Universals have traditionally thought to obey the identity of indiscernibles, that is, it has traditionally been thought that there can be no perfectly similar universals. But at least in the conception of universals as immanent, there is nothing that rules out there being indiscernible universals. In this paper, I shall argue that there is useful work indiscernible universals can do, and so there might be reason to postulate indiscernible universals. In particular, I shall argue that postulating indiscernible universals can allow (...) a theory of universals to identify particulars with bundles of universals, and that postulating indiscernible universals can allow a theory of universals to develop an account of the resemblance of quantitative universals that avoids the objections that Armstrong’s account faces. Finally, I shall respond to some objections and I shall undermine the criterion of distinction between particulars and universals that says that the distinction between particulars and universals lies in that while there can be indiscernible particulars, there cannot be indiscernible universals. (shrink)

David Armstrong's book is a contribution to the philosophical discussion about possible worlds. Taking Wittgenstein's Tractatus as his point of departure, Professor Armstrong argues that nonactual possibilities and possible worlds are recombinations of actually existing elements, and as such are useful fictions. There is an extended criticism of the alternative-possible-worlds approach championed by the American philosopher David Lewis. This major work will be read with interest by a wide range of philosophers.

This book espouses a theory of scientific realism in which due weight is given to mathematics and logic. The authors argue that mathematics can be understood realistically if it is seen to be the study of universals, of properties and relations, of patterns and structures, the kinds of things which can be in several places at once. Taking this kind of scientific platonism as their point of departure, they show how the theory of universals can account for probability, laws of (...) nature, causation and explanation, and explore the consequences in all these fields. This will be an important book for all philosophers of science, logicians and metaphysicians, and their graduate students. The readership will also include those outside philosophy interested in the interrelationship of philosophy and science. (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)

Resemblances obtain not only between objects but between properties. Resemblances of the latter sort - in particular resemblances between quantitative properties - prove to be the downfall of a well-known theory of universals, namely the one presented by David Armstrong. This paper examines Armstrong's efforts to account for such resemblances within the framework of his theory and also explores several extensions of that theory. All of them fail.

Structural properties are properties something has in virtue of its mereological structure in that they are properties whose instantiation by a particular involves the parts of the particular being propertied and related in the appropriate way. Most of the literature on structural properties has focused on problems that arise from the pairing of two assumptions: (1) structural properties are universals and (2) structural properties are, in some sense, composed of the properties they involve. Chief among these difficulties is David Lewis’ (...) claim that the conjunction of (1) and (2) require non-unique composition and hence entail the denial of the extensionality of parthood: butane, as well as methane, is composed of the universals carbon, hydrogen and bonded, yet they are distinct properties. This is the extensionality problem. In this paper I discuss a different problem for the conjunction of (1) and (2) and propose a single solution to both problems. First, in section two, I introduce the idea of multiple decomposition and suggest that at least some structural properties are multiply decomposable. In section three, I introduce the “problem of multiple decompositions.” This problem arises when it seems possible for a structural property to be composed of some xs and some ys even when the xs ≠ ys. Finally, in section four I show how both problems admit of a single solution by focusing on the parthood relation that holds between structural properties and their constituents. While the solution I propose is theoretically costly, I argue that this cost should be paid to retain both (1) and (2). (shrink)

In this paper I outline the main features of Karen Bennett’s (Australasian Journal of Philosophy 1–21, 2011) non-classical mereology, and identify its methodological costs. I argue that Bennett’s mereology cannot account for the composition of structural universals because it cannot explain the mereological difference between isomeric universals, such as being butane and being isobutane. I consider responses, which come at costs to the view.

A set of parameters for classifying composition operations is introduced. These parameters determine whether a composition operation is 1) universal, 2) determinate, 3) whether there is a difference between possible and actual compositions, 4) whether there can be singleton compositions, 5) whether they give rise to a hierarchy, and 6) whether components of compositions can be repeated. Philosophical implications of these parameters (in particular in relation to set theory) and mereology are discussed.

