Mereology is the philosophical study of parthood and composition. These are fairly commonplace relations. My legs are part of my body; the handle is part of the mug; Stewart Island is part of New Zealand. Canis Minor comprises two observable celestial bodies, Gomeisa and Procyon (itself a binary star system). Like all stars, Gomesia is composed of gases, mostly hydrogen and helium. The philosophical project is of course not concerned with creating a catalogue of the parts of things (although perhaps some philosophers will engage in conceptual analysis, reflective equilibrium, experimental philosophy, etc., to settle specific ‘compositional’ questions—a toy example being whether we ought consider, say, the ice cubes in the glass a proper part of the cocktail or not), but to inquire into the nature of the two relations, parthood and composition. Indeed, this is the ‘narrow’ understanding of mereology that Giorgio Lando adopts in Mereology: A Philosophical Introduction. Accordingly, mereological inquiry “is only about the formal features of the relation of parthood, and about identity and existence conditions for wholes” (p. 2, emphasis in original). Thus Lando leaves debate about other concepts in the vicinity such as essentiality, dependence, supervenience, and so on, to other areas of metaphysics. (I shall set aside questions about whether this move is legitimate or not—I will simply follow Lando’s narrowing of mereology’s domain in his book given its aims and scope.)
In the book, Lando introduces, motivates, and defends a theory about parthood and composition. It is not a novel theory, but a sensible tweak of the view dominant in twentieth century analytic philosophy, Classical Extensional Mereology (CEM), associated with Nelson Goodman, W.V.O. Quine, and David Lewis, among others. Despite its great influence (and its rejection by many contemporary scholars), this is the first book-length exposition and defence of CEM, filling a significant gap in the literature. The writing is clear and accessible, and thus the book deserves its subtitle; I cannot think of a better in-road into modern analytic mereology for the uninitiated reader than via an extended consideration of CEM. That said, there is also much in the book for the initiated. Participants in the debate will want to respond to Lando’s defence of CEM and thought-provoking critique of purportedly intuitive counterexamples.
CEM is the thesis that (1) parthood is transitive (i.e., if A is part of B, and B is part of C, then A is part of C), and (2) given some things, there is a unique thing composed by them. The first conjunct is thus the principle of transitivity applied to parthood; the second is the conjunction of the principles of uniqueness of composition and unrestricted composition. Lando articulates these latter two principles as follows: “given some things, there is at most one thing composed by them” and “no matter how heterogenous and disparate they are, there is at least one thing composed by them” (p. 1; emphasis mine). CEM is usually intended to be a unitary, exhaustive theory of composition and parthood (which has led Kit Fine to dub it ‘mereological monism’). However, Lando restricts its scope to concreta. Fair enough. In my view (admittedly, a nominastically inclined view), for any theory of mereology to be plausible it must do well when it comes to physical objects, first. I’ll return to this point later.
CEM is widely attributed to David Lewis, given his comments in his 1991 book, Parts of Classes. Lando’s defence, however, is not a mere recapitulation of Lewis’s views, since Lando and Lewis part ways on several key issues. Indeed, Lando takes these points of departure to be stances where Lewis’s version “stand at the basis of the discredit into which mereological monism has fallen” (p. 7). First, Lando disagrees that mereology is a logical doctrine. Of course, mereological theses can be axiomatised and expressed in some logical framework, but Lando points out that this does not identify mereology with logic. This issue is discussed in chapters 3 and 10.
Second, Lando emphasises mereological controversies, against Lewis’s claim that mereology is unproblematic, certain, perfectly understood. Plausibly, Lewis is best interpreted as making a normative claim: i.e., “that mereological monism should not be a topic of philosophical controversy” (p. 9). Lando argues that this normative claim too is wrong. The main purpose of the book, Lando writes, is to provide “an in-depth analysis and balanced assessment of mereological monism”, within a nominalistic framework that is “not everyone’s cup of tea” (p. 9).
Third, Lando disagrees about the application of CEM to abstracta. As noted, he explicitly restricts his application of CEM to spatiotemporal, concrete entities. After all, abstract entities (if they exist) are finicky. It is all too easy to use alleged abstracta to violate some mereological principle: one simply stipulates that some abstracta violates it. Lando hopes to show in the book that “abstract entities are both the most difficult and the least important field of application of mereological monism, and there is nothing surprising in the fact that counterexamples to mereological principles can be found among abstract entities. Concrete entities are the decisive field of application for mereological monism” (p. 10). Hear, hear.
