Bertrand Russell’s Bundle Theory of Particulars 9781472594167, 9781472512666, 9781474257022

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Preface Studying Bertrand Russell is fascinating in many respects, one of which is that most of the significant problems in the history of philosophy unfold as one reads his works and observes how his views have changed from one position to another. In my case, the problems that interested me were the problem of universals, whether we can know the nature and/or structure of reality, and, if so, could that knowledge be certain. In this book, I examine Russell’s later metaphysical and epistemological works, in particular Inquiry into Meaning and Truth (1940) and Human Knowledge (1948). In this period, Russell develops a realist bundle theory of particulars. So, this book should appeal to anyone who is interested in theories of particulars as well as to Russell scholars who are interested in Russell’s later work in these areas. Furthermore, my work is not independent of Russell’s more popular, earlier metaphysical and epistemological views, so it should also be of historical interest to philosophers who know the ontological and epistemological problems Russell grappled with, and who, therefore, would be interested in reading about how he solved these problems with the adoption of the bundle theory. In the introduction I will set up the general outlines of the contemporary metaphysical scene with a view to situate Russell’s theories of particulars. Readers familiar with the metaphysical terminology may happily skip the introduction. In the first and second chapters I will show which categories Russell’s theories fit into and why. Russell before 1905, when he published his theory of descriptions, views an ordinary particular, such as my cup, as an enduring substance. His theory of definite descriptions allowed him to rid his ordinary particulars of what he calls a ‘bulky essence’ but still left him with substrata, that is, immediate individuators, whose sole reason for existence was to individuate qualitatively alike particulars and account for persistence. Russell, however, succeeds in eliminating substrata all together in his later works, Inquiry into Meaning and Truth and Human Knowledge. It is this later period of Russell’s metaphysical and epistemological works that I study in this book. The third chapter is an exposition of the later Russell’s view on the epistemology of the bundles: Russell argues that we know some particulars by directly experiencing their qualities and others we know by inference. When making inferences to the effect that

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some particular must exist we rely on inferences that are non-demonstrative, mainly inductive inferences. But the justification of this kind of inference has been a problem for Russell, as well as many other philosophers. Russell formulates what today is called the new riddle of induction and in response argues that for any scientific knowledge about the external world to be possible we need to accept certain postulates as (probably) true in order that they may ground our non-demonstrative inferences that we do employ in scientific inquiry. These epistemological discussions will be followed by Chapters 4, 5 and 6 where I examine and respond to the major objections levelled against realist bundle theories, namely, the objection that the bundle theory is not able to account for the numerical difference of qualitatively alike particulars, that the bundle theory has the implication of turning all true propositions where a property is attributed to a subject into necessary truths, and that the bundle theory makes all subject–predicate sentences analytic. Chapter 7 argues that in Inquiry and Human Knowledge Russell’s neutral monism presented in The Analysis of Mind (1921) and The Analysis of Matter (1927) is not abandoned, but on the contrary, strengthened. Chapter 8 argues that Russell employed the philosophical method of logical atomism not just in the earlier works, such as ‘The Philosophy of Logical Atomism’ (1918), but also in Inquiry and Human Knowledge. Finally, I conclude with a summary and some preliminary remarks on the virtues of a realist Russellian bundle theory in comparison to alternative theories of particulars.

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Acknowledgements I would like to express my gratitude to a few people without whom this work would not have seen the light of day. This book is a reworking of my doctoral dissertation (McMaster University, 2009). Peter Loptson and Richard T. W. Arthur were my second and third readers, both of whom have helped a great deal with their comments during the initial writing stage. But surely, it was Nick Griffin, my dissertation supervisor, who had to carry most of the burden. Griffin not only helped guide my dissertation, but he also took the time to discuss with me how to improve it so that I could publish it as a book some day. Furthermore, there is one chapter in this book in particular, the one on the problem of individuation, which has especially benefited from our discussions and correspondence on this topic. I am grateful to Ken Blackwell and Sheila Turcon who helped with my research at the Russell Archives at McMaster University. I would also like to thank Ali Karatay, who many years ago, first introduced me to Bertrand Russell’s later metaphysical and epistemological work. My anonymous referee with Bloomsbury Publishing, with their questions on my book proposal, has helped me shape the project. In the process of addressing those questions, I believe that I have produced a far better product than the book would have been without. I thank both my official editors at Bloomsbury and my unofficial editor, Duncan Maclean, for the meticulous editing work they have done. And lastly, I thank my family, Halide Koç, Ismail Koç, Duncan Maclean, and Ada Maclean for their love and support.

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Introduction: Setting the Metaphysical Scene

In this section I give a very broad and simplistic outline of the various positions on properties and particulars for the purpose of characterizing Russell’s realist bundle theory in the contemporary language of analytic ontology. I made up the following chart of the various main positions one can take about categories of existence largely based on Michael Loux’s Metaphysics: A Contemporary Introduction (1998) in order that it may help the reader situate Russell’s theories of particulars in the contemporary metaphysical scene. Ordinary particulars (e.g. me, my cup, the Sun)

Endurance

Substance

Perdurance Class (bundle) of transient particulars (spatio-temporal parts)

Substratum

Bundle of qualities Class Universal qualities

complex tropes

Substratum plus qualities universal qualities

tropes

universal tropes qualities

Ordinary particulars, such as the moon or a painting, are particulars that persist through time. Some philosophers, austere nominalists as Loux (1998) calls them, take ordinary particulars to be fundamental entities, with no ontological structure. Others maintain that ordinary particulars have ontological structure.

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These philosophers differ over what kind of entities analysis of ordinary particulars yields and what the structure of an ordinary particular is like. But they all have to give an account of persistence, that is, what it means for an ordinary particular to persist over time. Perdurantists will explain persistence by appeal to a collection of transient particulars. Endurantists, on the other hand, will explain persistence by appeal to some substrata (immediate individuators which do not have any qualities of their own but which hold properties together) and its qualities or by appeal to substance which consists of some essential and accidental qualities. Accidental qualities are the ones that come and go as the ordinary particular endures in time. Perdurantists, having reduced the ordinary particular to some collection or class, have to give an account of these transient particulars that are members of these collections. Some take them to have substrata of their own and qualities; others take the transient particulars to be mere bundles of qualities, with no substrata accounting for the union of the qualities or for the individuation of the transient particular. Both camps, that is, the substratum theorists and the bundle theorists, further split among themselves depending on their take on the ontological status of qualities, particular qualities (tropes) versus universal qualities. Russell always maintained that ordinary particulars have structure and that they need to be analysed. However, his analyses yield different results at different times of his career. Russell’s view on ordinary particulars until Our Knowledge of the External World (1914) was that they exist as entities, but they cannot be known directly; they need to be inferred from the data of the senses. Thus, the early Russell thought that we can know ordinary particulars by inductive inference from our sensory experiences. This period, I think, qualifies as his endurantist period. Though as of 1914, Russell adopts a version of perdurantism. He abstains from making any existence claims about material objects. Rather, he constructs them. He takes an ordinary particular to be a series of classes of sense-data, and later of sensations. Each sensation is a transient particular and is further analysed into substrata and qualities, qualities which are instantiations of transcendent universal qualities. After ‘On Sensations and Ideas’ (1918) and The Analysis of Mind (1921), Russell is still a perdurantist, that is, an ordinary particular is a class of transient particulars. But what has changed is that these transient particulars are not exclusively sensations; they are events that are neutral between mind and matter. Russell defines an event as some entity which ‘is supposed to occupy some continuous portion of space-time, at the end of which it ceases, and cannot

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recur’ (HK 82–3). Russell as of 1918 seems to include purely mental events and purely physical events into the category of transient particulars that collectively make up ordinary particulars, which leads one to question the neutrality of his monism. Russell accepts events as an indispensable category between 1918 and 1940. And events, just like the sensations he discusses in 1914, are further analysed into substrata and qualities. After 1940, Russell decides that events are dispensable after all, because he is now able to explain events merely in terms of qualities, on the condition that events are not taken to have the property of non-recurrence of logical necessity (ibid. 83). Thus, Russell as of 1940 is a perdurantist, who holds that ordinary particulars are classes of transient particulars, whose further analysis this time yields merely qualities, and no substrata, which in the literature makes him a bundle theorist. Russell, though, is a bundle theorist of the realist persuasion, since the qualities that make up a transient particular in this late period are universal qualities, not particular qualities or tropes. And these universal qualities are immanent; they are not instantiations of transcendent universals.

Qualities: Realism with respect to universals As to the questions of whether qualities exist and how they exist, the two main positions are realism and nominalism. First, realists believe that qualities exist as universals. Some realists, such as the early Russell, believe that universals are abstract entities, in the sense that they are not located in space and time. These are called ‘transcendent universals’ (Armstrong, Universals Vol. 1 chapter 7). Such universals are exemplified in particulars, which are located in space and time. For instance, a male cardinal exemplifies the universal property of redness. The red cardinal is an instance of the universal redness. Other realists with respect to universals, such as the later Russell, believe that universals are abstract, though not in the sense of being non-spatio-temporal, but rather in the sense of being multiply occurrent. These universals are called immanent universals (ibid.). Realists introduce universal properties as a category to solve the problem of universals, which is ‘the problem of how numerically different particulars can nevertheless be identical in nature, all be of the same type’ (Armstrong, Universals Vol. 1 41). Once you accept universal properties, you can appeal to them in order to explain what it is that two particulars have in common.

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Another reason for postulating universals is based on a semantic argument. The claim is that if the referential theory of meaning and the correspondence theory of truth are true, then the constituents of propositions must correspond to entities in the world when the proposition is true. Thus, we need universals in order to explain how predicates are ascribed to subjects and what abstract singular terms refer to. Consider the proposition ‘this cardinal is red.’ The subject and predicate should both refer to something in the world in order for this sentence to be meaningful. And if the universal redness is indeed related to the entity referred to by ‘this cardinal’, then the proposition will be true. Furthermore, two tokens of the same predicate in different propositions should refer to a single entity so that the predicate can have the same meaning in both propositions (Loux, Metaphysics 20–30). And when abstract reference is in question, such as ‘Redness is a colour’, it is claimed that the abstract term refers to the universal redness.1 This kind of argument based on referential theory of meaning is one of Russell’s own arguments for the existence of universals. In The Problems of Philosophy (1912), Russell states that ‘when we examine common words, we find that, broadly speaking, proper names stand for particulars, while other substantives, adjectives, prepositions, and verbs stand for universals’ (53). In order not to posit universals redundantly, some realists, such as the later Russell, distinguish between basic and derivative (primitive and nonprimitive) predicates. They claim there to be universals, which are the referents of basic predicates; but they refrain from accepting universals for non-primitive predicates. The non-primitive predicates are defined in terms of the basic ones (Loux, Metaphysics 40–1). For instance, it is claimed that we do not need a universal for the predicate ‘is a dog’ once we have universals for predicates ‘barks’ and ‘is furry’. The justification empiricists give for such a distinction between basic and derivative predicates is epistemological: they maintain that the basic universals are qualities given to us in experience. The predicates that express what is given directly by sensory experience are classified as basic predicates that refer to universals and the remaining predicates are defined in terms of the basic predicates. Such a distinction between primitive and non-primitive predicates also comes in handy for the later Russell when faced with the problem of uninstantiated universals. One problem arises if the realist wants the basic predicates to refer to experienceable things. For there are many predicates that cannot be defined in terms of primitive predicates expressing sensory experiences. Such predicates are those employed in the theoretical sciences and ethics. Some contemporary realists, such as M. Loux, think that no predicates can be reduced to one another

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(Substance 15–16). First, Loux claims that there is not an absolute, neat distinction between primitive and defined predicates; the distinction is ‘system-relative’ at best. Second, Loux argues that even if we could draw an absolute distinction between primitive and defined predicates, ‘it would be perfectly harmless to speak of universals corresponding to defined predicates’ (Substance 15). Loux holds that there is some universal or other that corresponds to every predicate; he does not maintain that there has to be an irreducible universal corresponding to every predicate (ibid. 16). On the other hand, scientific realists, such as H. Putnam (1969), hold that there should be a distinction between primitive and non-primitive predicates, but what is directly experienced should not be considered as composing the basic predicates. The predicates necessary for physical theory should be the primitive ones. On the issue of non-scientific predicates, one view is that the non-scientific predicates of common sense do refer to their respective universals but ‘ontological priority should be given to the properties, kinds, and relations of physics’ (Loux, Metaphysics 46). Russell is not a scientific realist in this sense. First, he believes that we infer our knowledge of physics from what we experience. Second, the role Russell casts to science in philosophical studies is that of guidance in terms of method; he does not advocate that we accept the entities that science at one time or another deems ultimate as fundamental entities. In ‘On Scientific Method in Philosophy’ (1914), Russell says, ‘it is not results, but methods, that can be transferred with profit from the sphere of the special sciences to the sphere of philosophy’ (96). According to Russell, a philosopher should study the methods of science, and seek ways to use those methods in philosophy, as far as she can. An objection raised against realism with respect to universals is the famous ‘one in many’ problem, first raised in Plato’s Parmenides. It is claimed that it is problematic to say that a single universal can be multiply exemplified in different things at once. If it is the same thing at once in many places then ‘it would be separate from itself ’ (131b). And if it is not one in many, but parts of it are in many, such as a sail covering many people at the same time, then we end up with the absurdity that something large will be large in virtue of a small part of largeness (131c). But this objection assumes that universals are spatially located in particulars. The early Russell denies this assumption; for him universals are not in space and time. He argues that the relation ‘east of ’ in sentences such as, ‘Montreal is east of Toronto’ is not located anywhere or at anytime (POP 56). Russell says in The Problems of Philosophy that part of his metaphysics is Platonic realism (52). But the exemplification relation vanishes in his later work. One reason, though not the only reason, is that in his later work there are no more

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things (in the technical sense of the word) to exemplify universals. The thing, in his later work, is a series of transient particulars, which in turn, are bundles of universal qualities. However, Plato’s objection above may be a problem for immanent realists, such as the later Russell, who claim that universals are located in particulars. Their defence amounts to pointing out that the very nature of universals is such that universals can occupy many places at once. And they claim that the objection falsely presupposes that the spatio-temporal existence of universals is the same as that of particulars. Loux appreciates this reply; he explains that our understanding of spatial location is tied up with particulars. That is why we think that it is impossible for a universal to exist at different locations at once (Metaphysics 55). The later Russell would also reply that universals are such that they occur at many places and times. Russell writes, ‘when I say that redness can be at two places at once, I mean that redness can have to itself one or more of those spatial relations, which according to common sense, no “thing” can have to itself. Redness may be to the right of redness, or above redness, in the immediate visual field; redness may be in America and in Europe, in physical space’ (IMT 100). Contemporary Aristotelians, such as Loux, claim that while universals themselves are non-spatio-temporal, they belong to spatio-temporal things (Substance chapter 9). Universals are ontologically dependent on ordinary particulars. They do not exist independently of the particulars in which they inhere. Still there is some incoherence in the claim that something non-spatiotemporal is ‘in’ something spatio-temporal. Aristotelians explain that a universal’s being ‘in’ a particular is not a spatio-temporal relation. The preposition ‘in’ means something other than being spatially located. It means that the universal is logically dependent on a particular; it cannot be conceived without some particular or other. The later Russell’s universals are immanent like Aristotelian universals, but they are not Aristotelian in the above sense; a universal is not dependent on a particular, according to Russell. A universal, for example, ‘red’, is fully present at one point-instant, similar to Aristotelian universals. However, Russell’s universals do not belong to or depend on a particular; they make up the particular. And neither are his universals non-spatio-temporal. Among the realists, there is a division on the question whether there are any unexemplified properties. Platonists, on the other hand, argue that there should be unexemplified qualities. They claim there are some universals that are not exemplified by any particulars at all, for instance, a kind of animal that never has come into existence or a shape of which there is no example (Armstrong,

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Universals Vol. 1 65). Aristotelians claim that there are only exemplified universals. Universals are in the ordinary particulars; they do not exist independently of space and time like Platonic universals. The reason Aristotelians believe this is that once you posit universals in a realm of their own, one runs into two problems: first, the metaphysical problem of explaining how spatio-temporal ordinary particulars are related to non-spatio-temporal universals and second, the epistemological problem that since we human beings are in the spatiotemporal world there needs to be an explanation of how we can know of entities outside of space and time. A substratum theorist’s answer to the first problem is the exemplification relation. The early Russell’s answer to the second problem is his theory of acquaintance; Russell claimed we are acquainted with universals as well as the sense-data presumably caused by ordinary particulars.

Qualities: Nominalism The view opposing realism on the metaphysical status of properties is nominalism. Nominalists reject the existence of universal properties. One reason for this view, following Ockham, is to avoid postulating entities unnecessarily. While immanent realists, such as realist bundle theorists, try to reduce existents only to universals, nominalists try to reduce existents to particulars. Nominalists claim that they can explain attribute agreement, subject–predicate discourse, and abstract reference without any recourse to postulating universals (Loux, Metaphysics 54). That is, nominalists claim they provide a simple ontological theory for the phenomena to be explained. It is mostly philosophers with empiricist tendencies who are nominalists, since they tend to reject abstract objects, such as numbers, classes and propositions (as meanings or senses of sentences), because they are entities that cannot be experienced. Austere nominalists such as Rodriguez-Pereyra (2002) and Quine (1953) hold that only ordinary particulars exist. Rodriguez-Pereyra calls this type of nominalism ‘resemblance nominalism’. Russell formulates his objection to resemblance nominalism in The Problems of Philosophy. Russell argues that resemblance nominalism explains the fact that two things are both white by appeal to a resemblance relation between them. But these resemblance relations need to be explained as well, but resemblance nominalism cannot provide any explanation which does not result in a vicious regress.2 In response to this objection, which claims to prove the need to postulate universals, Quine argues that the fact that one thing is similar to another does not require any explanation.

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We should take it as a fundamental fact about the world that some things agree in their attributes: ‘That the houses and roses and sunsets are all of them red may be taken as ultimate and irreducible’ (‘On What There Is’ 10). On austere nominalist accounts, the truth-makers are ordinary particulars. The predicate ascribed to the subject does not refer to a universal. Instead, the predicate refers to the ordinary particular, too. The predicate is ‘true of or satisfied by’ the object (Loux, Metaphysics 60–4). Austere nominalists have an eliminationist strategy in explaining the phenomenon of abstract reference. They hold that sentences with subjects that seem to refer to abstract entities, such as in (i) ‘Courage is a virtue’, are ‘really just disguised ways of making claims about familiar ordinary particulars’ (ibid. 63). Hence, the quoted sentence actually claims that (ii) ‘Courageous people are virtuous.’ The problem with this account is that not all sentences can be translated in this manner because the truth-value of (i) changes when it is translated into (ii): (ii) may be false because some courageous people may lack other moral virtues, while (i) is true (ibid. 64). In response to this problem, some austere nominalists have held that abstract terms such as ‘courage’ refer to classes of ordinary particulars (Wolterstorff, ‘Qualities’ 98). This view has two problems, which were pointed out by Goodman and Carnap. The first is the imperfect community problem: suppose we have three things, an entity which has the properties of blackness and hardness, another of hardness and redness, and another of redness and sweetness. They satisfy the two conditions for the identity of a quality class, which are: (1) Any two elements of a colour class stand in the relation of similarity to one another. (2) There is no thing outside of a colour class which stands in the relation of similarity to all things in the class (Carnap, The Logical Structure §70). Yet, our three entities do not form a quality-class, because there is nothing common to all of them (Goodman, The Structure 118–19). As H. Hochberg has noted, Russell mentions a similar problem in Analysis of Matter (The Positivist 40), although there the construction is the other way around: a particular is constructed out of qualities. When you take the relation for construction to be 2-place, such as the similarity relation in the case of Carnap, or the overlapping relation in Goodman, you can construct a point in one-dimension, but not in two or more dimensions, because starting from the second dimension a two-term relation will allow the possibility that any two pairs in a group overlap, but not all of them do. Take lines A, B and C. If any two lines intersect and there is no line outside the group which intersects with all of them, then there will be a point they all have in common. But if we take

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planes, any two pairs of planes might have an area in common, even though there is no area common to all of them. That is why Russell explains that if the thing to be constructed is n dimensional, the relation for construction must be n+1 place (AMa 295)3. The other difficulty is pointed out by Carnap, and named ‘the companionship difficulty’ by Goodman. The austere nominalist view tries to construct quality classes out of ordinary particulars, whereas for Carnap, the individuals out of which quality classes are constructed are erlebs (total momentary experiences), not ordinary particulars (Carnap, The Logical Structure §67). But we can ignore that difference for our exposition of the problem. Suppose we have objects such that wherever blue is found red is found as well. Here blue is a companion of red. But there can be an object which is red, but not blue, and therefore does not belong to the colour class blue, and yet it would be similar in colour to all the objects in the class since all of them are red. In this case, the attempt to define the colour class ‘blue’ will fail because it does not satisfy the second condition for a quality class, which is that there should be nothing outside of a colour class which stands in the relation of colour kinship to all the things in the class (ibid. §70). There is another difficulty, which is also called the companionship difficulty by some philosophers, such as N. Wolterstorff. We will name this problem with a subscript: companionship difficulty2. (The problem is also called ‘the coextension difficulty’ (Rodriguez-Pereyra, 153).) The modern expression of this problem is through the ‘renate and cordate’ example. (‘Renate’: the property of having a kidney; ‘cordate’: the property of having a heart.) These properties are always found in the same ordinary particular, so one cannot form a class of ordinary particulars which would uniquely specify either of these properties. Their respective classes would have the same members; those properties would name the same class, leading to the consequence that the predicates ‘renate’ and ‘cordate’ mean the same thing (Loux, Metaphysics 84). Wolterstorff notes that one way to avoid the problems of companionship difficulty2 and imperfect community is to accept not only ordinary particulars as basic individuals, but also their aspects. Aspects are what Campbell calls ‘abstract particulars’ (20), and D. C. Williams calls them ‘tropes’ (7). For example, the ordinary particular Taj Mahal as well as one of its aspects, the pink of the Taj Mahal, will be a member of the colour class, that is, pink. The companionship difficulty2 will be solved because we will now have an ordinary particular, for example, a renate animal, as well as the renate aspect of that particular animal and another class with the same ordinary particular, but this time with the

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cordate aspect of that animal so that each will form a distinct quality class (Wolterstorff 101–2). This view leads to the way of trope theory, which is different from Wolterstorff ’s nominalism in the sense that trope theorists, when they explain abstract reference by reference to classes, would not include the ordinary particular as members, but merely the relevant tropes (aspects). According to trope theorists, each trope is numerically distinct. One red trope can never be numerically the same as another red trope. For instance, ‘the redness of this cardinal’ is a trope and not a universal like ‘redness’. The attribute agreement between two red objects is explained by the similarity of their tropes, and trope theorists hold that this similarity does not need explanation. Trope theorists claim that that some tropes resemble each other is a fundamental fact about the world. They maintain that the abstract singular term ‘red’ in ‘Red is my favourite colour’ refers to the class of resembling tropes (Loux, Metaphysics 80–3). The imperfect community problem and the companionship difficulties disappear on this view because the respective classes would include particular properties, not ordinary particulars with various shared properties (Campbell 33). The trope theorist’s response to a Russellian demand for an explanation of why two tropes are similar to each other would be simply that resemblance among tropes is a fundamental fact about the world, which does not warrant any explanation. One problem for the trope theory arises with the null class. Since, for instance, there is no trope for being a unicorn, the only class the term ‘unicorn’ can refer to is the null class. But then many other terms such as ‘angel’ and ‘griffin’ will also refer to the empty class, in which case we would be claiming all the three terms mean the same thing; but clearly they do not (Loux, Metaphysics 86). A more serious problem is one pointed out by Wolterstorff (‘On the Nature’ 176–81). Wolterstorff notes the difference between kinds and classes: ‘No class can have had different members from the ones it does have, whereas many kinds can have had different examples from those they do have; and classes are necessarily identical just in case there is no thing which is a member of one and not of the other, whereas there are pairs of non-identical kinds such that there is nothing which is an example of one and not of the other’ (ibid. 165). When redness is taken as a class of red things, it implies that there could not have been more red things than there actually are; it becomes a metaphysical impossibility for there to be more or less red things than there actually are (Loux, Metaphysics 87). But how many examples redness has is a contingent matter.

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Particulars: Substratum theory There are two main positions on the analyses of particulars: substratum theory and bundle theory. Locke used the term ‘substratum’ for that which acts as the bearer of properties in a substance, but which itself is not a property. Locke writes, ‘. . . not imagining how these simple ideas can subsist by themselves, we accustom ourselves, to suppose some substratum, wherein they do subsist, and from which they do result; which we therefore call substance’ (book 2, chapter 23 §1). According to substratum theories, there is a substratum in each particular (ordinary or transient), and it holds the qualities together to form a particular. A substratum is of a different category from that of qualities. It itself is not a quality; it is what bears qualities (Loux, Metaphysics 102). But as Locke puts it, ‘. . . of this supposed something, we have no clear distinct idea at all’ (book 2, chapter 23 §37). On a nominalist substratum theory, the substratum binds tropes together by simply ‘having’ them. On a realist substratum theory, a substratum exemplifies universal qualities. G. Bergmann (1967), E. Allaire (1963) and the early Russell are some of the proponents of the realist substratum theory. Substratum theorists may speak of ordinary particulars possessing properties. But strictly speaking, it is the substratum, not the ordinary particulars that bears the properties. Substratum theorists believe that the logical subject, or the bearer of properties, can be understood independently of the properties it bears. Its existence does not depend on the existence of its attributes. Therefore, the bearer of attributes cannot strictly be the ordinary particular. For the ordinary particular as a whole will include the properties; it does not have an identity independent of the properties (Loux, Metaphysics 95–6). Substratum theory is to be distinguished from the Aristotelian view of substance. Aristotelians do speak of ordinary particulars having properties. On the Aristotelian view of substance, the subject is not a substratum, that is, a constituent of the ordinary particular, but the whole substance. The Aristotelian substance is ontologically fundamental; it is not a whole made up of constituents. An Aristotelian ordinary particular has an essence; it belongs to a certain kind, such as being a human or a tree. The ordinary particular has various properties by virtue of belonging to a certain kind. For instance, an oak has broad leaves that rattle in the wind because it belongs to the kind oak tree. Kinds, on the Aristotelian view, are universals that cannot be reduced to any other properties (ibid. 119). On constructivist accounts, such as the substratum

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and bundle theories, ordinary particulars may also belong to kinds, but kinds are not essential. Each ordinary particular exemplifies certain kind-identifying properties such as having leaves that rattle in the wind, which results in the particular belonging to a certain kind, an oak tree. It is only properties and/or substrata that go into the constitution of the ordinary particular. In contrast, on the Aristotelian view of substances, since the ordinary particulars are irreducible entities, the kinds to which things belong are essential to them. The differences between the substance and the substratum theory are (1) on the substance view the ordinary particular is an irreducible entity, but on the substratum view an ordinary particular is reduced to a substratum and properties, and (2) on the substance view, the ordinary particular has an essence which is a certain kind that the individual belongs to and it also has accidental properties. The kind is an individuative universal. That a certain kind is instantiated twice means there are two individuals of that kind, that is, instantiation of kinds does the job of individuation (ibid. 123). But on the substratum theory, the task of individuation is on the properties and the substrata. Substratum theorists have two main arguments for the existence of substrata. The first is an argument from language: They argue that we need substrata in order to explain attribute ascriptions. Something has to serve as a logical subject of properties in order that our sentences correctly describe reality (ibid. 112–13). The second is an ontological argument; the substratum theorists who believe in the reality of universal properties argue that substrata explain numerical diversity. When there are numerically different but qualitatively indiscernible particulars, we need an explanation as to how they can be numerically different although they have all their properties in common. According to the substratum theorists, it is the respective substrata of the two particulars that individuate one from the other (Allaire 237). E. Allaire prefers the term ‘bare particular’ to ‘substrata’ and he argues that they are different notions. Allaire distinguishes his view as bare particularism. He argues that when we are acquainted with an ordinary particular, we are presented with its numerical difference, that is, its bare particular. When presented together, [two discs] are presented as numerically different. That difference is presented as is their sameness with respect to shape, colour, and so on. What accounts for the difference are the numerically different individuals. No character [quality] or group of characters can do that . . . To claim that both discs are but collections of literally the same universals does not account for the thisness and thatness . . . That is, the two collections of characters

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are, as presented, numerically different. Clearly, therefore, something other than a character must also be presented. That something is . . . a bare particular. (Ibid. 242)

Allaire warns that a bare particular is not to be misunderstood as a Lockean substratum, an ‘I know not what’. The basis for the distinction, he claims, is his adoption of the principle of acquaintance. He claims that we are acquainted with the numerical difference of a particular when we are acquainted with a particular. And this numerical difference is what he calls the bare particular. Hence, he argues, a bare particular is not an ‘I know not what’. It is something we can and do experience. And Allaire holds that Russell must have meant the Lockean substratum when he denied being acquainted with individuals. Allaire says, ‘To one who accepts the [principle of acquaintance], Locke’s phrase provides sufficient grounds for rejecting the entities he speaks of ’ (ibid. 244). Substratum theories, therefore, have been criticized on empiricist grounds. The claim is that ontologically fundamental entities should be things we can experience. What experience gives is properties. But we cannot experience this putative thing that bears properties in ordinary particulars. A substratum is not something given in experience. It is postulated in order to explain how various properties are held together in one object. The later Russell expresses this: ‘One is tempted to regard “This is red” as subject-predicate proposition; but if one does so, one finds that “this” becomes a substance, an unknowable something in which predicates inhere’ (IMT 97). Although the later Russell rejects the notion of substratum, the early Russell embraced it. In defence of the substratum theory, Loux suggests that the substratum theorist may, in response, accept that substrata are not experienced but argue that we should overlook this fact due to the overwhelming need to explain attribute ascriptions and numerical diversity (114). It seems that refurbishing the substratum view as Allaire’s bare particularism might save it from the objection based on lack of experience. When we perceive objects around us we do seem to perceive their number as well as their qualities. But this way of couching the substratum view makes it devoid of the metaphysical role that a substratum has, the immediate individuator. For on bare particularism the individuation of particulars is dependent on acquaintance or experience. That is, whether and how many particulars there are ontologically depends on perceivers. But this is not consistent with the realist position that substratum theorists generally take. In fact, the main reason why they are willing to admit to the existence of something not experienced is because they think

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there needs to be an entity which will immediately distinguish it from other things, independently of whether we can distinguish them as two. Thus, Allaire’s suggestion seems to have the consequence of making the number of things that exists depend on what we perceive. Another objection against the realist substratum theories is an extension of F. H. Bradley’s argument against the thesis that all relations are independent entities. A substratum is said to exemplify universal qualities and exemplification is a relation, which one would typically hold to exist independently of its terms, namely the substratum and the qualities it exemplifies (Loux, Metaphysics 39). But Bradley argues that if relations are supposed to exist independently of what they relate and not treated as properties of the related terms (relata), a vicious regress follows. There is a relation C, in which A and B stand; and it appears with both of them. . . . The relation C has been admitted different from A and B, and no longer is predicated of them. Something, however, seems to be said of this relation C, and said, again, of A and B. And this something is not to be the ascription of one to the other. If so, it would appear to be another relation, D, in which C, on one side, and, on the other side, A and B, stand. But such a makeshift leads at once to the infinite process. The new relation D can be predicated in no way of C, or of A and B; and hence we must have recourse to a fresh relation, E, which comes between D and whatever we had before. But this must lead to another, F; and so on, indefinitely. (Appearance 18)

The early Russell’s universals are transcendent, Platonic universals, that is, they reside in some third realm. A relation is a universal and gets exemplified by particulars when the relation relates two particulars. So when two things, A and B, are in a relation C, it must be that C is being exemplified by the particulars A and B. And since exemplification is yet another relation, it is a universal, independent entity, D. Now, if C is indeed exemplified by A and B by the exemplification relation D, then there must be a second-level exemplification relation, E, exemplifying D. And this chain of exemplification relations will have to go on infinitely, and thereby we will not have succeeded in explaining the first-level exemplification relation. Bradley is right that if exemplification is yet another relation just like any other, given the commitment to Platonic realism with respect to universals and the thesis that all relations are independently existing entities, the regress ensues. Something has to give. We need to reject one of the premises. Bergmann, for instance, rejected that exemplification is a relation on a par with other relations. According to

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Bergmann, the exemplification relation (nexus) is an ontological tie, which ties together the qualities of a particular. It is by stipulation such that it ‘does not need a further entity to tie it to what it ties’ (Realism 9). Bergmann assumes the nexus to be literally the same in every particular; it merely occurs many times. It is what differentiates a mere collection of properties from a unified particular (ibid. 9, 13). A nexus for Bergmann is a tie that connects particulars and properties; it is the result of ‘ontologizing exemplification’ (Hochberg, The Positivist 19). Russell’s reply to this objection in The Principles of Mathematics is that the infinite regress implied by the theory is harmless. Russell distinguishes between two kinds of infinite regress: the harmful (vicious) and the harmless. ‘There are no contradictions peculiar to the notion of infinity . . . an endless process is not to be objected to unless it arises in the analysis of the actual meaning of a proposition’ (§55). When it arises in the process of implications it is harmless. According to Russell, Bradley’s argument against the reality of relations is based on the endless regress that arises from ‘the fact that a relation which relates two terms must be related to each of them’ (§99); but, argues Russell, ‘the assertion of a relation between the relation and the terms, though implied, is no part of the original proposition, and . . . a relating relation is distinguished from a relation in itself by the indefinable element of assertion which distinguishes a proposition from a concept’ (ibid.). Russell accepts that the endless regress here is undeniable but he denies that it is of the vicious kind, and therefore does not think that a nexus is necessary,4 as Bergmann did. The regress seems to be vicious. Even if we make Russell’s distinction between the meaning of a proposition and its implications, it is still true that we won’t be able to give a proper explanation of how the two terms A and B are related to each other, since that explanation requires that we first go up one level and explain the exemplification relations between C, and A and B. And so on. Thus, the explanation of the meaning of ‘A is C-related to B’ can never be completed. In fact, the later Russell’s immanent view on universals helps in avoiding this objection. When universals are immanent they multiply occur as the numerically one and the same universal wherever they occur. They are not in some non-spatio-temporal waiting room to be exemplified by particulars. Hence, there is no exemplification relation that requires an explanation on the immanent universals view. This, then, is another virtue of Russell’s later theory of particulars that it is immune to Bradley’s regress argument against the thesis that relations are external to their terms, that is, that relations exist independently of the particulars they relate.

