Author’s Abstract
- Composition as Identity is the view that an object is identical to its parts taken collectively. I elaborate and defend a theory based on this idea: composition is a kind of identity.
- Since this claim is best presented within a plural logic, I develop a formal system of plural logic. The principles of this system differ from the standard views on plural logic because one of my central claims is that identity is a relation which comes in a variety of forms and only one of them obeys substitution unrestrictedly.
- I justify this departure from orthodoxy by showing some problems which result from attempts to avoid inconsistencies within plural logic by means of postulating other non-singular terms besides plural terms. Thereby, some of the main criticisms raised against Composition as Identity can be addressed.
- Further, I argue that the way objects are arranged is relevant with respect to the question which object they compose, i.e. to which object they are identical to.
- This helps to meet a second group of arguments against Composition as Identity. These arguments aim to show that identifying composite objects on the basis of the identity of their parts entails, contrary to our common sense view, that rearranging the parts of a composite object does not leave us with a different object.
- Moreover, it allows us to carve out the intensional aspects of Composition as Identity and to defend mereological universalism, the claim that any objects compose some object. Much of the pressure put on the latter view can be avoided by distinguishing the question whether some objects compose an object from the question what object they compose.
- Eventually, I conclude that Composition as Identity is a coherent and plausible position, as long as we take identity to be a more complex relation than commonly assumed.
Author’s Preface
- Our world contains a large number of material objects with parts. I am typing these lines by hitting some keys, which are part of a keyboard. The keyboard lies on a tabletop, which is part of a table standing in the philosophy department. On the shelf beside the table, there are several books, which have pages as parts. We call such objects ‘composite objects’ and say that they are composed, or made up, of their parts.
- The aim of this thesis is to develop and defend an account of composition as a kind of identity. Thereby, it connects to the position called “Composition as Identity”. The two central claims I am arguing for are that an object is identical to its parts taken collectively and that this identity relation is sensitive to the way the parts are arranged. I will present a formal system for these claims, which avoids some major problems of Composition as Identity discussed in the literature and brings out the intensional character of Composition as Identity. My aim is to give a detailed presentation of this view, with its costs and benefits singled out, and indicate open problems, which are still to be faced.
- Talk about identity and parthood is ubiquitous, which may suggest that we have a good understanding of these two notions. However, philosophers are still baffled by ancient puzzles such as the “the Statue and the Piece of Clay” or “the Ship of Theseus”. The fact that we are still troubled with these paradoxes shows that they are more than just means to puzzle first year philosophy students or unusual – and as I can tell from my own experience, rarely successful – icebreakers at parties. They show that this oversimplified picture of identity and parthood is mistaken and in need of clarification.
- Composition is what brings the notions of identity and parthood together, and hence, the key to shed light on these puzzles is to find out what composition is. The recent development of plural logic promises to give us the adequate logical tools to analyze composition with the help of formal methods. It allows us to finally use logical methods in order to tackle the ancient metaphysical problems. Since it is only fair to say that the development of plural logic is still in its initial phase, there are many open questions and problems to be explored.
- Part I, “Composition as Identity”, is a discussion of the motivations for and criticisms of the claim that a composite object is identical to its parts, as well as an analysis of different ways this assumption is spelled out in the literature. Eventually, I suggest elaborating on the point that composition is a kind of identity. This hypothesis hinges on understanding identity as a relation, which comes in different kinds.
- The idea of the varieties of identity is argued for in Part II, “From Plurals to Identities”. There, I will develop a formal system, which makes use of well-established principles and concepts of plural logic, i.e. a logic that allows the use of singular and plural terms. I show then that the traditional strategy to avoid certain inconsistencies, which follow from the basic principles of plural logic and innocuous empirical assumptions, has serious difficulties. An examination of these derivations and some commonly upheld principles on identity will lead me then to a denial of the thought that there is only one kind of identity. This makes it at least possible to hold on to a restricted version of “substitution” – the inference rule that allows substituting co-referring terms – such that it is still applicable within some contexts. By reflecting upon the lessons, which have been drawn from substitution failures in singular contexts, I conclude that some plural terms are non-rigid designators. Further, I suggest that predicates which are collective in an argument place are non-extensional in that argument place. Thus, substituting non-rigid designators in these argument places should not be considered as a reliable inference: In the case of predicates which are intensional in an argument place, only rigid designators can be substituted. On the basis of the theory of “Articulated Reference”, I propose that only terms, whose reference is articulated in the same way, can be substituted when we encounter predicates that are hyperintensional in an argument place. This allows us to reply to one of the criticisms raised against Composition as Identity, namely that objects necessarily have the parts they actually have.
