Introduction (Full Text)
- This book has two major aims. The first is to give a connected account of the various kinds of mereology, or formal theory of part, whole, and related concepts, which exist, widely scattered, in the literature. This aim is fulfilled mostly in Part I. The second and more important aim is to expose the philosophical defects of most of this tradition, and to suggest why, where, and how it should be put right.
- The standardly accepted formal theory of part-whole is classical extensional mereology, which is known in two logical guises, the Calculus of Individuals of Leonard and Goodman, and the Mereology of Lesniewski. Despite the discrepancies between the underlying logics of these two approaches, there is a precise sense in which both say the same things about parts and wholes. Classical extensional mereology (CEM) is subject to two major criticisms. The first is that, either out of conviction or for reasons of algebraic neatness, it asserts the existence of certain individuals, mereological sums, for whose existence in general we have no evidence outside the theory itself. The second and more fundamental criticism is that the theory is not applicable to most of the objects around us, and is accordingly of little use as a formal reconstruction of the concepts of part and whole which we actually employ.
- There are two reasons for this. The first is that the underlying logic of CEM does not have the resources to deal with temporal and modal1 notions in connection with mereology, such as temporary part, temporal part, essential part, or essential permanent part. This is not an internal criticism of CEM, since one could envisage suitably extending it to cope with temporal and modal2 concepts. However there is an internal reason why CEM is not suitable for such extension, and this concerns mereological extensionality. This is the thesis that objects with the same parts are identical (by analogy with the extensionality of sets, whereby sets with the same members are identical). If mereological extensionality is accepted, then two prima facie facts need to be accounted for. The first is that certain things, like human beings, have different parts at different times: they are mereologically variable or in flux. An object with different parts at different times cannot be identical with the sum of its parts at any time, for then it would be different from itself. The second problem is that some objects (again, like human beings) might have had some parts other than those they in fact have, and yet still have been the same objects. In other words, they are not modally3 rigid in their parts. If we accept mereological extensionality in a modally4 strengthened form, to the effect that objects with the same parts must be identical, then no object could have had parts other than those it actually has, a thesis called mereological essentialism, and associated with Chisholm.
- In the face of these two problems, a number of strategies may be adopted to preserve extensionality, some of them extreme. One may try revising the logic of identity, or denying that objects have undetached parts. The modal5 problem may be ignored by refusing to take modality6 seriously. If it is taken seriously, then it seems that mereological essentialism is the best option. One then faces the problem of explaining why it appears that ordinary objects are not modally7 mereologically rigid. Chisholm accounts for appearances by construing such objects as logical constructions out of objects for which mereological essentialism indeed holds.
- Since it is more difficult to ignore time than modality8, the problem of flux has been faced more often. The analogous solution to mereological essentialism is to deny that objects do vary their parts: they are mereologically constant. Chisholm holds that objects properly so called are indeed mereologically constant, and the appearance of variability among objects is to be explained by construing these, once again, as logical constructions. I argue that the price Chisholm pays is in each case too high to warrant upholding mereological extensionality.
- A second and more popular solution to the flux problem is to propose replacing the things (continuants) of our usual ontology by processes, which have temporal parts. I argue that the difficulties involved in such a revision have been greatly underestimated, and that in any case the move fails to save mereological extensionality because such four-dimensional objects fall prey to the modal9 argument.
- There are nevertheless places where extensional mereology is appropriate, in particular among events and among non-singular objects, that is, classes and masses: in the last two cases the full classical theory can apply. It emerges that `part', like other formal concepts, is not univocal, but has analogous meanings according to whether we talk of individuals, classes, or masses.
- It remains to be considered how mereology looks when extensionality is rejected. Part II considers the mereology of continuants, which may be in flux. The rejection of extensionality has as a consequence that more than one object may have exactly the same parts at the same time, and hence occupy the same position. Another somewhat controversial thesis defended is that an object may exist intermittently in special circumstances. These views are applied together to give a novel solution of the Ship of Theseus10 problem.
- Consideration of the conditions under which distinct things may be in the same place at the same time leads to a discussion of the nature of composition, constitution, and matter in their mereological ramifications. With the rejection of extensionality, it becomes possible to distinguish different concepts of proper-or-improper-part which enrich our conceptual palette and allow disputes to be resolved as turning on equivocation.
- Modal11 mereology has received almost no attention because the logical opinions of mereologists and modal logicians12 have usually been fundamentally opposed. Part III brings modality13 and mereology together as they are found in the work of Husserl at the beginning of the century and later in that of Chisholm. Mereological essentialism is rejected as a general doctrine, though again there are regions in which it is appropriate, essentially those where extensionality applies. For most continuants some parts are essential and others are not.
- Husserl used modal14 mereology as a tool in developing various concepts of ontological dependence of objects on other objects, a study which quickly leads into some of the central topics of ontology, concerning substance and conditional and unconditional existence. The modal15 approach developed here is used to re-examine traditional problems in this light, and to reassess Husserl's achievement in this field.
- The arguments have so far turned mainly on extensionality and what happens if it is rejected. In the last chapter I return to mereological sums, and ask what it is they seem to lack that other paradigmatic objects have. The leading idea here is that of a family of objects which is maximally connected under some relation; an object composed of such a family is integrated under the relation; such integrity — provided the relation involved is not merely formal — is what arbitrary sums and incomplete fragments lack. Among the kinds of relation constitutive of such integrity we consider forms of ontological and functional dependence, and give an account, based on work by Grelling and Oppenheim, of the characteristic structure or Gestalt of such integral wholes.
- A word should be said about the use of symbolic formulae and formal systems. Since most of the existing work on mereology uses such means of expression, their use is unavoidable if we are to survey such theories and compare their relative strengths. As for the rest of the book, since the aim is to discover the most suitable mereological concepts and the formal principles governing them, though it is in principle possible to do without symbols, in practice we need them for their brevity and clarity, and to enable us to test the consequences of formulae using the established means of formal logic. Nevertheless, I want to stress that this book is about ontology, not logic. The level of logical sophistication required to understand the text is not high: a journeyman's acquaintance with first-order predicate logic with identity will suffice. Even the modal16 sections require no more, provided one is prepared to indulge the fiction of possible worlds. The unfamiliar language of Lesniewski is introduced in such a way that a reader without foreknowledge may follow subsequent discussion; but in general I stay closer to predicate-logical means of expression. I have tried to make the notation as unfussy as possible; a survey of the notation used generally, in particular the conventions which allow parentheses to be almost entirely dispensed with, can be found in §2.2. Apart from this, the symbolically dense Chapter 2 is not a prerequisite for understanding the main argument. It is a survey exhibiting the riches of the predominant extensional tradition, and gathers material which is otherwise widely scattered.
- Finally, I should mention that the book does not deal with two areas where mereology overlaps with other important philosophical issues. The first is vagueness. Apart from some remarks in Part II, where mention of vagueness is unavoidable, this subject remains within the haven of bivalence. The second issue is whether there can be a mereology of abstract objects (if there are any). The discussion is confined to the concrete, except for a few remarks in §4.10. The reason for avoiding these two areas is that to discuss them with the required thoroughness would involve bringing in a good deal of material which is not in itself mereological, and which is also not relevant to the main argument, which is that extensional mereology is inadequate even for its primary intended sphere of application – concrete individuals.
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