Orthodoxy says that the thesis that composition is identity (CAI) entails universalism: the claim that any collection of entities has a sum. If this is true it counts in favour of CAI, since a thesis about the nature of composition that settles the otherwise intractable special composition question (SCQ) is desirable. But I argue that it is false: CAI is compatible with the many forms of restricted composition, and SCQ is no easier to answer given CAI than otherwise. Furthermore, in (...) seeing why this is the case we reveal an objection to CAI: that it allows for the facts concerning what there is to be settled whilst leaving open the question about what is identical to what. (shrink)

Composition is Identity is the thesis that a whole is, strict and literally, its parts considered collectively. Mereological Nihilism is the thesis that there are no composite objects whatsoever instead. This paper argues that they are equivalent, at least insofar as Composition is Identity is phrased in a particular way. It then addresses some consequences of such equivalence.

On the most popular account of material constitution, it is common for a material object to coincide precisely with one or more other material objects, ones that are composed of just the same matter but differ from it in sort. I argue that there is nothing that could ground the alleged difference in sort and that the account must be rejected.

Composition as identity, as I understand it, is a theory of the composite structure of reality. The theory’s underlying logic is irreducibly plural; its fundamental primitive is a generalized identity relation that takes either plural or singular arguments. Strong versions of the theory that incorporate a generalized version of the indiscernibility of identicals are incompatible with the framework of plural logic, and should be rejected. Weak versions of the theory that are based on the idea that composition is merely analogous (...) to identity are too weak to be interesting, lacking in metaphysical consequence. I defend a moderate version according to which composition is a kind of identity, and argue that the difference is metaphysically substantial, not merely terminological. I then consider whether the notion of generalized identity, though fundamental, can be elucidated in modal terms by reverse engineering Hume’s Dictum. Unfortunately, for realists about possible worlds, such as myself,... (shrink)

Mereological nihilism is the thesis that composite objects—objects with proper parts—do not exist. Nihilists generally paraphrase talk of composite objects F into talk of there being “xs arranged F-wise” . Recently several philosophers have argued that nihilism is defective insofar as nihilists are either unable to say what they mean by such phrases as “there are xs arranged F-wise,” or that nihilists are unable to employ such phrases without incurring significant costs, perhaps even undermining one of the chief motivations for (...) nihilism. In this paper I defend nihilism against these objections. A key theme of the paper is this: if nihilists need to employ such phrases as “there are xs arranged F-wise,” non-nihilists will need to do so as well. Accordingly, any costs incurred by the nihilist when she employs such phrases will be shared by everyone else. What’s more, such phrases are intelligible when employed by the nihilist, as well as when they are employed by the non-nihilist, insofar as analyses of such phrases will not essentially involve mereological concepts incompatible with nihilism. (shrink)

The paper defends a combination of perdurantism with mereological universalism by developing semantics of temporary predications of the sort ’some P is/was/will be (a) Q’. We argue that, in addition to the usual application of causal and other restrictions on sortals, the grammatical form of such statements allows for rather different regimentations along three separate dimensions, according to: (a) whether ‘P’ and ‘Q’ are being used as phase or substance sortal terms, (b) whether ‘is’, ‘was’, and ‘will be’ are the (...) ‘is’, ‘was’, ‘will be’ of identity or of constitution, and (c) whether ‘Q’ is being used as a subject or predicate term. We conclude that this latitude is beneficial, as it conforms with linguistic reality (i.e., the multiple uses actually in place) and also enables one to turn what is ordinarily perceived as a problem for universalist perdurantism viz., a commitment to all sorts of weird and gerrymandered temporally extended entities, into an advantage, for the richness in questions allows us to make sense of. (shrink)

In this paper I argue that we need to take irreducibly plural logic more seriously in metaphysical debates due to the fact that the verdict of many metaphysical debates hangs on it. I give two examples. The main example I focus on is the debate recently revived by Jonathan Schaffer over the fundamental cardinality of the world. I show how the three main arguments provided by Schaffer are unsound in virtue of an employment of plural logic. The second example I (...) give is a more general issue about the possibility of emergent properties of mereological wholes. Employing plural logic there is a new way to understand such cases. The upshot is that plural logic greatly matters to metaphysics and hence can no longer be ignored the way it has in this area. (shrink)

