosian 1998 outlines an answer to the Special Composition Question that isn’t quite as restricted as the one offered by van Inwagen 1990 (cited under Special Composition Question).

  • Markosian, Ned. “Brutal Composition.” Philosophical Studies 92.3 (1998): 211–249.

    DOI: 10.1023/A:1004267523392Save Citation »Export Citation » Share Citation »

    In response to van Inwagen’s Special Composition Question, Markosian argues against mereological nihilism and against mereological universalism. He presents an argument in favor of the intuitive response: sometimes. This paper can act as a fine entry point to the literature on this issue.

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Composition as Identity

According to proponents of Composition as Identity, a whole is the same as its parts. There is, though, no clear consensus about how this thesis should be defined. Some, for instance, maintain that a whole is identical with each of its parts distributively (i.e., the claim that identity can be a one-many relation), but not collectively, while others assert that a whole is identical with each of its parts distributively and collectively, and yet others argue that a whole is identical with each of its parts collectively, but not distributively. How we understand the nature of identity is, naturally, crucial to this debate—in addition to the part-whole relation. Van Inwagen 1994 discusses Composition as Identity and its connection with other mereological concerns. The papers in Cotnoir and Baxter 2014 (cited under Anthologies) push the Composition as Identity debate forward and in new directions; this volume can act as a fine starting point for newcomers, as can Wallace 2011a and Wallace 2011b.

  • Sider, Theodore. “Nothing Over and Above.” Grazer Philosophische Studien 91 (2015): 191–216.

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    Provides an analysis of what might be regarded as the central mantra of the Composition as Identity theorist: the whole is nothing over and above the parts. Is this slogan intelligible? Can its inherent vagueness be detailed away? Is it the case that Composition as Identity offers the best way of understanding the slogan? Sider aims to provide answers.

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  • van Inwagen, Peter. “Composition as Identity.” Philosophical Perspectives 8 (1994): 207–220.

    DOI: 10.2307/2214171Save Citation »Export Citation » Share Citation »

    A discussion of David Lewis on Composition as Identity, and on whether or not mereology is ontologically innocent.

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  • Wallace, Megan. “Composition as Identity: Part 1.” Philosophy Compass 6.11 (2011a): 804–816.

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    Wallace outlines the core aspects of the view known as Composition as Identity, distinguishes three varieties of the view, discussions popular objections against the view, and in the process notes reasons why some are motivated to endorse the view.

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  • Wallace, Megan. “Composition as Identity: Part 2.” Philosophy Compass 6.11 (2011b): 817–827.

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    Wallace discusses a common objection to Composition as Identity. In the process, she highlights different versions the objection has taken and assesses potential replies on behalf of the Composition as Identity theorist. A continuation of Wallace 2011a.

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Location

According to the substantivalist, there exists a duality of objects and regions; objects and regions are, then, bound by occupation or location relations (as material objects are “contained in” regions). You might be, for instance, partially located at some region. And, perhaps, you’re wholly located at a super-region of that region in which you’re partially located. Are all regions eligible candidates here? Uzquiano 2006 tackles this sort of question. What is the nature of these locative relations? Parsons 2007 offers a detailed account. There is a natural interplay between mereology and the ways in which an object may be located at different regions. Gilmore 2014 provides a nice overview, while Hawthorne and Sider 2006 and Saucedo 2011 give further discussion of the finer points. Furthermore, concerns about colocation and multilocation, naturally arise here. Kleinschmidt 2014 (cited under Anthologies) is essential reading for those interested in locative relations and the connections with mereology.

  • Casati, Roberto, and Achille Varzi. Parts and Places: The Structures of Spatial Representation. Cambridge, MA: MIT, 1999.

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    The authors aim to clarify how we understand the nature of space and the relations between spatial regions and that which occupies them (or occurs in them, in the case of events). In doing so, Casati and Varzi examine the interplay between mereology, topology, boundaries, and locative relations. Events, in addition to objects, are discussed. Mereological essentialism is also discussed (and endorsed).

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  • Gilmore, Cody. “Location and Mereology.” In The Stanford Encyclopedia of Philosophy. Edited by Edward Zalta. Stanford, CA: Stanford University, 2014.

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    Introduces and discusses locative relations, including the question of which locative relation should be considered fundamental, and concerns with multilocation. Gilmore also highlights how the issues here relate to mereology in general. The “additional arguments” appendix is easily overlooked, but worth reading.

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  • Hawthorne, John, and Theodore Sider. “Locations.” In Metaphysical Essays. Edited by John Hawthorne, 85–109. Oxford: Oxford University press, 2006.

    DOI: 10.1093/acprof:oso/9780199291236.003.0005Save Citation »Export Citation » Share Citation »

    The authors here examine the modal considerations of reifying locations and highlight some of the modal consequences of relationalism.

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  • Parsons, Josh. “Theories of Location.” In Oxford Studies in Metaphysics. Vol. 3. Edited by Dean Zimmerman, 201–232. Oxford: Oxford University Press, 2007.

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    In this thoroughly excellent paper, Parsons details his theory of location, which is designed to be neutral with regard to metaphysical disputes.

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  • Saucedo, Raul. “Parthood and Location.” In Oxford Studies in Metaphysics. Vol. 6. Edited by Karen Bennett and Dean Zimmerman, 223–284. Oxford: Oxford University press, 2011.

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    Saucedo considers how the mereological structure of the material world and the mereological structure of space-time might come apart. In the process, the ways in which the material world is located in space-time are discussed.