To be sure, despite his nominalist leaning, Lando does not outright deny the existence of all abstract entities. After all, debate about which (if any) abstracta exist falls outside Lando’s narrow conception of mereology. Rather, Lando concedes a restriction of the application of CEM to concreta. This is probably the right move for Lando to make. So, “the general thesis of the book is that Classical Extensional Mereology is a highly general theory of parthood and composition. Analogously, mereological monism is understood as the thesis that there is only one highly general theory of parthood and composition. Given these stipulations about terms such as ‘general’ and ‘monism’, the difficulties of mereological monism in the realm of abstract entities do not defeat it” (p. 11; emphasis in original). This is discussed in chapters 5, 8, 12 and 13.
Fourth, and finally, Lando departs from Lewis with respect to the Composition As Identity thesis. As far as Lando is concerned, Lewis’s contention that composition is (like) identity is not an integral part of a defence of CEM and nor is it constitutive of CEM. Although the Composition As Identity thesis has engendered an increasing literature, of which much is orthogonal to a defence of CEM, Lando aims to show that CEM can be presented and defended without a foray into identity, and without “its typical, obscure, tendentiously circular jargon according to which a whole is ‘nothing over and above its parts’, or ‘a whole and its parts are the same portion of reality’” (p. 12). This issue is discussed in the appendix, where Lando argues that the Composition As Identity thesis conflicts with his narrow conception of mereology. The idea is this: “Insofar as Leibniz’s Law is a constitutive principle of identity, to claim that a whole is identical to its parts is to claim either that they share all or some of their properties or that something similar is the case (e.g., that the features of a whole determine the features of its parts, and vice versa). This consequence has nothing to do with the formal features of parthood, and with the identity and existence conditions for wholes” (p. 12). Thus the Composition As Identity thesis “runs counter to the need to separate the explanatory scope of mereological monism from other areas of metaphysics” (p. 13).
So, in summary, Lando supports CEM—the thesis that parthood is transitive and that given some things, there is a unique thing composed by them—i.e., the general mereological framework associated with Lewis, except to say “mereology is not logic, but a problematic metaphysical doctrine; it fails to work for many abstract entities; and we should not say that a whole is identical to its parts. Still, mereological monism is a defensible and promising metaphysical doctrine about concrete entities. This—I contend—is the interesting core of mereological monism” (p. 13).
The book is split into three parts: The Methodology of Mereological Monism (Part One), Extensionalism (Part Two), and Unrestricted Composition (Part Three). I briefly outline each in turn.
Part One (chapters 1-4) explains what CEM, understood as a highly general thesis about composition and parthood, is all about, with an eye on methodological issues. In chapter 1, Lando notes the ambiguous nature of the English lexeme ‘part’ and its cognates. Lando places several constraints on parthood’s formal characterisation by considering some intuitive presuppositions about what it is to be part of something, in the literal sense; he distinguishes genuine, literal parthood (i.e., what mereologists are concerned with) from merely metaphorical parthood (e.g., when lovers proclaim they are both ‘part of’ one another) and other cousins of the notion of parthood at stake in mereological debate (e.g., selective parthood).
Chapter 2 explains why mereology matters: for example, mereological theses place constraints on, and can be used to refute, various metaphysical positions. Taking seriously certain mereological theses also restricts the range of available solutions to various philosophical puzzles. To give just one example that Lando mentions, David Lewis famously argued that set membership is not parthood, given that set membership violates the principle of transitivity, an essential aspect of CEM. The general idea goes as follows. Let L be the set of all Low records (the album by David Bowie), and let DB be the set of all sets of David Bowie records (which thus includes L, and also H, the set of all Heathen’s, E, the set of all Earthling’s, and so on). My copies of Low and Heathen are members of L and H, respectively, but they are not thereby members of DB. Indeed, DB has no records as members whatsoever, but sets. This refutes the hypothesis that set membership is formally equivalent to genuine, literal parthood (at least, if we are operating under CEM’s jurisdiction; that is, taking seriously CEM constrains the identity and existence conditions for wholes: having members is not identical to having proper parts).