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Bertrand Russell’s Bundle Theory of Particulars

Particulars: Bundle theory What is distinctive about bundle theories in general is that they reduce kinds of ultimate entities to one. The later Russell, Ayer (1954), Hochberg (1964), Castañeda (1974) are bundle theorists who are realists with respect to universals. D. C. Williams and Hume are nominalists with respect to universals. For the ultimate kinds are particular, unrepeatable, properties. Ordinary particulars and the notion of a universal are constructed; they are mere sets (Loux, Metaphysics 91–2). Bundle theorists deny the existence of substrata, mainly because of empiricist concerns. A supposed substratum is not something that can be experienced. The ordinary particular, according to a bundle theorist, is no more than the totality of some qualities. Realist bundle theorists, such as the later Russell, maintain that the ordinary particular is a series of transient particulars over space–time, each of which in turn are composed of universal qualities. What binds these properties together is the relation of compresence. The relation of compresence is considered to be an unanalysable, primitive relation. It is a contingent relation into which properties enter, which explains the contingent existence of transient particulars. Universals on this view are multiply occurring or repeatable entities. Universal properties do not need a subject such as a substratum to be exemplified. The ontologically basic category for realist bundle theorists is that of universal qualities. Universals for them are multiply occurrent entities; they are not entities that are exemplified by various substrata (Loux, Metaphysics 99). Nominalist bundle theorists, on the other hand, hold that ordinary particulars are composed of tropes, that is, particular properties, held together by the relation of compresence, or the ‘connection of location’ as D. C. Williams calls it (ibid. 80–1). Berkeley held the nominalist bundle theory for physical objects, but not for minds. In section 49 of his A Treatise Concerning the Principles of Human Knowledge Berkeley says, ‘. . . To me a die seems to be nothing distinct from those things which are termed its modes or accidents. And to say a die is hard, extended and square, is not to attribute those qualities to a subject distinct from and supporting them, but only an explication of the meaning of the word die’ (120). Hume held the bundle theory for both minds and physical objects. In ‘An Abstract of a Treatise of Human Nature’, Hume argues, ‘The mind is not a substance in which the perceptions inhere . . . We have no idea of substance

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of any kind since we have no impression of any substance either material or spiritual. We know nothing but particular qualities and perceptions’ (194). According to the bundle theory of particulars, whether realist or trope theorists, there is only one ontological category. The nominalist trope theorist takes this category to be that of the particular, such as tropes for D. C. Williams and Hume. On the nominalist bundle theory, the ontologically basic entities are the tropes that are particular properties, or ‘individual property instances’, as Russell would call them. For realist bundle theorists, this category is that of the universal, such as the later Russell’s universal qualities. Contemporary trope theorists typically identify abstract properties with classes of relevant tropes. Goodman, however, does not identify abstract properties with classes: ‘The nominalistically minded philosopher like myself . . . will so far as he can avoid all use of the calculus of classes, and every other reference to non-individuals, in constructing a system’ (Goodman, The Structure 25–6). Since Goodman rejects classes as entities, he follows Quine, who maintains that a certain property, such as blue, is a scattered individual; a discontinuous particular found here and there. Quine maintains, for example, that ‘“red” is on a par with “Cayster” [the river], as naming a single concrete object extended in space and time’ (‘Identity’ 69). I now turn to a brief introduction of the three major objections that a realist bundle theory faces. These problems will be discussed in detail in Chapters 4, 5 and 6. The first I will call the problem of individuation. The realist bundle theory faces the substratum theorists’ charge that the bundle theory is false because the principle of the identity of indiscernibles, to which the bundle theorist is committed, is false. Substratum theorists believe the principle is false because there can be indiscernibles which are not identical. It is claimed that the bundle theorist’s use of ‘constituents and wholes’ implies that the whole constructed is nothing more than the totality of what makes it up. The constituents of a particular are all its properties. There is nothing among the constituents of a particular that is not a property. Therefore, when two particulars share all their properties, there is nothing left to account for their distinctness (Loux, Metaphysics 107). In contrast, since on the substratum theory what differentiates one particular from another is its substratum, if it happens that there are two particulars with all their properties in common, their respective substrata will account for their distinctness. Another objection to the bundle theory is a reductio argument to the effect that the theory implies that all the properties of a particular are essential to its

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identity because if one of the properties had not been part of the complex that makes up the bundle, that bundle would not have existed. As a consequence, all true propositions ascribing properties to a particular, that is, subject–predicate propositions, become metaphysically necessary truths. But not all true subject– predicate propositions express necessary truths. Therefore, the bundle theory must be false. On the substratum theory, in contrast, every subject–predicate sentence makes a contingent claim. For the identity of a particular is constituted only by the substratum, not by any of its qualities so that none of its qualities are essential to its identity (ibid. 105–6). The third objection, the problem of analyticity, is that the bundle theory implies that all propositions ascribing a property to an individual are analytic propositions, therefore the bundle theory is not able to give a satisfactory account of subject–predicate discourse. When bundle theorists analyse the sentence ‘The cardinal is red’, they will hold that the subject is a bundle of properties and the relationship between the predicate and the subject is that of claiming that the property in question is a constituent of the bundle. But substratum theorists find this answer unsatisfactory in the sense that all true subject–predicate sentences become tautologies or analytic truths. Furthermore, assuming that grasping a bundle requires knowledge of all its constituents, they claim that no subject– predicate sentences can be both true and informative. If it were true that knowing the meaning of a bundle requires knowing all its constituents, we would know the truth-value of the sentence just by virtue of knowing the meaning of the word for the bundle (ibid.). Substratum theorists, on the other hand, do not face such a difficulty because the particular to which a property is attributed is bare. The motivation to salvage the realist bundle theory is mainly due to a desire for a sparse ontology. If we can give an account of the world based only on one category of existence, we should adopt that theory. But then why not accept merely individual properties as ultimate constituents instead of universals? Russell’s answer is, ‘retaining “things” does not enable us to dispense with qualities,5 whereas bundles of qualities fulfill all the functions for which “things” are supposed to be needed’ (Schilpp 697).

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The Substratum Theory (1903–40)

Ordinary particulars, that is, objects that persist over time, endure for the early Russell, until 1914. There is something that persists throughout the changes a particular undergoes. This something, I show in this section, is a substratum. Interpreting the early Russell to hold the substratum or bare particular view is supported by Loux (Metaphysics 98), Stace (‘Russell’s Neutral Monism’ 370) and hinted at by Hochberg (‘Things and Qualities’ 85, fn. 1; ‘Universals’ 88–9). As of 1913, however, the notion of an ordinary particular starts to fade away. Russell starts working towards a perdurance theory. When an ordinary particular, for example, a table, becomes a class of sense-data and sensibilia in 1914 the substrata are not completely laid off. They are employed as individuators of sense-data or events that make up the classes that stand for the ordinary particulars. However, substrata will be permanently unemployed as of 1940. As for our knowledge of ordinary particulars, in The Problems of Philosophy, the ordinary particular (material object) is an inference based on the sense-data presumably caused by the ordinary particular. The material object which gives rise to these sense-data and sensibilia is an inference to the best explanation (Griffin ‘Introduction’ 30). ‘What we call a “thing” . . . is a complicated inference from correlated sense-data’ (TK 94). Before we delve into the early Russell’s arguments for the substratum theory of ordinary particulars, a terminological introduction is in order. I divide terminology such as ‘terms’, ‘predicates’, ‘qualities’, ‘relations’, ‘particulars’ and ‘universals’ into three groups: (1) as part of a sentence (grammatical function),

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(2) as they are used in logic and/or semantics and (3) the ontological statuses they have. Terminology with examples: Parts of a sentence

Logic/Semantics

Ontology

Kent

Subject (proper name)

Term

Particular1

Kent flies.2

Predicate (verb)

Monadic relation

Universal

The wall is black.

Predicate (adjective)

Quality (monadic rel.) Universal

A violet is a flower. Predicate (substantive)

Quality (monadic rel.) Universal

Dogs chase cats.

Dyadic relation

Verb

Universal

Source: ‘The Philosophy of Logical Atomism’ 199–200.

What about properties? Russell does not use the word ‘property’ in a specific, consistent manner throughout his works. His logico-semantic terminology consists of terms and relations, and the latter are the same as qualities when they are monadic. I think Russell would treat ‘property’ as belonging to grammar, rather than logic/semantics, for he makes a distinction in My Philosophical Development between predicates and properties, which assumes the two belong to the same category. The conception of a property is wider than that of a predicate: ‘A predicate will be something that can occur in a proposition containing nothing else except a name – e.g. “Socrates is human”. A property will be what is left of any proposition in which a name occurs when that name is omitted or replaced by a variable. You may say, for example, “If Socrates had been more conciliatory, he need not have drunk the hemlock”. This may be considered as asserting a property of Socrates, but not as assigning a predicate to him’ (MPD 124). Thus, properties are wider than predicates in the sense that one can turn anything said about a subject into a property. For example, A flies; therefore, A has the property of flying. Again, A likes B, therefore B has the property of being liked by A, for example. Qualities include both sensible qualities and kind-identifying qualities, though the latter may be reduced to the former. In Problems of Philosophy, Russell defines ‘quality’ as ‘the universals represented by adjectives and substantives [nouns]’ (54). Qualities that are sensible are colours, sounds, tastes, sensations of touch, relations of position in a perceptual space, and of temporal order in perceptual time. The last two are considered as qualities only in the later period. Relations include all relations from 2-place to n-place.

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Russell’s arguments for substrata Logical subjects of subject–predicate sentences (POM) Russell’s notion of ‘term’ in The Principles of Mathematics suggests that he takes particulars to be substrata. In The Principles, anything that can be an object of thought is called a term, for example, a person, number, chimera, relation. They are individuals, that is, numerically diverse, and they are entities, that is, they have being in some sense. He regards terms as incapable of modification by having different relations. Russell holds that ‘a term is possessed of all the properties commonly assigned to substances or substantives’ (§47). He lists the commonly attributed properties as: being a logical subject, being immutable, and being indestructible: ‘What a term is, it is, and no change can be conceived in it which would not destroy its identity and make it another term’ (ibid.). Consider ‘Socrates is mortal’ and ‘Mortality is a person’s biggest worry.’ According to Russell, in the propositions expressed by these sentences both Socrates and mortality3 are terms. As logical subjects, they are supposed to have unchanging natures. Mortality, as a property is unchanging. But Socrates did change; he was young, then he aged. There are two ways in which Socrates could have such a nature: what we mean by Socrates is Socrates’ essence or all there is to Socrates is his substratum that bears various properties at different times. The term, Socrates, is also supposed to be numerically identical to itself and numerically diverse from everything else. But if Socrates is Socrates’ essence, unless the essence in question is an individual essence, that is, some property that only Socrates had, such as being the teacher of Plato or the identity property of being identical to Socrates, his essence will consist of properties such as being a rational man. Such a property is shared by a number of other individuals; so Socrates is not numerically diverse after all. Both the property of being the teacher of Plato and the property of being identical to Socrates are relational properties, and as such cannot be part of the logical subject. Therefore, the logical subject, Socrates, can only refer to a substratum.

Two things can be numerically diverse, while qualitatively identical. Something needs to account for this fact (POM and PP) Russell’s second argument for particulars is from the problem of individuation. This argument is given both in 1903 and in 1911. Russell in The Principles of Mathematics holds that every term is immediately diverse, without appealing to

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any properties or relations they have. And this can only be explained by things (individuals) having substrata or by their being at certain points and instants. In the quoted section that follows, Russell discusses numerical diversity: It is a sheer logical error to suppose that, if there were an ultimate distinction between subjects and predicates, subjects could be distinguished by differences of predicates. For before two subjects can differ as to predicates, they must already be two; and thus the immediate diversity is prior to that obtained from diversity of predicates. Again, two terms cannot be distinguished in the first instance by difference of relation to other terms; for difference of relation presupposes two distinct terms, and cannot therefore be the ground of their distinctness. Thus if there is to be diversity at all, it must be immediate diversity, and this kind belongs to points. (POM §428)

This argument concludes that there is something which gives terms ultimate diversity. Russell thinks terms must have unchanging natures in order that they may enter into relations with each other. There are two ways in general that terms have ultimate numerical diversity: (1) Every term is at a point and instant which are considered to be entities or (2) Every term has a substratum which is peculiar to it. And since in §428 the terms Russell is talking about are points, (1) seems to be the more likely option. Besides, during the time of The Principles of Mathematics Russell holds the absolute theory of space and time (§424), thus the points and instants as entities secure numerical distinctness. However, since in The Principles every term, including ‘a unicorn’, is numerically distinct, and no unicorn takes up a unique point in space or instant in time, it must be substrata which guarantee the numerical distinctness of all terms. Later in 1911 Russell holds the relational theory of space–time due to the theory of relativity, and yet still thinks terms must be immediately diverse. When he adopts the relational theory of space–time (in both perceptual and physical worlds), there are no more unique points and instants which could account for the numerical diversity of terms prior to their difference in qualities. This shows that around 1911 he still had to appeal to substrata. In 1911 Russell’s argument for the existence of particulars is the following. Suppose there are two patches of white in my visual field. They are qualitatively identical. If one assumes that perceptual space is absolute,4 then the different places of the two whites will account for the diversity. But Russell around 1911 takes perceptual space as relative, not absolute. ‘Absolute positions are not among objects of perception’ (‘On the Relation’ 116). When space and time are taken to be relative, there must be a way of distinguishing between two qualitatively

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identical things. For according to the relational view of space–time, there are no absolute points in space or absolute instants in time that individuals occupy. The location of each individual is determined by its relations to other individuals. Russell argues that two whitenesses cannot be distinguished in terms of their spatio-temporal relations to other things. This would require that the whitenesses are already numerically diverse, that is, unique particulars. Suppose there are two whitenesses, one surrounded by red and the other surrounded by black. We can distinguish the two whitenesses in terms of their relations of being surrounded by red or black. But for this distinction to be valid, we must know that it is impossible for something to be both wholly surrounded by red and wholly surrounded by black at the same time. This ‘presupposes the numerical diversity of our two patches of white’ (ibid. 117). Later in My Philosophical Development, Russell would write, ‘the two patches differ only in position, and since position is not a quality (or so I thought) it presupposes diversity and cannot constitute it’ (121). Russell thought in 1911 that ‘terms of spatial relations cannot be universals or collections of universals, but must be particulars capable of being exactly alike and yet numerically diverse’ (‘On the Relation’ 118). Russell here explains numerical diversity by the substratum each particular has. He requires particulars to have substrata as well as qualities just so that there can be numerically distinct but qualitatively identical things on a relational theory of space and time.

There needs to be numerically diverse elements to construct points and instants The third argument for the existence of particulars is from the construction of space–time series. Space–time is relative. Thus, no absolute points or instants exist. We have to construct them to form the space–time series. We need elements that are immediately diverse as elements of the classes that will stand in place of real point-instants. Particulars, which are numerically diverse, can be used to construct these classes, and these classes in turn will enable us to generate spatio-temporal series (MPD 121). It seemed to Russell that ‘the time series and the space of geometry could not be constructed without the use of materials that had unique spatio-temporal position, and that such materials could not be found if particulars were rejected’ (ibid.). Since as of Theory of Knowledge and Our Knowledge of the External World points and instants are classes, whose members are particular sense-data or particular events, it is the immediate distinctness of the events that belong to each class which secures the uniqueness of each ‘point’

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or class. To better understand this argument, we will go on a small excursion to Russell’s views of time that he advocates in Theory of Knowledge and resume the discussion of substrata afterwards. According to Russell’s view of time, what is objectively real is that some events happen earlier than others; some events succeed others. But the tensed time that we express with the present, past, and future tenses, such as ‘I am writing now’, is not an objective part of the world, but is dependent on our experience. Russell explains that there would not be a present, past or future if there were no experience, but there might well be earlier and later, even without experience. ‘There is no logical reason why the relations of earlier and later should not subsist in a world wholly devoid of consciousness’ (TK 73–4). Hence Russell’s view of time is what is called ‘the block view’ (or the B-theory), according to which temporal passage is not an objective part of the world. It is dependent on our perspectives. As Dainton describes the block view, ‘All moments of time are equally real, and there is no moving or changing present; nothing becomes present and then ceases to be present. The differences between past, present, and future are simply differences of perspective’ (Dainton 7–8). And the truthmakers of tensed propositions are not tensed facts, but rather tenseless facts (ibid. 32). Even though tensed sentences, such as ‘The sun is shining now’, do not describe tensed facts about the world, that is, objective properties of objects, they nevertheless describe relational facts. Tensed sentences express facts about the speaker and her relations to her immediate surroundings. Just as we hold that terms such as ‘far away’ or ‘taller than’ describe an existent’s relations to its immediate spatial surroundings, we should understand tensed sentences as expressing relations between a sentient being and the reality immediately around it. Since Russell accepts that there should be a relation ‘taller than’ as an objective fact, consistency demands that he maintain that tense terms, such as now and past, express further objective relations among the existents in the world. In fact, he does. The early Russell explains tenses by appeal to the relation between the sensing subject and the object.5 It is this relation that gives us the mental time, as opposed to the physical time. Relations of sensation and memory give time relations between subject and object. Physical time, on the other hand, depends on the relations between objects themselves. Relations of simultaneity and succession give time relations between objects (TK 64). Hence, to construct mental time series, Russell will need elements he can put in a succeeding order. Those elements are total momentary experiences, which are a collection of simultaneous objects of acquaintance.

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Russell explains the present tense by appeal to his theory of acquaintance. Sensation is the ‘kind of acquaintance with particulars which enables us to know that they are at the present time’ (ibid. 66). And something is now when it is simultaneous to a this, an object of sensation. Past tense is explained by memory (ibid. 65). And his argument for sensation involving presentness is the following: There cannot be any intrinsic difference between present and past objects. Sometimes, the object of sensation (sense-datum) and the object of imagination are the same, hence the difference between sensation and imagination cannot lie in their objects, but will lie in their being different relations between the subject and the object (ibid. 54). Similarly, there should be a different relation between subject and object when the object is past or present. We know by introspection which objects are past or present (ibid. 66). Thus, now is a relation between me and the object of my experience, namely sensation. Imagine me admiring the falling of the rain right now. Just as being admired by me is not an objective property of the rain, the nowness is not an objective property of the rain either. The liking is a relation between me and the rain in question. Similarly, when I see and hear the rain now, there is a certain relation between my sensory faculties and the rain in my vicinity. Later in Inquiry (1940), Russell will still explain presentness as based on a relation, but the subject is not a mind, it can even be a machine that says ‘“this is red” and “that was red” . . . on suitable occasions’ (IMT 111). For in The Analysis of Mind (1921), Russell rejects the subject (mind) as a substance, which enters a relation with an object. He appeals to the egocentric particular ‘this’ to explain now: ‘All egocentric words [I, here, now, past, present, future] can be defined in terms of “this” . . . “now” means the time of “this”’ (IMT 108). He says what differentiates past from present is the different causal relations involved in both cases. If there is a minimal causal chain between the speaker (or machine) and the stimulus, then it is present; if there is a longer chain, then it is past. Furthermore, the causes in perceptive use of a word and reminiscent use of a word are different as well. For instance, if I say ‘This is a cat’, that is, if I see a cat now, the perceptive stimulus will be a cat, but if the stimulus is reminiscent, that is, if I say ‘That was a cat’, there must also be some other present stimulus. Perhaps a friend asked me what I saw (ibid. 112). In explaining order in mental time, Russell (1913) uses total momentary experiences (‘tome’ hereafter), which is a correlate to an instant. A ‘tome’ is defined as ‘a group of objects such that any two are experienced together, and nothing outside the group is experienced together with all of them’ (TK 67). This definition of a tome at first sight seems to create a problem for the construction

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of mental time, since the ‘present’ becomes ambiguous if recurrence is possible. But it does not because recurrence does not happen in experience. Russell defines instants of physical time in a similar fashion to tomes. An instant is defined as a group of events, any two of which are simultaneous and nothing outside the group is simultaneous with all in the group. Then ‘an event is “at” an instant when it is a member of the class which is that instant’ (ibid. 74). Now in order to construct a physical time series, the relation of succession has to be asymmetric and transitive (ibid. 75). But if recurrence is possible then succession cannot be transitive, or even asymmetrical. Succession is not asymmetrical if A occurs before and after B. ‘If B occurs both before A and after C, while A occurs before C but never occurs after C, A will succeed B and B will succeed C, but A will not succeed C. Thus, succession will not be transitive’ (ibid.). If everything in the universe at one instant recurred after an interval, the anterior and posterior instant would be identical. Russell in TK argues that it is not a good answer to say it is improbable that everything in the universe at an instant should recur. But, interestingly, Russell of HK will find this answer acceptable. If it did recur, the early Russell says, there would be two occurrences that are not numerically identical. ‘It would be contrary to self-evidence to say that there was strictly one occurrence, which was anterior and posterior to itself. Without taking account of the whole universe, if a thing A exists at one time, then ceases, and then exists again at a later time, it would be more natural to say something similar reappeared than to say the same thing appeared’ (TK 76). Russell explains that there are two ways in which one could avoid the problem of recurrence in this series: One is to accept absolute time, that is, ‘admit that there is an entity called a “moment” which is not a mere relation between events, and is involved in assigning the temporal position of an object’ (ibid. 69). But since Russell does not hold time to be absolute any longer, he instead secures the non-recurrence of the elements of construction by invoking sense-data and sensibilia, or events. Since these are regarded as particulars, they cannot recur. They are immediately diverse. To define time series in physical time Russell uses the ‘simultaneity’ relation, which is ‘a relation between objects primarily, rather than between object and subject’; and he defines an instant as ‘a group of events of which any two overlap, . . . no event outside the group is simultaneous with all [events in the group], but all the events inside the group are simultaneous with each other’ (OKEW 124). But in the later period, he will drop simultaneity in favour of compresence, which is a relation between qualities that are present together. One reason for this change is the finding of the special relativity theory that simultaneity

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is actually ambiguous. Simultaneity of events experienced in the perceptual realm is not ambiguous, but simultaneity becomes ambiguous in the case of the physical realm. Russell explains that Einstein’s work showed that ‘simultaneity is ambiguous when applied to events in different places’ (HK 287). Two events may appear simultaneous from one perspective, but not simultaneous from another. Russell explains that ‘two events in distant places may appear simultaneous to one observer who has taken all due precautions to insure accuracy (and, in particular, has allowed for the velocity of light), while another equally careful observer may judge that the second preceded the first. This would happen if the three observers were all moving rapidly relatively to each other’ (ABC 35). Hence, the later Russell uses the relation of compresence both for the relation between qualities simultaneously experienced and for the relation between qualities that overlap in space–time (IMT 231). To recapitulate, the early Russell’s solution to the problem of recurrence is the adoption of particulars that persist for a finite period of time. These are transient particulars. Thus, the problem of recurrence of an instant, which is construed as a group of simultaneous events, is one reason why the early Russell opts for a substratum theory of particulars.

The qualities of a particular are instances of universal qualities In this early period, the analysis of an ordinary particular yields a substratum and some qualities. Qualities are universals. They are transcendent universals, which are instantiated in ordinary particulars. When they are instantiated, they are sense-data. In The Problems of Philosophy, he defines sense-data as ‘the things that are immediately known in sensation: such things as colours, sounds, smells, hardnesses, roughnesses, and so on’ (4). A sense-datum is an object of sensation, and sensation is a form of acquaintance (TK 66). Russell explains, ‘When I speak of a sensible object [a sense-datum], . . .what I mean is just that patch of colour which is momentarily seen when we look at the table, or just that particular hardness which is felt when we press it, or just that particular sound which is heard when we rap it’ (OKEW 83). Sense-data, then, are particulars. They are particular in virtue of their substrata though. They are not particular qualities or tropes. Universal qualities are instantiated or exemplified in particulars. There is an interesting exchange on this issue of instantiation between M. Weitz and Russell. Weitz argues that Russell held in the 1912 article

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‘Knowledge by Acquaintance and Knowledge by Description’ that qualities and relations have instances. Weitz writes, Russell is ‘so convinced that universal relations do have instances that he devotes most of his argument to the proof that we are acquainted with universal relations themselves. He writes, e.g., “Thus we must suppose that we are acquainted with the meaning of ‘before’, and not merely with instances of it”’ (Schilpp 69). However, Russell in reply denies that in 1912 he held the view that relations or qualities have instances and claims that he held this position continuously since 1902. Russell says, ‘when I say “A is human” and “B is human” there is absolute identity as regards “human” . . . there are no two humanities, nor two differences’ (684). I think this confusion arises because Russell does not make clear what he means by an ‘instance’. It might be interpreted to mean a specific property or relation, or it might be taken to mean the particular in which a universal property is exemplified or instantiated. Russell means the latter. When he says in this period that a particular is an instance of a universal, he means an ordinary (or transient) particular whose substratum, strictly speaking, exemplifies a universal. The view he rejects is that there are particular qualities or particular relations (tropes). Russell also has arguments against particular qualities or relations, or propertyinstances, as he calls them in The Principles of Mathematics and The Problems of Philosophy. The material object is the instance where certain universal qualities are exemplified. Strictly speaking, it is the substratum in an ordinary particular that exemplifies qualities. According to Russell, we are supposed to be acquainted with sense-data as well as with universal qualities themselves (POP 28).

Russell’s arguments against tropes The argument from the assumption of particular relations Russell’s argument against particular properties, and for universal properties, first appears in The Principles of Mathematics: Even if differences did differ, they would still have to have something in common. But the most general way in which two terms can have something in common is by both having a given relation [predication relation] to a given term. Hence if no two pairs of terms can have the same relation, it follows that no two terms can have anything in common, and hence different differences will not be in any definable sense instances of difference. (POM §55)

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Two specific differences would have to have something in common because, after all, they are both ‘differences’, and that has to be explained. If ‘difference’ refers to a class, that is, the class of all pairs that are different from each other, then all the pairs will have the same relation to the class-concept, ‘difference’, which is the class membership relation. And for something to belong to a class, it must fit some class intension, in our case, difference. The members will have to have the same relation, that is, same membership relation to the class, difference. But according to the particular properties view, there are no shared relations (Griffin and Zak 62). Griffin and Zak argue that this is a good argument as long as one wants to keep the notion of class intact. As D. Bostock explains, Russell did not make a distinction between classes and sets and maintained that classes have intensions independently of their extensions. But today there is a distinction made between sets and classes: ‘sets are to be conceived as “built out of their members” . . . whereas classes are conceived rather as the extensions of predicates, and therefore as given by our independent understanding of those predicates’ (Bostock 16). Thus, today a nominalist would put Russell’s argument aside by pointing out that difference is a set of particular differences, not a class of particular differences. Therefore, an explanation of why all pairs of differences belong to the same class is not called for. Granting that one wants to keep the notion of a class, Russell’s argument, according to Griffin and Zak, only shows that a theory where there are no universal relations at all would be false. It does not refute a mixed theory where all relations except for class membership are particulars. Therefore, this argument should not be considered as one that shows that all relations should be universals (ibid. 62–3). Indeed, all Russell argues for is that there must be a universal difference to explain what each specific difference has in common. It seems then that Russell’s argument does not exclude the possibility of a theory which countenances both specific differences and a universal difference. Such a mixed theory would, however, not appeal to any nominalist. One of the main arguments for nominalism is based on the virtues of a simple theory. But a theory where all relations except for class membership are particulars would not be a simple one since it would still posit two kinds of entities: particulars and universals. The nominalist’s response to the above argument would be to assert that difference, just like its opposite, similarity, is a fundamental fact about the world, and therefore, does not require explanation. That is, they would reject Russell’s suggested move of explaining the relation of difference by means of a

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class of pairs whose members are different, so that no problem of explaining the relation of class membership would ensue.

The infinite regress argument Russell has an argument in The Problems of Philosophy against resemblance nominalism, but which is also intended to serve as an argument against property-instances. He argues that the relation of similarity cannot be explained if all qualities and relations are explained by appeal to classes of ordinary particulars: If we wish to avoid the universals whiteness and triangularity, we shall choose some particular patch of white or some particular triangle, and say that anything is white or a triangle if it has the right sort of resemblance to our chosen particular. But then the resemblance required will have to be a universal. Since there are many white things, the resemblance must hold between many pairs of particular white things; and this is the characteristic of a universal. It will be useless to say that there is a different resemblance for each pair, for then we shall have to say that these resemblances resemble each other, and thus at last we shall be forced to admit resemblance as a universal. The relation of resemblance, therefore, must be a true universal. And having been forced to admit this universal, we find that it is no longer worthwhile to invent difficult and unplausible theories to avoid the admission of such universals as whiteness and triangularity. (POP 55)

Suppose we have an ordinary particular A and we call its colour ‘white’. Then we find another particular, B, which is also white because we see that it resembles A. And yet we find another particular, C, and it also resembles A and B in that respect. Now we have the same relation, ‘resemblance’, holding between three things. The ‘sameness’ of this relation can be explained either by a universal or by regarding each case of resemblance a particular one: R1: resemblance between A and B, R2: resemblance between B and C, R3: resemblance between A and C. Now R1, R2 and R3 resemble each other. The resemblance between these particular resemblances will also have to be explained. Again if the explanation is that this new resemblance between resemblances is particular, then the regress of resemblances will go on indefinitely. Even though aimed at resemblance nominalism, which does not countenance tropes but instead admits only ordinary particulars and explains qualities and relations by appeal to resemblance classes, this argument also serves as an argument against particular qualities and relations because at the second stage

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of the argument Russell supposes that a resemblance nominalist will explain the relation of resemblance by reference to a class of particular relations. Next he argues that such a move leads to a vicious regress because we are not able to explain the relation of resemblance that each of these particular white pairs have in common without having to climb up the infinite ladder of classes of resemblances. Rodriguez-Pereyra, a resemblance nominalist, denies that his position is committed to an infinite regress of resemblances (107–23). According to him, a regress does not start because the resemblances between pairs [A, B] and [C, D] do not need either a subsistent entity, ‘resemblance’, or another particular resemblance to account for the resemblances. It is A, B and C themselves that account for it. He reminds us that resemblance nominalism is an account of what makes ‘A is white’ true. On this account, what makes ‘A is white’ true is that A resembles B, which is also white (Rodriguez-Pereyra 110). And what makes ‘A resembles B’ true is the natures of particulars A and B. ‘If [A] and [B] resemble each other, then their resemblance is a fact because of their being the entities they are, and so [A] and [B] are the sole truth-makers of “[A] and [B] resemble each other”. There is then no need to postulate extra entities to account for facts of resemblance’ (115). On this account, what makes ‘A resembles B’ true will be the natures of A and B. But it seems to me that A and B cannot have any features to ground the resemblance. If there are no particular resemblances, then the nature of A does not include the property of resembling to B as a constituent, and neither does B include the property of resembling to A. If that is the case, then the natures of A and B should consist of qualities, which would provide grounds for making ‘A resembles B’ true. But there cannot be any qualities as part of the nature of A and B on this account because ‘A is white’ is made true, not by the white in the nature of A, but by the fact that ‘A resembles B’. Hence, the resemblance relation cannot be explained by the natures of A and B. Second, Rodriguez-Pereyra argues that Russell is also wrong when he argues that accepting one universal, resemblance, would make denying other universals pointless. Rodriguez-Pereyra points out the distinction between qualitative and quantitative economy. On qualitative economy, the goal is to keep the kinds of entities to a minimum, and on quantitative economy, we try to keep the number of entities in each kind to a minimum (107). And each has its virtues as argued by D. Nolan (1997). ‘A theory admitting n universals of resemblance [due to the regress of resemblances] would be quantitatively more economical than a full-blooded realism postulating a universal for each determinate property’

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(Rodriguez-Pereyra 122). I agree with Rodriguez-Pereyra on this point. If one accepts only the relation of similarity as a universal, and no others, this is still some achievement. It should be recognized as such. But Russell is right that it would not be as significant an achievement as reducing kinds of entities to one. There is a weakness, perhaps, in Russell’s argument. As pointed out by Bostock (243), Russell’s argument above based on the infinite regress of explanations is based on the premises of the correspondence theory of truth. Supposing A resembles B is true, what will explain its truth? According to Russell, there must be a fact to which the proposition, A resembles B, corresponds. Facts are complexes. The fact that A resembles B is constituted by A, B, and the relation of resemblance. The components of propositions refer to entities, such as particulars and universal properties or relations which make up facts. My first response6 to this was that the early Russell’s referential theory of meaning was another essential premise of his infinite regress argument. On the referential theory of meaning, in order for a proposition to be meaningful, the logical constituents of the proposition acquires meaning by standing for an entity. And the early Russell combines the correspondence theory of truth with the referential theory of meaning: A meaningful proposition is one which has a truth-value. In order for a proposition to be meaningful, that is, to have a truthvalue, each logical component of the sentence must refer to an entity. Thus, in order for the proposition ‘A resembles B’ to be meaningful, ‘A’, ‘resembles’, and ‘B’ must all refer to entities. And this is how ‘resemblance’ is explained; by positing a universal resemblance that the word ‘resembles’ stands for. I see now, however, that it is the correspondence theory of truth and the complex nature of facts which are the necessary assumptions for Russell’s infinite regress argument, not his theory of meaning. Otherwise one should not be able to mount the argument from a theory of meaning other than the referential one. But one can. In fact, the later Russell does in Inquiry. The later Russell disassociates his theory of meaning from his account of truth. He holds a causal/behavioural account of meaning of substantives, such as ‘box’ or ‘tree’, while still holding on to his correspondence theory of truth (chapters 13 and 15). And yet, he reiterates this very infinite regress argument in the last chapter of Inquiry. Thus, even though in the later period, Russell is in no obligation to posit entities to secure the meaningfulness of propositions, he reiterates his argument that the nominalist account of general words leaves the relation of similarity unexplained. Russell’s infinite regress argument seems to imply that resemblance is a fundamental relation since in the end we will have to admit that resemblance

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itself is a universal. But in fact it does not. On Russell’s realist view, resemblance is a derivative fact, not a fundamental fact. Yes, it is a fact that things resemble each other: my watch resembles my glasses with respect to colour. But this fact is derived from both of these items sharing the universal purpleness. What is fundamental is that my glasses are purple and so is my watch. That they resemble each other is a consequence of their both happening to have the same colour. When Russell argues against the nominalist requiring that there is a universal resemblance to account for the truth of ‘A resembles B’, this is on the assumption that we have picked an alternate route to explain other general worlds, such as whiteness or triangularity. It is only if one takes this alternative nominalist route that one will have to accept resemblance as a fundamental universal. If we follow Russell and explain first-level qualities such as whiteness in terms of universals, then we will have the tools to explain resemblance as a defined or derived universal from the first-level universals. What is required is that both A and B share a universal, yellowness. A universal of resemblance is not necessary as part of the ultimate furniture of the world. Many nominalists, whether resemblance nominalists or trope theorists, respond to Russell’s argument by arguing that there is no need to appeal to some further entity, such as a universal, to explain resemblances. The fact that things resemble each other is a fundamental fact about the world, and does not require any explanation. This is the point at which realists and nominalists seem to reach a stalemate. Realists about transcendental universal qualities insist that exemplification or instantiation is an ultimate fact about the world, whereas nominalists about universal qualities and relations insist that resemblance is a fundamental fact.