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  • Uzquiano, Gabriel. “Receptacles.” Philosophical Perspectives 20.1 (2006): 427–451.

    DOI: 10.1111/j.1520-8583.2006.00114.xSave Citation »Export Citation » Share Citation »

    Which regions of space are receptacles, wherein we might find objects? Uzquiano examines “the extent to which the answer to our question is constrained by various mereological relations on material objects and their interaction with the relation of exact location” (p. 427).

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Colocation and Multilocation

In cases of colocation, we seem to have two (seemingly distinct) things occupying the same region. In cases of multilocation, we seem to have one thing occupying multiple disjoint regions. While colocation and multilocation present separate worries, many consider both to be problematic: How can two seemingly distinct objects occupy the same region at the same time (think of the popular clay statue case)? How can one object exist at multiple disjoint regions (think of the enduring object, wholly located at many different times)? Passionate arguments can be found on both sides of both of these issues. Wiggins 1968 and Thomson 1998 are classic papers on colocation. Paul 2006 and Gilmore 2007 also focus on colocation; Barker and Dowe 2003, Balashov 2008, and Kleinschmidt 2011 all focus on multilocation and mereological problems. A greater appreciation of locative relations enables us to better understand positions in various debates in metaphysics. For instance, by employing a variety of locative relations, we can better appreciate the differences between competing theories of persistence, and a framework of locative relations allows us to solve certain problems—see, for instance, Daniels 2014 on this.

  • Balashov, Yuri. “Persistence and Multilocation in Spacetime.” Philosophy and Foundations of Physics 4 (2008): 59–81.

    DOI: 10.1016/S1871-1774(08)00004-1Save Citation »Export Citation » Share Citation »

    Lays out the main positions in the persistence debate, with an eye on modes of location, with the ultimate aim of adapting the theories of persistence for a Minkowski space-time.

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  • Barker, Stephen, and Phil Dowe. “Paradoxes of Multi-Location.” Analysis 63.2 (2003): 106–114.

    DOI: 10.1093/analys/63.2.106Save Citation »Export Citation » Share Citation »

    Barker and Dowe argue that endurantists face problems in virtue of how enduring objects are multilocated in time. For example, it seems that one can mereologically fuse an enduring object at all the times through which it persists; this fusion will surely be a 4D object. This appears problematic, since the enduring object here is meant to be a 3D object, but it will be identical to this 4D fusion.

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  • Daniels, Paul R. “Occupy Wall: A Mereological Puzzle and the Burdens of Endurantism.” Australasian Journal of Philosophy 92.1 (2014): 91–101.

    DOI: 10.1080/00048402.2013.820764Save Citation »Export Citation » Share Citation »

    Daniels response to the sort of problem raised by Barker and Dowe 2003 (Daniels focuses on a variant case that involves a time-traveling brick). Daniels argues that misunderstandings about the endurantist ontology and locative relations give rise to the alleged problem; by addressing these misunderstandings, a plausible endurantist solution is revealed.

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  • Gilmore, Cody. “Time Travel, Coinciding Objects, and Persistence.” In Oxford Studies in Metaphysics. Vol. 3. Edited by Dean Zimmerman, 177–198. Oxford: Oxford University Press, 2007.

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    Gilmore presents two cases—one involves a fictional time-travel scenario, the other merely utilizes cylindrical space-time. While the time-travel case is similar to the one discussed in Daniels 2014, here Gilmore argues that it gives rise to a problem for perdurantism.

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  • Kleinschmidt, Shieva. “Multilocation and Mereology.” Philosophical Perspectives 25.1 (2011): 253–276.

    DOI: 10.1111/j.1520-8583.2011.00215.xSave Citation »Export Citation » Share Citation »

    Presents cases that demonstrate that multilocation proves problematic for Minimal Mereology. (Minimal Mereology consists of the following axioms: the transitivity of proper parthood, the asymmetry of proper parthood, and weak supplementation.) Kleinschmidt also argues that relativizing parthood would provide no assistance here.

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  • Paul, L. A. “Coincidence as Overlap.” Nous 40 (2006): 623–659.

    DOI: 10.1111/j.1468-0068.2006.00627.xSave Citation »Export Citation » Share Citation »

    Do coinciding objects share their spatiotemporal proper parts? How can coinciding objects, which have all the same matter and locations, not also have all the same properties? In response, Paul argues that a property mereology is key; through it we can see that coinciding objects overlap with respect to their spatiotemporal proper parts, but not with respect to all their property parts.

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  • Thomson, Judith. “The Statue and the Clay.” Nous 32 (1998): 149–173.

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    Thomson defends the possibility of coincidence. She argues that an appeal to temporal parthood doesn’t help solve the problem of the statue and the clay.

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  • Wiggins, David. “On Being in the Same Place at the Same Time.” Philosophical Review 77.1 (1968): 90–95.

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    A classic paper on coincidence. Wiggins clarifies what we mean when we talk about coincidence.

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Mereotopology

Discussions of locative relations and mereotopology do not always overlap, but they do make natural bedfellows. Both, in a sense, concern the application of mereological concepts to various aspects of space-time. In this regard, Varzi 1996 sets the stage. In mereotopology, and elsewhere, concerns about boundaries—the absolute extremity of an object or region—arise. Do boundaries count as parts of what they bound? How should we handle vague boundaries, as in the case of a cloud? Varzi 1997 provides salient comments here. And what about holes, like those found in a block of Swiss cheese? See Lewis and Lewis 1970, as well as Casati and Varzi 2014, on this issue. These and related questions feature prominently in mereotopological discussions.

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