Let’s start with compositional pluralism. Elsewhere I’ve defended compositional pluralism, which we can provisionally understand as the doctrine that there is more than one basic parthood relation. (You might wonder what I mean by “basic”. We’ll discuss this in a bit.) On the metaphysics I currently favor, there are regions of spacetime and material objects, each of which enjoy bear a distinct parthood relation to members of their own kind. Perhaps there are other kinds of objects that enjoy a kind (...) of parthood relation other than the ones enjoyed by material objects and regions of spacetime. Perhaps, for example, there are facts; I’ve been wavering over whether to embrace these entities for years now. However, I’m reasonably confident that if there are facts than the kind of parthood relation that facts bear to that which composes them is not the kind of parthood relation enjoyed by material objects or regions of spacetime. More on why I am reasonably confident later. (shrink)

David Lewis famously takes mereology ‘to be perfectly understood, unproblematic, and certain". In this chapter, the author proceeds by articulating four theses that Lewis holds about composition. Three of them are familiar; Lewis himself explicitly articulates and relies upon them. The fourth remains implicit, but it is nonetheless important. The four theses include: composition is unique (the same things cannot have two different fusions); composition is unrestricted (any two things whatsoever have a fusion); composition is ontologically innocent (composed entities do (...) not "count" beyond their parts); and composition is unmysterious (it is not problematic to treat it as primitive, and can function in demystifying explanations). The author devotes a section to each thesis: explaining what it says, pointing to the texts that illustrate that Lewis believes it, and explaining why Lewis believes it. Lewis uses the label ‘uniqueness’ and explicitly endorses the thesis. (shrink)

This paper develops co-ordinated multiple-domain supervenience relations to model determination and dependence relations between complex entities and their constituents by appealing to R-related pairs and by making use of associated isomorphisms. Supervenience relations are devised for order-sensitive and repetition-sensitive mereologies, for mereological systems that make room for many-many composition relations, as well as for hierarchical mereologies that incorporate compositional and hylomorphic structure. Finally, mappings are provided for theories that consider wholes to be prior to their parts.

The article develops and extends the theory of Glenn Kessler (Frege, Mill and the foundations of arithmetic, Journal of Philosophy 77, 1980) that a (cardinal) number is a relation between a heap and a unit-making property that structures the heap. For example, the relation between some swan body mass and "being a swan on the lake" could be 4.

Many philosophers have declared that everything which exists is a particular. There is a weak interpretation of this doctrine which I believe to be a true proposition, and a strong one which I believe to be false.

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)

Lewis has objected to Armstrong's notion of a structural universal on the grounds that it violates the Principle of Uniqueness of Composition (PUC), which says that given some parts, there is only one whole that they compose. This paper reviews Armstrong's case for structural universals, and then attempts to reconcile structural universals with PUC by arguing for the existence of arrangement universals. The latter are not only a key to defending structural universals against Lewis' objection, but are in fact essential (...) to Armstrong's conception of structural universals in general. Three objections to my proposal are deflected, and two alternative proposals are shown to be inferior to it. (shrink)

‘‘Thus I believe that there is no part of matter which is not—I do not say divisible—but actually divided; and consequently the least particle ought to be considered as a world full of an infinity of different creatures.’’ (Leibniz, letter to Foucher).

Some argue that theories of universals should incorporate structural universals, in order to allow for the metaphysical possibility of worlds of 'infinite descending complexity' ('onion worlds'). I argue that the possibility of such worlds does not establish the need for structural universals. So long as we admit the metaphysical possibility of emergent universals, there is an attractive alternative description of such cases.

I argue that, despite van Inwagen’s pessimism about the task, it is worth looking for answers to his General Composition Question. Such answers or ‘principles of composition’ tell us about the relationship between an object and its parts. I compare principles of composition with criteria of identity, arguing that, just as different sorts of thing satisfy different criteria of identity, they may satisfy different principles of composition. Variety in criteria of identity is not taken to reflect ontological variety in the (...) identity relation; I discuss whether variety in principles of composition should be taken to reflect ontological variety in the composition relation. (shrink)

Armstrong holds the Supervenience Theory of instantiation, namely that the instantiation of universals by particulars supervenes upon what particulars and what universals there are, where supervenience is stipulated to be explanatory or dependent supervenience. I begin by rejecting the Supervenience Theory of instantiation. Having done so it is then tempting to take instantiation as primitive. This has, however, an awkward consequence, undermining one of the main advantages universals have over tropes. So I examine another account hinted at by Armstrong. This (...) is the Operator Theory of instantiation, by which I mean the theory that universals are operators, and that a particular instantiates a monadic universal because the universal operates on the particular, resulting in the state of affairs. On this theory the state of affairs supervenes on the instantiation rather than vice versa. In the second part of the paper I develop this theory of universals as operators, including an account of structural universals, which are useful for accounts of modality and of mathematics. (shrink)

Argues that a set is the mereological whole of the singleton sets of its members (following Lewis's Parts of Classes), and that the singleton set of X is the state of affairs of X's having some unit-making property.