A substratum theory of transient particulars (1914–40) Perdurance: Ordinary particulars are classes (1914) Russell refuses to accept material substance in Our Knowledge of the External World (1914). What he has in mind in rejecting substance is the inferred entity, material substance, which was composed of a substratum and qualities. He denies the need to accept permanent material objects as causes of sensedata. Russell’s main reason for rejecting substance is that there is no empirical evidence for it. All we are acquainted with are sense-data; we are not acquainted with the material substance that presumably causes them. The early Russell’s

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analysis of an ordinary particular yields the substratum and qualities. Russell aims, so far as possible, for the logical simples of analysis to be things we are acquainted with (TK 119). However, a substratum is not something that we can be acquainted with. Therefore, Russell drops the substratum theory of ordinary particulars in 1914. The substratum of an ordinary particular ensured the persistence of the same object through time. But now Russell thinks that since all we have as data to believe that some table is the same table used on a previous occasion is all the similarities of appearances and the similarity of the correlations of those appearances, we should build our knowledge of the external world strictly on this basis. We should not make inferences to existents for which we have no direct evidence, such as the material substance. Russell notes though that he is not denying the existence of material objects, and neither is he affirming it. He says there is no empirical evidence for either position (PLA 273–4). Russell thinks we have no good reason to hold that material objects are permanent. For example, we have no reason to believe that ice when melted is the same substance. What we directly know is that the appearance we call ice has been replaced by the appearance we call water, and we can formulate laws as to how each behaves. But that is all. We have no reason to accept that the two appearances are of the same substance (OKEW 110). He no longer believes that the best explanation of our experiences requires that we infer the existence of enduring material objects. In 1914, having decided that the material object with its substratum and qualities is empirically inaccessible, Russell rejects affirming its existence. He tries to construct ordinary particulars out of sense-data, instead of inferring their existence. Russell claims that ‘the persistence of things through time is to be regarded as the formal result of a logical construction, not as necessarily implying any actual persistence’ (ibid. 153). Russell wants to have empirically given things, that is, sense-data, at the foundation of knowledge and then logically construct the entities we call material objects. He admits that conceiving ‘a system of correlated particulars, [i.e., a class of sense-data] hung one to another by relations of similarity and continuous change and so on’ is complicated (PLA 273), but argues that we should nevertheless construct the external world since such a system of correlated appearances (objects of sensation) is what is empirically given to us as data.

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Transient particulars: Sense-data Russell defines a thing (an ordinary particular) as ‘a certain series of appearances, connected with each other by continuity and by certain causal laws’ (OKEW 111). These appearances are now the transient particulars which are the members of the class which we call an ordinary particular. Russell takes wallpaper as an example. To assume that there is a permanent entity, the wallpaper, which ‘has’ the various fading colours, is just ‘gratuitous metaphysics’ (ibid. 112). Such a substance is not empirically given to the perceiver. Instead he defines the wallpaper as ‘the series of its aspects’ (ibid.). By doing so, he uses Ockham’s principle that advises us not to ‘multiply entities without necessity’ (ibid.). We find the entities that we cannot do without, which are the successive appearances in experience, and then define any other purported entity in terms of these appearances (PLA 280). A piece of wallpaper is a series of classes. The class is a collection of all the appearances of the wallpaper from different perspectives at a time. We logically construct a series out of the classes of the appearances of the wallpaper at each moment. This series stands for the material object wallpaper (ibid. 275). There is no need to assume a persistent substance (ibid. 276). Thus, at this stage, the enduring ordinary particular with its substratum has been eliminated. However, we need to pay attention to the fact that Russell is not yet able to completely rid his theory of substrata. We know perceptual and physical space–time were relational for Russell since at least 1911, and until 1940. However, since space–time is relational in Our Knowledge of the External World, this means there are no instants or points as entities to provide numerical diversity between qualitatively alike groups of appearances. So, he still needs elements which are numerically diverse to construct point-instants. These elements are the particular sense-data (TK 55), just like the events to follow in The Analysis of Mind and The Analysis of Matter. Sense-data are the transient particulars that make up a class, which replaces an ordinary particular. What Russell refuses the existence of in Our Knowledge of the External World is the view of an ordinary particular as an enduring material object, with its substratum and qualities. But the substratum flag now has passed on to these fleeting, private appearances, which Russell calls sense-data. In The Analysis of Mind and The Analysis of Matter, events will carry the flag. Events are going to be the transient particulars that make up the class of an ordinary particular. Stace correctly notes that Russell in The Analysis of Mind succeeds in eliminating the ‘substrates’ – or ‘Ding-an-Sich’ as Stace calls them – of an ordinary particular. But the Ding-an-

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Sich has been transferred to the aspects, particular sensations. ‘The unverifiable character of the old solid “physical object” is simply transferred to the new airy and fluttering “aspects”’ (Stace 370).

Transient particulars: Events (1919–40) From sense-data to sensations Russell in The Problems of Philosophy claimed we could be acquainted with objects of sensation (sense-data) and then infer the existence of material objects. Hence, the having of sensations was a form of knowledge for Russell in The Problems. However, he realizes in 19197 that his earlier view that sensation is cognitive had led him to distinguish between sensing (sensation) and what is sensed (sense-data), which in turn required a perceiving mental substance, a subject in a cognitive relation with an object, that is, the sense-data (AMi 141). But once he has decided that there is no good ground for assuming mental substance to exist, he let the distinction between sensation and sense-data go in 1919. Without the subject, who through sensation knows sense-data, sense-data are no longer objects of knowledge. Sensation and sense-data are not distinguished from each other (ibid. 142). ‘The sensation that we have when we see a patch of colour simply is that patch of colour, an actual constituent of the physical world’ (ibid.). Later on Russell regards sensations as causes of knowledge, but he does not regard them knowledge in themselves any longer (AMi 144). One reason why sense-data (appearances) as elements of the construction of particulars is abandoned is that when you confine ultimate existents to actual and possible appearances, you leave out physical entities such as electrons which cannot appear to anyone. When I hear a sound, the sound-waves that travel are not appearances of any kind. Yet they must exist (Bostock 194–5). What we have, as of 1919, in place of sense-data, are sensations. And sensations are events, but not all events are sensations. Events are short-lived, transient particulars. In Logical Atomism (1924), Russell writes, The world consists of a number, perhaps finite, perhaps infinite, of entities which have various relations to each other, and perhaps also various qualities. Each of these entities may be called an ‘event’ . . . Every event has to a certain number of others a relation which may be called ‘compresence’; from the point of view of physics, a collection of compresent events all occupy one small region in spacetime. One example of a class of compresent events is what would be called the contents of one man’s mind at one time- i.e. all his sensations, images, memories,

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thoughts, etc. which can coexist temporally . . . Every part of his visual field is compresent with every other part, and with the rest of ‘the contents of his mind’, at that time, and a collection of compresent events occupies a minimal region of space-time. (341)

Events, Russell wishes to argue, are neutral in their nature; they are neither mental nor physical. Russell now abandons dualism on the nature of the ultimate reality in favour of neutral monism. Events are presented or perceived either in mental terms or physical terms depending on the kind of causal laws involved. Laws of physics yield classes that stand for physical entities, laws of memory and perspective yield classes which stand for mental entities. Russell, as of 1919, believes that neutral monism, according to which sensations are fundamentally neutral (events which can obey both mental and physical laws), is a better ground for bridging the gap between the world of sense and the world of physics. Earlier in Our Knowledge of the External World, the stuff of the world of sense, that is, sense-data was of the same kind, that is, physical, with the stuff of physics, and thereby sense-data constituted the bridge between the world of sense and the world of physics. But now that sense-data are abandoned, neutral events will take the place of common ground between the two worlds. The mental and physical ordinary particulars are constructed out of the neutral stuff, namely sensations. A physical thing is a class of sensations arranged according to physical causal laws. First the laws of perspective bring together the sensations of one thing at one time from different places to form a momentary thing, and then laws of dynamics bring together such classes of sensations to form one thing. For instance, Jones is a series of occurrences bound together by causal laws, not similarities, though various appearances of Jones will quite likely be very similar. But the causality here is not one of ordinary scientific causation, where Jones would have been considered the ‘real’ cause of all the appearances presented to different observers (AMi 97). Russell instead takes the whole class of sensations as actually being Jones (ibid. 98). What bring together the various appearances of Jones are such physical causal laws as the laws of perspective, reflection, and diffraction of light. This is the same for all physical objects (ibid. 99) and all physical objects are systems of particulars (ibid. 102). In the world of psychology, first the laws of dynamics collect together successive sensations of one thing, and then such classes of sensations are brought together to form an experience or biography (ibid. 126). Russell, having

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denied that there is a subject, a mental substance, which is supposed to be in relation with the physical world, explains the subject as a construct of sensations and images, which are causally dependent upon sensations. Bostock correctly argues that the main problem with the phenomenalist account of perception in The Analysis of Mind and Our Knowledge of the External World is that it does not give us any scientific explanation, that is, it does not tell us why perception occurs. On this theory, all we know is that perception occurs in certain regularities. So, we can make predictions, but are not provided any explanations (Bostock 194).

The qualities of events: Instantiations of universals Events, according to Russell, are particulars; they are entities designated by proper names (Schilpp 698; AMi 193). As explained earlier, Russell needs entities that cannot possibly recur in order to construct the point-instants of the space–time series; and events serve this purpose well. These particulars have qualities. The question now is: What is the nature of these qualities? Are they still instantiations of transcendent universal qualities? In The Analysis of Mind, Russell abandons his earlier The Problems of Philosophy view that one needs to be acquainted with universals in order to be able to use general ideas appropriately. In chapter 11 of The Analysis of Mind, Russell argues that the fact that we can use general ideas or thoughts does not show, on its own, that the reason why we can do this is that we have directly experienced them. We cannot experience universals. What we experience are particular events (AMi 228). I should note, however, that at this stage, Russell is still discussing a transcendental or Platonic understanding of universals. A transcendent universal is what he now believes cannot be experienced. He is not yet considering immanent universals. This rejection of a form of direct knowledge of transcendent universals, I argue, does not amount to the rejection of their existence. Russell still maintains that the qualities or relations of particular events are instances of universal qualities and relations. Universals are part of the world, ‘though an inferred part’ (ibid.) since we cannot experience them. Russell has always maintained that universals are real, a part of reality. What has changed is his account of our knowledge of universals. There are two ways of knowing universals. One is a lower kind of knowledge, where the determination depends on appropriate reaction to stimuli. And the higher kind of knowledge relies on recognition of similarities and differences,

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which are used to make inferences to universals. This is a theory of how we acquire knowledge of universals, not a theory as to whether universals exist or not. Just before the passage I quoted, Russell says, ‘I think a logical argument could be produced to show that universals are part of the structure of the world, but they are an inferred part, not a part of our data’ (ibid.). I do not know why he italicized ‘think’ here. But my interpretation of his views in this period, given his position on truth throughout his whole career is that he must, even in this period, believe that there are universals, for they are his truth-makers. He believes that there is a world existing independently of what we think or claim to know about it. Thus, there are facts about this world, which make our propositions true or false. And these facts have a complex structure. So, there must be universals as part of these facts, to make our claims about the world true or false. That he now thinks that we cannot have direct knowledge of the universals does not change or clash with his conviction that they must exist. Landini in ‘On What There Isn’t’ (2009) also maintains that universals are still part of Russell’s ontology as of 1918. Landini explains that after Russell adopted neutral monism, he ‘decided that universals are distinguishable only by their causal powers and have a predicable nature only. A predicate can only occur in a predicate position, not in a subject position. Thus, Russell has to abandon his thesis that a mind can stand in a relation of “acquaintance” to a universal’ (27). To recapitulate, then, ordinary particulars, such as tables or trees, perdure as classes of transient particulars starting from Our Knowledge of the External World (1914) until and including his last major metaphysical and epistemological work, (1948) Human Knowledge. From Our Knowledge of the External World up to Inquiry (1940), the transient particulars are not bundles; they require substrata, some immediate ontological individuators as constituents. Hence, Russell’s transient particulars fall in the category of substratum view in this period. In the next chapter, we will see that Russell’s account of transient particulars becomes a bundle theory as of Inquiry. Each transient particular will be constituted merely of qualities.

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The Bundle Theory (1940–8)

A bundle theory of transient particulars In My Philosophical Development, Russell explains that his view of particulars in The Principles of Mathematics led to a substratum view and he looked for a way to escape it: There was another class of difficulty which was connected with the wellestablished objections to the notion of substance. It seemed as if the particulars which I had denoted by small Latin letters would have to be substances in a syntactical sense, though they would not need to have the property of indestructibility which substances were traditionally supposed to possess. If the statement that x has such and such a property1 is always significant, and never analytic, it seems to follow that x is something different from the sum of all its properties, and it must differ from another particular, y, purely numerically, so that it should be logically possible for the two particulars, x and y, to share all their properties and yet be two. We could not, of course know that they were two, for that would involve knowing that x differs from y, which y does not do: x, in fact, would become a mere unknowable substratum, or an invisible peg from which properties would hang like hams from the beams of a farmhouse. Such considerations make the concept of ‘particulars’ difficult, and invite a search for some way of escape. (MPD 119–20)

Russell explains that he discussed the bundle theory in his 1911 paper (‘On the Relation’ 118) as a way to escape the ‘invisible peg’, but was convinced back then that the bundle theory was not satisfactory because he thought that this theory is not able to explain numerical diversity between two qualitatively alike bundles and he could not see a way of constructing point-instants of the space–time series without invoking entities that are particulars (MPD 120).

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Addressing the problem of numerical diversity The later Russell recognizes that position in perceptual space is absolute, and not relative as in non-perceptual space. So, now he sees an opportunity to abandon particulars as composed of substrata and universal qualities in favour of bundles of universal qualities, where qualities will include positional qualities. When perceptual space is taken to be absolute, there are location qualities in the perceptual space that one can use to distinguish two bundles of qualities that are alike. For instance, a bundle of blue and round qualities will have the quality of centrality (due to being in the centre of my visual field) while another blue and round bundle will have the quality of dexterity (due to being to the right of the centre of my visual field). These positional qualities will distinguish two blue and round bundles. It seems at first that the distinguishing power of positional qualities is confined to qualities experienced by me. But that is not the case. If I am perceiving two blue and round bundles, one compresent with the quality of dexterity and the other compresent with the quality of centrality, then, given Russell’s assumption of structural similarity2 between percepts and their non-perceptual causes, there must be a relation between the blue and round complexes in the world that cause my perception of them, a relation which corresponds to the positional qualities of the bundles in my perceptual field. Therefore, positional qualities in perceptual fields also help distinguish complexes in the non-perceptual world. Another aspect of the problem of numerical diversity is on a theoretical basis, in distinction from the problem of distinguishing two bundles presented in perception. If the bundle theory is correct about the nature of particulars, then qualities must in principle suffice to distinguish between two things. In other words, the principle of identity of indiscernibles must be true. But philosophers such as Wittgenstein (Tractatus 5.5301–3) and later M. Black have argued that it is logically possible for there to be two things that share all their properties. Counterexamples such as Black’s two similar iron spheres in an otherwise empty symmetrical universe seem to imply that in fact qualities are not enough for numerical diversity. In response, Russell accepts that there is such a logical possibility. But he nevertheless argues that we need to accept the principle of identity of indiscernibles, otherwise identity becomes indefinable and enumeration impossible (IMT 102). This problem will be discussed in detail in Chapter 4, ‘The Problem of Individuation’.

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Addressing the need for non-recurring elements for construction of point-instants We have seen earlier that since physical space–time is relative, there are no absolute points or instants to construct the space–time series from. Therefore, Russell needs to construct point-instants. But such a construction seems to require elements that cannot recur in order that the space–time series can be transitive. For that reason until Inquiry, Russell takes events as ultimate particulars, which serve as the elements of construction of point-instants. Russell in Human Knowledge first discusses the construction of instants and points from events, and he explains that in this construction he made three assumptions: ‘that a single event may occupy a finite amount of space-time, that two events may overlap both in space and time, and that no event can recur’ (HK 293). This view takes events as particulars, which have ultimate numerical diversity (ibid. 269, 292–3). But Russell was uncomfortable with having to admit events as ultimate kinds, because they retained the notion of substratum. In Human Knowledge, looking back, he explains that when constructing points and instants from events, events were provisionally taken as particulars. And as particulars, they are unknowable substances in which qualities inhere (ibid. 293). It is difficult to see how something so unknowable such as a particular would have to be required for the interpretation of empirical knowledge. The notion of a substance as a peg on which to hang predicates is repugnant, but the theory that we have been advocating [the construction of points and instants from events] cannot avoid its objectionable features. I conclude, therefore, that we must . . . find some other way of defining space-time order. (Ibid. 294)

This ‘some other way’ will be constructing them out of complete complexes of qualities. That is, in order to avoid the unknowable substance, Russell rejects events as the raw elements of construction. In their place he puts complexes of qualities. Thus, in the later chapters of Human Knowledge, Russell argues that events should not be ultimate kinds; instead we should explain events in terms of qualities, namely, as ‘incomplete complexes of compresence of qualities’, whereas ‘particulars’ which are the elements of space–time order would be ‘complete complexes of compresence of qualities’. Russell states that constructing points, instants and particles from qualities has the advantage of not having to accept any kind of particulars, things or events, as ultimate constituents.

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In Inquiry and Human Knowledge, Russell keeps the distinction between ordinary particulars, that is, ordinary particulars which seem to persist through time, such as a person or a book, and transient particulars, which are spatiotemporal slices of an ordinary particular. Russell repeats this view in Inquiry by pointing out that a proper name, say ‘Caesar’, does not refer to the individual entity that lived long ago; instead it refers to a series of occurrences involving Caesar in the continuous stretch of space–time that he lived (IMT 33). Thus, an ordinary particular is still to be constructed, but the members of the construction, that is, transient particulars, are not themselves further constructions; instead they are real quality-complexes. Thus, the persistence of an ordinary particular is still explained by a perdurance theory. It is not that we have one entity which endures through time, takes on some properties and leaves behind others. Instead, there are transient bundles composed of qualities, and a series of sufficiently similar and causally related such bundles make up an ordinary particular. The novelty that comes with the bundle theory is that the occurrences referred to above were events, but now they are bundles of qualities. Now that the substratum is rejected in the case of transient particulars as well, Russell will need a unifier for the transient particular. The relation of compresence will avail itself for the task. Qualities then are the ultimate constituents of reality in the later period. And Russell claims he can construct point-instants from qualities, which by their nature are recurring entities. Russell’s position on this is to accept the logical possibility that a complete complex of compresent qualities might recur, but insist that this is highly improbable given that positional qualities can be parts of complexes of compresent qualities (HK 294, 295, 298). ‘If we take a sufficiently large bundle of qualities, there will be no empirical instance of recurrence. Non-recurrence of such bundles may be accepted as a law of physics, but not as something necessary’ (ibid. 83).

The rejection of substratum in linguistic terms In this section, we will study Russell’s statement of his bundle theory in linguistic terms, that is, how he thinks the bundle theory, as a theory of what kinds of things exist, is reflected in language. Russell, putting it in linguistic terms, explains that the issue whether there are particulars as well as universals or merely universals boils down to what we mean by ‘this’, assuming that we are able to define all other egocentric particulars (indexical expressions) in terms of ‘this’. Is ‘this’ an

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ultimate or not? Does it stand for an ultimate kind of reality, that is, a simple particular or could we define it in terms of something else? Do we have to have it as part of our minimum vocabulary? Russell explains, ‘If “this” is ultimate, the following are significant, [i.e. non-tautologous]:

(a) This is exactly like that. (b) This might have other qualities than it has (i.e., false propositions of the form “This has the quality q” are not self-contradictory). If “this” is not ultimate, the following are significant:

(α) This has occurred before, or elsewhere. (β) This is identical with that. In either case the propositions in question are not significant on the opposite hypothesis.’ (Russell, Appendix to HK 291)

Russell, as of Inquiry (1940), argues that ‘this’ is dispensable. What ‘this’ refers to can be explained in terms of the qualities it is composed of. As a consequence, propositions α and β above become significant. ‘This’ is something which is in principle repeatable. The consequence that (a) and (b) will not be significant will be discussed in Chapters 4 and 5 respectively. For the later Russell, particulars, such as what ‘this’ denotes, are not fundamental unrepeatable entities. The ultimate ontological constituents are universal qualities. He compares two views of qualities: (1) as universals: a quality can exist at various times and places. (2) as instances of one universal: each quality exists only once. The later Russell chooses the first view that qualities are universals. On this theory, ‘what would otherwise be instances of the quality become complexes in which it is combined with other qualities’ (HK 265). This distinction is the distinction between immanent (1) and transcendent (2) universals, as Armstrong would later call them. A quality, linguistically, is not a predicate anymore, since there is no bare subject to which we could attribute qualities. ‘This is red’ or ‘Socrates is Greek’ should not be treated as subject–predicate propositions, where some quality is ascribed to a substance. These propositions express relations between wholes and their parts. ‘This’ and ‘Socrates’ refer to complexes, groups of qualities. Redness is one of the qualities of the complex I am attending to, which I call ‘this’, and being Greek is one of the qualities of the complex, Socrates. Thus, a complex of compresence is something that can have a name, just as the qualities composing it can, but according to Russell, names are primarily those of qualities. As he puts it, he is suggesting ‘an unusual extension for the word “name”’ (IMT 97).

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In Inquiry, Russell explains that since on a bundle theory the particular is completely defined when all its qualities are given, one might think that the name for the whole (the particular) is unnecessary because the bundle can be completely described by its parts (331). Russell agrees with a qualification. He argues that in theory every bundle can be defined by its properties; but in practice, we need names for the wholes. We need the names of complexes to carry out, and then report on, our analysis of the wholes. Bundles are wholes with parts. We can experience a whole, name it, but not know its parts. And as wholes they need to be analysed. When we perceive that a whole has parts, the propositions we make about that whole (particular) do not only describe the parts and their relations, but also describe the relation of the parts to the whole (ibid. 334–5). Thus, Russell argues that we cannot do without propositions of the form ‘P is part of W’ because they are used in analysing the wholes (ibid. 328–30). In Human Knowledge, Russell claims that such propositions ‘only arise through ignorance, and that, with better knowledge, our whole W can always be described by means of its constituents. [He] thinks, therefore, though with some hesitation, that there is no theoretical need for proper names as opposed to names of qualities and of relations’ (303). That is, theoretically we need proper names for the qualities and relations, but not for the bundles they make up. Every bundle can, in theory, be defined by the totality of its qualities. But since we are not omniscient, we need proper names for the particular bundles in practice (ibid. 308). We may symbolize the desiderata as follows: a-h: names of qualities, complexes of qualities and classes of qualities i-z: variables for qualities, complexes of qualities and classes of qualities A-H: names of relations (2 or more places) I-Z: variables for relations Scheme of abbreviation: a: this; b: Socrates; f: red; g: Greek; c: colour; d: Plato; e: square; h: soft A: ___ teaches ___ ; C: ___is a constituent of/member of ____; L: a multi-place compresence relation.

Sample sentences followed by their symbolizations: Red is compresent with square and soft. L (feh) There is a relation that holds between red, square and soft. ƎX X (feh)

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This is red. Socrates is Greek. Something is Greek Red is a colour. Socrates taught Plato.

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C (fa) C (gb) Ǝx C (gx) C (fc) A (bd)

Red is a constituent of this if and only if this is identical to a compresence of red, square and soft. C (fa) if and only if a = L (feh)

In the above symbolization,3 I tried to reflect Russell’s views in the later period on the ontological status of particulars and universals. Universals are the ultimate constituents of existence for him, so all qualities are symbolized by names. (Although for the later Russell words for qualities are names, they are different from ordinary proper names in the sense that names of qualities ‘do not designate a region which is spatio-temporally continuous’ (HK 84) the way ordinary proper names do.) Subject–predicate propositions are to be treated as expressing inclusion in a complex or as membership in a class. Thus, the sentence ‘This is red’ will be understood as stating that the quality red is included in the complex referred to by ‘this’. Rather, the quality, red, is a constituent of this complex. I assigned the same kind of symbolization to single qualities, such as being red, and complexes of qualities, such as ‘this’, with a view to reflect the parity in ontological status between qualities and ‘particulars’. I have ‘C’ as an ambiguous relation between being a constituent of a complex and being a member of a class because Russell’s transient particulars are complexes but his ordinary particulars are classes. Furthermore, we need class membership as a relation to express the relation between subject and predicate in abstract reference propositions such as ‘Red is a colour’ or ‘Animals are mortal.’

Qualities as immanent universals In ‘On the Problem of Universals’ (1946), Russell explains that on his view a thing is a bundle of qualities. Qualities are universals, but they are not transcendent universals; that is, they do not reside in some third realm. They exist in the actual world. These are called immanent universals in Armstrong. Immanent universal properties do not need a subject such as a substratum to be exemplified. Rather, immanent universals are multiply occurring entities or repeatable entities. One

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quality may exist in more than one place, or rather, in more than one perceptible area. Russell writes, ‘The colour itself exists wherever (as we should commonly say) there is something that has that colour’ (HK 303). Universals are multiply occurrent entities in space–time. As Kinney also notes, a universal for the later Russell is something which can recur or ‘that which can exist simultaneously with itself in disjunct [disjoint] loci’ (81). It is not the case that there are independently existing universals and their spatio-temporal instances. Rather, there are spatio-temporal qualities4 (IMT 102). However, qualities as immanent universals are different from qualities understood as scattered individuals. On the latter view we have one particular, which has parts wherever we find the quality in question. But on the former view, there is one universal which is wholly present wherever we find the quality in question. Immanent universals are not abstract in the sense in which transcendent universals are abstract. Transcendent universals are not in space–time, but immanent universals are. But when I say they are ‘in’ space–time, I do not mean it literally. Space–time is the result of the relations between complexes of compresent qualities. A complete complex of compresent bundles of qualities (universals) is itself a point-instant. Russell writes, ‘Complete complexes of compresence are the subjects of spatio-temporal relations in physical spacetime . . . A complete complex of compresence counts as a space-time pointinstant’ (HK 304). The kinds of qualities which constitute a bundle are sensory qualities, such as ‘redness’ or ‘softness’. There is also evidence suggesting that kind-identifying qualities such as ‘being a human’ go into the bundles as well. Russell states that ‘an instance of man “has” other qualities besides humanity: he is white or black, French or English, wise or foolish, and so on’ (ibid. 298). Russell points out that his notion of qualities is wider than it is generally supposed: He includes among qualities positional qualities, such as ‘being dexterous’, that is, being to the right of the centre of a visual field. Note that this is not a relational property. Suppose I see bundles A and B. Both have the qualities of being white and square. A is to the left and B is to the right of the centre of my visual field. The quality that bundle B has as a constituent part is not the relational property of being to the right of A, even though it is true that it is to the right of A, but instead B has the quality of a certain position, namely, being to the right of the centre of my visual field. This positional quality is a coordinate quality confined to each perceptual field. Russell in effect uses these absolute places in perceptual fields to individuate qualitatively alike bundles. M. Weitz makes two criticisms of this view: First,

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Weitz argues that coordinates are not experienceable qualities, and therefore they are not an improvement over the substrata in that sense. Russell retorts that we do experience coordinate qualities in the perceptual space. ‘If a fly tickles me, I know, without looking, whereabouts I’m being tickled, because, in tactual space, a touch on one part of the body causes a sensation differing in quality from a touch on another part’ (Schilpp 685). Weitz’s second criticism is that the coordinates, regarded as separate qualities, are particulars ‘in the sense of being the denotation of proper names’, though not in the sense of being instances of universals. Weitz holds that Russell has merely substituted coordinates for the substrata. ‘If Russell admits that spatial coordinates are particulars and their symbols are proper names, the whole point of his realism is lost, because the relation of predication is readmitted: all qualities become predicates of their coordinates’ (Schilpp 81, fn. 96). Here’s Russell’s reply: The theory that he [Weitz] is examining does not reject the dualism of universals and particulars; all that it does is to place qualities among particulars. If C is a shade of colour, C is a particular; but ‘visual’, ‘auditory’, etc. are predicates. The affinities of the theory are not with Plato, but with those who aim to get rid of ‘substance’. All the well-known difficulties of substance remain so long as we retain a ‘this’ which is not a bundle of qualities. (Schilpp 685–6)

As I understand it, Russell in this reply, explains that particulars, in the sense of denotation of proper names, are not coordinates, but bundles of qualities, which have coordinate qualities as parts. Although coordinate qualities could be particulars (again in the syntactical sense), what Russell wants to do, I think, is to replace transient particulars by a group of qualities, not just a coordinate quality. That would indeed be quite similar to a substratum, except that coordinate quality in perceptual spaces would be experienced. But why does Russell resort to absolute positions in perceptual space? Couldn’t he have included spatio-temporal relations or such relational properties in a bundle?

Relations The reason why spatio-temporal properties, such as being to the right of a, are not included in a bundle is that (1) such a view entails that an individual might have contradictory properties; (2) the account of a particular would be circular,

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that is, we would have to assume a when constructing b, and assume b when constructing a; (3) some relations (spatio-temporal relations) would have been reduced to properties of particulars. One argument for the view that relations cannot be part of the bundle comes from Plato, who noted that Socrates is shorter than Simmias because ‘he happens to have tallness’. But it is not in his nature to be tall; tallness is not one of the qualities that make him Simmias. ‘It is not, surely, the nature of Simmias to be taller than Socrates because he is Simmias but because of the tallness he happens to have’ (Phaedo 102c). That is, relations themselves cannot be part of what makes a particular that particular or a bundle. Otherwise we would have particulars with contradictory properties housed in one individual, for example, Socrates would have both the property of being taller than and the property of being shorter than as properties that make him the particular that he is. Hence, relations should exist independently of the particulars they relate. The early Russell accordingly, argues that relations exist in a transcendent sense: ‘The relation “north of ” does not seem to exist in the same sense as Edinburgh and London exist. If we ask, “Where and when does this relation exist?”, the answer must be “Nowhere and nowhen”. There is no place or time we can find the relation “north of ”’ (POP 56). Thus, relations for the early Russell are transcendent universals. The relation ‘north of ’ subsists as a transcendent universal; they are exemplified by their terms (POP 57). But once Russell abandons the Platonic understanding of universals, and adopts an Aristotelian one, according to which universals are immanent, he will need to situate spatio-temporal relations, such as ‘being north of ’, in the world. The second argument is that reducing relations to properties of bundles would make the account of a particular circular, since any relational property will depend on the existence of a bundle, and yet relational properties are treated as constituents of a bundle on the proposal that relational properties be included in a bundle. Hochberg makes a suggestion in order to avoid the circularity. Instead of including the property of being to the right of something in the bundle a, Hochberg suggests that we include being to the right of a bundle of properties. For instance, say both a and b are white and square and a is to the right of b, then we can include being to the right of a white square into the bundle a (Hochberg ‘Things and Descriptions’ 73). This solution, at first sight, seems not to give rise to a circular account of particulars because it does not invoke the name of the white, square bundle. However, circularity remains, as the white and square bundle is a complex of compresence, that is, a particular, whether it is named or not.

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The third kind of argument against relations being part of a bundle is Russell’s arguments against theories of relations which take relations to be properties of either the whole they compose or the terms they relate. Leibniz and Bradley denied that relations have independent existence. Leibniz reduced relations to the properties of related terms,5 while Bradley reduced relations to the properties of the wholes they composed. Russell, on the other hand, argues for the irreducibility of relations (Winslade 85). Against Bradley’s monistic theory of relations, Russell gives an argument from asymmetric relations: The proposition ‘a is greater than b’, we are told, does not really say anything about either a or b, but about the two together. Denoting the whole which they compose by (ab), it says, we will suppose, ‘(ab) contains diversity of magnitude’. Now to this statement . . . there is a special objection in the case of asymmetry. (ab) is symmetrical with regard to a and b, and thus the property of the whole will be exactly the same in the case where a is greater than b as in the case where b is greater than a . . . Thus, the distinction of sense, i.e., the distinction between an asymmetrical relation and its converse, is one which the monistic theory of relations is wholly unable to explain. (POM §215)

Russell gives the same objection in 1946 against the monistic view of relations that the relation of being above really is a property of the whole composed of the two bundles (‘The Problem of Universals’ 270). Russell explains that this monistic view comes from the fact that the relation ‘above’ seems to be dependent on the existence of at least two bundles. ‘Unless at least two [bundles] exist there cannot be a fact requiring the word “above” for its statement’ (ibid. 269). Russell acknowledges this, but argues that the monistic theory, by making relations properties of wholes, loses the sense or direction of asymmetrical relations. One of the arguments Russell gives against Leibniz’s monadistic theory of relations is that it cannot give a satisfactory account of asymmetrical relations either (Weitz in Schilpp 61). Consider L is (greater than M): ‘the supposed adjective of L [the words in parentheses], involves some reference to M, and this is merely a cumbrous way of describing a relation. Or, to put the matter otherwise, if L has an adjective corresponding to the fact that it is greater than M, this adjective is logically subsequent to, and is merely derived from, the direct relation of L to M’ (POM §214). Russell’s complaint is that regarding an asymmetrical relation as a property of a particular does not actually eliminate relations. An adjective formed to express such a relation has to logically presuppose the relation.

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Thus, relations, if they exist, need to be external to the bundles. However, Russell in his later work does not confidently argue for the independent existence of universal relations, although he certainly seems to think that realism with respect to universal relations is nevertheless the best of all alternative theories. What is clear is that Russell accepts relational facts, since a proposition that lists two objects and another proposition that expresses a relation between these two objects will be made true, if at all, by facts of different kinds. What is also clear is that, according to Russell, relation-words are necessary linguistically and logically to express relational facts. We need to take relations into account when describing the world; we cannot do just with qualities. For we find qualities in some patterns in the world. ‘The relations of up-and-down, right-and-left, are just as much part of what is perceived as are the actual colours; if this were not so, photographs would not seem as like their originals as they do’ (‘The Problem’ 269). Consider the relation of being above something. Suppose we have two bundles a and b. Bundle a is located above bundle b. Russell argues we do need the word ‘above’ to express the fact that a is above b. We can perceive that a is above b just as we can perceive a and b. According to Russell, then, the following two claims are true: (1) There are relational facts; (2) Logic and language require relation-words for the expression of relational facts. However, Russell does not seem to settle on one way of analysing these relational facts without reservation, though he is inclined towards a view which acknowledges the independent existence of relations. Russell explains in 1957 that the question, ‘Are there relations as universals?’, is ambiguous between two senses of existence (‘Logic’ 174–5). Russell, as early as 1905, distinguishes between such two senses of existence (‘The Existential’ 98–9): (i) as it occurs in philosophy or ordinary language, as when we ask if God exists or affirm that Hamlet existed (ibid. 98), and (ii) as it occurs in symbolic logic or mathematics, that is, taken as an existential quantifier. Russell explains that to say that a exists in this sense means that ‘[a] is a class which has at least one member. . . . In this sense [ii], the class of numbers (e.g.) exists, because 1, 2, 3, etc. are members of it; but in sense [i] the class and its members alike do not exist: they do not stand out in a part of space and time, nor do they have that kind of super-sensible existence which is attributed to the Deity’ (ibid. 99). In 1957, Russell maintains that relations do exist in sense (ii), since ‘we certainly cannot do without variables that represent predicates or relationwords’ (‘Logic’ 175). However, Russell argues that existence in sense (ii) does not imply existence in sense (i).