Chapter 3 is a foray into formality, explicating connections between mereology and formal ontology, and distinguishing various characterisations of formality. Chapter 4 discusses several key concepts (transitivity, reflexivity, and antisymmetry) standardly taken to be features of the parthood relation. Again, take transitivity, an essential feature of genuine parthood, according to CEM. Lando discusses some potential counterexamples; firstly, the idea due to Nicholas Rescher that according to biologists, a mitochondrion is a part of a cell, the cell is a part of a tissue, but the mitochondrion is not a part of the tissue. Lando puts the apparent force of this objection down to a curious feature of the English language. He suggests that removing the indefinite article preceding ‘part’ clears things up: “the mitochondrion is part of the tissue”; after all, “it is in it in a spatial sense” (p. 48, emphasis mine). Transitivity is preserved. Secondly: “The left arm of a Kemalist MP is part of her; the Kemalist MP is part of the parliament. But it seems definitely wrong to claim that the arm is part of the parliament” (p. 49, emphasis in original). The contention that this is an intuitive counterexample, Lando claims, is due to the polysemy of ‘parliament’ (e.g., the building wherein MPs discuss matters, or the social institution of parliament). Note that on whichever equivocation one has in mind, the claim is no longer a viably sensible one about genuine parthood. Alternatively, if ‘parliament’ is taken to mean set of parliamentary members, then we are back in the set theoretic domain of membership, not the mereological domain of parthood. And Lando says set membership “seems to work exactly as the relation between an MP and its parliament” (p. 50). This seems sensible enough to me.
Part Two (chapters 5-9) considers the uniqueness of composition—the principle that given some things, there is at most one thing that all of these things compose—and extensionalism—the connected idea that complex (i.e., multi-part) entities that comprise the same proper parts are numerically identical. Uniqueness of composition implies extensionalism, but not vice versa.
In chapter 5, Lando connects extensionalism to his nominalistic framework. According to the framework adopted, structure is not part of an entities’ composition. The pile of playing cards on my bookshelf comprises 52 cards; were I to build a house of cards, I would not have thereby brought something new into existence (contra mereological pluralists who wish to preserve some variety of realism about structure). The card-house and card-pile are composed of the same parts; they are the same complex entity, just with a different spatial arrangement at different temporal stages. Structure, then, is ‘safely obliterated’. Lando distinguishes his approach from Nelson Goodman’s, and argues that CEM respects Kit Fine’s four principles of obliteration (absorption, collapse, levelling, and permutation).
Chapter 6 distinguishes the uniqueness of composition from extensionalism, and discusses some cases in which the two diverge (so-called ‘fake’ ways of respecting extensionalism but not uniqueness of composition). Thus Lando introduces the reader to the useful Hasse diagram machinery. In chapter 7, Lando argues that alleged counterexamples (ones in which a structured entity and its co-located portion of matter are concerned: e.g., the infamous ‘statue and clay’ example) are reconcilable with extensionalism. The literature on these sorts of cases is massive. Lando argues that as far as these cases are concerned, either some given structured entity and its co-located portion of matter are not in fact distinct (but—following Lewis—can be thought of from different perspectives which select for different modal profiles when considering different counterfactual situations, or which make certain properties—e.g., aesthetic properties—salient), or that they are non-identically composed after all (and thus there is a difference with respect to their parts). He then argues that controversial cases involving change over time, like the Ship of Theseus, do not pose special problems for extensionalism. And in chapter 8, Lando distances extensionalism as a plausible principle about concreta from being a plausible principle about abstracta. He outlines several strategies for reconciling abstracta (e.g., linguistic types) with extensionalism: deny the existence of the abstract entity at stake, deny that the entity is abstract, deny that the entity is involved in the parthood relation at all, or revise the application of parthood so that extensionalism is not violated. Non-extensionally composed abstract objects, were they to exist, would pose a remaining problem for Lando’s view, and he concedes as much. Chapter 9 explores some alternative (non-classical, non-extensional) mereological theories. Lando concludes that although some of these theories are “technically irreproachable and relatively conservative” (p. 65), they are otherwise not well motivated.
An aside: when I began reading this book I assumed that Part Three would be where Lando and I part ways. I can accept parthood’s transitivity and Lando’s nominalism, and the counterexamples to extensionalism/uniqueness of composition do not move me. However, unrestricted composition—the principle that no matter how disparate/heterogeneous some given collection of things are, there is something that these things compose—is, pretheoretically at least, outright bizarre (not to mention overly ontologically profligate). To his merit, Lando goes a long way to offset this worry. My main complaint will be the short shrift given to alternatives, especially mereological nihilism.
