Giorgio Lando: Mereology: A Philosophical Introduction

Mereology: A Philosophical Introduction Book Cover Mereology: A Philosophical Introduction
Giorgio Lando
Bloomsbury
2017
Paperback $35.96
240

Reviewed by: Alessio Persichetti (University of Aberdeen)

Mereology studies the nature and relationships of parthood in objects, considered in the most general way. The book by Giorgio Lando, “Mereology: A Philosophical Introduction,” aims to provide an oriented introduction to the topic.

The literature on the subject does not lack examples of introductory volumes. However, monographs until now have had two weaknesses: they were either too focused on a specific aspect of mereology or provided merely a broad-spectrum summary. Regarding the former, there are F. Moltmann’s Parts and Wholes in Semantics (1997) regarding linguistic structures,  A. Varzi and R. Casati (1999) and Kleinschimdt (2014) on parts and space, and C. Calosi and P. Graziani (2014)’s collection on mereology and special sciences. In the latter case, there are the good — but outdated —  introductions of P. Simons (2000) and M. Libardi (1990), and the recent H. Burkhardt et al. Handbook of Mereology (2017). Lando’s book is the first real attempt to present an accessible general introduction to the problems of the field from a precise standpoint. In particular, this book adopts the perspective of CEM (Classic Extensional Mereology), the theory of parts and parthood that has its roots in Nelson Goodman’s A World of Individuals (1956) and David Lewis’ Parts and Classes (1991) and On the Plurality of Worlds (1986).

The book is organised into one introductory chapter, three main parts, and an appendix. The first part describes how mereology works and which relations and features a mereological theory must satisfy; the second part defends the idea that CEM is the only correct theory of mereology (i.e. argues for monism); the final part defends and clarifies the core principle of Unrestricted Composition from different kinds of criticisms.

The introduction (Chapter 0) expounds the main concepts of Classic Extensional Mereology. CEM is the theory according to which: 1) parts are in transitive relationships with other parts; 2) given n objects, there exists another thing n+1 composed by the n objects; and 3) given some objects, there exists only one fusion of them. Giorgio Lando then distinguishes the semantical senses of the term “mereology”: mereology can be intended as the sub-discipline of metaphysics that studies parts, as a theory that explains the parthood relation, or as the correct theory that describes parts. Lando identifies mereology with the third sense; specifically, he chooses CEM as the best candidate for being a unique and proper mereological theory. In this perspective, Lando claims that he has oriented his explanation towards a defence of CEM. Afterwards, he explains how the CEM arises from David Lewis’s attempt to develop a topic-neutral tool to solve problems concerning classes. Lando’s primary aim is to develop Lewis’ account into a full metaphysical theory with ambitions of generality. At the same time, the secondary goal is to clarify CEM and monism against the most common objections.

The first part, “Methodology of Mereological Monism,” is dedicated to methodological remarks concerning the scope of mereology — and the role CEM plays in it. Chapter 1 explores the semantic sphere of mereology: it starts by clarifying the semantics of the term “part” and formulating criteria a part must satisfy.  Lando argues that a part should satisfy spatial location, selectivity and formality. A part is spatially located when it has a spatio-temporal location relationship through the same region of space.  In addition, a part must satisfy selectivity, that is, it must have clear boundaries in order to be identified. Finally, a part must stand in a binary relation with another part; in this sense it must satisfy formality. Furthermore, Lando wants to make clear that mereology concerns literal parthood, not metaphorical cases. For example, the notion of parthood invoked in the sentence “You are part of my heart” is not a genuine example of parthood as investigated in mereology, because it is not literal.

Chapter 2 defends mereological monism and shows why CEM could be useful in a range of different cases. Lando argues in favour of monism that it gives clear and unambiguous criteria to decide what is a part and what is not a part. This is an advantage that pluralism, in which one accepts multiple mereological theories, does not have. Because pluralism accepts numerous ways to discriminate parthood, each different from the others, it offers no unified notion of part.

Chapter 3 elucidates the relationship between mereology and formalism. The fact that mereology aims at generality and must be characterized as neutral does not imply that mereology is a kind of logic. Mereology aims to describe parthood in the broadest way possible. In this sense, it must be understood as formal: mereology can be applied to every part-whole relationship, independently from what “part” means in the context. Consequently, Lando argues, CEM is the best candidate to achieve the ambition of generality.

Having described the overall requirements and goals of a mereological theory, Chapter 4 argues in favour of the axioms of CEM. Here, Lando expounds and justifies the axioms of Transitivity, Reflexivity, Antisymmetry, and the Proper-Parthood definition.