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Neither, Russell argues, can we conclude that there are relations as entities from the fact that there are relational facts. He argues that it does not follow that there is an actual ingredient in the world which is denoted by the word ‘above’6 from the relational fact that a is above b (‘The Problem’ 269). That is, Russell’s 1946 and 1957 articles both leave the question of whether relations exist in sense (i) open (‘The Problem’ 272 and ‘Logic’ 175). But interestingly in My Philosophical Development (1959) he refers the reader to the last chapter of Inquiry to learn ‘what he has to say on the ontological status of universals’ (175), and in that chapter Russell gives his famous infinite regress argument for the existence of universals, due to the inability to explain the relation of similarity. Given that there are relational facts, there are two main ways of accounting for relations: nominalist or realist. In Inquiry, Russell considers the resemblance nominalist’s proposal of explaining all qualities and relations, including asymmetrical relations, in terms of similarity classes or ordinary particulars. Thus, on this view, all wholes where the relation-word ‘above’ is correctly used have a certain kind of resemblance. But Russell argues that we have to account for the resemblance relation itself, and this attempt leads us to infinite regress of the vicious kind7 (‘The Problem’ 271–2; IMT 346). Let us recapitulate the discussion on the ontological status of universals. There are relational facts and we need relation-words to express relational facts. A resemblance nominalist account of relations does not successfully explain relational facts. On the realist camp, we have three options: relations are to be reduced to properties of the wholes, relations are to be reduced to properties of the particulars they relate, and relations exist independently of particulars. Relations, as we have seen, Russell argues, cannot be reduced to properties in either sense. So, we are left with the option of holding that relations exist independently of the bundles they relate. Yet, Russell argues this option does not have a good enough argument supporting it, other than the argument by elimination that we just stated. The only reasons we have in its favour are that there are relational facts and we know that we need relation-words in language and logic. But our linguistic or logical needs are not sufficient to determine what exists in reality. This seems to be where Russell stands. It seems to me that Russell already has a straightforward argument at his disposal for the existence of universal relations: (1) The correspondence theory of truth is true, that is, there are facts that are truth-makers of propositions, whatever the nature of propositions is, as long as they are admittedly complex. (2) Facts are complex. (3) There are relational facts. (4) Since in the later period particulars are bundles of qualities, analysis of relational facts must yield either

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qualities and relations, or merely qualities, where some would be relational ones. (5) Relations cannot be reduced to qualities of bundles, given Russell’s arguments against internal relations. Therefore, constituents of facts must be both qualities and relations, which exist as truth-makers of propositions. I suspect that the reason why Russell does not fully endorse such an argument is that he recognizes that there is a tension involving the notion of independently existing universal relations. It is, as Russell points out, obvious that relations would not exist if there were not any bundles to relate in the first place. It is logically possible to have just one quality in existence, for instance, yellow, and nothing else. Thus, qualities seem fundamental in the sense of being ontologically independent from anything else. But any relation would require the existence of things to relate. Thus, the existence of relations, in fact, is not independent of any other entities. It seems that qualities are ontologically independent existents, but the existence of relations is dependent, that is, real but not the kind of thing that can exist independently of anything else. The problem facing us is that we have good reason to believe that there are relations in the world, as holding between qualities or bundles of qualities. We also have a good reason to maintain that relations are fundamental, that is, ultimate existents of the world, since listing all the bundles of qualities in the world would not be an accurate or complete list of facts. We also need to list the relations between the bundles. Yet relations are ontologically dependent. The relation of ‘being the mother of ’ exists between many pairs of bundles; but it is ontologically dependent, that is, it may exist only if there are at least two people, at least one of which is female. That is, there seems to be a tension between the fundamentality of relations and their ontological dependence because we have been, along with the tradition, assuming that fundamentality is sufficient and necessary for ontological independence. But once we divorce these meta-ontological concepts, as E. Barnes suggests, the tension is resolved. Barnes argues that the class of fundamental entities is not coextensive with the class of ontologically independent entities, and neither is the class of derivative entities coextensive with the class of ontologically dependent entities (874). Barnes does not give a definition of fundamentality, but gives examples to explain what she means. For instance, fundamental entities are ‘those which truthmake their own existence, and which are capable of serving as truthmakers for the existence of other (derivative) entities’ (Barnes 876–7). She gives tropes as example of fundamental entities on a trope bundle theory, while the existence of table is derived from that of the relevant tropes and a relation (of compresence

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or mereology) between them. Derivative entities ‘derive their existence from the fundamental entities’ (ibid. 877). A derivative entity is ‘no part of fundamental reality’ (ibid. 883). Barnes explains ontological independence as follows: ‘If the existence of x does not, at each moment of its existence, rely on some other entity or entities, then x is ontologically independent. So the ontologically independent entities are those capable of “lonely existence”. . .’ (882). Barnes identifies the class of entities which are fundamental but not independent as emergent entities (ibid.). Thus, if my mind is an entity emerging from my brain matter, that my mind exists will be true if there is such a further entity. It will not be enough that there exists my brain matter arranged in suitable ways. If that were enough, my mind would be a derivative entity on Barnes’s conception. At the same time my mind is not ontologically independent for it depends on the existence of my brain matter arranged in suitable ways for its own existence (ibid. 885; 887). J. Kim presents the ideas generally associated with emergentism as follows: (1) The whole has properties that emerge from the parts and their relations, as well as properties that merely result from those parts and their relations, and that these emergent properties cannot be explained or predicted from the knowledge of the parts and their relations. (2) The wholes bring into the world new causal powers and structures (Kim 5–6). What motivates emergentism is a need or desire to recognize an ontological kind that a whole belongs to as distinct from the ontological kind of its parts, as opposed to reductionist views which maintain that the ontological kind of the whole is the same as that of the parts. For instance, in the case of mind, an emergentist recognizes the kind, mental, as distinct from physical, which is the kind of the parts out of which minds emerge. Yes, the whole, for the emergentist, has causal powers that are distinct from the causal powers of the parts. But this difference lies in ontological kind. We should, as Barnes argues, separate the fundamental versus derivative distinction from the ontologically dependent versus independent distinction, so that we can have room for fundamental entities, such as relations, which are ultimate parts of reality but ontologically dependent because they are dependent on the existence of qualities. But a Russellian bundle theory cannot follow Barnes all the way. We should not equate the class of fundamental and ontologically dependent entities with the class of emergent entities, as Barnes does (884–5). Admitting that relations are fundamental but ontologically dependent does not imply that relations are

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emergent entities. First, an emergent entity is generally considered to be a ‘byproduct of the activity of its parts, an entity that is new, over and above its parts’ (ibid. 873–4). But some relations, such as, the mixing of egg, flour and milk produce a by-product, while others, such as ‘being to the north’, do not produce any entity over and above Edinburgh and London. Furthermore, an emergent entity is a result of some collective activity of its parts. But again, not all relations are a result of compresent quality-complexes engaging in some collective activity. My books are stacked one on top of another, but they are not engaged in any collective activity to yield the relation of being above or under. Lastly, it seems that the notion of emergence encompasses the idea that what emerges out of some fundamental elements is necessarily of a different ontological kind. But Russell’s relations, which relate bundles of qualities, are of the same ontological kind as qualities. Russell mentions emergent properties in a footnote in The Analysis of Matter. He notes that analysis in science yields ‘structure such that the properties of the complex can be inferred from those of the parts*’ (AMa 285–6). And here is the starred footnote: Dr. C.D. Broad, in The Mind and its Place in Nature, lays stress upon what he calls ‘emergent’ properties of complexes – i.e. such as cannot be inferred from the properties and relations of the parts. I believe that ‘emergent’ properties represent merely scientific incompleteness, which would not exist in the ideal physics. It is difficult to advance any conclusive argument on either side as to the ultimate character of apparently ‘emergent’ properties, but I think my view is supported by such examples as the explanation of chemistry in terms of physics by means of the Rutherford-Bohr theory of atomic structure. (Fn. on p. 286)

Russell argues that adequate analysis of a complex whole yields parts with a certain structure and knowing these parts and how they are structurally related is sufficient to infer the properties of the whole. He explains that some properties of complexes seem emergent, because they cannot at the moment be explained by appeal to the parts and their relations. But this only shows incompleteness in our knowledge of the complex, its parts, and how the parts relate to each other, not a fact about the complex itself. Russell’s logical atomism demands further and further analyses of wholes. But Russell does not retain the whole which has been analysed as yet a further entity over and beyond its parts and relations. He always eliminates any ontological commitment to a whole whenever he is able to successfully make do with its parts and their relations. Examples are numbers, ordinary particulars, transient

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particulars. So Russell is very far from an emergentist. He replaces constructions with inferred entities whenever suitable and in some cases he is content with the complex formed out of the simples, and does not require a construction. There is a hierarchy in his ontology, but the entities on levels higher than the logical simples are merely derivative entities, they are not fundamental, not part of the ultimate furniture of the world. All God needs in creating the world, as Barnes would put it, are the logical simples. Thus, wholes are not emergent entities for Russell. The kinds of entities for whose ontological status I want to appeal to the fundamental yet dependent distinction are those of relations between wholes, that is, bundles. I conclude thus that relations are fundamental entities according to Russell, and they are ontologically dependent at the same time, that is, dependent on the existence of qualities. Relations exist as immanent universals, just like qualities do. Qualities and relations are universal entities; they multiply recur. They are not transcendent universals, that is, they do not have existence independently of any instantiations whatsoever. If tomorrow we discover a new relation, the novelty of the relation will not be explained by its being exemplified for the first time, but by our recognizing this relation for the first time. But one might object that it is quite clear that I acquire new relations every day, relations that did not exist yesterday, but does today. For instance, my desk was located right next to a window, but now it is located next to a wall. Russell in response will point out that space–time is a four-dimensional block, with events laid out with relations of being earlier than or later than, or simultaneous with. It seems to me, from an anthropocentric point of view, that I was not the relatum of a relation in the past but now I am. In actuality, my desk and I are in that relation in a tenseless sense on the space–time continuum. All events and their properties and relations in it are as real as another, regardless of the subjective feelings of pastness, presentness or futurity that percipients associate with them. One relation, which is of great significance to the bundle theory of particulars, is that of compresence. The compresence relation is a relation that holds between qualities. Other relations of significance to the bundle theory are causal and spatio-temporal relations. For instance, hotness causes pain or the quality of whiteness in a transient particular causes a quality of whiteness in me. Quality of hotness, in most occasions, temporally precedes the quality of pain. We should note that compresence has an epistemological advantage over the substratum. The compresence relation is not something unexperienced, like a substratum. We do experience various qualities or events in a compresent

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manner all the time. I hear the water in the pool next door splash at the same time as I feel the hot humid air in my room, which is also accompanied by an itch on my knee. Thus, the compresence relation is something we experience, unlike the ‘that which holds properties together’. And the relations of compresence among qualities experienced by no one are inferred from our experiences of compresent qualities. The relation of compresence is considered to be an unanalysable, primitive relation (IMT 104). Russell takes this relation to have ‘a merely ostensive definition’ (HK 296). Compresence of qualities takes place in our perceptual spaces and in the physical space.8 In physical space, compresence is the overlapping of qualities in space–time (ibid. 304). In private space, the qualities of a book that I perceive at a moment would comprise a transient particular, a spatio-temporal slice of my book on my table. And, according to Russell, ‘there is no difficulty of principle in constructing complexes of compresence, where there are no percipients’ because a camera from that very perspective would record that perception (ibid. 297). Being a relation, compresence should also be a universal. But is it another constituent of the bundle? No. ‘A complex of compresence . . . is determinate when the qualities constituting it are given’ (ibid. 306). There is no mention of the compresence relation as another component of the complex. The components entirely consist of qualities. Furthermore, it seems that the relation of compresence should not be another component in the bundle because if it is it will lead to an infinite regress. All the qualities and the compresence relation will need a further compresence relation to unify them; and this second-level relation of compresence will also be a relation and therefore that second-level bundle will require a third relation of compresence to combine them, and so on infinitely. Here is another occasion to employ Barnes’s distinction in the effort to give a consistent account of Russell’s bundle theory. There is no doubt that Russell takes compresence to be a primitive relation, and it is a relation of crucial importance to the bundle theory of particulars. But at the same time, it is clearly a relation whose existence depends on there being at least two qualities in existence; hence it is an ontologically dependent relation. If we stick to the traditional coextension of fundamentality and ontological independence we will have difficulty in explaining the ontological status of the compresence relation.

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Bundles as point-instants Complexes (bundles) of compresent qualities yield transient particulars. Such bundles, when they are causally related and spatio-temporally ordered by physical or psychological laws, form a series, which stand in place of ordinary particulars. Complete complexes of compresence, on the other hand, yield pointinstants. A complex of compresent qualities is complete when all the qualities in the group are compresent and there is no quality outside the group, which is compresent with every quality in the group. Ever since his adoption of the relative theory of space and time, Russell constructs points and instants. In Our Knowledge of the External World, they are constructed out of appearances, in The Analysis of Mind and The Analysis of Matter out of events, and Russell’s final position in Human Knowledge is that they are to be constructed out of qualities. In the later period, the relation of simultaneity is given up, and the relation of overlapping, and later compresence, takes its place. Here’s Russell’s initial definition of a point-instant in The Analysis of Matter: ‘A group of events having the following two properties:

1. Any two members of the group are compresent. 2. No event outside the group is compresent with every member of the group.’ (AMa 295) This definition, however, created a problem. Russell could use the definition in constructing instants because time is a single dimension. But when the thing to be constructed has more than one dimension, as in the case of a plane, a 2-place compresence relation does not suffice. If you take three planes, where any two overlap with each other, it is possible that there is no region common to all three of them.9 Thus, for constructing points or point-instants he needed a different definition. Russell’s solution was to change the first condition in the above definition. The new recipe for constructions is that for all constructions, if the thing to be constructed has n dimensions, the number of events any of which has to be compresent should be n+1. Thus to construct a point-instant, which is fourdimensional, the first condition requires that any five events in the group are compresent (ibid. 299).

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Russell maintains this definition later in Human Knowledge when discussing the construction of point-instants out of events: ‘In n dimensions the definitions are the same, except that the original relation of copunctuality has to be between n+1 regions’ (HK 280). A point-instant is reached by determining all the events that overlap in space–time. The relations of overlapping or compresence are given in experience, just as events are (ibid. 277). ‘“Overlapping” is not itself to be defined logically; it is an empirically known relation, having . . . only an ostensive definition’ (ibid. 279). Take events A and B, and some part of A overlaps with some part of B, you look for other events, say C which will have a part that overlaps with both A and B. You will continue this process as long as possible, that is, ‘until there is no event remaining which overlaps with all the events already in our group . . . when this stage has been reached, the group of events that has been constructed may be defined as an instant’ (ibid. 271). However, in the later sections of Human Knowledge, after Russell settles on the view that it must be qualities that are ultimate constituents, and not events, he gives yet another definition. The first condition does not restrict the number of elements that need to be compresent, since the elements of construction are not events on this definition, but qualities which multiply recur. Russell needs to restrict the number of elements that are compresent when the elements already possess some uniqueness, as events as particulars do, because what he wants to construct is a point-instant. Therefore, the uniqueness or ‘particularity’ must be a result of construction, not assumed at the outset, as would be, for instance, if we gave a definition which required all events to be compresent. Thus, Russell’s definition of a point-instant when elements of construction are qualities is the following: (1) All members of the group must be compresent; (2) there is no member outside the group which is compresent with all. Complexes of compresent qualities can be complete or incomplete. Pointinstants are complete complexes, and events, which are transient particulars, are incomplete complexes of compresence. The definition of a complete complex, that is, a particular as a point-instant is: ‘a) all the members of the group are compresent, b) nothing outside the group is compresent with every member of the group’ (ibid. 294). The first condition requires that some properties overlap in space–time or be experienced simultaneously. The second condition is meant to delineate the complex as distinct from other qualities or groups of qualities. When there is a complex whose qualities are together sufficient to individuate it as one particular, that complex is complete. ‘Every increase in the number of qualities combined in a complex of compresence diminishes the amount of space-time that it occupies’ (Russell, HK 306). The more defining characteristics

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the better chance at distinguishing a grouping of properties as one particular. The amount of space–time does not have to diminish with more properties, because two properties may coincide spatio-temporally in the region occupied by the complex of compresence. Russell should have said that an increase in the number of qualities may either diminish or leave the same the amount of space–time it occupies.10 The difference between Russell’s early view of particulars and the later one we have just outlined is that particulars in the early period are particulars in the sense that each instance is unique with its own substrata but in the later period particulars do not come already numerically diverse; it is the complexity of their qualities that particularizes them. A complex is complete in the sense that there is no other quality outside the group with which every quality in the complex is compresent. The compresence relation in perceptual terms is the simultaneity and overlapping of experience, and in physical terms it is the overlapping of qualities in physical space–time. It is the very same relation in both realms. And in fact, as I will argue in Chapter 8 on neutral monism, these realms are epistemological distinctions; in reality there is only one realm and it is neutral between mind and matter. The definition of compresence seems to be circular, though. A particular point-instant is a complete compresence of qualities. But compresence is being co-present, that is, taking up the same spatio-temporal position. Thus, it seems that the existence of spatio-temporal positions is ontologically prior to the compresence of qualities. But Russell wants these positions to result from compresence of qualities. Russell’s response is to point out that ‘compresence is needed in defining spatio-temporal position . . . Complete complexes of compresence are the subjects of spatio-temporal relations in physical space-time’ (ibid. 304). These ‘particulars’, that is, point-instants, are used in constructing space–time. Compresence is a relation of togetherness of qualities; but the locations of these complexes are not already determined. Qualities are together in a spatio-temporal sense; but this does not mean that the spatio-temporal positions are given or determined beforehand. We do misleadingly say that a quality is at a space–time point. But it would be more accurate to say that this quality is part of the complex forming that point-instant (ibid. 305). Russell again constructs physical space–time series and perceptual space–time series. A perceptual space-time series is constructed of tomes (total momentary experiences) (ibid. 295). A tome counts as an instant in perceptual time for Russell, so that an instant in perceptual space–time is directly experienced. But

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a point-instant in physical time will have to be inferred. A transient particular is a bundle of compresent qualities. Since Russell identifies a point-instant with a complete complex of compresent qualities, if the whole group of qualities recurs that would mean the point-instant recurs, in which case we cannot construct a series of successive point-instants. Considering a momentary percept, there is no danger of recurrence because he regards the space of perception as absolute in the sense that the centre of one’s visual field may be taken as the reference point with spatial relations determined by reference to it. According to Russell, the qualities in our visual fields have positional qualities. ‘At every moment, what is in the center of my field of vision has a quality that may be called “centrality” what is to the right “dexter”, what to left “sinister”, what above “superior”, what below “inferior”’ (ibid. 298–9). Therefore, at least in visual spaces, it is guaranteed that when a sensory quality recurs it will also be compresent with one of the above positional qualities which will help distinguish it from other occurrences of the sensory quality in one’s percept. However, the complete complexes of physical space do not directly enjoy the advantage that perceptual bundles do in terms of avoiding recurrence. Russell accepts that ‘it is logically possible for [a complete complex of compresence] to occur more than once, but [he] assumes that if [the complex] is sufficiently complex, there will not in fact be recurrence’ (ibid. 306). Russell will have bundles of qualities sufficiently complex that they will not recur. And he can thereby construct space–time order out of nonrecurring particulars (ibid. 293). What also contributes to the individuation of point-instants in the construction of the physical space–time series is that, based on the postulates of non-demonstrative inference, it is highly probable that the spatiotemporal relations in physical space will be approximately corresponding to the spatio-temporal positions in perceptual spaces. That is, the spatial qualities used in individuating bundles in perceptual spaces will indirectly and approximately help the individuation of bundles to be used in the construction of the physical space–time. ‘Two simultaneous parts of one visual percept have a certain visual spatial relation which is a component of the total percept; the physical objects which correspond to these parts of my total percept have a relation roughly corresponding to this visual spatial relation’ (ibid. 320).

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Particulars: Complex versus class According to my interpretation of Russell’s theory of particulars in the later period, ordinary particulars are logical fictions, classes, while transient particulars, which are the members of the classes that make up ordinary particulars, are not classes; they are complexes. Russell’s history of replacing logical fictions for inferred entities lends support to the interpretation, which we encounter in Bostock, that both the ordinary and the transient particular is a class, a logical fiction. Bostock seems to treat transient and ordinary particulars on a par in his exposition of the bundle theory (240), and therefore it seems that he interprets transient particulars, that is, complexes of compresent qualities, also as a class, a logical fiction. But this view is mistaken. Neither a complete complex of compresence nor a mere complex of compresence is a class. A transient particular is not to be identified with a class of qualities; it is rather a unit. ‘It is something which exists, not merely because its constituents exist, but because, in virtue of being compresent, they constitute a single structure’ (Russell, HK 297). It is defined when its constituents are given, but it does not exist merely because its constituents exist. The qualities need to be in a compresence relation. Hence, the particular is not a class; members of mere classes are not related to each other by compresence.11 Moreover, a class is an abstract entity, whereas a complex of compresence is not. A complex is just as real as its components. The reason that Russell in Human Knowledge emphasizes that transient particulars are complexes, not classes, arises from a tension when one considers the requisites of his ontology and epistemology. In the later period, the right interpretation is that Russell infers some transient particulars instead of constructing them. Strong support for this interpretation comes from the fact that a tension arises when some key propositions that he seems to hold to be true are taken in total. 1. 2. 3. 4.

A particular is a complex of compresence (HK 298–9). A particular is a construction (Assumption for reductio). A construction is not of the same logical type as data (Appendix to HK 257). A complex is of the same logical type as its constituents (ibid. 293).

If all of the above are true, then we have a complex, which is a construction, and it is both of the same logical type as its constituents (4) and is not of the same logical type as its constituents (3). Therefore (2) has to be false. We must infer

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the existence of (some) particulars. Our knowledge of them will be through descriptions. There are three main methods that Russell generally discusses for arriving at the knowledge that something exists: we could directly experience that it exists, we could infer its existence or we can construct something to stand for what we would otherwise infer as existing. Russell typically prefers construction over inference whenever possible. Russell claims that if a construction is available concerning the existence of a certain kind of entity, ‘this very fact invalidates the inference’ we would be normally inclined to make, ‘since it shows that the supposed inferred entity is not necessary for the interpretation of the propositions of the science in question’ (Schilpp 699). Russell used the method of construction extensively in Our Knowledge of the External World, The Analysis of Mind and The Analysis of Matter. Construction, as Russell takes it, yields an entity which is of a different logical type than its constituent elements. One ‘can never construct anything of the same logical type as data’ (Russell, Appendix to HK 257). For instance, a material object in Our Knowledge of the External World is regarded as a class, and therefore of a different logical type than what it is constructed of, namely, sensibilia. Russell explains the difference between construction and inference as follows: ‘In a construction, a logical structure is formed of known elements. In an inference, an entity of the same type as known entities is inferred. E.g. instants in Newton and classes of events’ (ibid. 287). Transient particulars in the later period are either known directly or inferred, not constructed. In 1948, Russell writes, ‘At one time, I hoped that science could be content with constructions in place of inferences. I now no longer think this possible’ (‘Non-Deductive Inference’ 129). He thought he could explain our perceptual experience by positing a class of sensations as the seeming cause of our perceptions. But this method did not work, as Bostock explains, because the definition of the ordinary particular as a class of sensations was circular. The class of sensations, that is, the ordinary particular, relied on there being sensations from certain perspectives which are at certain places. Yet the places of the perspectives are not given, they are to be constructed as well. One cannot construct both. Either the same ordinary particular or the places of the perspectives need to be given (Bostock 162–3; 167). Thus, a satisfactory account of perception in AMa required that we accept the existence of entities which cause our perception. But these entities, whose existence we are admitting, are not material things, ordinary particulars that persist over time; instead they are transient particulars, which cause our

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perceptions, but which no one can directly experience. Because we cannot experience the transient particulars, we infer their existence. So, in the later period, Russell reverts back to the causal theory of perception. Consequently, the transient particulars that Russell is concerned with in the later period are the ones at the beginning of a causal chain and the ones that are part of the intermediary process of perception between an object external to a mind and the mind itself. For instance, when I see a tree, I need to presume that there are some transient particulars which are composed of the physical and chemical qualities of the tree that no one can directly perceive, as the cause of our perception of the tree. There are also other transient particulars in the causal chain emanating from the tree and ending in my mind, which are not directly perceived by anyone, such as the refracted light waves. But towards the end of the causal chain of perception there are transient particulars that we directly experience. Thus, it is not for all kinds of transient particulars that we need inferences; only for the ones that no one can directly experience, but we think must exist as a requisite of the best explanation of our perceptual experiences. Note the difference in the treatment of point-instants as well. Until 1948, pointinstants were classes, logical fictions. But in Human Knowledge he argues they are complete complexes of compresence. Russell writes, ‘As for points, instants, and particles, in so far as they are not logical fictions similar considerations apply’ (HK 299).

Reductive versus eliminative identity Russell identifies transient particulars with a bundle of compresent qualities. But what is the nature of this relation of identity? I argue in this section that the later Russell’s transient particulars are not reduced to bundles of qualities, but eliminated. Russell is defending a theory on the nature of particulars. He is maintaining that the ontological category of particulars that we thought was ineliminable in fact can be identified with a group of universals. Thus, it is an identity claim between kinds of things: particulars (immediately individuated transient particulars) and complexes of universals (universal qualities). One can regard this identity relation as a reduction so that particulars may be reduced to universals; in which case one would keep both ontological kinds in their inventory. For instance, in physics we identify heat with high kinetic molecular energy. This

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kind of identification may be called reductive, that is, heat is reduced to high kinetic molecular energy. On the other hand, we may identify one entity with another (entity or construct) with a view to eliminate one. This may be called eliminative identity. Such identification results in elimination of one of the kinds. Elimination of one kind leaves the theorist with a sparse ontology. I maintain, along with Bostock and Landini, that Russell’s ontological identity claims fall in the latter category. He eliminates the entity from his ontology. Bostock, in Russell’s Logical Atomism (153), and Landini, in Wittgenstein’s Apprenticeship with Russell (14–15) and in ‘Russell On What There Isn’t’ (7–8), argue that when Russell provides a logical construction for an entity, he does not intend to keep the kind of entity for which a construction has been provided. That is, Russell’s identification of unknown entities with logical constructs is an eliminative one; and not a reductive one. Thus, when Russell defines the number 2 as a class of couples, he does not claim a reductive identity relationship between the number 2 and a certain class. Russell, in Introduction to Mathematical Philosophy (1919) explains that the two are distinct entities. ‘There is no doubt about the class of couples: it is indubitable and not difficult to define, whereas the number 2 . . . is a metaphysical entity, about which we can never feel sure that it exists . . . It is therefore more prudent to content ourselves with the class of couples . . .’ (Russell, IMP 18; repeated in PLA 269–70). Thus, it is ontologically economical and prudent to replace numbers with what we know to exist, that is, classes. In Our Knowledge of the External World (1914), a material object at a time is the class of all its possible and actual appearances. A material object over time, that is, an ordinary particular, is a temporal series of such classes (OKEW 111– 12; Bostock 164, fn. 26). Bostock argues, and I agree, that matter in OKEW is defined as the class of actual and possible appearances but again not identified, in the sense of reduction, with this class. This class is a replacement or a ‘substitute notion that should replace the original notion of matter’ (Bostock 164). Where my interpretation differs from that of Bostock’s in this discussion is that Bostock claims that logical constructions are provided in place of all the eliminated particulars (240). But as I argued in the earlier section, I maintain that it is not constructions, but complexes, which replace transient particulars in Russell’s later works. The category of particulars is eliminated in favour of complexes of universal qualities. One might wonder here if there is any conflict between the claim that Russell infers the existence of transient particulars and the eliminativist interpretation

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that I have been defending. It seems that on one hand, I claim that Russell eliminates transient particulars; on the other, I argue that he infers their existence. But the worry should be dispelled by the following clarification. Russell does eliminate transient particulars, what we have, ontologically speaking, are not particulars, but only qualities and quality-complexes. We know of or about these quality-complexes in two ways: acquaintance and inference. The qualitycomplexes at the beginning of a causal chain are known by inference, through description, and the quality-complexes towards the end of the causal chain of perception are known by direct experience. Thus, what we infer to exist is a quality-complex, not a particular. To recapitulate, that Russell has gone back to inferring particulars is not a problem in terms of the bundle theory because what he is inferring is that there is a complex of compresent qualities which is the cause of my perception of the table. He is not inferring the existence of a particular in the old, substratum plus qualities sense. Such inferences, however, are not demonstrative. Inductive arguments inferring the existence of a transient particular do not demonstrate their conclusions. And demanding demonstrative certainty from induction leads to circularity, as we have learned from Hume. Therefore, Russell sees that demanding certainty in our scientific reasoning leads either to scepticism or to an unreasonable science. Recognizing that in science we do reason successfully for the most part, despite the fact that the reasoning involved is not demonstrative, Russell argues that we need to first analyse the way we actually reason in science with a view to enumerate the principles of reasoning that we use, and determine which ones are reliable and which ones are not, such as hasty generalization, and embark on the project of justifying these principles once we know which non-demonstrative principles of inference we use in science (Garvin 39–41). As Garvin explains in his ‘Russell’s Naturalistic Turn’, Russell reasoned that since insisting on demonstrative inferences in science leads to scepticism, and since many successful and fruitful inferences are already being made in science, we need to widen the class of acceptable and reasonable inferences so as to include non-demonstrative inferences that are actually invoked in physical sciences (42–3). But Russell did not advocate that we should therefore accept all the non-demonstrative principles of actual science as valid. They are to be accepted as valid for the purposes of analyzing the kind of inferences involved in physical sciences (HK 182). Whether these non-demonstrative inferences are indeed truth-conducive is still a question that the critical epistemologist needs to work on.

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Hence, even though Russell had the precursors of naturalized epistemology such as the acceptance of the impossibility of a satisfactory response to the sceptic, the acknowledgement of the success of non-demonstrative inferences in science, and the recognition that the epistemologist needs to carry out the task of identifying the principles that we actually use in scientific inferences, Russell is not quite the naturalized epistemologist that Quine is (Garvin 36; 47–9). I have argued that the later Russell’s metaphysical position on the nature of particulars, either transient or ordinary, is that they do not exist as a different kind of entity from universal qualities and relations. But we still live and talk as if there are particulars: I have a cup of coffee. The cup seems to be a particular, an entity distinct from its repeatable properties such as being hard, and being oval-shaped. For all I know, it is the same cup I use when I come to the office every morning. Such seeming persistence of particulars will need to be explained as a feature of the way we know about the world and things in it. The world in fact consists only of repeatable entities, that is, universal qualities and relations. But we treat some combinations of qualities as unique entities, for in our experience, such a combination seems to be a unique one. And acting on the assumption that it is the same cup that I use every morning has been successful in terms of fulfilling my overall goals. Thus, there are constraints on how we know about the world due to our standpoint of experience and practical requirements of language and behaviour. It makes communication and thought easier to treat a series of similar and causally related complexes of qualities as a persisting thing. Russell’s structure of knowledge and justification is still foundational in the later period. But it is a moderate version, where foundational beliefs based on perceptual experiences are not indubitable; only highly likely to be true. Thus, the justification they confer upon any inferences made from them comes in degrees. We make two kinds of inferences from foundational beliefs: deductive (demonstrative) and non-demonstrative. Non-demonstrative inferences include, but are not exhausted by, inductive inferences.

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The Epistemology of the Bundles: Non-demonstrative Inference

Each particular is a bundle of compresent qualities. Some particulars we know by direct experience. For instance, I see a bundle of the colour green and treelike shape, when I look outside my window. Other particulars I cannot directly experience, such as the qualities that make up the tree, which, according to common sense and physics, cause my perception of the tree. That is, I do not directly experience the cause of my perception when I look outside my window. This move from what we perceive to what exists is an inference we routinely make in common sense and physics. The epistemological question is how do we justify such an inference? The cause of perception may be regarded as an ordinary particular, a persisting substance or as some transient particular(s). Knowing ordinary particulars, the phenomenalist Russell in Our Knowledge of the External World argues, is merely a matter of knowing a series of similar and causally related transient particulars. We cannot know them by inference, since we have no good reason to believe that they are there to be known by inference. We can explain perception without positing such ordinary particulars as causes and we should not multiply entities unless our theory is unable to account for perception without such posits. Thus, Russell maintains in Our Knowledge of the External World that we could construct the actual tree as a class of some transient particulars, which are actual and ideal percepts. Looking back at phenomenalist construction of ordinary particulars of the external world, Russell states in The Analysis of Matter that it ‘employs analogy and induction, it refrains from assuming causality’ (399). The kind of causal inference that Our Knowledge of the External World refrains from was one where we would infer a transient non-percept or an unperceivable

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subsisting material object to exist as the cause of a percept. Russell uses causal reasoning when it comes to inferring that other percepts (actual or ideal) must exist, since he needs them to account for perception. A causal claim, such as ‘A-type events cause B-type events’, is the conclusion of a causal inference. In order to arrive at such a conclusion, we need several premises. One should be a premise stating a positive correlation between the occurrence of A-type events and B-type events. Another should maintain that the occurrence of As is temporally prior to, or simultaneous with (OKEW 218), the occurrence of Bs. A third premise should be a subconclusion to the effect that other possible causes for B to come about have been ruled out. A fourth one should be a subconclusion to the effect that coincidence of As with Bs have been ruled out. To achieve the last one, one must have designed a controlled study with appropriate test and control groups. And most importantly, we have the implicit premise in all causal inferences that laws of nature are uniform. If all these conditions are satisfied, then we can infer that As (with a high probability) cause Bs in the ordinary scientific sense. The first two of the above premises are the ones that Russell discusses most in Our Knowledge of the External World. Russell explains his notion of a causal law as ‘invariable sequence’, that is, correlation and temporal priority: ‘By a causal law, I mean any general proposition in virtue of which it is possible to infer the existence of one thing or event from the existence of another or a number of others. If you hear thunder without having seen lightning, you infer that there nevertheless was a flash, because of the general proposition, “All thunder is preceded by lightning”’ (ibid. 216). Note that the sound of thunder and sight of lightning are both percepts. Since we have observed a positive correlation between percepts of thunder and percepts of lightning, and since we have observed that sight percepts have occurred prior to the sound percepts, we infer that the next observed case of sound percept must have been preceded by a sight percept, even if we have not perceived it. We infer the existence of one percept from another. We do not go beyond percepts, whether actual or ideal, in our inferences until we get to the Analysis of Matter. In Our Knowledge of the External World, Russell explains the attitude which philosophers, such as Kant, have traditionally taken towards causation: ‘The law of causation, according to which later events can theoretically be predicted by means of earlier events, has often been held to be a priori, a necessity of thought, a category without which science would be impossible’ (235–6). Russell finds this view ‘excessive’ in its scope, on the grounds that the law of causality has been verified in scientific studies, but not so well in human volition so far

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(OKEW 236). Russell takes the law of causality to be ‘an empirical generalization from past instances in which it has been found to hold’ (ibid. 28). Thus, Russell in Our Knowledge of the External World invokes causal inferences, but does not accept the law of causality as an a priori principle. At the same time, Russell agrees with J. S. Mill that inference to unobserved events ultimately depends on induction, specifically induction by simple enumeration. The reasoning is such that inference to unobserved events depends on the law of causality, and that in turn is based on induction by simple enumeration: So far we have observed that numerous events have had causes, and we have observed no event which does not have a cause. Therefore, all events, including the unobserved ones, have causes (An Outline 281). ‘It is thus the principle of induction, rather than the law of causality, which is at the bottom of all inferences as to the existence of things not immediately given’ (OKEW 226). Enumerative inductive inferences have in common with causal inferences the implicit premise that laws of nature holding for unobserved cases will be similar to the laws that hold for the observed cases. An inductive inference is the kind of inference we make when we are trying to establish a correlation between two kinds of things or events. We aim to conclude a correlation between two classes; or intensionally speaking, between two kinds of properties. For example, ‘All Cretans are liars’: we claim that there is a positive correlation between being a Cretan and being a liar. Any member who belongs to the class of Cretans also belongs to the class of liars. And since correlation is one of the premises of a causal argument, and correlation relies on enumerative induction, justifying causal inferences we make requires a justification of induction. Since in Our Knowledge of the External World, Russell relies on the validity of induction in order to justify his causal claims, he needs to justify inductive inferences. He accepts Hume’s argument, the conclusion of which is that such an attempt leads to circular reasoning. Hume shows that if we want to argue that induction is a rational form of reasoning, where rational means a form of reasoning which yields deductive certainty, then we are bound to fail. The reason is that any such reasoning will require the premise that unobserved cases always resemble the observed cases, or the principle of uniformity of nature. But we cannot justify our belief in this premise. We cannot justify it a priori, since there is nothing logically contradictory about unobserved cases not resembling the observed ones. Neither can we justify our belief in this premise empirically, since that would require inductive reasoning, which is exactly what we are trying to validate, hence we are led to circular reasoning.