In Part Three, then, Lando considers the various arguments in favour of unrestricted composition and finds them convincing. He also analyses, and finds unconvincing, the kind of objection mentioned above: that unrestricted composition is exasperatingly counterintuitive. The defender of CEM need not think that there is any interesting or salient entity that is composed of, say, Big Ben and my red pen. That entity is neither spatially continuous nor causally efficient. But, the idea goes, claiming that these two parts compose something is perhaps little more odd than the idea that Procyon (11.46 light years from Earth) and Gomesia (162 light years from Earth) compose something: Canis Minor. But because Canis Minor is listed in Ptolemy’s 48 constellations (and for other reasons), I for one find it interesting (even though it is not spatially continuous or causally efficient). I cannot say the same for Ben-pen (reluctantly supplying a specific natural-language sortal predicate for this mereological fusion). But perhaps this is a contingent matter.
Mereological fusion can thus be thought of as a function (or, in Goodman’s terminology, a ‘generating relation’) from parts to wholes. CEM does not require of wholes that they “play any explanatory role, participate in causal links, or play any role in an exhaustive description of the world” (p. 193). Wholes do not “instantiate any interesting, autonomous properties. They would inherit the properties of their parts” (p. 193). If a window were to get hit by a cricket ball, it would be redundant to claim that it was hit by something in addition to the arrangement of its parts; the ball and the parts that comprise the ball are co-located. There is no additional matter that CEM claims exists as well as the whole’s parts—so as far as physical stuff is concerned, the principle of unrestricted composition is not as ontologically profligate as some might think (indeed, Lewis thinks of his version, which includes an additional commitment to the Composition As Identity thesis, as ontologically innocent; wholes on this view are an ‘ontological free lunch’, to use David Armstrong’s expression), and is happily compatible with nominalism (it does not say anything about what kinds of entities exist, just that of the things that exist, any combination forms a mereological whole). Since Lando’s theory does not include a commitment to the Composition As Identity thesis, it may turn out on his view that unrestricted composition is less ontologically innocent than Lewis supposes: on the list of things that exist, we might need to include the cricket ball in addition to all of its parts (and in addition to all of the possible merelogical sums of its various parts, and so on), violating the eleatic principle. The proof will be in the pudding. Nonetheless, about allegedly intuitive counterexamples to unrestricted composition, note that just as using the word ‘car’ allows us to pick out a familiar object composed of various parts, using the expression ‘Ben-pen’, then, allows us to pick out a (less commonsensible, admittedly) entity composed of parts. The difference is just that we would not be inclined to talk about Ben-pen outside of philosophical discourse. Indeed, Lando admits that the principle of unrestricted composition vindicates all manner of “heterogeneous and redundant entities that are never to be mentioned outside of philosophy” (p. 193). That said, Ben-pen, trout-turkeys and car-bouquets “could become relevant, and begin to fall under certain sortal predicates” (p. 199).
Chapter 10 provides Lando’s preferred way of formalising unrestricted composition (i.e., with plural quantification) and distinguishes it from less perspicuous alternatives. Chapter 11 clarifies Lando’s definition of ‘fusion’ and provides a discussion of its formulation in first-order logic. Chapter 12 considers some counterexamples to unrestricted composition (à la Ben-pen), and chapter 13 provides an argument in support of it (largely following the ideas of Lewis, Sider, Quine, and Donald Williams—the ‘argument from vagueness’) according to which mereology should be neutral. It shouldn’t distinguish between ‘interesting’ fusions like mugs and people and Canis Minor and ‘uninteresting’ ones like Ben-pen. The basic idea comes from Lewis. If you accept that things have parts, and that parts comprise wholes, there is no precise, non-arbitrary stopping point. Now, ‘Big Ben exists’ is not a vague sentence; “nothing in the sentence that expresses the existence of a fusion is vague. By contrast, the conditions under which we would want to restrict composition are vague: this means that these conditions cannot be satisfied” (p. 180, emphasis in original), because although certain predicates are vague, existence is not. Chapter 14 wraps up by discussing some upshots for non-Quinean metaontology.