Peter Geach famously holds that there is no such thing as absolute identity. There are rather, as Geach sees it, a variety of relative identity relations, each essentially connected with a particular monadic predicate. Though we can strictly and meaningfully say that an individual a is the same man as the individual b, or that a is the same statue as b, we cannot, on this view, strictly and meaningfully say that the individual a simply is b. It is difficult (...) to find anything like a persuasive argument for this doctrine in Geach's work. But one claim made by Geach is that his account of identity is the account most naturally aligned with Frege's widely admired treatment of cardinality. And though this claim of an affinity between Frege's and Geach's doctrines has been challenged, the challenge has been resisted. William Alston and Jonathan Bennett, indeed, go further than Geach to argue that Frege's doctrine implies Geach's. If Alston and Bennett are right, then those who favor a broadly Fregean treatment of cardinality have no choice but to adopt Geach's doctrine of relative identity. And because contemporary set-theoretic accounts of cardinality are essentially Fregean in all respects relevant to this issue (see §11 below), it follows from Alston and Bennett's claim that virtually every standard modern treatment of cardinality requires a 'relativized' treatment of identity. The purpose of this paper is to argue against the implication claimed by Alston and Bennett. Despite some superficial similarities between Frege's treatment of cardinality and Geach's treatment of identity, the two doctrines are fundamentally opposed. Frege's account of cardinality, and its set-theoretic descendants, are all inconsistent with the claim that identity is 'relative' in Geach's sense. (shrink)

The traditional Lewis–Stalnaker semantics treats all counterfactuals with an impossible antecedent as trivially or vacuously true. Many have regarded this as a serious defect of the semantics. For intuitively, it seems, counterfactuals with impossible antecedents—counterpossibles—can be non-trivially true and non-trivially false. Whereas the counterpossible "If Hobbes had squared the circle, then the mathematical community at the time would have been surprised" seems true, "If Hobbes had squared the circle, then sick children in the mountains of Afghanistan at the time would (...) have been thrilled" seems false. Many have proposed to extend the Lewis–Stalnaker semantics with impossible worlds to make room for a non-trivial or non-vacuous treatment of counterpossibles. Roughly, on the extended Lewis–Stalnaker semantics, we evaluate a counterfactual of the form "If A had been true, then C would have been true" by going to closest world—whether possible or impossible—in which A is true and check whether C is also true in that world. If the answer is "yes", the counterfactual is true; otherwise it is false. Since there are impossible worlds in which the mathematically impossible happens, there are impossible worlds in which Hobbes manages to square the circle. And intuitively, in the closest such impossible worlds, sick children in the mountains of Afghanistan are not thrilled—they remain sick and unmoved by the mathematical developments in Europe. If so, the counterpossible "If Hobbes had squared the circle, then sick children in the mountains of Afghanistan at the time would have been thrilled" comes out false, as desired. In this paper, I will critically investigate the extended Lewis–Stalnaker semantics for counterpossibles. I will argue that the standard version of the extended semantics, in which impossible worlds correspond to maximal, logically inconsistent entities, fails to give the correct semantic verdicts for many counterpossibles. In light of the negative arguments, I will then outline a new version of the extended Lewis–Stalnaker semantics that can avoid these problems. (shrink)

I argue via examples that there are cases in which things that are not two distinct things qualitatively differ without contradiction. In other words, there are cases in which something differs from itself. Standard responses to such cases are to divide the thing into distinct parts, or to conceive of the thing under different descriptions, or to appeal to different times, or to deny that the property had is the property lacked. I show these responses to be unsatisfactory. I then (...) gather and systematize available ways of talking about such cases with phrases like ‘insofar as’, ‘qua’, ‘to the extent that’, ‘in some respect’, etc., while paying special attention to the scope of ‘not’ when used with these phrases. This allows me to show how we can speak of self-differing without contradiction. (shrink)

This essay interprets Butler’s distinction between identity in the loose and popular sense and in the strict and philosophical sense. Suppose there are different standards for counting the same things. Then what are two distinct things counting strictly may be one and the same thing counting loosely. Within a given standard identity is one-one. But across standards it is many-one. An alternative interpretation using the parts-whole relation fails, because that relation should be understood as many-one identity. Another alternative making identity (...) relative to sort fails, because whole and parts can be of the same sort. (shrink)

In _Real Natures and Familiar Objects_ Crawford Elder defends, with qualifications, the ontology of common sense. He argues that we exist -- that no gloss is necessary for the statement "human beings exist" to show that it is true of the world as it really is -- and that we are surrounded by many of the medium-sized objects in which common sense believes. He argues further that these familiar medium-sized objects not only exist, but have essential properties, which we are (...) often able to determine by observation. The starting point of his argument is that ontology should operate under empirical load -- that is, it should give special weight to the objects and properties that we treat as real in our best predictions and explanations of what happens in the world. Elder calls this presumption "mildly controversial" because it entails that arguments are needed for certain widely assumed positions such as "mereological universalism". Elder begins by defending realism about essentialness. He then defends this view of familiar objects against causal exclusion arguments and worries about vagueness. Finally, he argues that many of the objects in which common sense believes really exist, including artifacts and biological devices shaped by natural selection, and that we too exist, as products of natural selection. (shrink)