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Russell’s response to this problem in Our Knowledge of the External World was to accept inductive inferences to be valid as an a priori logical principle. Russell formulates the principle of induction as follows: ‘If, in a great number of instances, a thing of a certain kind is associated with a thing of the other kind, it is probable that a thing of the one kind is always similarly associated with a thing of the other kind; and as the number of instances increases, the probability approaches indefinitely near to certainty’ (OKEW 225). Later in The Analysis of Matter, however, Russell realizes that phenomenalist construction of ordinary particulars is not in fact able to give a satisfactory account of perception without appealing to non-perceptual causes. Phenomenalism accepts the testimony of other people, that is, accepts their mental events as data. And Russell relies on arguments based on analogy to infer that there are minds other than his own and their testimonies as to what sense-data they have (‘The Relation of Sense-data to Physics’ 150). But what is problematic is the reliance on testimonies of other minds, even if we assume other minds are validly inferred to exist. Russell explains in The Analysis of Matter that relying on the testimonies of other minds tacitly assumes causality in the sense that another mind is a cause and the testimony I hear its effect. It is assumed that other people use their words the same way I do, to express what they perceive. Bostock gives us the other reasons: First, when causes are constructions, they are mere sets with no causal powers. But this is not a criticism of Russell’s constructions since the phenomenalist Russell does not hold sets of sensedata to have causal powers anyway (Bostock 191). Second, constructing ordinary particulars requires that places and times are immediately distinct. But Russell claims places and times are constructed as well. So, Russell’s construction of ordinary particulars in Our Knowledge of the External World becomes circular (ibid. 167). Third, ‘unperceived, ideal appearances’ had to be appealed to when stating a causal law. In support, Bostock makes the following quotation from The Analysis Matter: ‘The great difficulty in the above theory of “ideal” elements is that it is hard to see how anything merely imaginary can be essential to the statement of a causal law’ (Russell 214). Bostock explains that, ‘If these “ideal” elements do not actually exist, then the “real” laws of physics cannot rely upon them, and this must make it very difficult to state those laws’ (194). Russell in The Analysis of Matter abandons phenomenalism and adopts the ordinary scientific view of perception in explaining the inferences from percepts to what exists in the physical world. Russell now assumes that ‘percepts have causes which may be not percepts’ (399). Causality is still accepted based on

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the validity of induction. And induction is again believed on a priori grounds. The novelty in The Analysis of Matter with regard to the principle of induction, however, is that now it is accepted as a postulate of science; it is not a logical principle, which holds universally true (168). By a postulate, Russell means ‘something not very different from a working hypothesis, except that it is more general: it is something which we assume without sufficient evidence, in the hope that, by its help, we shall be able to construct a theory which the facts will confirm’ (AMa 167). Russell adds that science does not require any of its postulates to be necessarily true. It is enough that they are often true. Hence, Russell announces that he accepts the validity of induction, while acknowledging that he has no conclusive argument for it (ibid.). Causal inferences are justified based on the postulated validity of inductive inferences. Russell argues that the law of induction is an a priori (not based on experience) belief that we have, not a priori knowledge; for if it were a priori knowledge it would always be true (ibid. 174–5). In The Analysis of Matter, there is a slight change in the formulation of Russell’s understanding of a causal law. Causal laws are no longer considered to be invariable sequences; they state tendencies (ibid.; MPD 146). According to the view that causal laws are invariable sequences, A causes B means that events of type A are invariably followed by events of type B. One problem with this view is that sometimes events may be tokens, not types; that is, A may not be repeated at all but nevertheless cause B (HK 490). Russell’s views on the epistemological status of induction remains the same in Human Knowledge. Induction, which is an inference which gives probability, not certainty, to our inductive generalizations, is still a postulate required for scientific knowledge. What is significant in Human Knowledge with respect to induction is that Russell formulates a new problem of induction, which later N. Goodman (1955) will call ‘the new riddle of induction’. Russell argues that accepting induction as a postulate is not enough to make our inductive inferences, and therefore, causal inferences, truth-conducive. He realizes that without any prior reason for believing that all As are Bs, sheer positive correlation between As and Bs and temporal sequence is not sufficient to yield true conclusions more often than false ones. Here is Russell describing enumerative induction: ‘Given a number n of α’s which have been found to be β’s, and no α which has been found to be not a β, then the two statements: (a) the next α will be a β, (b) all α’s are β’s, both have a

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probability which increases as n increases, and approaches certainty as a limit as n approaches infinity’ (HK 401). Russell points out, however, that induction by enumeration is erroneous as it is, since ‘it can be shown that the conclusions of inductive inferences from true premises are more often false than true’ (MPD 153). Let a1, a2, . . . an be the hitherto observed members of α, all of which have been found to be members of β, and let an+1 be the next member of α. So far as pure logic is concerned, β might consist only of the terms a1, a2, . . . an ; or it might consist of everything in the universe except an+1 ; or it might consist of any class intermediate between these two. In any of these cases the induction to an+1 would be false. (HK 404)

This point is made later (1955) by Nelson Goodman (Fact 74–5) with his famous ‘grue’ example. The class α is the class of emeralds. The class β is the class of green things. The members of α have been observed so far to be members also of β. So we would like to conclude that the next emerald (an+1) will be green. But as long as classes are taken extensionally, we can also conjure up a class βʹ whose members are grue things; where something is grue if and only if either it is green and has been observed before today or it is blue and observed after today. And therefore, we would also be able to conclude that the next emerald will be grue. Thereby, we would predict that the next emerald to be both green and grue, but if the next emerald is grue, then it is blue, not green. That is, Goodman makes the same point that ‘this traditional form of induction allows the inference of incompatible conclusions from the very same evidence’ which Russell had made in HK (Aune 132). Russell explains that this problem shows that the classes α and β need to be treated intensionally, not extensionally; ‘the class β must have certain characteristics, or be related in some specific way to the class α’ (HK 404–5). Russell explains this with a better, that is, easier to understand, example in a note on non-demonstrative inference in 1959: You have, let us suppose, a growing boy whose height you measure on the first day of every month. You may find that, for a certain period, his rate of growth is constant. If you knew nothing about human growth, you might infer by induction that he would continue to grow at this rate until his head strikes the stars. There are, in fact, an infinite number of formulae which will fit any finite set of facts as to your boy’s growth. Pure induction, if valid, would lead you to regard all these formulae as probable, although they contradict each other. (Russell, ‘Note on Non-Demonstrative’ 139)

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All the above examples show that without some initial reason to believe that ‘All emeralds are green’ or ‘All human beings grow 2 inches every year’, inductive inference to such generalizations based on mere positive correlation of As and Bs is not truth-conducive. Russell turns to J. M. Keynes for the solution to the problem above. Keynes requires that there must be an antecedent probability for the generalization we want to test. That is, before we observe its instances, the generalization should have ‘something to be said in its favor, so that at any rate it is worth examining’ (HK 435), unlike, I suppose, the generalization that ‘All emeralds are grue.’ To satisfy this requirement, Keynes formulates a postulate called ‘the postulate of limited variety’, which is a form of the assumption of natural kinds (ibid. 318). Keynes maintained that the things we will generalize about, α’s, belong to certain natural kinds (‘generator properties’), and these kinds are of a limited number, even though the individuals which belong to those kinds may be infinitely many. And some properties (‘apparent properties’) arise out of each natural kind. So, the β that we want to associate with α will have to be one of those properties that arise out of the kind α. Suppose the generalization in question is ‘All copper conducts electricity.’ Knowing that copper belongs to the kind metal, we check what kind of properties other metals have; we see that the property of conducting electricity arises out of the kind property of being a metal. So we think that there is an initial probability for our generalization that all copper conducts electricity to be true (HK 435 and 441; Keynes chapter 22.3). Keynes supposes that ‘it is possible to pick out a finite set of fundamental properties, such that when we know which of these properties an individual possesses, we can know (at least in theory) what some, at least, of his other properties are, not because there is a logical connection, but because in fact certain properties never occur except in conjunction with certain others’ (Russell, HK 442). Russell does not, however, accept Keynes’s postulate as it is. Russell notes that biology does not accept precise natural kinds ever since the theory of evolution. Russell describes a natural kind as ‘a class of objects all of which possess a number of properties that are not known to be logically interconnected’ (ibid. 317). Russell in fact held this view since 1914: ‘Darwin’s Origin of Species persuaded the world that the difference between different species of animals and plants is not the fixed, immutable difference that it appears to be. The doctrine of natural kinds, which had rendered classification easy and definite, which was enshrined in the Aristotelian tradition, and protected by its supposed necessity for orthodox dogma, was suddenly swept away forever out of the biological world’ (OKEW 22). Neither in physics, Russell argues, are there any natural kinds

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apart from subatomic particles, such as protons (HK 444). Furthermore, Russell points out that J. Nicod showed that ‘Keynes’s postulate was not sufficiently stringent, and in making it more adequate made it less plausible’ (‘NonDeductive Inference’ 122). This leaves Russell searching for a better postulate (or postulates) which will provide the finite antecedent probability needed to validate inductive inferences.1 This is revealed in the second part of the note on non-demonstrative inference mentioned above: Keynes, in his Treatise on Probability shows that under certain circumstances an induction is valid if the generalization in question has a finite probability before any instances of its correctness are known. Accepting this view, I conclude that induction, in so far as it can be validly employed, is not an indemonstrable premiss, but that other indemonstrable premises are necessary in order to give the necessary finite probability to inductions which we wish to test. The conclusion is that scientific inference demands extra-logical postulates of which induction is not one. (Russell, ‘Note on Non-Demonstrative Inference’ 139)

Thus, Russell concludes that in order to be able to use inductive inferences in a cogent way, we have to have some reason, independent of the correlation between As and Bs, to think that the generalization about As with reference to Bs is probable. In fact, Russell concedes this point even back in 1927: ‘It may be said that all inferences to something unobserved are only probable, and that their probability depends, in part, upon the a priori probability of the hypothesis’ (AMa 16–17). This is similar to the move Russell has had to make when trying to justify our beliefs about particular facts. It may be that we have a group of beliefs about particular facts which cohere very well with one another. But unless each belief is initially credible, coherence among them will not raise the probability that what these beliefs describe about the world is in fact true. Unless I and everybody else have actually existed for a while and we have had the experiences we believe to have had, total coherence among our beliefs will not amount to any approximation to truth. I might have as well just dreamed up a wonderfully coherent story. Thus, the beliefs about particular facts that we use as data when making our inferences towards scientific generalizations must be initially credible. Russell assigns this credibility to our beliefs by accepting memory as a postulate (or ‘premise’ as he calls it) of knowledge. By a premise of knowledge, Russell means something you have to accept as true in order that knowledge about the external world may be possible at all, even though you do not have any independent justification for it. A claim describing a particular fact, then, is more probable than not if it is remembered. Any proposition remembered

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has more credibility than any other not remembered (HK 188; Van Cleve, ‘Why Coherence’ 168). Russell in the later period espouses what Bonjour would call moderate foundationalism. Russell still believes that coherence alone cannot justify our beliefs. But he now argues for a compromise view between pure foundationalism and coherentism. He defines a datum as ‘a proposition which has some degree of rational credibility on its own account, independently of any argument derived from other propositions’ (HK 392). And ‘it may thus happen that a body of propositions, each of which has only a moderate degree of credibility on its own account, may collectively have a very high degree of credibility’ (ibid. 157). Russell likens the structure of knowledge ‘to a bridge resting on many piers, each of which not only supports the roadway but helps the other piers to stand firm owing to interconnecting girders. The piers are the analogues of the propositions having some intrinsic credibility, while the upper portions of the bridge are the analogues of what is only inferred. But although each pier may be strengthened by the other piers, it is the solid ground that supports the whole, and in like manner it is intrinsic credibility that supports the whole edifice of knowledge’ (ibid. 396). Hence, just as in order for coherence to enhance justification each belief about particular facts has to have some initial credibility, a generalization needs to be initially plausible before we use inductive reasoning to draw that generalization as a conclusion. And similarly, a causal claim, being a kind of generalization, needs to be initially plausible in order that a causal argument can confer likelihood to its conclusion. Since ‘induction cannot prove causation unless causation is antecedently probable’ (ibid. 455), Russell suggests we analyse the inferences we do make in science, and once we identify them, accept them as postulates (MPD 153). Russell formulates five such postulates.

The postulates of scientific inference Russell’s postulates are synthetic, contingent and a priori. They are synthetic and contingent because they ‘depend, for their truth, upon characteristics of the world, not upon logical necessities which must be the same for all possible worlds’ (‘Non-Deductive Inference’ 121). Thus, the postulates are claims about what the world is like; and if they are true, their truth is contingent on what the actual world is like. We accept the truth of the postulates on a priori grounds.

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The postulates give the finite a priori probabilities, concerning causal laws and other kinds of generalizations, which Russell needs in order to justify inductive inferences we employ in arriving at these generalizations (HK 487). Russell writes, The postulates that I shall require will therefore state that generalizations of certain specified kinds are finitely probable before there is any evidence in their favour. If the postulates are admitted, it will follow that inductive evidence can confer a high degree of probability upon any generalization of one of the specified kinds. (‘Non-Deductive Inference’ 131)

1. The law of quasi-permanence. ‘Given any event A, it happens very frequently that, at any neighboring time, there is at some neighboring place an event very similar to A’ (HK 488). A series of such events gives us the persisting ‘thing’. ‘In every natural process, there is a finite probability that there is something that persists’ (‘Non-Deductive Inference’ 126). This quote suggests at first sight that what is inferred is the ordinary particular, but that is not the case. Russell explains that what he means by the quasi-permanence of a thing is that we should regard a thing not as a ‘single persistent substantial entity, but as a string of events having a certain kind of causal connection with each other’ (HK 458). Remember that back in Our Knowledge of the External World Russell rejected the permanence of material objects. This work was an attempt to gain knowledge of the external world using merely deductive inference, which gives certainties. But later he finds deductive inferences insufficient. He argues for the need for non-demonstrative inferences, such as that ensured by the postulate of quasi-permanence. Russell confesses that ‘The method of Cartesian doubt, which appealed to me when I was young, and may still serve as a tool in the work of logical dissection, no longer seems to me to have fundamental validity. I have come to accept the facts of sense and the broad truth of science as things which the philosopher should take as data, since, though their truth is not quite certain, it has a higher degree of probability than anything likely to be achieved in philosophical speculation’ (MPD 153). According to Russell, one shortcoming of relying on purely deductive inferences as he did in Our Knowledge of the External World was that it led to solipsism. Russell takes the data of percipients other than myself as data in my construction of the external world. But just as I do not have any logical grounds to infer that anything outside me exists, I do not have any logical grounds to believe in the existence of other people with percepts either. That is, Russell is

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not licensed to use other people’s percepts as data for his construction. Russell explains later in An Outline of Philosophy: I have been assuming that we admit the existence of other people and their perceptions, but question only the inference from perceptions to events of a different kind. Now there is no good reason why we should not carry our logical caution a step further. I cannot verify a theory by another man’s perceptions, but only by means of my own. Therefore, the laws of physics can only be verified by me insofar as they lead to predictions of my percepts. If then, I refuse to admit non-mental events because they are not verifiable, I ought to refuse to admit mental events in everyone except myself, on the same ground. Thus, I am reduced to what is called ‘solipsism’, i.e., the theory that I alone exist. This is a view which is hard to refute, but still harder to believe. (319)

Recognizing this problem, in Human Knowledge Russell accepts ‘quasipermanence’ as a postulate we need in order to be able to make scientific inferences to gain knowledge about the external world. But the difference between the traditional notion of permanence of an ordinary particular and Russell’s notion of quasi-permanence is that the postulate of quasi-permanence does not maintain that every ordinary particular persists, but instead that it is highly probable that every transient particular will be associated with another to which it is similar in structure and/or quality. Also, every transient particular is a complex of compresence of qualities; they do not need a substratum to exemplify them, as the old notion of persisting transient particulars would require. But sometimes there will be many events at a neighbouring time which are similar to A at a given time, such as in the case of peas in a pan. To be able to identify one pea, A1, as the same one at a neighboring time, A2, instead of B2 or C1, Russell calls for the second postulate of causal lines (HK 487). 2. Causal lines. ‘It is frequently possible to form a series of events such that from one or two members of the series something can be inferred as to all the other members’ (ibid. 489). Such a series, Russell calls a causal line. This postulate enables us to say that when there are many events at a given time similar to A, ‘there is usually one which has a special connection with A, of the sort which makes us regard it alone as part of the history of the “thing” to which A belongs’ (ibid. 488). Russell explains that it is by similarities between a person at time t and a person at time tn that we recognize that the two transient particulars are identical. But what accounts for their identity over time, that is, what makes them belong to the same series of transient particulars, is that there is causal continuity between them, as well as qualitative and/or structural similarity (ibid. 458).

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Causal lines are also postulated between an object of perception and my perception of the object (ibid. 458–9). 3. Spatio-temporal continuity. ‘When there is a causal connection between two events that are not contiguous, there must be intermediate links in the causal chain such that each is contiguous to the next, or (alternatively) such that there is a process which is continuous in the mathematical sense’ (ibid. 491). For instance, when I hear what a friend says, there must be intermediary regions between the sounds my friend makes and the sounds that my ear receives, which, according to physics, are sound waves. This postulate again aids in making an inference to transient particulars, missing pieces in the causal chain of perception. 4. Structure. ‘When a group of complex events in more or less the same neighborhood all have a common structure, and appear to be grouped about a central event, it is probable that they have a common causal ancestor’ (ibid. 464–5). For instance, when we watch a performance at a theatre, the common causal ancestor of our perceptions would be the event of an actress doing her part. The reason he admits this postulate is that we will be able to assume that there is something in the external world which is the cause of our perceptions, when several people experience perceptual events similar in structure. This postulate implies that the structure of the cause of the percept is the same as that of the perceptual counterpart (ibid. 474). Structure is important for explaining quasi-persistence, which will otherwise be unexplained since the notion of substance is rejected. Russell writes, ‘persistence is a very common feature of natural processes . . . structure is what is most apt to persist’ (ibid. 473). It seems that structure gives the finite antecedent probability that we need to justify inductions that we use in making causal inferences with respect to perception. Identity of structure, especially when the structure is very complex, gives a finite probability of common causal origin. The reason is that the presumed causes of perception are often quite different in their qualities than the qualities of their effects in us as percepts. Take, for example, the quality of a sound I hear and the quality of sound wave. How can we justify the claim that it is the sound wave which causes my percept of a certain sound, when the two are qualitatively unlike each other? It is because the structure of the percept and the non-percept is the same. If there were no similarity at all, either one of quality or structure, between what I perceive and what presumably causes my perception, why should I think that particular non-percept is the cause of my percept? In fact, the importance of structural similarity is stressed as early as The Analysis of Matter. Russell argues that the a priori probability of a hypothesis may be strengthened ‘when we infer something similar to what we know

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than when we infer something dissimilar’ (AMa 16). This is why we need the structural postulate. Accepting that there is structural similarity between nonperceptible causes and perceived effects gives the initial credibility for our causal claims which aim to infer that some unperceived transient particular must exist based on our knowledge of the structure of our percepts, that is, the transient particulars that we perceive. Admitting that qualities of a percept are different from the qualities of a nonpercept, which causes it, seems to be inconsistent with my thesis that Russell was a neutral monist in the later period. But we talk of perceived qualities and unperceived qualities as qualitatively different from an epistemological point of view only. The inference from common sense to physics is an inference from one way of knowing to another. What ties the different ways of knowing is that in both cases we work on the assumption that the structure of what we know, that is, the unperceived cause, in the second way of knowing, is the same as the structure of what we know in the first way of knowing. 5. Analogy. ‘Given two classes of events A and B, and given that, whenever both A and B can be observed, there is reason to believe that A causes B, then if, in a given case, A is observed, but there is no way of observing whether B occurs or not, it is probable that B occurs; and similarly if B is observed, but the presence or absence of A cannot be observed’ (HK 493). This postulate is required for justifying the belief that there are other minds, understood as classes of transient particulars, not as mental substances (HK 483). We observe in ourselves that when we have a certain belief, or when we are in a certain physical or mental state, we tend to behave in certain ways. And we observe similar behaviour in other people, so we infer that the cause of their behaviour should be something similar. For instance, I smile when I have a pleasant thought, so when I see my friend smiling, I infer that she must be having a pleasant thought (ibid. 483). Russell notes that this postulate is also useful in inferences that do not draw conclusions about other minds. For instance, we generally associate the feeling of hardness of an object when touched with certain visual appearances; certain shapes and contours of objects seem to be accompanied most of the time with a feeling of hardness when we touch them. This habitual association leads us to expect and infer that a similar visual appearance will be accompanied the next time we touch something and it feels hard (ibid. 494). With the help of these postulates, Russell can now infer the probable existence of transient particulars in the physical world. Suppose I have a percept of an orange, O10, sitting on the left-hand side corner of the kitchen table. Based on

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the law of quasi-permanence, I infer that there is a great likelihood that I will have percepts O11, . . ., On similar to O10 if I do not change my position and anything else about the circumstances. Based on the structural postulate and the postulate of causal lines, I infer that there must be a transient physical orange, O1, which causes O10, and which has a similar spatio-temporal structure to O10. It seems that structure is what grounds the causal line between the transient physical orange O1 and my perceptual orange, O10. Suppose after perceiving O10, I hear the phone ringing and answer it. Afterwards I go back to the kitchen only to see O11. With the postulate of quasi-permanence and spatio-temporal continuity, I infer that ‘the orange’ must have been sitting where it was all along. And therefore, I conclude that O10 is the same ‘thing’ (ordinary particular) as O11, that is, belongs to the same series of transient particulars as O11. Russell admits that future study may show that the postulates he has given are not necessary for scientific inference, but he claims they are sufficient (ibid.). To know these postulates, in the sense of ‘animal knowledge’ (ibid. 495), is to know the general connections between particular facts. Furthermore, he notes that these postulates need not be certain. ‘In order that the postulates . . . fulfill their function it is not necessary that they should be certain; it is only necessary that they should have a finite probability’ (ibid. 149). Has the admittance of these postulates brought Russell in a full circle back to Kant? Not quite. On the face of it, they both maintain that there is synthetic a priori knowledge, that is, knowledge about the world acquired by non-empirical means. But what they each mean by knowledge is different in this context. Kant argued that there is synthetic a priori knowledge, in the sense of certainty. Russell, on the other hand, argues there is synthetic a priori knowledge, where knowledge means ‘animal knowledge’ or ‘habitual knowledge’. This kind of knowledge is akin to ‘synthetic a priori beliefs’. Russell explains in The Analysis of Matter that Kant’s claim was that we have knowledge, in the sense of certainty, about the world and we acquire this knowledge by non-empirical means. But Russell holds that we have beliefs about the world which rely on non-empirical means (174). Nevertheless, Russell’s account of knowledge is indeed Kantian in the sense that in order for scientific knowledge of the world to be possible at all, one must accept the truth of some propositions, even though they differed on the details of these propositions. The most important difference in their views is that Kant thought these propositions must be necessary truths, while Russell thought they only need to be probably true.

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4

The Problem of Individuation

In this chapter we will discuss the problem of individuation which arises for the later Russell’s realist bundle theory. Individuation seems to pose a problem for the bundle theory because it relies on the principle of identity of indiscernibles and according to this principle, two things having the same qualities is sufficient for them to be identical. Some philosophers, led by M. Black, argue that the principle of identity of indiscernibles is false and therefore the bundle theory must be false. On the realist bundle theory, the constituents of a particular are merely qualities. Therefore, the theory has the consequence that if two particulars have all their qualities in common, then they have to be numerically identical. There is nothing among the constituents of a particular which is not a quality. Hence when two particulars share all their qualities there is nothing left to differentiate the two (Loux, Metaphysics 108). There are three kinds of particulars that we need to examine in relation to the problem of individuation: The problem of individuation with respect to (1) particulars which are point-instants, necessary for constructing space–time series, (2) particulars in the ordinary sense (ordinary particulars) such as Caesar as an object that persisted through time, and (3) particulars as spatio-temporal slices (transient particulars), such as one of the complexes of compresent qualities which make up the series Caesar, the ordinary particular. But all these particulars share one feature: they are not particulars in the traditional sense; they are either complexes or sets of qualities. The problem of individuation with respect to ordinary particulars, that is, what is in general called ‘the problem of identity’ is the question of determining criteria for when one ordinary particular can be regarded as the same thing over time, what changes it can go through and remain the same thing. Ordinary particulars, for Russell, are ordered sets of transient particulars. We know them

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as chains of bundles of qualities, which are causally connected to each other. Hence, Russell’s answer to this problem would be that two transient particulars should be regarded as the same ordinary particular, that is, as belonging to the same series, if there are causal chains connecting one to the other, which would track the loss and gain of various qualities in time. If any two series have all the same quality-complexes as members in the same order, then, according to Russell, there is one series, not two. The problem of individuation with respect to point-instants is that construction of a space–time series requires that we have units that do not recur. For instance, if we have complete complexes of qualities a, b and c as candidates for being particulars as point-instants, and if they share all their qualities, then there will not be a transitive relation of succession between them to form a temporal series. Could there be two complete complexes of compresent qualities that share all their qualities? Russell admits this is a logical possibility. On the individuation of point-instants, Russell says that another complex with the same properties can recur but never will; he only maintains that it is empirically impossible for the same complex to recur. He accepts that ‘it is logically possible for [a complex of compresence] to occur more than once, but [he] assumes that if [the complex] is sufficiently complex, there will not in fact be recurrence’ (HK 306). The more complex the compresence, the less likely that the same particular will recur. And the problem of individuation with respect to transient particulars is determining criteria to distinguish one particular from another at a space–time point − others of the same kind or of different kinds. A transient particular is a complex of compresence, but not a complete complex of compresence, which for Russell counts as a point-instant. A transient particular is, for instance, a spatio-temporal part of one of the books on my table. The criteria we have for the identity of a transient particular is the compresence, that is, coexistence, of certain qualities. In the case of transient particulars, since they are incomplete complexes of compresent qualities, there is an even stronger chance that a complex may recur. But how does Russell’s allowance of logical possibility of recurrence of a bundle mesh with his other commitments, namely, the commitment to the necessary truth of the principle of identity of indiscernibles and the necessary truth of the bundle theory? Russell devotes a chapter to the problem of individuation in Human Knowledge. However, what he mainly discusses is the individuation of a certain type of particular, a point-instant, that is, a complete complex of compresence (1). For what is important to him is the construction of a space–time series, where

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one needs elements that will not recur. Furthermore, answering the question for point-instants, in effect, answers it for ordinary and transient particulars. It seems to me, after a thorough consideration of all the arguments for and against the principle of the identity of indiscernibles, that Russell, like J. O’Leary-Hawthorne later on, regarded it as a logical consequence of the bundle theory that if a and b are transient particulars that share all their qualities, then they would be the same particular. So, he would not be surprised if he were presented with logically possible universes with ‘two’ qualitatively identical ‘things’. Another way to put this is that since Russell’s particulars are eliminated, Russell’s bundle theory of particulars does not entail the principle of identity of indiscernibles (PII hereafter) in its original formulation. It only entails that if two complexes of qualities share all their qualities, then such complexes are identical. What Russell admits the logical possibility of is another complete complex of compresence with a different name; that is, he accepts the principle as a logical truth if the predicative function in the statement of the principle ranges over identity properties as well, not merely qualities. Now let us survey the discussion of the relation between the bundle theory and the PII. Armstrong gives one of the traditional arguments against the realist bundle theory based on the falsity of PII: If it is true that a particular is a bundle of properties, and if properties are universals, then these truths are necessarily true. If so, then, necessarily, if particulars a and b have exactly the same properties, then a and b are the very same particular. That is to say, identity of indiscernibles is necessarily true. But on no interpretation does it appear to be a necessary truth. Therefore, it cannot be a necessary truth that a particular is a bundle of universals. But if this is not a necessary truth, it is not a truth at all. (Universals Vol. 1 91)

The explanation for the first premise is that bundle theorists in general hold the theory to be true of particulars necessarily, since they claim that it is impossible for there to be substrata as constituents of particulars (Loux, Metaphysics 107). A. Casullo challenges this claim and argues that the later Russell held the bundle theory to be only contingently true of particulars. Casullo distinguishes between weak and strong reduction, and claims that Russell’s reduction to particulars is a weak reduction, that is, ‘particulars are only contingently identical’ to complexes of properties (‘The Contingent’ 527). Armstrong, on the other hand, assumes that any truth put forward as a theory explaining the nature of particulars in metaphysics must be put forth as a necessary truth. This is what he means when he says, ‘If this [that a particular is a bundle of universals] cannot be a

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necessary truth, it is not a truth at all.’ But Casullo objects that Russell did not mean to formulate a necessary truth about particulars. Russell did not claim that a particular, in all possible worlds, is a bundle of universals (ibid.). It seems to me that we need to accept Armstrong’s first premise as true because Russell formulated the realist bundle theory as a theory to apply to any particular. According to Russell, modality applies primarily to propositional functions,1 and on this view, ‘It is necessary that a particular is a bundle of compresent properties’ would translate into ‘For all x, if x is a particular then x is a bundle of compresent properties.’ And this universal claim must be what Russell had in mind when he proposed the bundle theory. He could not have proposed a theory which would only be possible: There is an x such that x is a particular and x is a bundle of properties. Thus, Russell is committed to the necessary truth of the principle of identity of indiscernibles due to his commitment to the bundle theory. We will see now that he is also committed to the necessary truth of the principle because he accepts that principle as a logical truth: it is in terms of this principle that Russell defines identity.

Russell on identity Russell did not consider identity to be a relation until 1900.2 In 1897, he claims, ‘every relation involves a diversity between the related terms’ (An Essay On §208). Since identity does not relate two diverse terms, it cannot be considered as a relation. Again in 1899, he says relations may be between two or more terms but ‘identity of content’ does not have this formal condition of relations, for it is ‘mere self-sameness’ (‘The Classification’ 140). Diversity is required for a relation, and diversity requires at least two terms (ibid. 141). In 1903, Russell accepts identity as a relation. ‘Since there is such a relation as identity and since it seems undeniable that every term is identical with itself, we must allow that a term may be related to itself ’ (POM §95). Two terms are identical ‘when the second belongs to every class to which the first belongs’ (ibid. §26). However, after POM, he decided he had to find a definition for identity. He thought the principle of identity of indiscernibles together with Leibniz’s Law would be the right one. In Principia, Russell and Whitehead’s definition of identity is: ‘x and y are to be called identical when every predicative function satisfied by x is also satisfied by y’ (13.01). Russell defines identity in logic and mathematics on the basis of

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the principle of identity of indiscernibles, on the assumption of the axiom of reducibility.3 Therefore, he must be taking the principle to be a logically necessary truth. However, in Principia, the function ranges over relational properties as well as qualities; in particular, it ranges over the property of being identical to a. Let us use the abbreviation PIII for this wide notion of the principle of identity of indiscernibles, and PIIR when predicates range over both qualities and relational properties, except for the property of being identical to a, and let us use the abbreviation PIIQ for the narrow sense, when the predicate variable ranges over only qualities. Wittgenstein objects to Russell’s definition of identity by means of the principle of identity of indiscernibles: ‘Russell’s definition of “=” won’t do; because according to it, one cannot say that two objects have all their properties in common. (Even if this proposition is never true, it is nevertheless significant)’ (Tractatus 5.5302). Ayer explains that ‘in saying that this proposition is at least significant Wittgenstein implies that it is not self-contradictory’ (Philosophical 27). Since ‘two objects have all their properties in common’ is not self-contradictory, the principle of identity of indiscernibles cannot be a logical truth. But the reason that it seems as if the claim is not self-contradictory is that Wittgenstein is not including identity properties as one of the properties that any two objects may have in common. If we did, then it would indeed be self-contradictory to say that there are two objects, with all the qualities and relations and they are even represented by the same name: ‘a is not identical to b even though a has the property of being identical to b and b has the property of being identical to a’. Furthermore, regardless of whether Wittgenstein had PIIQ or PIII in mind, it seems to me that Wittgenstein ignores the fact that the phrase ‘two objects’ is a variable which may or may not stand for the same individual. In his 1911 article, ‘On the Relations of Universals and Particulars’, Russell denies PIIQ as a logically necessary truth. Even if two particulars had the same qualities, they would be different particulars on his earlier view. Russell says, ‘Terms of spatial relations cannot be universals or collections of universals, but must be particulars capable of being exactly alike and yet numerically diverse’ (‘On the Relations’ 118). ‘It is logically possible for two exactly similar patches of white, of the same size and shape, to exist simultaneously in different places. Now whatever may be the exact meaning of “existing in different places”, it is self-evident that, in such a case there are two different patches of white’ (112). This shows that for Russell PIIQ was not true, but denial of PIIQ does not imply the falsehood of PIII. Since his particulars have substrata in this early period, Russell can get

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identity properties from them. In general, the identity property can be grounded on the substratum each particular has or can be derived from the particular. If the identity property is dependent on the particular, then it would be circular to hold that a particular is individuated by its identity property. Hence, it must be the substrata that were the individuators. A particular a will have the property of having a’s substratum and b will lack that property. Hence, there will be a property that distinguishes the two otherwise qualitatively alike particulars. The logical truth of PIII would be preserved. The later Russell seems to hold PIIQ to be necessarily true, since now he holds the bundle theory to be true. If two particulars share all their qualities then they are identical, where qualities include positional qualities, such as being to the right of the centre of a visual field. Russell in Inquiry (1940) gives an argument from verifiability for holding PIIQ to be logically true. He claims enumeration would be theoretically impossible without the principle of identity of indiscernibles. If I want to count objects A, B, C, D, E and if B and C are indiscernible, then I would give B and C the same name and count them as one, and conclude there to be only four objects. Therefore, ‘if there be a concept of identity which allows indiscernibles to be not identical, such a concept can never be applied, and can have no relation to our knowledge’ (IMT 130). I find this argument sound. There might as well be 16 objects in reality, but I would still count 4 objects since only 4 would be distinguishable from one another. Thus, enumeration does indeed become impossible. A substratum theorist might argue that Russell is begging the question here. The only way Russell would give the same name to B and C and count them as one particular is if he already assumes that B and C are identical because they are indiscernible. According to Russell, we would give B and C the same name, because they would be composed of the same qualities; they would have to be the same quality-complex. Russell will give the same name to the qualitycomplexes because he is assuming that there is nothing more to a particular than its qualities. If he held the substratum theory, each quality-complex would have a bare, simple particular that differentiates it from other similar quality-complexes, and in that case, he would not give the same name to B and C, because B and C would have different substrata to account for their distinctness. But the problem with this response is that since substrata cannot be experienced, they would serve no role in our distinguishing between objects. All we have as tools to distinguish one thing from another are properties. Even if the said objects had substrata we would not be able to recognize them. We cannot perceive the presumed substrata of objects. Thus, it is true that denying

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the principle of identity of indiscernibles makes enumeration impossible, for the fact that enumeration depends on making distinctions based on qualities. On the face of it, since Russell takes the principle of identity of indiscernibles to be necessarily true, his version of the realist bundle theory will face M. Black’s objection to the effect that it is not true that the principle is necessarily true. The version of the principle that Black argues against is PIIR, since he allows the predicate variable to range over qualities and relational properties, but not over any identity property, such as being identical to a.