The second part, on “Extensionalism,” enters into fine-grained details in responding to examples against Extensionalism and the Uniqueness of Composition. Chapter 5 analyses why uniqueness of composition and extensionalism are not negotiable points of CEM, and how these two points are essential to a nominalist account of structures of parts. Lando claims that nominalism is necessary in order to have a general mereological theory that is independent of single structures. By “structure” Lando means the configuration and order of individual parts. If a mereological theory is case-sensitive regarding structures, then it would lose some degree of generality.

Chapter 6 clarifies the conceptual distinction between Extensionalism and Uniqueness of Composition: firstly, how they differ in their formalization; secondly, which tasks the quantifiers in the formulations cover.

Chapter 7 offers a concrete application of CEM in order to show its virtues. Taking the example of a mountain, Lando demonstrates that CEM is able to: a) distinguish parts (e.g. the trees on its surface) from the proper parts of the mountain; b) give a clear account of cases of counterparts; and c) settle the issue of overlapping objects, that is, the mountain and the “mountmatter” on it, such as rocks, forests, rivers, etc.

Chapter 8 faces the most difficult mereological cases, which relate to abstract objects. For Lando, a theory that aims for generality must also be able to explain parts of abstract entities, such as numbers and sets. But a problem for CEM arises when one allows for the stipulation of entities that the theory cannot accommodate, namely facts and propositions. In what sense does a fact have parts, or does a word share the same letters with other words? Lando solves the issue claiming that these sorts of objects do not belong to mereology: abstract entities have their own identity criteria, independent from those of CEM.

Chapter 9 examines alternatives to Extensionalism useful for fictional and controversial scenarios. These include, for instance, objects without clear boundaries among their parts (e.g. forms), or scenarios where it is no clear relationship involved (e.g. reciprocal parts). Nevertheless, non-extensional variants must be employed if and only if there are strong metaphysical motivations to apply them.

The third part of the book, “Unrestricted Composition,” is dedicated to defending the principle of Unrestricted Composition. Chapter 10 treats the notion of fusion and its relationship with ontological economy. Specifically, Lando settles the issue regarding how quantifiers in Fusion’s axiomatization have plural variables as domain. Chapter 11 refines further this formal definition of the concept of Fusion. Chapter 12 upholds the existence of counterintuitive fusions, like that of the Statue of Liberty and a chair. However, Lando stresses that CEM accepts the plurality of fusions only as long as the parts involved are actual existing parts.

Chapter 13 examines the problem of vague fusions. Unrestricted Composition could give rise to disquieting consequences like spatial or temporal disconnected fusions. However, the principle accommodates many of our standard intuitions, for instance, the case of spatially distributed things. A classic example is that of a fleet, in which the sum of the ships is not spatio-temporally contiguous. Despite this non-contiguity, on Unrestricted Composition, each ship counts as a part of the fleet.

Finally, Chapter 14 evaluates the consequences of Unrestricted Composition for meta-ontology. In particular, Lando examines how the principle interacts with Quinean meta-ontology, Meinongianism, Williamson’s conception of being, and Kit Fine’s meta-ontology. In the brief Appendix that closes the book, Lando argues against the equivalence between Composition and Identity in mereological monism.

Giorgio Lando’s book has the virtue of offering a clear introduction to mereology from CEM’s perspective. It explains what the methodology of the discipline is, and what is required for a theory of parthood. Every axiom of the theory is expressed and explained with clarity, and supported by a multitude of useful examples. Furthermore, it does this from the specific point of view of monism and CEM theory. In this sense, Lando covers an important gap in the literature: here we have a monograph that expounds a major topic and at the same time suggests to the reader a definite approach to follow.

This approach avoids a deficiency possessed by many other introductions. Quite often, they are merely compendia of positions and notions. In contrast, this book starts by immediately giving reasons why CEM is the best candidate among competitor mereological theories. This is helpful in two ways: on the one hand, it benefits newcomers by offering a precise way of facing mereological problems; on the other hand, it helps the expert reader evaluate from the beginning whether CEM is convincing or not.  Regarding the defence of CEM, Lando’s arguments are solid: he succeeds in defending the main principles of CEM from classic objections. His criticism regarding fusion and the unrestrictedness and uniqueness of composition — the most contentious points of CEM – is especially strong. The volume is also successful in upholding monism as respectable choice in meta-mereology: for example, by demonstrating why pluralism has problems in managing criteria of identity about parts and objects.  In this regard, Giorgio Lando has reached his goal.