In this short text, a distinguished philosopher turns his attention to one of the oldest and most fundamental philosophical problems of all: How it is that we are able to sort and classify different things as being of the same natural class? Professor Armstrong carefully sets out six major theories—ancient, modern, and contemporary—and assesses the strengths and weaknesses of each. Recognizing that there are no final victories or defeats in metaphysics, Armstrong nonetheless defends a traditional account of universals as the (...) most satisfactory theory we have.This study is written for advanced students, but as Armstrong goes considerably beyond his earlier work on this topic, it will interest professional scholars as well. Carefully plotted and clearly written, Universals is both a paradigm of exposition and a case study on the value of careful analysis of fundamental issues in philosophy. (shrink)

In this important study D. M. Armstrong offers a comprehensive system of analytical metaphysics that synthesises but also develops his thinking over the last twenty years. Armstrong's analysis, which acknowledges the 'logical atomism' of Russell and Wittgenstein, makes facts the fundamental constituents of the world, examining properties, relations, numbers, classes, possibility and necessity, dispositions, causes and laws. All these, it is argued, find their place and can be understood inside a scheme of states of affairs. This is a comprehensive and (...) rigorously this-worldly account of the most general features of reality, argued from a distinctive philosophical perspective, and it will appeal to a wide readership in analytical philosophy. (shrink)

P. T. Geach, notoriously, holds the Relative Identity Thesis, according to which a meaningful judgment of identity is always, implicitly or explicitly, relative to some general term. ‘The same’ is a fragmentary expression, and has no significance unless we say or mean ‘the same X’, where ‘X’ represents a general term (what Frege calls a Begriffswort or Begriffsausdruck). (P. T. Geach, Mental Acts (London: Routledge and Kegan Paul, 1957), p. 69. I maintain that it makes no sense to judge whether (...) things are ‘the same’, or remain ‘the same’, unless we add or understand some general term - ‘the same F’. (P. T. Geach, Reference and Generality, third Edition (Ithaca, N.Y.: Cornell University Press, 1980), pp. 63f. I am arguing for the thesis that identity is relative. When one says ‘x is identical with y’, this, I hold, is an incomplete expression; it is short for ‘x is the same A as y’, where ‘A’ represents some count noun understood from the context of utterance - or else, it is just a vague expression of a half-formed thought. (P. T. Geach, ‘Identity,’ Review of Metaphysics 21 (1967-8), p. 3.) One of the ways Geach seeks to support this is by tying it to the well nigh universally admired Fregean thesis about cardinality. (shrink)

Arguments that ordinary inanimate objects such as tables and chairs, sticks and stones, simply do not exist have become increasingly common and increasingly prominent. Some are based on demands for parsimony or for a non-arbitrary answer to the special composition question; others arise from prohibitions against causal redundancy, ontological vagueness, or co-location; and others still come from worries that a common sense ontology would be a rival to a scientific one. Until now, little has been done to address these arguments (...) in a unified and systematic way. Ordinary Objects is designed to fill this gap, demonstrating that the mistakes behind all of these superficially diverse eliminativist arguments may be traced to a common source. It aims to develop an ontology of ordinary objects subject to no such problems, providing perhaps the first sustained defense of a common sense ontology in two generations. The work done along the way addresses a number of major issues in philosophy of language and metaphysics, contributing to debates about analyticity, identity conditions, co-location and the grounding problem, vagueness, overdetermination, parsimony, and ontological commitment. In the end, the most important result of addressing these eliminativist arguments is not merely avoiding their conclusions; examining their failings also gives us reason to suspect that many apparent disputes in ontology are pseudo-debates. For it brings into question widely-held assumptions about which uses of metaphysical principles are appropriate, which metaphysical demands are answerable, and how we should go about addressing such fundamental questions as "What exists?". As a result, the work of Ordinary Objects promises to provide not only the route to a reflective understanding of our unreflective common-sense view, but also a better understanding of the proper methods and limits of metaphysics. (shrink)