Black’s argument Black argues that it is logically possible for there to be numerically different but qualitatively identical things, thereby showing that the claim that PIIR is a necessary truth is false.4 Black imagines a symmetrical universe which consists of only two spheres. The spheres are qualitatively identical: each has a diameter of 1 mile, and both are made of iron and have the same temperature and colour. Every relational property of the one is also had by the other. Two such spheres cannot have properties of being in different places, because their places are qualitatively the same too, since they are in a symmetrical universe. Black says, ‘to say the spheres are in “different places” is only to say that there is a distance between the two spheres’ (‘The Identity’ 156). Since it is logically possible for there to be two different things sharing all their properties, the principle of identity of indiscernibles is false (ibid.). Thus, Black’s counterexample seems to refute the principle as a necessary truth, therefore rendering the bundle theory false. A way in which one might hold that the principle is a necessary truth, that is, to counter the possibility of there being numerically different but qualitatively identical particulars, is by appealing to haecceities or identity properties. Then each particular sphere in Black’s example would have a property that the other does not have, namely, being that particular. The non-qualitative property of haecceity, or the non-qualitative property of being identical to a, may be used to differentiate between two spheres. In Principia, the early Russell argues that the property of being identical with a certain particular can individuate two things that are qualitatively the same. ‘It should be observed that by “indiscernibles” he [Leibniz] cannot have meant two objects which agree as to all their properties, for one of the properties of x is to be identical with x, and therefore this property would necessarily belong to y if x and y agreed in all their properties’ (PM,

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introduction, chapter 2 §6). This shows that the early Russell admitted identity properties as properties that can individuate qualitatively similar particulars. This is consistent with his adoption of the substratum view in the same period. The substratum each particular has individuates it, which is effectively the same as haecceity for the early Russell. However, the later Russell cannot accept the identity property as an individuative property, mainly because he has now dropped the substratum view and adopted the bundle view of particulars, unless he derives it from the existence of a bundle of qualities. But he cannot include the identity property in a bundle as an individuative property since that would make the account of particulars circular. The identity property assumes the concept of a certain particular. But on the bundle theory, particulars are constructed out of their constituents, so the constituents cannot presuppose the concept of a certain particular (Loux, Metaphysics 109–10). In any case, Black does not allow the spheres to have properties such as being identical to this sphere or that sphere. For he thinks treating such properties as individuative properties is just repeating the hypothesis that the two spheres are different. Black writes, ‘All you mean when you say “a has the property of being identical with a” is a is a . . . In fact you are merely redescribing the hypothesis that a and b are different by calling it a case of “difference of properties”’ (155). Neither does Black allow subjunctive properties, such as ‘If there were an observer, then one sphere would be on her left the other on her right.’ Black argues that we would be ‘just pretending to use a name’ (157). We have seen that qualities such as being black or being a sphere can make up a particular. But relational properties, which involve a reference to a particular, such as being 2 metres away from a particular sphere, b, or being 2 metres away from another black sphere cannot be constituents of a bundle. Russell does not include spatio-temporal properties in a complex in the regular sense. Instead of invoking properties such as being to the right of b, he allows into the makeup of bundle qualities such as dexterity, that is, being to the right of the centre of a visual field. Russell calls such qualities positional qualities. These qualities do not involve any reference to other particulars; hence do not pose a problem of circularity. Russell writes, I hold that a ‘thing’ is nothing but a bundle of qualities, and that therefore, two different things cannot be exactly alike. But I hold this only because I regard position in space as defined by means of certain qualities not usually recognized as such . . . if I see two things at once, they cannot both be in the center of my field

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of vision; if one is so, the other is to the right or left of it, and above or below it . . . It is in virtue of these qualities that my visual field has spatial characteristics. The space of physics is partly constructed, partly inferred, from the space of visual and other immediate objects of perception. (‘The Problem’ 260–1)

Positional qualities, however, require a perceiver or a perspective, according to which one bundle would be dexter and the other sinister. However, it is one of Black’s conditions that no perspective is allowed. If Russell were allowed to bring in a perspective, he would not have the problem of individuation between the two spheres. Black explains that if an observer were introduced, the spheres would have the properties of being to the left or right of the observer which would distinguish one from the other. The spheres would have ‘acquired new relational characteristics’ (157). That is, Russell’s reply assumes an observer. However, Black does not allow any observers or potential perspectives into his logically possible world. Black says that this would change the conditions of his counterexample. So, Russell’s reply from the absoluteness of perceptual spaces cannot address cases where there is no perspective of any kind but only two objects in a symmetrical universe. Perhaps we could reply on Russell’s behalf by pointing out that Black’s disallowance of any perspectives is begging the question against Russell’s version of the bundle theory. Hochberg makes this point when he says that Black’s counterexample is not really an argument against Russell, ‘for it simply denies the existence of the non-relational location properties5 or pairs of coordinate properties that are crucial for Russell’s bundle analysis’ (The Positivist 45). Casullo defends PIIQ by giving an argument from conceivability to show that Black’s counterexample is not possible. Casullo claims that assuming that possibility is grounded on conceivability, we cannot conceive of these two spheres unless we have a mental image of them (‘A Fourth’ 135). Indeed, conceiving something that is essentially physical requires that we entertain an image of it. The two spheres in a symmetrical universe are physical objects. Thus, when I conceive of them I cannot help but form a mental image, which immediately gives me a point of reference, that is, the centre of my imaginary visual field. B. Blanshard and A. J. Ayer also join Casullo in making such a criticism of Black’s spheres. Blanshard argues the two spheres are not intelligible because we are not allowed to call one ‘this’ and the other ‘that’ (397). For that would give them different locations with reference to an observer. And Ayer argues that the reason we can imagine such universes is that we ‘bring into the picture a point of observation with respect to which the two halves of the universe are differently situated’ (33).

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In response to such arguments based on the unverifiability of his scenario, Black argues that in fact we can verify that there are two spheres. ‘We could know that two things existed without there being any way to distinguish one from the other’ (162). To support this claim Black appeals to the fact that we can verify that there are in a region of space two stars by observing their gravitational effect which result in the region as a whole even though we cannot inspect one in isolation from another, just as physicists say that they can verify that there are two electrons in a given region without being able to cite any property had by one and not by the other. Black claims it would be a property of the whole, composed of the two stars with the space between them, that there are two, even though no property of each star would be different from the properties of the other star. Now if this is true for Black’s scenario then there is a property of the whole of this symmetrical universe with qualitatively alike spheres that they are two. In response to this, I think that Russell would hold that there in fact is not an emergent property that the whole has, such as sheer numerical difference; instead, such a scenario shows that our physics is not yet able to identify all the properties of the two spheres (or electrons) and the relations between them. Otherwise, we should be able to infer all the properties of the complex from the properties of its parts and their relations. That is why it seems to us that there is an emergent property of being two. Together with Black, S. French argues that the objection based on verifiability confuses thinking about a possible state of affairs and the state of affairs itself. He admits that the ‘I’ who does the imagining will definitely be involved in imagining a two-sphere universe, but ‘it is possible for me to imagine a situation in which the universe existed but “me” did not’ (152). Granted, conceivability does not have to involve mental imagery. One can take a conceivable state of affairs as a set of logically consistent propositions which merely describe a scenario. But the non-question-begging descriptions of the scenario do not seem to yield the conclusion that there are two spheres. Description (1): There are exactly two spheres. Any given sphere has qualities F, G, H. Description (2): There are at most two spheres. Any given sphere has qualities F, G and H. Description (3): There is at least one sphere. Any given sphere has qualities F, G and H. Description (1) is obviously assuming what it needs to prove. It assumes that there are two spheres, instead of proving that there are two. Descriptions (2) and (3) leave the question open as to how many spheres there are. But there is at least one on the third scenario. Still, Black cannot prove that there are two due to the argument made by I. Hacking below.

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Hochberg’s response, by pinning down the problem on the description of the scenario, points in the direction of Hacking’s argument. Hochberg argues that Black’s argument does not show bundle theories to be false. All the argument establishes is that ‘no definite description that we can give, under the conditions assumed, will apply to only one of the spheres; hence any such description must fail.’ Any definite description we form will be satisfied by both spheres. So we cannot label them, for that would require a definite description such as ‘Let the label A apply to the sphere such that . . .’. ‘This does not show that the spheres are indistinguishable in that they do not stand in different relations, but only that, given the limited resources we are allowed, we cannot distinguish them by description’ (The Positivist 46). Admittedly, we cannot describe them as different. This is exactly the problem. We cannot describe them as two distinct things merely by appeal to their properties (including relational ones). I. Hacking shows that the properties Black allows in the description of his possible world underdetermine the claim that such a possible world has two individuals in it. Hacking argues that the same evidence could support either of two theories: (1) There are two individuals in Euclidean space and therefore the principle of identity of indiscernibles is not true; or (2) There is one individual in a Riemannian curved space and therefore the principle of identity of indiscernibles is true. If the space the spheres are in were a Riemannian one, then the relational property of being a certain distance away from would not require that another particular, that is, a sphere, exists. Since a Riemannian space is curved, drawing a line away from one sphere would lead us back to the same sphere. So, Hacking continues, since the evidence does not singularly determine any one of these claims, the truth or falsity of the principle cannot be established by such counterexamples (249). As a defence of Black’s argument, R. M. Adams replies that a Riemannian world with one sphere would be a different logically possible world. The difference does not have to be a difference in description but can be regarded as a difference in possible realities (16). Following Adams, R. C. Hoy holds that one cannot claim that the same logically possible world can sometimes be described in accordance with principle of identity of indiscernibles or not described in accordance with it. ‘If one world contains only one ball bearing and another contains two aren’t they different logically possible worlds? So a cogent complaint seems to be: Hacking is not redescribing a logically possible world; he is inventing a new one’ (Hoy 279–80). G. Landini and T. R. Foster also criticize Hacking for not distinguishing ‘logically possible worlds and principle of identity of indiscernibles from

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physically possible worlds and the principle of identity of indiscernibles’ (58). But even if we are discussing examples in the realm of logically possible worlds, any such world will have to conform to some laws of physics, either Euclidean or Riemannian. We are not entertaining worlds which conform to no physical or geometrical laws whatsoever, since we are conceiving of spheres, which are physical objects, which means they have to abide by some physical/ geometrical laws, whatever they may be. Thus, what Hacking’s point shows is that any logically possible world will conform to some laws; if these laws involve Euclidean geometry then Black is begging the question with his imagined universe. Since in a Euclidean world the only way a sphere can have the property of being 2 miles away from a sphere is if there indeed is another in that universe. In which case, by including such a property as one of the properties of a sphere he is assuming that there are two spheres, instead of proving it. Thus, I hold, following Hacking’s footsteps, that Black is begging the question in his article, and therefore he has failed to establish that PIIR is false. Another kind of response but one which also stresses the significance of the description of the scenario comes from O’Leary-Hawthorne. He claims that if we describe this world based on the commitments of a realist bundle theorist, then the description yields only one particular. Since the properties of the bundle are immanent universals, spatio-temporally located in particulars, any combination of properties are also universals, and therefore ‘can be fully present at many places at once. Thus, it is possible by the bundle theorist’s own lights that, say, the bundle consisting of F, G, and H be five feet away from itself ’ (O’Leary-Hawthorne 193). Black’s universe would be described as ‘a world in which a single bundle of universals – the universals of solidity, mass, shape, colour, etc. collocated in one of the spheres – is at some distance from itself’ (Zimmerman 306). Therefore, that the principle of identity of indiscernibles is logically true is not a problem for the realist bundle theorist. It expresses exactly what the theory wants to maintain. In Black’s imagined universe, there is only one particular, not two. The immanent universals are such that they can be wholly present at many places at the same time. For instance, the numerically same greenness is in my cactus, in the spinach in my fridge and in the olives hanging from a tree in Assos. Therefore, the property of greenness can be at a certain spatial distance from itself. O’Leary-Hawthorne argues that since the bundle is a group of properties, it also is repeatable. It follows that Black’s symmetrical spheres do not work as a counterexample which defeats the bundle theory; on the contrary, they are a straightforward and welcome consequence of the theory. There is numerically

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one group of properties in two different places just as there is numerically one green in many different places (O’Leary-Hawthorne 193). Just as greenness can be a certain distance from itself, so can a bundle of properties, including greenness, be a certain distance from itself. Therefore, if we describe Black’s universe as containing one bundle of universals which is at a distance from itself, then the bundle theory is not refuted (ibid. 194). O’Leary-Hawthorne, in anticipation of the objection that to say that the same group of properties is at a certain distance from itself is contradictory, points out that if being the same distance from itself is contradictory then the idea of immanent universals should also be contradictory (195). D. Zimmerman agrees with O’Leary-Hawthorne that if the bundle theorist is granted immanent universals, then it is not inconsistent to describe the universe with only one sphere. Black would be begging the question against the bundle theorist by insisting that there are two distinct spheres (306). But, unfortunately, the substratum theorist can make the same complaint against the bundle theorist. She can say that Hawthorne’s response assumes the truth of the bundle theory, by interpreting a particular as a complex of properties, and that therefore, it does not show that Black’s argument is flawed. Yes, as a matter of fact, not only the bundle theorist, but also the substratum theorist is begging the question. The debate as to the truth of the principle of identity indiscernibles boils down to a disagreement on the nature of a particular. For, once we are committed to a certain understanding of particulars, our description of the universe, and therefore, the number of the spheres in such a universe is determined accordingly. Thus, O’Leary-Hawthorne’s arguments support Hacking’s conclusion that the principle cannot be refuted by means of such counterexamples. For any putative scenario requires some assumptions to be made for its description and the assumptions skew the results. Even though, for his own version of the realist bundle theory, Russell does not need to defend the bundle theory as O’Leary-Hawthorne does, that is, by giving an account of relational properties, such as, being at a certain distance from itself, O’Leary-Hawthorne’s seems to be closest to Russell’s views in the later period. Russell would admit that the same bundle of qualities may recur in such a universe, on the assumption that we are not allowed any perspective whereby we could appeal to positional qualities that employ the centre of field of vision as a reference point. That the same bundle may recur follows logically from taking qualities to be immanent universals, which the later Russell does. Just as a property can wholly be at different places at a time, so can a group of them.

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Hawthorne’s response helps us see what exactly a realist bundle theory of particulars, and in particular an eliminativist one, entails and does not entail. An eliminativist realist bundle theory of particulars does not entail PIIQ, but instead entails what I will call PIIC, the principle of identity of indiscernible complexes: If two complexes of compresent qualities share all their qualities, then they are identical. We need to appropriate the principle of identity of indiscernibles based on the commitments of the eliminativist realist bundle theory. Neither of PIIQ, PIIR or PIII is appropriate within the context of the eliminativist bundle theory. The variables x and y in the above formulations of the principle do not range over individuals (particulars), since they are eliminated in favour of quality-complexes. Hence the need for PIIC, where variables x and y range over complexes of qualities (as well as qualities). According to Russell, ‘a particular is constituted by qualities; when all its qualities have been enumerated, it is fully defined’ (HK 292). Thus, the bundle theory of particulars, which maintains that compresence of a group of qualities is sufficient for the identity of a transient particular, commits the later Russell to PIIC. I conclude that an eliminativist realist bundle theory is not troubled by Black’s counterexample because the version of PII Black is attempting to refute is not what our bundle theorist is committed to. Nevertheless, I hold that the best response to Black’s counterexample is to point out that his example begs the question, due to the arguments made by Hacking and Hawthorne. Interestingly, the early Russell had given an argument similar to Black’s, arguing against the bundle theory. The following is his argument from ‘On the Relations of Universals and Particular’ (1911). It may be said that two patches are distinguished by the difference in their relations to other things. For example, it may happen that a patch of red is both to the right of something and to the left of something. But this does not imply that the patches are two unless we know that one thing cannot be both to the right and to the left of something (‘On the Relations’ 117). 1. Two patches of red are distinguished by the difference in their relations to other things. (Supposition: bundle theorist’s claim) 2. Red (redness) both has the relation of being to the left of X, that is some reference point, and the relation of being to the right of X. (From 1) 3. One thing cannot be both to the left and to the right of X. (Supposition) Therefore, (4) there are two reds. Russell argues that (3) is required in order for (4) to follow; but assuming (3) is, in effect, assuming numerical diversity, whereas numerical diversity is supposed to result from the different relations the qualities have.

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Furthermore, Russell argues that (3) is false. If red surrounds X completely, then red would be both to the left and to the right of X. Therefore, (4) does not follow.6 Therefore, two things cannot be distinguished by their relations. Therefore, the bundle theory is wrong. One problem with this argument is that the supposition (1), on the face of it, would be wrong on the later Russell’s account. The bundle theory does not maintain that relations individuate qualities or bundles of qualities in perceptual space. It maintains that coordinate qualities do. Dexterity and sinisterity are qualities, not relations. So if red is dexter, that means two qualities, that is, redness and dexterity, are compresent. It may be the case that red is also compresent with sinister. There is nothing in the bundle theory that excludes that. For red is the same thing when compresent with dexterity and when compresent with sinisterity. Another problem is that it attributes a position to the bundle theory that it actually rejects. The bundle theorist does not assume (3). On the contrary, the bundle theory denies (3). It is the characteristic of immanent qualities that they can recur: red can both be to the right and to the left of X. The worst problem is that Russell, at the second stage of his argument, is begging the question against the bundle theory, just as Black does. The early Russell’s argument seems very similar to Black’s argument. Two things that are qualitatively alike are the spheres with certain shared qualities, and the corresponding ‘two things’ in Russell’s example are the two red patches. Both the spheres and red patches are presumed to share their relational properties as well. Black shows how this is possible with his symmetrical universe. If the universe is symmetrical, then one sphere can be a certain distance from another sphere, and hence the two spheres will share their relational properties as well. And the early Russell points out that one thing, namely, a red patch, can have the same relations with another if red surrounds X. Thus, red will have both the properties of being to the left of and to the right of, and hence those properties will be shared by ‘both’ reds. Therefore, relational properties do not help individuate the spheres or the reds. But just as Black does, the early Russell assumed at the outset that there are two reds. So, we end up with the bundle theory unable to explain how there are two things, that is, two reds or two spheres. We have examined the problem of individuation that the bundle theory is charged with. I conclude that (i) to insist against Russell that it is logically possible to have a universe with no perspectives whatsoever is to beg the question against his version of the bundle theory of transient particulars. (ii) Nevertheless, if (i) is denied, we can, by appeal to O’Leary-Hawthorne, show that on a realist bundle theory, if the same complex of properties recurs, it will have to be the same particular, not a different one. That is, Russell’s bundle theory is committed to PIIC, not PIIR. (iii) PIIR is not refuted by Black after all, thanks to Hacking’s argument.

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The Problem of Necessity

The bundle theory maintains that the identity of a particular is determined by its qualities. And on the realist version of the bundle theory qualities exist necessarily. This invites the question as to the modal status of particulars, that is, whether particulars are necessary existents or not. Accordingly, one objection to the bundle theory is that all particulars become necessary existents on this theory. The constituents of a particular are universal properties, and as such they are necessary existents. Therefore, the argument concludes, the whole they compose is a necessary entity. Russell’s bundle theory is immune to this objection because it requires the qualities of a bundle to be compresent. So, regardless of whether an ordinary particular or a transient particular is in question, what ensures that contingent entities remain as such is the contingent nature of the compresence relation that binds the qualities of a transient particular, which in turn may be a member of the set that makes up an ordinary particular. Therefore, the bundle is a contingent existent. Another modal concern is over the necessary or contingent truth of propositions involving particulars. Most propositions about particulars express contingent truths. For instance, take the proposition that Russell did not die young. This proposition is true, and it is contingently true in the sense that he might have died young. But if the bundle theory of particulars is true it seems that this proposition will have to express a necessary truth. Identifying a particular with a set or a complex of compresent qualities seems to imply mereological essentialism, and as a consequence, propositions which attribute a property to a particular all become necessary truths. Van Cleve argues that when particulars are identified in a reductive sense either with sets or mereological sums (complexes), mereological essentialism follows

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(‘Three’ 97). Mereological essentialism is defined by R. Chisholm as follows: ‘for any whole x, if x has y as one of its parts then y is part of x in every possible world in which x exists’, or ‘every whole has the parts that it has necessarily’ (66). I argue that in order for the mereological essentialism involved in the nature of a set or a complex to create a problem of necessity for a bundle theory of particulars, two assumptions must be made, namely, that the identity involved is of the reductive kind and that the bundle theory is proposed as a necessary truth about particulars. Thus, mereological essentialism, and therefore, the problem of contingent predication, ensues for the bundle theorist only if both of the following conditions hold: (1) the bundle theory in question maintains that particulars are reduced either to classes of qualities or to complexes of compresent qualities; (2) the bundle theory in question maintains that it is necessarily true that each particular is identical to a certain bundle of qualities. Russell identifies ordinary particulars with sets, and transient particulars with complexes. When a particular is reductively identified with a set of qualities, the qualities become essential to the particular. Since sets exist only if their members do, all the members of a set are essential to the identity of that set. And if a particular is necessarily identical to such a set, then any quality will be essential to the identity of the particular. Therefore, predicating a property to a particular expresses a necessary truth about the particular. When a particular is reductively identified with a complex of compresent qualities, again the qualities become essential to the particular. Since there is nothing more to the identity of a complex other than its qualities, if any of the qualities were not part of the complex, then it would cease to be that complex. And if a particular is necessarily identical to such a complex, then each quality becomes essential to the particular. Therefore, any proposition attributing a property to a particular, again, expresses a necessary truth about the particular. Van Cleve expresses this objection nicely with an analogy: ‘It [is] not true of any individual that it might have existed with properties other than the ones it actually has: we cannot suppose that a complex whose constituents are F, G, and H might have existed with F, G, and J as constituents instead. Thus, the bundle theorists’ world . . . is a Leibnizian one in which every individual has just the properties it does necessarily. Adam need not have existed at all, but once in existence could not have done otherwise than eat the apple’ (‘Three’ 124). Russell himself would not take seriously an objection to the effect that the bundle theory does not leave room for contingent predication, since he rejects de re modalities, whatever theory of particulars he happens to hold, be it

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a substratum or a bundle theory. Nevertheless, let us see what this objection amounts to. I hold that Russell’s theory avoids the problem of accounting for contingent predication because it does not reduce particulars to either classes or complexes; instead he eliminates particulars and puts classes or complexes in their place, since on this view, there is no particular which could either have its properties necessarily or contingently. This solution of opting for an eliminativist bundle theory as opposed to a reductionist one is suggested by Van Cleve, who explains that when individuals are eliminated, the problem of accidental or necessary predication also disappears, for there are no individuals which could have their properties essentially or contingently (103; 128). But Van Cleve does not seem to have recognized that this is exactly the later Russell’s version of the bundle theory (130). This might be because he took for granted the interpretations of Russell’s views as promoting reduction, as opposed to elimination, by Russell scholars, such as Pears (63). Nevertheless, I will first show that if Russell’s identification were a reductive one, he would not be able to escape the problem because he holds that it is necessarily true that each particular is identical to a certain bundle of qualities.

Supposition of a reductive identity Russell in Principles explains that there are two kinds of wholes. First are aggregates.1 An aggregate is a whole which is definite as soon as its constituents are known. ‘Classes [i.e. sets] are to be interpreted as aggregates’, except when a class contains one term or none (§139). Second are unities. A unity is a whole which is not completely specified when its parts are all known. Unities ‘contain relations or . . . predicates, not occurring simply as terms in a collection, but as relating or qualifying’ (ibid. §135 and §136). A unity is not a class. The parts of a whole as a unit are identified by analysis (ibid.). The later Russell’s wholes in the case of ordinary particulars are aggregates, and in the case of transient particulars unities (HK 297). Enumeration of the qualities in a transient bundle does not suffice to determine the bundle. The qualities need to be in a compresence relation. The compresence relation itself is not a member of the bundle but it is a relation that binds the qualities in a bundle. And ordinary particulars are series of transient particulars linked to each other with causal chains.

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One formulation of the reductio argument against the bundle theory to the effect that all properties of a bundle are essential to it is based on the assumption that particulars are reduced to classes. If particulars are reduced to classes, then the truth of the bundle theory, it is argued, implies that its qualities are essential to the particular. As Van Cleve puts it, ‘if a thing were a set of properties, all of its properties would be essential to it: not only could it not change its properties, but it could not have different properties to start with. This is because it is essential to a set that it contains the very members it does’ (‘Three’ 96). An ordinary particular, for Russell, is in fact a set, an ordered set. If Russell reduces an ordinary particular to a set, then he seems to be committed to mereological essentialism with respect to ordinary particulars. As ordinary particulars are sets of transient particulars, each transient particular will be essential to the set, since sets have their members essentially. If two sets differ even in one member, they are not identical. And since each transient particular is a quality-complex, it will follow that each ordinary particular has its qualitycomplexes, therefore, qualities, necessarily. But we need to notice that the reason that qualities end up being essential to an ordinary particular is that the identity between a particular and a class is taken to be a necessary relation. Casullo concurs that Russell’s ordinary particulars are series of transient particulars (he calls them momentary particulars or temporal parts). Casullo argues that even if we accept that a transient particular has its properties essentially, it does not follow that the ordinary particular, which has this transient particular as a part, has those properties essentially unless mereological essentialism is accepted with respect to ordinary particulars (‘A Fourth’ 129). Casullo argues that Russell is not committed to mereological essentialism because he interprets Russell’s identity claim as a reductive contingent relation so that the qualitycomplexes (transient particulars) are not essential to the identity of an ordinary particular because the identity between the ordinary particular and the set of quality-complexes, Casullo argues, is not necessary (ibid. 130). The problem of accounting for contingent predication arises also on the level of transient particulars, which are identified, by supposition, reductively, with a quality-complex. Since a quality-complex is constituted by its qualities, if one of the qualities had not entered into the constitution of the complex, it would not have been that quality-complex. And if transient particulars are necessarily identical to quality-complexes, then the qualities will be essential to the transient particular as well. That is, the mereological essentialism with respect to complexes seems also to taint the contingency of a transient particular’s qualities.

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The relation of identity: Necessary versus contingent On the assumption that the identity claim of the bundle theory is a reductive one, it seems that the quality-complexes that belong to the set to which an ordinary particular is identical would be essential to its identity if the identity relation between an ordinary particular and the set of complexes of compresent qualities is taken as a necessary relation. For an individual would then be identical to the same set of bundles across all possible worlds. If an individual a is necessarily identical to a set of certain bundles of compresent qualities in the actual world, it will also have to have the same bundles in any other possible world in which it exists. It seems, therefore, that if a Russellian could maintain that the identity relation between an ordinary particular and a series of bundles of qualities is contingent, she could thereby escape the problem of accounting for accidental predication, as Casullo suggests. After all, if an ordinary particular is contingently identical to a set of bundles of compresent qualities, then an ordinary particular of this world would be a series of complexes of certain qualities. So, it would leave the possibility open that this ordinary particular is identical to some other set of quality-complexes in another possible world. Assuming that the identity relation between an ordinary particular and a set of quality-complexes is a reductive one, would Russell maintain that it is a contingent or a necessary relation? In fact, since Russell assimilates metaphysical necessity to logical necessity, we need to rephrase our question accordingly: Assuming that the identity relation between an ordinary particular and a set of bundles of qualities is reductive, would Russell think that it was a logically necessary relation? Casullo argues that it is contingent (‘The Contingent’ 527). Casullo makes a distinction between weak bundle theory and strong bundle theory, where in the former the identity is contingent, and in the later it is necessary (ibid. 528). But he makes this distinction for the purpose of showing a defence of a Russellian bundle theory in the face of another objection, the problem of individuation (ibid. 536). He does not use the distinction to solve the problem of accidental predication. According to Russell, the identity relation is logically necessary. It is a relation that a thing has to itself. He expresses it with the propositional function, x = x (PM 22). It is expressed as a relation either between (logically) proper names and variables: ‘The principle of identity itself [i.e. x = x] fails to hold for descriptive

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terms, although it continues to hold for variables and name letters’ (Kalish, Montague and Mar 396). Since a bundle of compresent qualities is referred to by a definite description, such as ‘the bundle such that . . .’, the identity between a particular and a certain bundle of qualities will be expressed as a relation between a proper name and a definite description. And when Russell analyses the reference to the definite descriptive phrase, ‘the bundle’, away, the final analysis yields an identity between a proper name and a variable. Suppose, a particular a is identical to the bundle of properties F, G and H. The restatement will yield, ‘There is an x (a complex) such that ((x has the properties F, G, and H) and (for all y, if y has properties F, G, and H, then y is identical to x) and x is identical to a).’ Thus, after a Russellian analysis of a statement of the identity relation between a particular and a bundle of qualities, the remaining identity relation, namely (x = a), is a necessary relation. Therefore, I do not think that we can interpret Russell’s bundle theory of particulars as stating a contingent relation between a particular and a bundle of qualities, as Casullo does. The particular is asserted to be the same entity as the bundle of qualities. We have one entity, which is identical to itself. One argument in favour of the claim that a bundle theorist must hold the identity relation between a particular and its qualities to be a necessary one comes from Armstrong (Universals Vol. 1 91)2: When one is proposing a metaphysical theory about the nature of particulars, it must be a metaphysically necessary truth that they are proposing. Otherwise, their theory is not metaphysically significant. Physics is in a better position to tell us what the nature of particulars is like in the actual world. Russell would agree with Armstrong on this point. In ‘On Scientific Method in Philosophy’ (1914), Russell says, ‘In the first place a philosophical proposition must be general. It must not deal specially with things on the surface of the earth, or with the solar system, or with any other portion of space-time . . . a philosophical proposition must be applicable to everything that exists or may exist’ (106). Thus, Russell must have proposed the bundle theory of particulars as a necessary truth about particulars. But this does not mean that Russell accepts properties such as being necessarily identical to a. Russell accepts that it is a necessary truth that everything is identical to itself. For all x, x = x. And it is a tautology that ‘a = a’, that is, it is logically true. But he would argue that the necessity in the latter is derivative. Therefore, we cannot conclude that a has the property of being necessarily identical to a, as Barcan-Marcus and Kripke do. Barcan-Marcus (‘The Identity’ 2.32) and Kripke (‘Identity’ 136) have argued that all identity statements are necessary. On the

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face of it, I do not think Russell would disagree with them, since on Russell’s theory, any identity statement which has ordinary proper names will have to be translated to sentences which substitute a definite description in the place of the ordinary proper name, which will mean that the only identity statements that remain will be between logically proper names and variables. And identity statements involving logically proper names and variables are necessary for Russell. Russell would hold that the necessity of the identity relation in ‘a = a’ is derivative because modality applies primarily to propositional functions, not to propositions. Individuals, such as a, do not have any properties necessarily. Russell, in the quoted text below, claims that one cannot accept predicates that properly apply to propositional functions as properties of individuals: Much false philosophy has arisen out of confusing propositional functions and propositions. There is a great deal in ordinary traditional philosophy which consists simply in attributing to propositions the predicates which only apply to propositional functions, and still worse, sometimes in attributing to individuals predicates which merely apply to propositional functions. This case of necessary, possible, impossible, is a case in point . . . Propositions are only true or false. (Russell, ‘The Philosophy of Logical Atomism’ 231)3

Even if we did accept modality directly applies to propositions, E. J. Lowe explains that (1) ‘It is true of a that it is necessarily identical with a’, does not follow from (2) ‘It is necessarily the case that a is identical with a.’ What should follow from (2), according to Lowe, is (1)*, ‘It is true of a, in particular, that it is necessarily identical with itself’ (86–7). However, one may have other grounds for accepting such properties as being necessarily identical to a. Here is another argument from Kripke which aims to get at this property: Ordinary proper names are Millian, that is, the only function of ‘a’ is to refer to a. Ordinary proper names are rigid designators, that is, ‘a’ designates a in all possible worlds in which a exists. Therefore, a particular, a, has the property of being necessarily identical to a (Naming 3). That is, it is because names are taken to be rigid designators that there is such a property as being necessarily identical to a. But Russell does not hold names to be rigid designators. Thus, the reductive identity relation between an ordinary particular and a set of quality-complexes, that is, transient particulars, is a necessary one. And so is the reductive identity relation between a transient particular and a bundle of compresent qualities. Therefore, if Russell in fact held the relation between

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particulars and either sets or complexes to be a reductive one, he would be committed to mereological essentialism with respect to particulars. But in fact Russell’s ordinary particulars are eliminated in favour of classes, not reduced to classes. When there are no particulars, either ordinary or transient, there is no particular about which the question of accidental predication can arise.