- With the aim to overcome the shortcomings of the conventional systems of plural logic, some of its doctrines are dismissed, while additional principles as well as further concepts will be introduced instead. These are then used to promote a formal system, which allows to define a general identity relation and its nine kinds. The different kinds of identity relations are distinguished syntactically and semantically, based on the kinds of terms they take as arguments and on the number of objects these refer to. After presenting some theorems of this formalism, two further objections to Composition as Identity can be met. The assumption that there are different kinds of identity relations might appear to be a high price to pay for a defense of Composition as Identity, yet the benefits outweigh the costs.
- Eventually, we see in Part III, “Arrangement Matters”, that the previously developed view cannot deal with examples where the parts of a composite object are rearranged in such a way that they compose a different object. In order to meet this criticism put forward against Composition as Identity, I propose to modify the system from Part II. By taking the way objects are arranged as a condition for which object they compose these difficulties can be overcome. Thereby, the idea that Composition as Identity is built upon an intensional view gets further support and criticisms of it that are implicitly asking it to be extensional dissolve. All that remains is the questions of arrangement. Moreover, this account of composition provides us with reasons to embrace the view that any objects compose some object1. The final chapter concludes with some remarks on why the account of composition I develop does not turn out to be a disguised form of mereological nihilism, which claims that no objects compose.
- Much of what I say about some objects composing an object applies mutatis mutandis to some objects composing some objects. However, I will not provide a complete account of composition, which can handle these cases due to its complexity and the space available. The analysis of composition given here is incomplete in a further respect by considering material objects only. Whether there are composite non-material objects, and how or under what conditions they compose are interesting questions but will be ignored in what follows. Some of the examples I provide may suggest the contrary, but they are intended to be read from a materialist standpoint. I shamelessly assume that composition is an irreflexive relation, i.e. no object composes itself. In my opinion, we cannot make sense of “self-composition”, which is why I am happy to exclude it from my analysis. Further, although plural logic will be introduced in Part II, we will rely on some of its resources already in Part I, where we will occasionally use plural variables ‘uu’, ‘vv’, ‘ww’, ranging over plural terms, such as ‘Anna and Frege’ or ‘the authors of Principia Mathematica2’, referring to more than one object at once.
- I would like to give some final remarks concerning a methodological issue. Discussions of metaphysical theories are often confronted with the question how to evaluate the different positions. For instance, on the basis of what are we to decide whether it counts in favor of a metaphysical theory that it entails a certain other metaphysical view? Or, on the basis of what do we judge one metaphysical view to be better or more appropriate than another? As a quick look at the references I used already might suggest, my views are heavily influenced by the works of David Lewis and Willard Van Orman Quine. I take myself to be working broadly in the tradition of Lewis and Quine, where considerations of parsimony are lent considerable, though not exclusive, value. Yet, I should emphasize that there are ample points of disagreement, so that it would be unfair to these philosophers to say that they would agree with all the claims I am arguing for. Nevertheless, some of their views should be seen as a starting point of my investigation, in particular, the appreciation of the principle of parsimony, and so I hope to make a contribution to this bigger project with the theory we are about to develop.
- Additionally, I should mentioned that, from a historical point of view, mereology and plural logic have been within a nominalistic framework. Since the principle of parsimony is a key point of nominalism, the following discussion is intended to contribute to the work that has been in this tradition. In order to avoid the impression that we are making arbitrary decisions at certain points in the following discussion, I think it is crucial to stress that considerations of parsimony will play an important role and that it will be one of the basic principles I shall use to evaluate different positions along the way we are about to go.
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In-Page Footnotes
Footnote 1:
- In certain places, I will simply say that objects compose. This should be understood as short for some objects compose some object.
Footnote 2:
- For the ease of exposition, I will use the abbreviations ‘PM’ for ‘Principia Mathematica’, ‘OD’ for ‘On Denoting’, and ‘Grundgesetze’ for ‘Grundgesetze der Arithmetik’.
Footnote 3:
- Where two years are given, the first indicates date of original publication. Each entry is followed by a bracketed list of the pages on which it is cited.
- In due course I intend to add links where I have these works and to investigate those I don’t have that look relevant to my researches.
Footnote 4:
- I've downloaded - but not logged - this work.
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