Although the book is an extremely welcome addition to the study of mereology, it is not perfect. The first flaw is theoretical, while the second concerns the third part of the book, and the third regards some choices in the exposition. As already mentioned, Lando provides good arguments in favour of both monism and extensionalism. However, his account fails in its treatment of abstract objects. Lando’s justification of CEM is successful only in the case of spatio-temporal located entities. A mereological theory aspiring to be the single correct theory and the most general explanation does not have this luxury. Lando claims in Chapter 8 that CEM cannot treat stipulated cases violating its principles, or that abstract things such as numbers and words lack definite identity criteria. Thus, his argumentative strategy is to maintain that abstract objects are not in the scope of CEM. Nonetheless, on this issue he is not persuasive: CEM in conjunction with monism and the pretence of topic-neutrality cannot rule out abstract objects. Otherwise, CEM would lose its status of generality or one would be forced to admit that abstract entities require different mereological criteria. These are two unpleasant outcomes for a monist mereology. Excluding a class of entities from a theory is a respectable move, but it cannot be accepted as long as the goal of the theory is generality.

About the second flaw of the book: as mentioned earlier, most of the book is accessible; however, the third part becomes a bit complex for a beginner. In particular, from Chapter 13 to 15, the discussion presupposes knowledge of many metaphysical positions. Despite the fact that they are summarized briefly, this treatment is insufficient for understanding these positions. The non-expert reader or philosopher with a different background will have some difficulties in following the explanation. This renders the last part more appealing to a philosopher already engaged in the debate than to a student with no expertise in the subject. My last critical remark concerns the space given to the pluralistic arguments: the discussion would have gained even more from the confrontation of CEM with other types of theories and pluralistic options. A deeper comparison of CEM with the competing alternatives would have been beneficial for the introductory purposes of the monograph. But I suppose that precise editorial requirements might have led the author not to include material on these different perspectives.

To sum up, “Mereology: A Philosophical Introduction” is a fundamental addition to the extant literature on mereology: it describes systematically the basics of Classical Extensional Mereology, and the relevant arguments in its favour. It is the first introduction explicitly oriented to monism in the literature. Moreover, it addresses the classic objections to CEM; this makes the book valuable also for specialists interested in defending this approach. Moreover, the book discusses with completeness collateral issues like meta-ontological consequences, nominalism, etc. Nevertheless, it has some limits, theoretically speaking. Giorgio Lando is able to defend CEM in the case of spatio-temporal objects; however, it appears that there is a difficulty in treating abstract objects and defending CEM’s generality at the same time. Moreover, a confrontation with different theories would have been preferable for two reasons: it would have emphasized the strength of CEM in comparison and, simultaneously, would have informed the reader about opposing views in the field. An opinionated introduction does not mean that other positions must be excluded. Finally, the third part is sometimes too difficult for introductory purposes. Nevertheless, I warmly recommend the book, perhaps not to newcomers in metaphysics, but to a graduate student or philosopher with metaphysical commitments, who wants to deepen his or her understanding of CEM.

Bibliography

Burkhardt, H., Seibt, J., Imaguire, G., Gerogiorgakis, S. (Eds.), 2017. Handbook of Mereology, Analytica. Philosophia Verlag GmbH, Munich.

Calosi, C., Graziani, P. (Eds.), 2014. Mereology and the Sciences. Parts and Wholes in the Contemporary Scientific Context, Synthese Library. Springer, Cham Heidelberg New York Dordrecht London.

Goodman, N., 1956. A World of Individuals, in: Bochenski, J.M., Church, A., Goodman, N. (Eds.), The Problem of Universals. A Symposium. Notre Dame University Press, Notre Dame, pp. 13–31.

Kleinschmidt, S., 2014. Mereology and Location. Oxford University Press, Oxford, New York.

Lewis, D., 1991. Parts of Classes. Blackwell, Oxford.

Lewis, D., 1986. On the Plurality of Worlds. Blackwell, Oxford.

Libardi, M., 1990. Teorie delle parti e dell’intero. Mereologie estensionali, Quaderni del Centro Studi per la Filosofia Mitteleuropea. Trento.

Moltmann, F., 1997. Parts and Whole in Semantics. Oxford University Press, Oxford.

Simons, P., 2000. Parts. A Study in Ontology. Oxford University Press, Oxford.

Varzi, A., Casati, R., 1999. Parts and Places. The Structures of Spatial Representation. MIT Press, Cambridge MA, London.

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