Russell’s views on modality The eliminativist interpretation of Russell’s particulars is also consistent with Russell’s views on modality in general. Russell denies that necessity or possibility applies to propositions at all. According to Russell, these modal properties are properly attributed to propositional functions. There seems to be no true proposition of which there is any sense in saying that it might have been false. One might as well say that redness might have been a taste, and not a colour. What is true, is true; what is false, is false. (POM §430)

In his 1905 article, ‘Necessity and Possibility’, Russell considers several theories of necessity available to him at that time. (1) The theory that confounds metaphysical necessity with aprioricity. On this view, we tend to think that what we know empirically could have been otherwise so we call those truths contingent and we think what we know a priori could not have been otherwise, and we call those truths necessary (510). (2) The theory according to which a proposition is necessary if it is implied by another proposition (512). (3) A necessary proposition is an analytic proposition, where analytic propositions are those ‘which are deducible from the laws of logic’ (516). (4) The view that necessity can only properly apply to propositional functions,4 not propositions. Russell denies (1) because on this view propositions do not have any ‘notable logical characteristics’ that make them necessary or possible (ibid. 510). He denies (2) because on this view all propositions become necessary, since any proposition will follow from another (512). Russell rejects (3) because there are propositions which seem to be necessary, but which are not analytic, such as ‘If a thing is good, then it is not bad’ (517). (4) is the view Russell espouses.5 A proposition is necessary ‘when it is an instance of a type of propositions all of which are true’ (517). Russell imagines taking a London cab which has a number plate with five figures, and then he thinks, ‘This London cab could have had a 4-digit number plate.’ What is meant by this proposition is ‘This is a London cab, and some London cabs have numbers

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consisting of four figures’ (518). The subject of the proposition is to be regarded as an indeterminate object, represented by a variable, according to Russell. That is why he claims necessity is properly a predicate of propositional functions, not propositions. To determine whether a proposition is necessary or not, we need to replace constants with variables, and determine if it is true that the property attributed to the constant is true for all values of the variable. Take, ‘Socrates is mortal.’ The propositional function would be ‘x is mortal’, and its universal closure, ‘For all x, x is mortal’ is necessary throughout the class human. ‘The propositional function “x has the property ϕ” is necessary if it holds of everything; it is necessary throughout the class u if it holds of every member of u’ (518). Then on this theory, a proposition about a particular, as derived from its corresponding propositional function, cannot be necessary per se, but has to be necessary relative to a class. Russell writes, ‘“x is mortal” is necessary throughout the class man’ (518). It follows then that a propositional function can be both necessary and possible depending on which class we take as our reference. Take, ‘Socrates is smart.’ If I take the class of men as the class u, then the corresponding propositional function will be possible because some men are smart, but not all. But if I take the class u to be the class of eminent philosophers, then it would be necessary. This account of modality, then, seems to take modality to be a relation between two classes. And this sounds very close to the later Russell’s view of probability as a relation between propositional functions. Perhaps that is why even in 1905 he considers the possibility of explaining modalities in terms of a theory of probability. The subject of probability is one which is naturally associated with modality: the probability of a proposition’s being true may be supposed to be a measure of its greater or less degree of possibility. Thus, it would be necessary, in order to show that modal distinctions are never required, to produce a theory of probability in which no such distinctions are invoked. I am not prepared, in this paper, to advocate any view on such a thorny question as probability; and I confess that I do not know any view which strikes me as tenable. (‘Necessity’ 519)

Russell in Human Knowledge discusses a tenable theory of probability by Keynes. However, Russell does not connect probability to modality in this work. But it seems to me that this is the most fitting theory of modality for his later philosophy, although I will not attempt to show it here. I will only note that such a theory of modality is hinted at by Bigelow, Collins and Pargetter in ‘The Big Bad Bug: What Are the Humean’s Chances?’, showing the possibility of linking

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modality to probability: ‘. . . think of “Chtw (−) =1” and “Chtw (−) > 0” as modal operators like necessity and possibility. That is, we interpret “□A” as meaning “Chtw (A) =1”, and take “◊A” to mean “Chtw (A) > 0”’6 (458). I have argued earlier in Chapter 2 that when Russell identifies particulars with bundles of qualities, he eliminates particulars. This view is compatible with Russell’s understanding of modality as primarily applying to propositional functions and has room for giving an account of the contingency of our attributions to particulars. Remember the proposition that Russell did not die young. If we want to apply necessity to this proposition, we will first have to apply necessity to the propositional function, ‘x did not die young’, so that we have: ‘For all x, x did not die young.’ If the reference class is human beings, this universal statement is not true, since it is not true that everything is such that if it is a human being it does not die young, as counterexamples, such as Ramsey’s short life, abound. Thus, the proposition that Russell did not die young, derivatively, expresses a contingent truth. The contingency of the proposition is derived from the contingency of the propositional function: There is something such that it is a human being and it did not die young. That is, as Russell understands the matter, necessity and contingency are relations between two groups of properties, in this case between the property of being a human being and the property of not dying young. If being a member of the first class is sufficient to be a member of the second, then we have a necessary proposition, when the variable is replaced by an appropriate constant. But the fact that something has the property of being a human is not sufficient to conclude that this something will not die young. Thus, our example is a contingent proposition. When we attribute a contingent or necessary property to a certain particular, we do it by virtue of one of the properties of the particular. It is contingent that Russell did not die young because this is a consequence of Russell’s having a certain property, that is, being a human being. It is this property that allows him to die either young or old. Thus, Russell’s view of modal notions is consistent with an eliminativist interpretation of his bundle theory of particulars because on this version particulars are eliminated altogether and we are left with qualities, their complexes and relations between them. Thus, any seeming attribution of either a necessary or contingent property to a particular is in fact a statement of a relation between two classes of qualities.

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The Problem of Analyticity

Substratum theorists charge that the bundle theorist cannot explain subject– predicate discourse, since the bundle theory implies that all propositions about particular facts are analytic, when in fact most are not. Since a bundle theorist has denied a metaphysical holder of properties, in a proposition which seems to be of a subject–predicate form there is no subject that the attribute is ascribed to. Thus, the bundle theorist needs to explain what is going on when an attribute seems to be ascribed to a particular (Loux, Metaphysics 103). Take the sentence, ‘Caesar had curly hair.’ The questions are: what is the attribute said to be related to and what is the relationship between the subject and the attribute? On the later Russell’s theory the attribute is related to the particular referred to by the name ‘Caesar’. The relation between the two is a part–whole relation in the case of transient particulars, that is, quality-complexes (or a spatio-temporal slice of Caesar), so the attribute is one of the constituents of the particular. And the relation between the attributes which constitute a particular is a compresence relation. In the case of ordinary particulars, such as Caesar considered as a persisting thing, the relation between the ordinary particular and the qualitycomplexes that constitute the ordinary particular is a relation of inclusion or membership in a set. When the bundle theorist answers that attribute ascription consists in pointing out that an attribute is one of the constituents of a whole or membership in a set, the substratum theorist objects that this implies that those propositions, when true, are analytic truths. One could get the result that the bundle theory makes all propositions about particulars analytic if one makes the assumption of a theory of meaning

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(a definition), according to which the meaning of a word, including proper names, is revealed by its analysis. Against this objection, I will first show that Russell, before 1905, did make this assumption, but not the later Russell. Next, I will present the later Russell’s defence against the charge, which consists of pointing out that we actually define proper names by a definite description, not by analysis. Finally, I will appeal to a nominal description theory of names to save Russell’s bundle theory from the incrimination. According to a classical account, going back to Kant at least, a proposition is analytic if the property attributed to the subject is contained in the meaning of the subject term. Analyticity applies primarily to a certain type of proposition. Russell, like Leibniz before him, calls them ‘the genus-species type’, that is, ‘Red is a colour.’ The definition of the subject term contains the predicate term. Another type of proposition where a property is attributed to a particular is called the species-individual type, that is, ‘Socrates is Greek’ (The Philosophy of Leibniz 15–17). An analytic proposition, according to Leibniz, must be of the genusspecies kind. Russell explains that ‘this is the reason why every proposition about actual individuals is, in Leibniz’s opinion, contingent’ (ibid. 17). However, the early Russell argued that some of Leibniz’s premises force Leibniz to the conclusion that even species-individual-type propositions are analytic. When we come to the Identity of Indiscernibles, we shall find that Leibniz himself, by holding a substance to be defined by its predicates, fell into the error of confounding it with the sum of these predicates. That this was from his standpoint an error is sufficiently evident, since there would be no ground for opposing subjects to predicates, if subjects were nothing but collections of predicates. Moreover, if this were the case, predications concerning actual substances would be just as analytic as those concerning essences or species. (Russell, The Philosophy of Leibniz 50)

Similarly, the later Russell’s realist bundle theory faces a version of this objection. The later Russell, in Human Knowledge, explains that the premises which led to the conclusion that the species-individual-type propositions were analytic on Leibniz’s account were (1) the principle of identity of indiscernibles, and (2) the claim that every proposition has a subject and a predicate (HK 299). The later Russell seems to be in the same predicament. The following is an analogous argument against the realist bundle theory: A particular is defined by all its qualities (derived from PII). Therefore, any proposition where a predicative quality is attributed to the subject is analytic.

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Both the early and the later Russell deny that all propositions are of the subject–predicate form.1 In opposition to Leibniz, Russell maintains that propositions in which one term is related to one or more terms, as in ‘Socrates is shorter than Plato’, should not be treated as subject–predicate propositions. So since relations are not part of the particular according to Russell, many propositions about particulars in which a relational property is attributed to a particular are synthetic. The remaining propositions where a quality is attributed to a particular, such as ‘Socrates is white’, are not analytic for the early Russell because back then he subscribed to the substratum view. The later Russell, however, analyses ‘Socrates is white’ as expressing a relation between a whole and one of its parts. It seems that denying that relational properties are part of the particular reduces the number of species-individualtype propositions that become analytic but does not eliminate them. We seem to be left with the consequence that propositions in which a quality is attributed to the particular, as in ‘Socrates is white’, are analytic, unless we adopt the substratum theory. The reason is that the early Russell required that the meaning of a word be given by a philosophical definition, that is, analysis. On a realist bundle theory, the analysis of the particular yields all its qualities. Therefore, a sentence where a quality is attributed to a particular, or where a quality is claimed to be a constituent of a particular, is analytic if one holds the view that the meaning of a proper name is given by the analysis of the particular the name stands for, since the meaning of the predicate will be contained in the meaning of the subject term. In contrast, on a substratum view, a sentence where a quality is attributed to a particular is not analytic even if one assumes the view that meaning of a name requires analysis, because the analysis of the particular yields a mere bare particular or substratum. So, the crucial assumption required in order to mount the charge of analyticity against the realist bundle theory is not the assumption that all propositions are of the subject–predicate form. As long as one defines, or gives the meaning of, a proper name by listing all its qualities, it may be argued that the proposition ‘Socrates is white’ is analytic, even though one treats all propositions in a relational form. The bundle theory maintains that ‘Socrates is white’ is not of the subject–predicate form; instead it expresses a part–whole relation, namely, one part, that is, whiteness, is a constituent of the whole, Socrates, supposing that here we are treating Socrates as a spatio-temporal slice. If one assumes that the definition or meaning of the whole consists of analysing the whole, then the part will be revealed as a mere result of conceptual analysis; hence the proposition

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will be analytic. The crucial assumption required to mount the objection of analyticity then is the definition of proper names as analysis. The early Russell thought that ‘definition is only possible in respect of complex ideas. It consists, broadly speaking, in the analysis of complex ideas into their simple constituents’ (Philosophy of Leibniz 18). The definition of a subject term, for the early Russell required an adequate analysis of it, which included all the properties that could be truly attributed to the subject, though not its relations (Griffin, ‘Some Remarks’ 80). Russell writes, ‘If A and B are component parts of the concept in question, both are always necessary to definition; if they are relations, neither is necessary’ (‘The Axioms of Geometry’ 410). Russell in 1899 distinguishes between two kinds of definitions: the philosophical and the mathematical. He thinks that the meaning of a word may be given only by the philosophical definition, that is, definition as analysis. A mathematical definition consists of any relation to some specified concept which is possessed only by the object or objects defined. In this sense, the projective straight line was defined above by its relations to points and planes. . . . Philosophically, a term is defined when we are told its meaning, and its meaning cannot consist of relations to other terms. It will be admitted that a term cannot be usefully employed unless it means something. What it means is either complex or simple. That is to say, the meaning is either a compound of other meanings, or is itself one of those ultimate constituents out of which other meanings are built up. In the former case, the term is philosophically defined by enumerating its simple elements. But when it is itself simple, no philosophical definition is possible. The term may still have a peculiar relation to some other term, and may thus have a mathematical definition. But it cannot mean this relation. (Ibid.)

For instance, if we define ‘this table’ by listing all the qualities this table is constituted by, such as hardness, brownness and squareness, this would be a philosophical definition of the table. But if we define ‘this table’ as the thing in the middle of my room, this would be a mathematical definition, since I would specify the table as a unique particular by its relation to other things. So when a mathematical definition is given for a term, no such analysis is involved; only a correct uniquely identifying relational description is given. Since the philosophical definition of a term includes all the qualities of the thing, one consequence seemed to be that the meaning of the subject term includes the meaning of the predicate term, unless the proper name does not have a meaning, as would be the case if it referred to a bare particular or substratum.

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Even though he never cared for essences, Russell before 1905 seemed to be stuck with them due to this analytical notion of definition. With his new theory of denoting (1905), Russell ceases to demand that a definition of a term involve an analysis of the term. In a letter written in 1953 to R. S. Hartman, who was seeking an explanation for Russell’s distinction between philosophical and mathematical definition employed in POM, Russell replies, I cannot at this date justify the passage on page 63 of The Principles of Mathematics about which you inquire. At the time when I wrote that passage I still believed what I had been taught that a definition should be a conceptual analysis and that one definition could be better than another even when both uniquely determine the same object. All this seems to me now a confused legacy of the muddleheaded concept ‘essence’. What I think about definition now is put forth in the Introduction to Principia Mathematica2 . . . You will realize that The Principles of Mathematics was written before I arrived at my theory of descriptions which I published in Mind of October 1905. That theory made everything that I had previously said about definition obsolete. (17 May 1953)

So before 1905, when his new theory of descriptions appears, he had to accept a bulky essence with all the qualities of a particular. But as of 1905, Russell could use definite descriptions to define an ordinary proper name, and correlatively reduce the particular to a bare substratum which exemplifies qualities. For instance, the ordinary proper name ‘Caesar’ is to be defined by appeal to a definite description such as, ‘The emperor who crossed the Rubicon’, that is, there is an x such that (x is an emperor and x crossed the Rubicon) and (for all y, if y is an emperor and y crossed the Rubicon, x and y are identical). The variables, x and y, refer to logical subjects, and these logical subjects in this period range over irreducible particulars, which are mere substrata, as I argued earlier in Chapter 1. So when Russell switches to the substratum theory of particulars, leaving a version of the substance view behind, he thereby solves the problem of analyticity, for with his theory of definite descriptions he finds an alternative way of giving the meaning of ordinary proper names. For the later Russell a proposition is analytic if and only if it is a logical truth (tautology) or can become a logical truth by substitution of mathematical definitions, not philosophical definitions, that is, analysis. By a logical truth, Russell means propositions which can be proved by logic, that is, ‘they show that certain different classes of symbols are different ways of saying the same thing, or that one class says part of what the other says . . . It is obvious that a proposition which is a tautology is so in virtue of its form, and that any constants which

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it may contain can be turned into variables without impairing its tautological quality’ (AMa 171–2). We also see Russell invoking the mathematical definition for meanings of words in his later work Human Knowledge. For when defending his bundle theory against the analyticity charge, he appeals to definite descriptions we use for ordinary proper names. But note that the logical subject, denoted by the variable x, in the logical analysis of a true sentence containing a definite description, does not refer to some particular or other with a substratum. If the sentence in question is true, the variable refers to some quality-complex or other. Consider ‘This is red.’ The ‘this’ we refer to is a whole, a complex, and red and probably other qualities are parts of this complex. Russell says ‘“this” is equivalent to a description; e.g., “what is occupying the center of my visual field”. To say that this description applies to redness is to say something which is clearly not analytic’ (HK 300). And in the case of an ordinary proper name, we can define it by a definite description. Consider ‘Caesar crossed the Rubicon.’ We do not define the word ‘Caesar’ by enumerating all the events that comprise Caesar, partly because we do not know all his experiences (ibid. 301). We define ‘Caesar’ by some of his prominent characteristics. Russell writes, ‘Suppose P is some property which has belonged to only one person; then we can say, “I give the name ‘A’ to the person who had the property P”. In this case, the name “A” is an abbreviation for “the person who has the property P”. It is obvious that if this person also had the property Q, the statement “A had the property Q” is not analytic unless Q is analytically a consequence of P’ (ibid.). That is, if we define ‘Caesar’ with only a subclass of his qualities, such as the man who ruled Rome and was killed by Brutus, then the property of having crossed the Rubicon would not be contained in the definition of Caesar. Russell even gives a nominal theory of definite descriptions: ‘Every person has a number of characteristics that are peculiar to him; Caesar, for example, had the name “Julius Caesar”’ (ibid.). So the name ‘Caesar’ is an abbreviation of ‘the person whose name was “Julius Caesar”’. Hence, the later Russell does not hold that statements about particular facts, that is, propositions where a property is ascribed to the particular, are analytic (ibid. 497). Synthetic propositions ‘include not only all statements of particular facts but also all generalizations which are not logically necessary, such as “All men are mortal” or “All copper conducts electricity”’ (ibid.). Russell holds the description theory both as a theory of meaning and reference for proper names. As a theory of reference, definite descriptions are

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the means by which a link between a proper name and a particular is established. As a theory of meaning, the semantic contribution a proper name makes to a sentence in which the name occurs is through a canonical definite description. For his defence against the analyticity charge, the later Russell only needs the description theory as a theory of meaning to use it in defining proper names. Kripke argues against the description theory both as a theory of reference (he accepts in some cases of initial baptism, however, that a description does fix a referent) and as a theory of meaning for proper names on the grounds that it gets modal facts wrong (Naming 106). Russell’s version of the description theory allows one to substitute a single description for a name, and Searle’s version allows a disjunction of definite descriptions to be substituted for a name. In either case, Kripke argues, substitutions result in making the properties of the particular necessarily belong to it. ‘If one has the description “the man who taught Alexander” as the description of Aristotle, then the statement “Aristotle taught Alexander” will be tautologous, although it is not actually tautologous for it is something we could discover to be false’ (ibid. 30). This proposition about Aristotle becomes analytic, and therefore becomes a necessary proposition. And if we substitute ‘Aristotle’ for a disjunction of definite descriptions, attribution of most of Aristotle’s properties to him would result in an analytic proposition, and therefore a necessary truth, as Searle accepts: ‘It is a necessary fact that Aristotle has the logical sum, inclusive disjunction, of properties commonly attributed to him: any individual not having at least some of these properties couldn’t be Aristotle’ (172). Russell would have to accept that in those cases when the definite description is the same as the predicated property, the sentence is analytic, and therefore necessary. The later Russell admits this when providing a reply to the criticism he himself raises against Carnap’s view, where Napoleon is described as a region of space–time, the sentence ‘Napoleon was for a period of time in Elba’ becomes analytic. Russell gives retort to the criticism: Yes, that statement is analytic but other statements about Napoleon are not, such as ‘Napoleon wore a cocked hat’ or ‘This position of space-time is a person’ (HK 80). Philosophers such as W. Kneale (1962), B. Loar (1976) and K. Bach (1981) have suggested a nominal description theory instead of the regular one, so that the name ‘Aristotle’ would be substituted with ‘the person called “Aristotle”’ or ‘the bearer of “Aristotle”’. On this version of the description theory, the only property attributed to the particular analytically would be the property of being called ‘Aristotle’. Russell probably would accept this view because as we have

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seen in the quote above he regards, ‘the person who was called “Julius Caesar”’ as a definite description which could give the meaning of ‘Caesar’. Against nominal descriptions as a theory of meaning, Kripke argues that ‘being called “Caesar”’ is non-rigid, since the man we pick out as ‘Caesar’ in this world might have a different name in another world (Naming 49). This objection, however, would be begging the question against a Russellian theory of proper names, since proper names are not rigid designators on Russell’s view. Thus, Russell’s theory of meaning of proper names as definite descriptions, rather nominal definite descriptions, protects his theory against the charge that the bundle theory implies that all propositions attributing a property to a particular becomes analytic. Since none of the qualities of a particular, to which we would refer by a proper name, is contained in the meaning of the proper name, true propositions attributing a quality to a particular do not express analytic truths. Before we end this chapter, we should also note that there is another related objection to the realist bundle theory to the effect that if the bundle theory of particulars were true then propositions ascribing a property to a particular would be uninformative on the grounds that one who knows what the term used to refer to a particular means would already know the property attributed to it (Loux, Metaphysics 103). On the later Russell’s theory of understanding one does not need to know all the components of the referent of a term in order to know what the term means. Russell explains that we can know a complex without knowing its parts. Here is how he expresses the point in Human Knowledge: I maintain that I can perceive a complete complex of compresent qualities without necessarily perceiving all the constituent qualities. I can give the name ‘this’ to such a complex, and then by attention observe that redness, say, is one of its constituent qualities. The resulting knowledge I express in the sentence, ‘This is red’, which, accordingly, is a judgment of analysis, but not, in the logical sense, an analytic judgment.3 (Russell, HK 302)

We should note that the idea that we can know the complex without knowing its parts is not a view that the later Russell has formulated just to defend his bundle theory. For even in 1913, Russell accepted that we can know complexes without knowing their constituents: ‘Analysis only raises problems because we may be acquainted with a complex without knowing what its constituents are’ (TK 120). I have argued in this chapter that the later Russell does not have to accept the consequence that all propositions ascribing properties to particulars are analytic.

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One way in which this consequence would follow is if the later Russell defined ordinary proper names via analysis. I showed that the later Russell appeals to denotational (mathematical) definitions of names as their meanings, with the result that substitution of definite descriptions for names of particulars does not yield analytic propositions. But as Kripke shows, this solution does not work for all propositions where a property is attributed to a particular. As a solution, I suggested that we appeal to a nominal description theory. On this theory, no propositions about particulars are forced to be analytic, if in fact they are not, for there is nothing to the meaning of a proper name, apart from ‘being called such-and-such’ that could contain the predicate attributed to it.

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Neutral Monism

Russell’s neutral monist period is widely known as the period of The Analysis of Mind (1921) and The Analysis of Matter (1927). But Russell scholars have differing views as to whether Russell was indeed a neutral monist in this period. Whereas R. M. Sainsbury argues Russell was a neutral monist, W. T. Stace and D. Bostock argue that Russell’s neutral monism was an impure one at best. These philosophers, though, concur that any neutral monist views Russell may have held during The Analysis of Mind and The Analysis of Matter are abandoned later in Inquiry and Human Knowledge. I argue in this section that Russell was a neutral monist in all his later works as of The Analysis of Mind. Neutral monism is a theory as to the nature of substance. It states that there is only one kind of substance in existence, hence the monism, and that this kind of substance is neutral in nature; it is neither mental nor physical. I will quote Russell’s definition of neutral monism from his (1914) ‘On the Nature of Acquaintance’, which is a collection of three chapters, including one on neutral monism, from his posthumously published Theory of Knowledge, written in 1913. Neutral monism is ‘the theory that the things commonly regarded as mental and the things commonly regarded as physical do not differ in respect of any intrinsic property possessed by the one set and not by the other, but differ only in respect of arrangement and context’ (138).

The merits of neutral monism One of the merits of this theory is that it abides by Ockham’s principle of simplicity and reduces the number of the kinds of entities we accept (‘On the Nature of Acquaintance’ 145). Apart from its ontological appeal, Philip Jourdain shows us

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the logical significance of Ockham’s razor. In his 1919 short piece in The Monist where he discusses the application and significance of Ockham’s razor with respect to the indefinables of the deductive system of Russell and Whitehead’s Principia, Jourdain argues that the logical ground for preferring a deductive system with fewer indefinables is that when we are able to reduce primitive ideas to a fewer number, we are thereby able to show that some dependence relation in fact holds between the ideas that we previously thought were primitive. This is the logical importance of Ockham’s principle (450). Thus, if neutral monism can succeed in reducing kinds of ultimate entities to one, it will thereby have shown us the relation between the mental and the physical, which we previously thought were ontologically independent of one another. Another merit of neutral monism, according to Russell, is that it does not define physical as ‘what is in space’, as the dualists do. Russell finds this way of defining the physical problematic because the notion of space has become ambiguous. Mathematics has constructed many possible spaces; psychology constructs space from various senses; and physics assumes space as a working hypothesis. Since space is ambiguous between these different accounts, ‘what is in space’ cannot be the criterion to distinguish the mental from the physical (TK 22). In fact, for this reason, Russell defines physical as ‘whatever physics deals with’. For instance, in 1914 in ‘The Relation of Sense-data to Physics’, he explains that when he says sense-data are physical, he means that they are ‘part of the actual subject matter of physics’ (143). A third merit often attributed to neutral monism is that it dissolves the interaction problem faced by Cartesian dualist views on the nature of substance. Since, according to neutral monism, and in other varieties of monism, there is only one kind of substance, their interaction does not raise the question as to how different kinds of substances can interact at all. Largely based on the above reasons, Russell as of 1919 (‘On Propositions’) thinks it is wise to reject dualism and adopt neutral monism, which distinguishes the mental from the physical based on causal laws. Russell’s position in AMi is that dualism is ‘not metaphysically valid’ and the residual dualism we find in the world depends on our observation of the world. ‘The dualism is not primarily as to the stuff of the world, but as to causal laws’ (AMi 137). In The Analysis of Mind, Russell explicitly adopts a version of neutral monism along with the rejection of the mental substance. There is no mental substance holding the sensations together. Sensations are the neutral stuff (particulars) that constitute both the physical and the mental worlds. Sensations are the particulars which occur in perspectives, whether actual or potential. An example Russell

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gives of a particular is: ‘the visual sensation which occupied the center of my field of vision at noon on January 1, 1919’ (ibid. 193). Russell ends The Analysis of Matter by the following remarks: ‘Percepts are the only parts of the physical world that we know otherwise than abstractly. As regards the world in general, both physical and mental, everything that we know of its intrinsic character is derived from the mental side, and almost everything that we know of its causal laws is derived from the physical side. But from the standpoint of philosophy the distinction between physical and mental is superficial and unreal’ (402). Thus, there is no difference between mental and physical in terms of their metaphysical nature. But there is a difference in ways of knowing what exists, whose nature is neutral between mind and matter.

Neutral monism in The Analysis of Mind and The Analysis of Matter In substance dualism, as we find it in Descartes, there are two kinds of substances, ordinary particulars, namely, mental substances and physical substances, as well as two kinds of properties and relations (property dualism). In Russell’s The Analysis of Mind and The Analysis of Matter there are no ordinary substances, which Russell could be neutral or dualist about; but there are transient particulars, that is, events. Now then the dualist versus monist question applies to these events. Devoid of their properties and relations an event is a mere substratum. As such there is no significance in distinguishing between mental and physical substrata. Substance dualism or monism is significant when the ‘substances’ in question are not bare particulars, but they are substances in the Aristotelian or Cartesian sense, that is, with some essential qualities. To make a qualitative distinction (mental vs physical) in something which does not have any qualities of its own is meaningless. So, it cannot be that it is the substrata of events that Russell is neutral monist about. It must be their qualities. Besides, Stace notes that the other motive for neutral monism is empiricism. Stace writes, ‘The stuff of the neutral monists is never any kind of hidden unperceivable “substance” or Ding-an-sich’ (Stace 354). The stuff for the neutral monists is something we can directly experience such as sensations or sense-data. Russell also seems to have this empiricist motive. If so, we have another reason to eliminate an

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interpretation of Russell’s neutral monism where only the substrata are neutral, since the substratum is something we cannot experience. Thus, we are left with two plausible interpretations of Russell’s neutral monism: (a) What Russell is neutral about are the qualities of events. The qualities are neutral between mind and matter, but the relations the events get into are of a dual nature. (b) Russell’s neutral monism is about qualities and relations. It is both the qualities and relations themselves that are of a neutral kind. Option (a) is Stace’s interpretation of Russell’s neutral monism (Stace 379). Stace argues that Russell was not a pure neutral monist (363). One of his arguments is based on the definition of neutral monism as a theory of mind and matter where both are made of the same stuff, but there is a distinction based on the relations between this stuff (353). This definition wrongly suggests that there is one kind of qualities of events, but two kinds of relations between any given kinds of events. Stace goes on to argue that such a neutral monism would not be pure since it would have entities, namely relations, which are of two different kinds. Relations have always been real and external to the entities they relate for Russell. Hence, they will have to have some metaphysical nature or other, either a neutral or a dual one. But Stace’s inference is wrong because the definition he works with is ambiguous and leads to misinterpretation. The relations in the definition need to be narrowed to causal relations. The neutral monist Russell holds that only certain relations are of two kinds, namely, causal relations. All other relations should have the same ontological status as qualities. But this does not mean that Russell makes an exception for the ontological status of certain relations. Causal relations are not irreducible relations, according to Russell; they are taken to be statements of general laws. Thus, what we have two different kinds of are generalizations of a certain sort, not a certain kind of entity, relation, that comes in two different natures. Russell argues that he can construct a mind as a class of events, arranged according to mnemic laws, and a material object as a series of events, arranged according to physical laws. But this method of construction based on different kind of laws leads others, in a similar way, such as Stace, to infer that Russell must have acknowledged at least two different kinds of relations (380). Again we need to keep in mind that causation, either mnemic or physical, is not actually a real relation for Russell. That A causes B is not part of reality. What occurs in reality is that A-type events are typically followed by B-type events. Therefore, the fact that Russell appeals to mnemic laws and causal laws is not an indication that he admits two different kinds of relations into his ontology.

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Furthermore, this interpretation is not compatible with Russell’s general treatment of qualities and relations as logically on a par; he treats qualities as monadic relations. So, there is nothing in his philosophy that can explain the putative difference in nature, as mental versus physical, between qualities and relations. More importantly, as Stace points out, if Russell admits that there are two different kinds of relations, he is back to dualism. Thus, he will not have achieved the goal of neutral monism (379). Argument by elimination leads us to option (b) as the most plausible interpretation. But how can we explain on this interpretation, (1) why these relations, even though themselves of a neutral nature, give rise to mental and physical events when they relate events in different ways, and (2) why some events, such as images, seem to be purely mental, and others such as electrons, seem to be purely physical. These questions are also the basis of another argument against the purity of Russell’s neutral monism. Both of the questions above can be answered by appeal to an epistemological distinction among qualities and relations. Different ways of knowing qualities and relations leads us to group some as purely mental, others as purely physical, and some things can be known in both ways, so we group them in both classes, that is, mental and physical. Events are the way they are in reality. The duality in the way the events are arranged is a matter for epistemology. This interpretation explains why relations can give rise to these categories of the mental and the physical even though they are not distinct in reality as such. It also explains the fact that electrons seem to be purely physical. They can never be known by direct observation, hence cannot be mental. They can only be known by inference. I argue that this version of neutral monism is the one Russell aimed at in The Analysis of Mind and The Analysis of Matter and actually arrived at in Inquiry and Human Knowledge. Stace’s second argument, which Bostock also points at (175), to the effect that Russell is not a pure neutral monist is based on Russell’s explicit recognition that some particulars seem to be purely mental and others purely physical. Images seem to be of a purely mental nature and unobserved material objects or events purely physical. Stace (363) in support quotes Russell, where Russell writes that sensations are neutral; whereas ‘images belong only to the mental world, while those occurrences (if any) which do not form part of any “experience” belong only to the physical world’ (AMi 25). But the ‘physical world’ and the ‘mental world’ in the above quote should not be taken to mean realms of different nature. The mental and physical worlds are constructions based on different causal laws. The doom of dualism is

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overturned when we look at how Russell defines images. He finds the traditional way of distinguishing between images and sensations based on their force and vivacity, and coherence with past experience practically useful, but not ultimately satisfactory. Russell argues that the best way to define images is by appeal to their causes (ibid. 145–51). Thus, the difference between images and sensations is not a difference in kind of stuff, but a difference in causal laws they fall under. Images obey only psychological laws, and unperceived material objects obey only physical laws; sensations, however, obey both laws (OP 299). In fact, Russell’s causal definition of images and sensations is very close to the functionalist accounts of the mind in the late twentieth century. Functionalism defines a mental event by virtue of its causal roles. J. Fodor states that ‘in the functionalist view the psychology of a system depends not on the stuff it is made of (living cells, mental or spiritual energy) but on how the stuff is put together’ (114). Furthermore, Stace argues that images are not neutral; they are purely subjective, even though they could be derived from sensations, and that therefore Russell’s neutral monism is not pure (362). It seems to me that there is an inconsistency in this statement. Since Stace accepts Russell’s claim that images can be derived from sensations, this should be consistent with the definition of neutral monism, which maintains that everything should be constructed out of the neutral stuff. Thus, images are constructed out of sensations. It is irrelevant that once derived or once constructed we only have them in the ‘mental groupings’ of the neutral stuff. I think that in order to convincingly argue that Russell’s neutral monism is not purely neutral due to the need to give a correct account of images Stace needs to deny that images can be derived from sensations. Only then, can he argue that there are some entities which cannot be constructed from sensations, i.e., the neutral stuff. More importantly, an interpretation of Russell’s views in The Analysis of Mind as accepting that there are still things in reality which are only mental and others which are only physical makes Russell’s arrangements of events according to different kinds of laws an ad hoc solution to bridge the gap between perceptions and physics. For then the construction of the mental world and of the physical world according to mnemic laws and physical laws respectively will only apply to sensations, not to images or particulars experienced by no one. So, it must be that the mental and the physical constitute epistemological categories, based on how we know particulars. The reason why we call an entity mental or physical depends on which class it belongs to, the class composed

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according to laws of perspective and mnemic laws or the class composed according to the laws of physics. Another argument of Stace’s relies on the assumption that one of Russell’s motivations in adopting neutral monism was to avoid the Cartesian interaction problem (354). We should note though that it is not dualism about the nature of substances and their properties alone that gives rise to the problem of interaction we encounter in Descartes. It is also the metaphysical principle that a cause must be similar in kind to its effect. For otherwise one might maintain that the mental and the physical do interact, but hold that this is not mechanical causation where physical bodies enter relations with other physical bodies; but some kind of nonmechanical causation (Miles 476–7). Once the likeness principle is accepted, it indeed becomes difficult to explain how my will, which is presumably of a purely mental nature, can cause my body, which is presumably purely physical in kind, to act in a certain way. Russell was a dualist until On Propositions and neutral monism does dissolve the problem of interaction. But I do not think that the dissolution of the interaction problem on the neutral monist account was one of the major attractions for Russell, since Russell was able to account for interaction on a dualist account by appeal to a combination of his regularity account of causation and the metaphysical likeness principle. Descartes and Russell both maintained that there is a world existing independently of our minds. And they both accepted a distinction between how the world appears to us and how it is in reality. Thus, if our beliefs about the external world and inferences based on these beliefs are to be truth-conducive there had to be some underlying metaphysical principle to guarantee that the causes of our perception are similar in some way to our percepts. Otherwise, there is no reason to think perception gives knowledge of the world outside of our minds. Since the nature of what we perceive does not seem to be similar in quality to the nature of what causes our perception, one way out is to hold that the cause and effect are indeed similar – but in structure, not in their nature. Thus, Russell’s account satisfies the likeness principle in virtue of similarity in structure. Russell has always maintained that there is a structural resemblance between our perception of physical objects and physical objects themselves. Hence, the early Russell was thereby able to hold a dualist position on the nature of substance and account for the interaction between the mental and the physical. A causal

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interaction between mental substances and physical substances is viable through the likeness of structure between them, even if not quality. It might be thought that the dualist Russell was able to avoid the problem of interaction solely because he did not share Descartes’ traditional notion of causation. Descartes had a deterministic understanding of causation, where the occurrence of a cause was both necessary and sufficient for the effect to occur, whereas Russell’s is Humean; constant (or frequent) conjunction of events. Since causation, and therefore the interaction between mind and body, is reduced to a regularity of certain kinds of events, that some of the causes of events are mental while their effects are physical might be considered to be unproblematic. But even on the regularity account of causation, one has to explain why certain events are regularly followed by other events. Russell maintains that when it seems that my will to drink coffee causes my neurons to fire in a certain way to make my arm to pick up a mug, in fact all that occurs is that the willing of coffee has been followed by the firing of a certain neuron in a certain way. But this regularity account alone does not really help Russell in explaining the interaction between the mental and the physical. Russell needs the willing of coffee to be similar to the neural event that causes my hand to pick up the mug. Otherwise, he cannot account for why that particular type of willing is frequently conjoined with that particular type of neural firing. Russell’s explanation is that the mental cause and the physical effect have a similar structure. Another argument to the conclusion that Russell’s neutral monism was an impure one at best comes from Bostock, who argues that the change in Russell’s account of causation in The Analysis of Matter resulted in ‘the demise of Russell’s neutral monism’. Bostock also notes that Russell himself does not seem to have recognized that he abandoned neutral monism in AMa (197). I think that the reason Russell seems oblivious is that he in fact did not abandon neutral monism. Russell rejects the physical substance in The Analysis of Matter, in favour of a class of ‘physical’ events. At the same time, Russell reverts back to inferring the causes of perception. However, it is not the persisting physical substance which he is inferring the existence of. It is physical events that we cannot or do not experience. It is the unobserved transient particulars that we infer to exist as causes of our perceptions. Bostock argues that this move results in the abandonment of neutral monism because by admitting an inference to an unobserved entity, an unobserved event, Russell has introduced entities into his ontology which are not neutral between mind and matter. Bostock explains that Russell recognized the importance of the causal theory of perception, and this

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recognition caused him to reconsider what can be causes, and this led him to abandon the neutrality of his monism (Bostock 190). Bostock argues for the same point in the following lines: When Russell infers the existence of the cause of perception in The Analysis of Matter, he ‘abandons the identification on which neutral monism depended, for it now accepts that perceptions do have physical causes and are not the same as those causes. So if minds are still to be constructed then they will of course be constructed from the perceptions, and not their causes, whereas if bodies are still to be constructed (rather than postulated) they will be constructed from these physical causes, that are supposed to exist in space whether or not they do cause a perception in a sentient body, and not from the perceptions. In consequence, there is no longer anything which is supposed to be an ingredient of both constructions, and neutral monism has finally disappeared’. (Ibid. 195–6)

Bostock and Stace, in arguing for the failure of Russell’s neutral monism, are helped by Russell’s own writing. Russell writes about ‘physical causes’ and ‘mental effects’. But we need to read The Analysis of Matter and his later work with the proviso in mind that when he uses ‘mental’ and ‘physical’ as descriptors of events he does not mean that there is a metaphysical distinction among kinds of events. These descriptors are mainly epistemological, about how we group events, according to different kinds of causal laws, that is, different kinds of regularities, which we have observed. Yes, it is in The Analysis of Matter that Russell has adopted the ordinary scientific causal theory of perception, but this did not lead to his abandonment of neutral monism. On the causal theory of perception, my perception of a computer is caused by the computer itself. The computer, as an ordinary particular, is still a set of events, a logical construction. But it is not this set that causes my perception of the computer. As Bostock explains Russell cannot both have the computer as a logical construction, that is, a set, and have that set cause my perception of the computer, since sets cannot cause perceptions because sets depend on their members for their existence, and most of their members are percepts (191). The cause of my perception of the computer is only some of those events that make up the set, namely the ones at the beginning of the causal series. And there is no problem in some events causing other events. These events are neutral, metaphysically speaking. The ones at the beginning of the chain, which are not directly observed by anyone are typically what we would call physical, the ones towards the end of the causal chain of perception are the events that we would typically call mental. But these adjectives describe

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epistemological distinctions, based on our groupings of data, not metaphysical distinctions.