Hailed by the Bulletin of the American Mathematical Society as "undoubtedly a major addition to the literature of mathematical logic," this volume examines the essential topics and theorems of mathematical reasoning. No background in logic is assumed, and the examples are chosen from a variety of mathematical fields. Starting with an introduction to symbolic logic, the first eight chapters develop logic through the restricted predicate calculus. Topics include the statement calculus, the use of names, an axiomatic treatment of the statement (...) calculus, descriptions, and equality. Succeeding chapters explore abstract set theory—with examinations of class membership as well as relations and functions—cardinal and ordinal arithmetic, and the axiom of choice. An invaluable reference book for all mathematicians, this text is suitable for advanced undergraduates and graduate students. Numerous exercises make it particularly appropriate for classroom use. (shrink)

Things and Their Place in Theories Our talk of external things, our very notion of things, is just a conceptual apparatus that helps us to foresee and ...

This is a short response to Aaron Cotnoir's 'Composition as General Identity', in which I suggest some further applications of his ideas, and try to press the question of why we should think of his 'general identity relation' as a genuine identity relation.

This book, based on Jaegwon Kim's 1996 Townsend Lectures, presents the philosopher's current views on a variety of issues in the metaphysics of the mind...

The Fourth Edition of this long-established text retains all the key features of the previous editions, covering the basic topics of a solid first course in ...

Thomas Reid was a philosopher who founded the Scottish school of 'common sense'. Much of Reid's work is a critique of his contemporary, David Hume, whose empiricism he rejects. In this work, written after Reid's appointment to a professorship at the university of Glasgow, and published in 1785, he turns his attention to ideas about perception, memory, conception, abstraction, judgement, reasoning and taste. He examines the work of his predecessors and contemporaries, arguing that 'when we find philosophers maintaining that there (...) is no heat in the fire, nor colour in the rainbow … we may be apt to think the whole to be only a dream of fanciful men, who have entangled themselves in cobwebs spun out of their own brain'. Written by one of the Scottish Enlightenment's most important thinkers, this work brings to life the intellectual debates of the time. (shrink)

In this study of events and their places in our language and thought, Bennett propounds and defends views about what kind of item an event is, how the language of events works, and about how these two themes are interrelated. He argues that most of the supposedly metaphysical literature is really about the semantics of their names, and that the true metaphysic of events--known by Leibniz and rediscovered by Kim--has not been universally accepted because it has been tarred with the (...) brush of a false semantic theory. (shrink)

Two things become one thing, something having parts, and something becoming something else, are cases of many things being identical with one thing. This apparent contradiction introduces others concerning transitivity of identity, discernibility of identicals, existence, and vague existence. I resolve the contradictions with a theory that identity, number, and existence are relative to standards for counting. What are many on some standard are one and the same on another. The theory gives an account of the discernibility of identicals using (...) phrases like “insofar as”. And it holds that standards for counting remain or shift depending on our purposes. (shrink)

In this important study D. M. Armstrong offers a comprehensive system of analytical metaphysics that synthesises but also develops his thinking over the last twenty years. Armstrong's analysis, which acknowledges the 'logical atomism' of Russell and Wittgenstein, makes facts the fundamental constituents of the world, examining properties, relations, numbers, classes, possibility and necessity, dispositions, causes and laws. All these, it is argued, find their place and can be understood inside a scheme of states of affairs. This is a comprehensive and (...) rigorously this-worldly account of the most general features of reality, argued from a distinctive philosophical perspective, and it will appeal to a wide readership in analytical philosophy. (shrink)

are synthetic a priori judgements possible?" In both cases, i~thas usually been t'aken for granted in fife one case by Kant that synthetic a priori judgements were possible, and in the other case in contemporary,'d-". philosophical literature that contingent statements of identity are ppss. ible. I do not intend to deal with the Kantian question except to mention:ssj~".

Friends of states of affairs and structural universals appeal to a relation, structure-making, that is allegedly a kind of composition relation: structure-making ?builds? facts out of particulars and universals, and ?builds? structural universals out of unstructured universals. D. M. Armstrong, an eminent champion of structures, endorses two interesting theses concerning composition. First, that structure-making is a composition relation. Second, that it is not the only (fundamental) composition relation: Armstrong also believes in a mode of composition that he calls mereological, and (...) which he takes to be the only kind of composition recognized by his philosophical adversaries, such as David Lewis. Armstrong, accordingly, is a kind of pluralist about compositional relations: there is more than one way to make wholes from parts. In this paper, I critically evaluate Armstrong's compositional pluralism. (shrink)

"This book is valuable as expounding in full a theory of meaning that has its roots in the work of Frege and has been of the widest influence.

Provides comprehensive coverage of logical structure as well as the techniques of formal reasoning.