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)

The objective probability of every physical event is fixed by prior physical events and laws alone. (This thesis is sometimes expressed in terms of explanation: In tracing the causal history of any physical event, one need not advert to any non-physical events or laws. To the extent that there is any explanation available for a physical event, there is a complete explanation available couched entirely in physical vocabulary. We prefer the probability formulation, as it should be acceptable to any physicalist, (...) though some reject the explanation formulation.) (3) Causal Exclusion. (shrink)

If the property _being a methane molecule_ is a universal, then it is a structural universal: objects instantiate _being a methane molecule_ just in case they have the right sorts of proper parts arranged in the right sort of way. Lewis argued that there can be no satisfactory account of structural universals; in this paper I provide a satisfactory account.

I want to join Dummett in saying that the reality of the past (and, by analogy, the reality of the future) is an issue of realism versus anti-realism: (Dummett 1969) If you affirm the reality of the past, you are a realist about the past. If you deny the reality of the past, you are an anti-realist about the past. (And likewise, in each case, for the future). It makes sense to think of these issues by analogy with realism about (...) the external world, unobservable objects, mathematical objects, universals, and so on. These are all properly described as ontological issues. (shrink)

In the past fifteen years or so there has been a lot of attention paid to theories of “sparse” universals, particularly because of the work of D. M. Armstrong. These theories are of particular interest to those of us concerned with the distinction between natural and non-natural properties, since, as David Lewis has observed, it seems possible to analyze naturalness in terms of sparse universals. Moreover, Armstrong claims that we should conceive of universals as being “immanent” as opposed to “transcendent”, (...) and if universals are immanent then, as we will see, there is pressure to admit they are sparse as well. But I will argue that neither of these alleged reasons to accept a sparse conception of universals succeeds: the outlook for a fully general analysis of naturalness in terms of universals is not good, and the apparent advantages of immanence over transcendence are illusory. (shrink)

Do properties have intrinsic properties of their own? If so, which second-order properties are intrinsic? This paper introduces two competing views about second-order intrinsicality: generalism, according to which the intrinsic–extrinsic distinction cuts across all orders of properties and applies to the properties of properties as well as the properties of objects, and objectualism, according to which intrinsicality is a feature exclusive to the properties of objects. The case for generalism is then surveyed along with some proposals for distinguishing intrinsic second-order (...) properties from extrinsic ones. After addressing these broad questions about the nature of second-order intrinsicality, the Problem of Accidental Intrinsic Properties of Properties is introduced and put to work as a case study for the significance of second-order intrinsicality. The connection between this problem and the metaphysics of quantitative properties is then examined. (shrink)

The dominant theory of parts and wholes – classical extensional mereology – has faced a number of challenges in the recent literature. This article gives a sampling of some of the alleged counterexamples to some of the more controversial principles involving the connections between parthood and identity. Along the way, some of the main revisionary approaches are reviewed. First, counterexamples to extensionality are reviewed. The ‘supplementation’ axioms that generate extensionality are examined more carefully, and a suggested revision is considered. Second, (...) the paper considers an alternative approach that focuses the blame on antisymmetry but allows us to keep natural supplementation axioms. Third, we look at counterexamples to the idempotency of composition and the associated ‘parts just once’ principle. We explore options for developing weaker mereologies that avoid such commitments. (shrink)

Are the sparse properties drawn from all the levels of nature, or only the fundamental level? I discuss the notion of sparse property found in Armstrong and Lewis, show that there are tensions in the roles they have assigned the sparse properties, and argue that the sparse properties should be drawn from all the levels of nature.

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 paper explores the mereology of structural universals, using the structural richness of a non-classical mereology without unique fusions. The paper focuses on a problem posed by David Lewis, who using the example of methane, and assuming classical mereology, argues against any purely mereological theory of structural universals. The problem is that being a methane molecule would have to contain being a hydrogen atom four times over, but mereology does not have the concept of the same part occurring several times. (...) This paper takes up the challenge by providing mereological analysis of three operations sufficient for a theory of structural universals: Reflexive binding, i.e. identifying two of the places of a universal; Existential binding, i.e. the language-independent correlate of an existential quantification; and Conjunction. (shrink)

In his last book, David Armstrong sets out his metaphysical system in a set of concise and lively chapters each dealing with one aspect of the world. He begins with the assumption that all that exists is the physical world of space-time. On this foundation he constructs a coherent metaphysical scheme that gives plausible answers to many of the great problems of metaphysics. He gives accounts of properties, relations, and particulars; laws of nature; modality; abstract objects such as numbers; and (...) time and mind. (shrink)