Let’s say that you agree with Lando that composition can’t be non-arbitrarily restricted. You might still reject unrestricted composition, by denying that composition is a relation that is ever instantiated. The main opponents of unrestricted composition are mereological nihilists, who say just this (or something very close to it). According to Peter van Inwagen, chairs do not exist—only the mereological atoms (‘simples’) exist. A so-called chair is thus merely simples-arranged-chairwise. (Likewise, so-called Ben-pen is merely simples-arranged-Ben-penwise). For van Inwagen, living entities are a non-arbitrary, principled exception to mereological nihilism; on his view, composition only occurs in organisms. The pros and cons of this move cannot be discussed here. For Theodore Sider, composition does not even occur then. For Sider, the only wholes are the limit case (i.e., a simple is a whole, comprising only itself)—no objects with proper parts exist. Mereological nihilism is not directly opposed to transitivity or the uniqueness of composition (these being trivially true according to the view), just unrestricted composition. Other mereological positions claim that composition is restricted in a rather brutal way, or that existence is vague, to mention a few. Lando does not push against these views, “partly due to space constraints and partly because the motivations and the articulation of these stances do not belong to mereology [as a discipline] according to the narrow understanding of it” (p. 199). This is unfortunate.
Take mereological nihilism. Lando says that it “requires a massive strategy of reconciliation with our referential and cognitive practices, which seem to involve lots of complex entities with parts, and perhaps no mereological atom at all” (p. 199). Yet it’s not obvious to me why it can be so easily cast aside in a book-length treatment of mereological monism. Many theorists distinguish between the ‘manifest image’ of, say, a table, and the ‘scientific image’. We are all aware that tables are made up of ‘simples’ (fundamental particles, or whatever is there at the fundamental level) and are thus mainly empty space, and yet we percieve the table as a solid object and refer to it as such. That’s fine, and is by and large part of ‘folk knowledge’ these days. And it might be more straightforward to reconcile just how we perceive and refer to middle-sized ordinary objects like tables and chairs with nihilism than Lando supposes. If perceiving a chair and referring to it with the term ‘chair’ are re-described in light of the scientific image as perception of, and reference to, the ‘manifestation’ of simples-arranged-chairwise, mereological nihilism comes off as less revisionary. It need not matter that we don’t directly perceive the fundamental particles themselves. (Of course I admit a much more sophisticated discussion is needed than this to fully allay Lando’s worries, but also it is true that CEM has revisionary implications!)
There is the thought that we have no need to posit a commonsense entity in addition to what the scientific image tells us is there: arrangements of fundamental entities. Simples arranged tablewise do the same causal work that tables do; tables, that is, are casually redundant. And by getting rid of tables from their ontology, nihilists can appeal to a principle of parsimony. Since Lando avoids commitment to the Composition As Identity thesis, he may be committed to the existence of tables in addition to simples-arranged-tablewise, and yet, this commitment appears redundant: the simples arranged tablewise (the entities that the scientific image vindicates) do all of the explanatory and causal work that tables do, and have scientific credentials. If composition is identity, then wholes are an ontological free lunch, but one’s ontology is just as good without them. And if composition is not identity, there is good reason to cut mereological wholes from our ontology. A commitment to wholes begins to look suspect, one might think.
So is nihilism the better option? I can’t here adjudicate on this issue further. The literature on alternatives to CEM is vast after all. But deciding which side to come down on seems to be a matter of one’s intuitions and balancing of theoretical virtues. Both mereological nihilism and CEM are counterintuitive theories: nihilism denies the existence of tables (unlike CEM), but at least it doesn’t vindicate Ben-pen (as CEM does). Defending brutalism or the vagueness of existence comes with other unsavoury implications. And so the debate in the literature has turned largely metametaphysical: about whether (say) parsimony is an appropriate theoretical virtue for deciding between various options, and about whether it is appropriate to demand a fact-of-the-matter answer to the question of whether wholes exist. But these questions, of course, are beyond Lando’s intended scope.
Time to wrap up. Lando’s Mereology: A Philosophical Introduction introduces, motivates, and defends a tweaked version of an influential thesis, CEM, in the domain of concrete entities. And this Lando does extraordinarily well. The book would well suit a higher-level undergraduate course on mereology (probably supplemented with a reading or two on mereological nihilism, brutalism, etc.) or a postgraduate seminar focused on the prospects and pitfalls of CEM. Its clarity and depth of explanation would be welcomed by students and instructors alike.