Neutral monism in Inquiry and Human Knowledge According to Stace and Bostock, Russell was never a proper neutral monist. According to Sainsbury, Russell has ‘abandoned neutral monism by the time of HK’ (268). I argue that, on the contrary, Russell’s neutral monism achieved its mature form in Human Knowledge. In fact, Russell in the later period gives a clearer explanation as to why we regard certain events as mental and others physical, even though the stuff out of which the world is constructed is of a neutral kind. It is a matter of epistemology. Russell in Human Knowledge distinguishes in the world ‘a stuff and a structure. The stuff [consists] of all the simples denoted by names’ (259). The simples denoted by names being qualities, qualities are the neutral stuff of this later period. In The Analysis of Mind the neutral stuff consists of sensations; in The Analysis of Matter events are the neutral stuff, without any significant change of meaning. Russell switches to ‘events’ in The Analysis of Matter because ‘sensation’ has phenomenological connotations that Russell wants to avoid. However, after Inquiry the neutral stuff cannot be events anymore, since events are not the ultimate constituents any longer. Qualities are the neutral stuff. As an object of knowledge studied under physical laws, they are physical; as an object of knowledge studied under psychological laws they are mental. A causal chain of perception includes both mental and physical qualities. The qualities that are part of the receiving end of the causal chain are part of percepts, mental transient particulars. A percept is ‘what happens when, in common sense terms, I see something or hear something or otherwise believe myself to become aware of something through my senses’ (HK 203). My seeing the sun is a percept, and it is not identical with the sun itself. These two are the far ends of a causal chain. Percepts are located in the brain. ‘Their location in causal chains is the same as that of certain events in the brain’ (ibid. 209). Russell holds that it is probable that physical objects differ from percepts in terms of their qualities. Hence, he notes that this might be thought to lead to the problem of interaction of the mental and the physical since percept is considered to be mental and the material objects physical. However, Russell explains that his metaphysical view is that there is no distinction between the mental and the physical, but epistemologically, there is a distinction: ‘My own belief is that the

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“mental” and the “physical” are not so disparate as is generally thought. I should define a “mental occurrence” as one which someone knows otherwise than by inference; the distinction between “mental” and “physical” therefore belongs to theory of knowledge, not to metaphysics’ (ibid.). Thus, mental occurrences are what we know directly, without any inference (ibid. 201), whereas physical occurrences we can only know by inference. What enables Russell to infer that a certain perceptual effect is caused by a certain unperceived complex of qualities is the assumption of the likeness principle; same cause same effect, and what is similar between the two marginal ends of a causal chain of perception is their structure. There is something strictly the same between a mental event and its physical counterpart, that is, its structure. ‘In many natural processes there is a constancy of space-time structure in spite of complete change in the intrinsic character of the ingredients of the structure’ (‘Non-Deductive Inference’ 124). One of the postulates the later Russell assumes in order for scientific knowledge to be possible is the principle of constancy of structure. He explains that the principle ‘implies that in circumstances which occur frequently but not invariably, the structure of a percept is the same as that of each of a series of occurrences leading backward in time to an original occurrence, before which there were no spatio-temporally connected events having the structure in question’ (HK 473–4). And based on the assumption of the likeness principle (same cause, same effect and different cause, different effect), we can infer the structure of a physical cause from the structure of its phenomenal effect (ibid. 254). Structure is a logical concept. ‘To exhibit the structure of an object is to mention its parts and the ways in which they are related’ (ibid. 250). Examples of structure are the structure of a map and how it relates to the region of which it is a map and the structure of a gramophone record to the sound it produces (AMa 249). In the latter, ‘what is nearer to the center on the record corresponds to what is later in the music’ (HK 253). What Russell means by structural similarity between percepts and nonpercepts is best illustrated by his example of someone making a broadcast. The broadcaster produces sounds of a certain structure, and those sounds turn into electromagnetic waves when they reach the microphone, which are then turned back into sounds by a radio that receives them which then become audible by human beings. Throughout the changing qualities of the waves that are transmitted, their structure remains the same, that is, the structure of the sound waves and the structure of the electromagnetic waves are the same. Russell says,

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‘When we examine causal sequences, we find that the quality of an event may change completely in the course of such a sequence, and that the only thing constant is structure’ (ibid. 467). In fact, Russell argues that such a structural postulate is necessary earlier in The Analysis of Matter (249). Russell also argues there that what we can know about physical events is only their structure (254). M. H. A. Newman (1928), however, criticizes Russell’s view that nothing but structure of the external world is known, since that would not give us any empirical knowledge about the world. If all we can say is, ‘There is a relation R such that the structure of the external world with reference to R is W’, such a statement expresses only a trivial property of the world. Any collection of things can be organized so as to have the structure of W, provided there is the right number of them. Hence the doctrine that only structure is known involves the doctrine that nothing can be known that is not logically deducible from the mere fact of existence, except (‘theoretically’) the number of constituting objects. (Newman 144)

In his reply to Newman, Russell admits that he should not have maintained that it is only structure that could be known about the physical world. Russell writes that he actually assumes ‘spatiotemporal continuity with the world of percepts, and even that one could pass by a finite number of steps (from one event to another compresent with it) from one end of the universe to the other. And co-punctuality I regarded as a relation which might exist among percepts and is itself perceptible’ (Letter to Newman). Accordingly in Human Knowledge, Russell makes the changes to his account as to what can be known about the external world. He maintains that we can know the relation of compresence that holds between qualities and the relation of earlier and later, as well as the structure (HK 332). He acknowledges that ‘since physics is intended to give empirical truth, the ordering relation must not be a purely logical one, such as might be constructed in mathematics, but must be a relation defined in terms of experience. If the ordering relation is derived from experience, the statement that space-time has such-and-such a geometry is one having a substantial empirical content, but if not, not. . . . I suggest that the ordering relation is contiguity or compresence, in the sense in which we know these in sensible experience’ (HK 329). I will not discuss here whether his response is a satisfactory one or not. But I want to note that it is not fair to hold that Russell did not attempt to explain how non-structural knowledge about the external world can arise, as W. Demopolous and M. Friedman argue (632). Yes, in Human Knowledge, Russell states we can

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assume that there is spatio-temporal contiguity or causality between percepts and non-percepts. But this is not an ad hoc solution. He arrives at the conclusion that we need to accept some principles, namely his scientific postulates, as true, in order that we may have non-trivial knowledge, that is, not merely structural, about the external world, after having discussed how for any of our inductive inferences to conclusions about the nature of non-percepts to be truth-conducive we need a priori reasons for thinking that those conclusions have ‘something to be said in their favour’. And such a priori reasons, he argues, can only be provided by way of postulating them. However, it is difficult to reconcile my interpretation above that we can know the nature of non-percepts by inference, with the following remark Russell makes in Human Knowledge: ‘Physical events are known only as regards their space-time structure. The qualities that compose such events are unknown – so completely unknown that we cannot say either that they are or they are not different from the qualities that we know as belonging to mental events’ (HK 231). I interpret the uses of ‘know’ in this passage as direct knowledge so that we cannot directly know what the qualities of the non-percepts are like, but we can acquire indirect knowledge of the nature of non-percepts. And such indirect knowledge is made possible by the assumptions that there is a structural similarity between percepts and non-percepts and that both percepts and non-percepts are in fact of the same kind; they are neutral between mind and matter. I have argued in this section that Russell is a neutral monist in all of his later work, including Human Knowledge and that structure plays an important role in making inferences from the ‘mental’ to the ‘physical’. He does not hold there to be a metaphysical distinction between mind and matter and he maintains that the distinction between mind and matter is an epistemological distinction. What we know directly are percepts, which are quality-complexes, and their structure, which is the same as the structure of non-percepts. Even though we cannot directly know the qualities of non-percepts, which presumably cause those percepts, our inferences with respect to their existence as causes and their qualities, as well as structure, are reliable because our inferences are grounded on the postulated truth of structural similarity and causation between percepts and non-percepts.

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8

Logical Atomism

Bertrand Russell is known to have changed his epistemological and metaphysical views frequently, which raises the question as to whether there was any single theory or philosophical method he consistently held throughout the changes. I hold that the metaphysical theory Russell consistently held on to is the theory of universals; but in this section I would like to discuss the philosophical method that Russell consistently employed. Gregory Landini argues in Wittgenstein’s Apprenticeship with Russell (Chapter 2) that Russell’s main research programme was logical atomism. Landini writes, ‘In spite of the rather radical changes Russell made from The Problems of Philosophy to Human Knowledge: Its Scope and Limits, none mark any change whatsoever in what he meant by his philosophy of logical atomism’ (40). Even though Landini claims that Russell was always a logical atomist, including the later period of Inquiry (1940) and Human Knowledge (1948), he focuses on Russell’s work from ‘On Denoting’ (1905) to Analysis of Matter (1927) to support this claim. Bostock, on the other hand, in his recent book Russell’s Logical Atomism (2012) counters Landini’s view by stating that Russell’s positive views on particulars (reduced to complexes of universals) in Inquiry and Human Knowledge ‘evidently falls outside Russell’s period of logical atomism, and cannot contribute to our understanding of it’ (236). I support Landini’s claim by showing how the later Russell’s bundle theory of particulars espoused in Inquiry and Human Knowledge also fits the logical atomist pattern, contra Bostock, who claims that these works can have no contribution to our understanding of Russell’s logical atomism. The bundle theory, the theory of particulars which Russell espouses in the later period, is one of the periodic views Russell held on the nature of particulars. But the method by which he arrived at the bundle theory is a permanent feature of Russell’s philosophy, that is, logical atomism. It is logical analysis with the aim

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of reaching logical simples with structure. The uncontroversial key elements of Russell’s logical atomism are logical analysis, atomism (pluralism) and logical construction. The method used in arriving at the bundle theory in Russell’s later period should be viewed as an application of logical analysis at the level of particulars. Logical analysis shows Russell that particulars need not be recognized as ultimate simples: we can eliminate any particular and replace it with a bundle of compresent qualities. Thus, analysis, in the later period, yields merely qualities as logical simples (atoms).

Russell’s different views on the nature of particulars As we have surveyed Russell’s works from The Principles of Mathematics (1903) to Human Knowledge (1948), we have found that Russell has frequently changed his views on the nature of particulars and how we know them. In the early period between 1903 and 1905, based on Russell’s referential theory of meaning, anything we could meaningfully talk about had to pick out a particular, a substance. After the publication of ‘On Denoting’ in 1905, only logically proper names, such as the demonstratives, ‘this’ or ‘that’, could pick out particulars. All references made to ordinary particulars, such as people and chairs, by way of proper names or definite descriptions were now to be analysed away as references to variables, that is, undetermined logical simples, and universal qualities and relations. Thus, in this early period, we have a dual ontology with particulars and universal qualities and relations. And we can know only some particulars directly, that is, what is immediately presented to us in sensation; most of the ordinary particulars, such as a table, on the other hand, are known by description. For instance, I know the table as something which gives me sensations of brownness, hardness and rectangularity. Thus, the particulars that we know directly are called sense-data between 1912 and 1918. Those are the referents of the demonstratives, ‘this’ or ‘that’. We infer the existence of ordinary particulars in Problems of Philosophy (1912). But two years later in Our Knowledge of the External World we learn we ought to refrain from affirming or denying the existence of ordinary particulars. In their stead, we have logical constructions. The nature of particulars was two-fold in this early period between 1903 and 1918, that is, Russell was a dualist, acknowledging both mental and physical particulars. But the period between 1919 and 1927 is taken to be Russell’s neutral monist period, where particulars are all of one kind, of a neutral kind. Russell in The Analysis of Matter (1927) explains that his aim is to bring physics and

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psychology together, ‘not by subordinating one to the other, but by displaying each as a logical structure composed of . . . neutral stuff ’ (10). Fundamental particulars in this period are events, and they are neutral, that is, they are neither mental nor material in nature. Ordinary particulars in this period are constructions, classes whose members are the transient particulars. Russell explains the difference between the mental and the physical based on how we know something. If we know an event directly, without inference, he calls it ‘mental’; if we know it by inference, he calls it ‘physical’. Thus, there is nothing metaphysically different between the mental and the physical. ‘What there is’ is of one kind, neutral between mind and matter. But we make an epistemological distinction among the stuff of the world (HK 224). When we reach Russell’s later period, that is, Inquiry and Human Knowledge, we find that Russell explains transient particulars solely in terms of qualities. Hence, the need for the category of particulars, either in the case of ordinary particulars or in the case of events, is obviated. An ordinary particular, such as a car, is a series of transient particulars, which can be considered as spatiotemporal slices of a car through its entire career. Transient particulars, in turn, are mere complexes of compresent qualities. Thus, a spatio-temporal slice of my car is a complex composed of qualities such as being black, having a certain roundish shape, four wheels and so on. These qualities are compresent, that is, they occur at the same space/time. When these qualities are compresent they make up a transient particular.

Logical atomism Throughout all these changes on the nature of particulars, Russell has consistently adopted a philosophical method, that of logical atomism. The uncontroversial key features of the programme of logical atomism are logical analysis, atomism and logical construction. It is controversial, however, whether the theory of acquaintance is a further essential component of logical atomism. One famous application of Russell’s logical atomist programme is his theory of definite descriptions. When Russell considered propositions such as, ‘the present King of France does not exist’ a difficulty for him arose due to his commitment to a theory of meaning and truth whereby a sentence is meaningful (has a truthvalue) only if its constituents refer to entities in the world. For instance, ‘Socrates is wise’ is a meaningful sentence if there is such a thing as Socrates and a property as being wise in the world. So, in order for the sentence ‘The present king of

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France is bald’ to be meaningful, the grammatical subject ‘the present King of France’ needs to refer to an entity in the world. But it does not. Yet, the sentence seems to be meaningful. To solve this puzzle, Russell argued that the linguistic analysis of a proposition can be misleading; we should instead carry out a logical analysis of a proposition and find out the logical subject of the sentence. So, Russell gave a logical translation of this sentence, which yielded only a variable, an undetermined constituent, as the logical subject of the sentence, and thereby the seeming reference to the present king of France is eliminated. Russell writes, ‘The fact is that, when the words “the-so-and-so” occur in a proposition, there is no corresponding single constituent of the proposition, and when the proposition is fully analysed the words “the-so-and-so” have disappeared’ (LA 328). Thus, the logical simples arrived at after the logical transformation are an undetermined constituent and several properties, namely, being present, and being a king of a country called ‘France’. Now, let us try to understand the various components of the programme of logical atomism. By logical analysis, we mean the analysis of a concept or entity with the aim of reaching its simples and revealing its structure. The simples are not necessarily what we experience as simple. Russell allows for the possibility that what we may think as a simple constituent may turn out to be complex after further analyses. In ‘Logical Atomism’ (1924), Russell expresses this view as follows: ‘When I speak of “simples”, . . . I am speaking of something not experienced as such, but known only inferentially as the limit of analysis. It is quite possible that by greater logical skill the need for assuming them could be avoided’ (337). When Russell calls his logic ‘atomic’, what he means is that his logic is pluralistic, as opposed to monistic. The logic that his teacher, Bradley (along with Spinoza, Leibniz, Hegel) had available to him was Aristotelian logic, which parsed all propositions into the subject–predicate form. According to Russell, this logic leads one to an absolute monistic metaphysics, where all there is in existence is the Absolute, and every other seeming plurality in the world is explained as predicates of this one subject, ‘since the fact that there were several substances (if it were a fact) would not have the requisite form’ (LA 331). That is, if it were true that there are several substances we would not be able to express this fact in subject–predicate form. One of Russell’s arguments against absolute monism is based on its inability to account for asymmetrical relations such as ‘being bigger than’. For example, the sentences ‘A is bigger than B’ and ‘B is bigger than A’ will both have to be

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expressed with the subject–predicate sentence, ‘The whole composed of A and B has the property of being bigger than’. But this misses the direction of the relation; it is not able to express the difference in meaning between As being bigger than B versus Bs being bigger than A. The monistic theory, therefore, cannot explain the distinction between an asymmetrical relation and its converse (POM §215).1 In ‘On Scientific Method in Philosophy’ (1914), while arguing that philosophy should be concerned with the general features of the world, and not any specific thing, Russell tries to clarify what he means by distinguishing his view, logical atomism or absolute pluralism, from absolute monism. Absolute monism, takes the whole universe to be the subject, and assigns philosophy the task of studying the ‘peculiar predicates’ that only apply to the whole and not to any particular thing. Russell, on the other hand, maintains that there are many subjects and their properties. The totality of the universe is not yet a further entity. The business of philosophy is to determine the general propositions which are true of each particular thing in the universe, not of the whole universe collectively. Logical atomism, ‘while maintaining that there are many things, [it] denies that there is a whole composed of these things’ (‘On Scientific’ 107).

The theory of acquaintance In Problems of Philosophy (1912), Russell states an epistemological theory, the theory of acquaintance.2 Russell explains the relation of acquaintance as a kind of experience ‘between a subject and object which need not have any community of nature. The subject is mental . . . the object may be a sensible particular, or a universal, or an abstract logical fact. All cognitive relations – attention, sensation, memory, imagination, believing, disbelieving, etc. – presuppose acquaintance’ (‘On the Nature’ 127). Russell advances this view as rival to (1) the neutral monist view, according to which there is no mental subject that enters into a relation of acquaintance, (2) the theory that both the subject and the object of acquaintance is mental and (3) the theory that when a subject is in the relation of acquaintance, what it is immediately acquainted with has to be mental – the content of an object (ibid.). D. Pears argues that the theory of acquaintance is an essential component of Russell’s logical atomism. According to Pears, Russell’s theory of understanding coupled with logical analysis and atomism implies that these atoms must

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be things we are acquainted with. Russell holds a theory of understanding according to which in order for a subject to understand a proposition she needs to be acquainted with the constituents of that proposition.3 And in accordance with logical analysis, when we analyse a proposition, which purports to express a fact, we find its logical constituents or simples. Therefore, if I understand the proposition in question, the simples of the proposition will have to be things that I am acquainted with (The False, Vol. 1 63). Landini, on the other hand, argues that the theory of acquaintance is not an essential component of logical atomism. Landini shows that, according to Russell, being acquainted with an object is neither a necessary nor a sufficient condition for being a logical simple. Being acquainted with an object is not a sufficient condition for being a simple since according to Russell we can be acquainted with complexes (facts) as well. And being acquainted with an object is not necessary for being a logical simple either, because Russell admits that it is possible for there to be logical simples we are not acquainted with (PLA 202; MPD 165; Landini, Wittgenstein’s 31–3). Pears is right that if one does combine the epistemological theory of acquaintance with Russell’s logical and metaphysical method of logical atomism, one gets the result that logical atoms should be the things we are acquainted with. But Landini argues that one does not have to combine these views, and more importantly Russell does not argue for a necessary relation between the two. Russell does not maintain a logically necessary relationship between the epistemology of the atoms and their logical or ontological status. The two can be independent of each other. Landini, therefore, convincingly argues that logical atomism is a research programme and it should be distinguished from Russell’s epistemological views, such as the theory of acquaintance, in PLA (Wittgenstein’s 40). As Landini points out, Russell’s early theory of acquaintance as a relation between a mind and sense-data, universals, and complexes was the ‘feature of an epistemic theory he couched within his logical atomist research program – a theory he abandoned in favor of neutral monism’ (39). Further support against a necessary connection between the experience of atoms as simple and their being in fact simple comes from Russell’s understanding of a philosophical proposition. In ‘On Scientific Method in Philosophy’ (1914), Russell argues that a philosophical proposition must be a priori, and by a priori he means that it ‘can be neither proved nor disproved by empirical science’ (107). The assertions a philosopher makes about the world should be ‘equally

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true however the actual world were constituted’ (107). Thus, Russell would not hold that the ontological atoms of the world must necessarily be things we are acquainted with. Such a position would be antithetical to his well-entrenched rejection of anthropomorphic philosophies.

Logical construction: The maxim of ‘constructions over inferences’ Logical construction seems to be an essential component of Russell’s programme of logical atomism. In ‘Logical Atomism’, Russell writes, ‘The business of philosophy, as I conceive it, is essentially that of logical analysis, followed by logical synthesis’ (341). Logical analysis is the method of analysing a concept or entity to find its atoms, its constituents. As Bostock explains, once we find the atoms we may want to construct a replacement for the original entity. This is the synthesis part. The replacement is a class of some kind (153–4). Why and when would we want to construct a replacement for an entity? When we have some good reason to think that some entity must exist, but we cannot verify it to exist. For the sake of ontological economy and caution, it would be more prudent to work with a replacement instead of the entity whose existence is desired but unknowable. Consider material substances for illustration. What we experience, when we perceive a table, are its qualities and its relations to other things, but we do not perceive some material substance, in which all the properties of the table inhere. We may infer the existence of such a material substance. This is a case where we seem to have good reasons to think that there should be some such substance. Our reasons for the inference are that (1) there needs to be something that unifies the properties of the table, (2) such a thing would also explain the persistence of the table as it is going through changes over time. Yet, we do not experience this material substance itself; all we experience are properties. Russell, as of Our Knowledge of the External World, advises against making inference in this way to unknown entities, that is, material substances. Rather, we should logically construct fictional entities to stand in their place. As long as our construct has the same logical properties of the table, it will serve all the purposes for which we need the entity, the material substance. Hence, Russell’s famous maxim of constructions versus inferences: ‘Wherever possible, substitute constructions out of known entities for inferences to unknown entities’ (LA 326).

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In ‘The Philosophy of Logical Atomism’ (1918), Russell explains the process of logical construction as follows, What I can know is that there are a certain series of appearances linked together, and the series of those appearances I shall define as being a desk. In that way the desk is reduced to being a logical fiction, because a series is a logical fiction. In that way all the objects of ordinary life are extruded from the world of what there is, and in their place as what there is you find a number of passing particulars of the kind that one is immediately conscious of in sense. I want to make clear that I am not denying the existence of anything: I am only refusing to affirm it. I refuse to affirm the existence of anything for which there is no evidence. (273)

Russell gives other examples of the applications of this maxim in ‘Logical Atomism’. One is Frege’s definition of number. Numbers4 are substituted by classes of collections whose members can be matched into a one-to-one relationship. Thus, instead of accepting the existence of numbers as entities, we construct replacements for them. The number 2, for instance, is the set of all classes that are similar to a given set, which is a class with couples. The similarity is determined by one-to-one mapping of the members of the classes. For example, we can take the set that has only Tom and Jerry as members. All sets that are similar to this given set will form a further set, this set will be the number two (327). Other examples are from Russell’s The Analysis of Mind (1921) and Our Knowledge of the External World (1914). In The Analysis of Mind, Russell replaces the persisting mind, mental substance, by another logical construction, a construction out of mental events, such as thoughts, images or sensations (LA 330). In Our Knowledge of the External World, material substances, that is, ordinary particulars, are replaced by classes of sensations and sensibilia. And later in The Analysis of Matter (1927), ordinary particulars, as well as points and instants of the space–time order, are constructed out of events, instead of sensations (244–5). Thus, construction has accompanied most of Russell’s logical analyses in all his works where he followed the logical atomist research programme. The theory of definite descriptions, however, offers merely an eliminative analysis of definite descriptions; the analysis is not followed by a replacement of any kind. This point is recognized by Bostock as well who writes, ‘Some analyses are purely eliminative, and do not provoke a succeeding synthesis’ (281), and he gives Russell’s analysis of definite descriptions as an example.

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Logical atomism and the bundle theory Logical atomism, then, comprises three essential elements: logical analysis, atomism and logical construction. Whether the theory of acquaintance is yet another element is debated. As far as the theory of acquaintance is concerned, I find Landini’s argument convincing. That is, the epistemological theory needs to be kept separate from the philosophical research programme of logical atomism. If so, my thesis that Russell’s later work should also be considered as part of this programme stands, since, first, in his later work, Russell no longer holds the theory of acquaintance, as it was originally formulated, to be true,5 though he maintains a distinction between knowledge by direct experience and knowledge by description. Second, I can assert that logical atomism is an ongoing research programme for Russell which extends to his later work even though as of The Analysis of Mind some particulars, such as the transient particulars which cause our perceptions, are constituted of atoms, that is qualities, which no one can directly experience. Logical atomism, as a philosophical method, advises us to work on logical analyses of propositions that purport to be about reality and thereby arrive at the ultimate constituents of reality. How these atoms can and should be known is a different matter. The theory of acquaintance suggests we require the mental subject to be acquainted with, have some direct knowledge of these atoms, in order that she can be said to understand the propositions which invoke these atoms. Alternatively, understanding a proposition may merely require appropriate use of the words that stand for these atoms, and in fact this is the position Russell takes in the later period. Thus, the epistemology of the atoms can be worked out in different ways. In its original formulation, ‘acquaintance’ expressed a relation between a mental subject and an object, which could be a material object, a universal or a mental object in introspection. But after 1921, the subject is no longer a mental substance which enters into relations of acquaintance with material or mental objects. As of 1940, the subject and the object are just complexes of ‘mental’ and ‘physical’ qualities respectively. Interestingly, Russell, in the later period, still invokes the distinction between direct knowledge and knowledge by description, as is evident from the following passage in Human Knowledge: ‘The sun and the moon, my house and garden, my dog and my cat, Stalin and the King . . . are known to me by description, not by acquaintance. And the description has to be in terms of my experiences’ (88).

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What Russell means here is not exactly knowledge by acquaintance as it was originally formulated because the relata of the relation of direct knowledge are no longer different kinds of substances; in fact they are not even substances at all. An example of immediate knowledge given in Inquiry is the state one is in when they notice a sensible experience, which they may or may not express in a proposition. When I have a sensible experience, such as hotness, the mere having of the experience is not knowledge, according to the later Russell. If I notice the experience, attend to it, then I know it. This is an immediate kind of knowledge. And I may express this knowledge as ‘There is hotness’ (Inquiry 47–9). The distinction between knowledge by acquaintance and knowledge by description in the later period merely reflects Russell’s foundationalism and internalism in his epistemology. In Inquiry, Russell divides knowledge into two kinds. First is the kind of knowledge that we have similar to animals, mainly consisting of appropriate response to environmental stimuli. The second is what he calls empirical knowledge, which, Russell claims, properly belongs in the area of epistemology or theory of knowledge: ‘Epistemology, must arrange all our beliefs, both those of which we feel convinced, and those that seem to us only more or less probable, in a certain order, beginning with those that, on reflection, appear to us credible independently of any argument in their favor, and indicating the nature of the inferences (mostly not strictly logical) by which we pass from these to derivative beliefs’ (ibid. 15). A theory of knowledge, according to Russell, should not be preoccupied with the causes of a belief, but with its grounds. The kind of knowledge where having the appropriate causes of belief is satisfactory for justification is the kind of knowledge that we share with animals. Thus, Russell in the later period, still holds on to an internalist understanding of justification and knowledge when it comes to theory of knowledge proper. And this internalism is reflected in the distinction between knowing by acquaintance and knowing by description. Russell still has the Cartesian subjective starting point. I know that there is a moon by inference, an inference from my immediate sensible moon-ish experiences. We find both logical analysis and atomism (pluralism) in Russell’s later work. Whereas it was facts which were analysed in Russell’s ‘Philosophy of Logical Atomism’ (1918) lectures, and the analysis yielded terms (particulars), qualities and relations,6 in the later period between 1940 and 1948, what gets analysed are transient particulars and the analysis yields universal qualities as atoms. The construction component of logical atomism, however, seems to conflict with my thesis that Russell’s later metaphysical work follows the logical atomist

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programme since in this later period transient particulars are analysed away, but no logical construction is provided in their place. A stronger reason for Bostock’s exclusion of the later period from Russell’s logical atomist period might be the fact that Russell in The Analysis of Matter reverted back to inferring the causes of perception to exist, as opposed to constructing them as advised by logical atomism. I hold, in contrast, this move does not imply that Russell has abandoned logical atomism. For logical atomism advises that constructed entities take the place of inferred entities, whenever possible. If and when we have reason to think it is not possible, we are not going to opt for construction instead of inference. At the time of The Analysis of Matter, Russell realized that he could not give a satisfactory account of perception merely based on logical constructions and that he had to admit the existence of some entities as causes of perception, as the ordinary scientific view of causation suggests. Thus, Russell in this work was still abiding by the motto ‘employ constructions over inferred entities, whenever possible’. It was not an intentional move to cease to employ the philosophical method of logical atomism. It just was not possible to give a satisfactory account of all phenomena, in particular, relating to perception, merely by appeal to logical constructions. In fact, we can see that Russell continued to practise the method of logical atomism in his further analysis of transient particulars in Inquiry and Human Knowledge. The Analysis of Matter analyses an ordinary particular into series of events, which are transient particulars. These transient particulars, Russell of Inquiry and Human Knowledge recognizes can be further analysed, and thereby the substrata of events can be eliminated. When Russell analyses transient particulars into merely qualities he fulfils the logical atomist programme. Bostock gives a short account of the bundle theory of particulars in his book in the chapter on universals. He presents Russell as providing bundles of qualities as logical constructions to replace particulars (Bostock 240). But this is partially true as we saw in Chapter 3. Yes, Russell eliminates particulars from his ontology and bundles of qualities do replace particulars; but these bundles of qualities are not classes in the case of transient particulars. I must provide a point of clarification here. When I claim that logical construction does not seem to be carried out in the later period, my remark applies only to transient particular and point-instants, which were earlier taken to be particulars. Russell is still constructing an ordinary particular. It is constructed out of transient particulars, which are quality-complexes.

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The difference between The Analysis of Matter and Human Knowledge with respect to the status of point-instants is that in the former what provided the elements of construction were particular events, while in the latter, the elements of the complete complex, which is a point-instant, are not particulars, they are universal qualities. And these qualities do not make up classes or constructions; they make up complexes of compresence. We can form groups of qualities having the following two properties: a) all members of the group are compresent; b) given anything not a member of the group, there is at least one member of the group with which it is not compresent. Any one such complete group of compresent qualities constitutes a single complex whole, defined when its constituents are given, but itself a unit, not a class. That is to say, it is something which exists not merely because its constituents exist but because, in virtue of being compresent, they constitute a single structure. One such structure, when composed of mental constituents, maybe called a ‘total momentary experience’. (HK 297)

Thus, in Inquiry and Human Knowledge, point-instants and transient particulars are identified with complexes of qualities, and thereby eliminated as ultimate kinds. I hold that Russell’s later metaphysics still follows the logical atomist programme even though neither transient particulars, that is, spatio-temporal slices of an ordinary particular, nor point-instants are constructions since the maxim that advises logical construction is vacuously true in the later period as far as particulars are concerned. One key feature of the maxim is that we are encouraged to replace constructions for inferences to unknown entities only when ‘the subject is sufficiently useful to be worth constructing’ (LA 330). In the later period, Russell does not think that it is sufficiently useful to construct transient particulars anymore. Constructing transient particulars, in the later period, is not called for, since now Russell argues that we have no reason to recognize them as ultimate entities either as inferred entities or constructions. However, when it comes to ordinary particulars, which seem to persist through time, Russell still employs construction. For instance, I am a series of transient particulars, each of which is a mere complex of compresent qualities. Earlier Russell had argued that we need events as particulars in order to explain individuation. The problem of individuation arises especially in the construction of the space–time order which requires elements that cannot or at least does not recur. Each unit in the series needs to be distinct from each other. Hence, the need for these elements to be particular events. But the later Russell was not satisfied with this view that recognizes unanalysable particulars

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since particulars as such cannot be known or defined (HK 293– 4). And positing something unknowable as a fundamental in his interpretation of empirical knowledge was not acceptable for Russell (ibid. 294). Consequently, in the later period, Russell denies particulars altogether and explains individuation without recourse to unanalysable particulars. Individuation relies on the truth of the principle of identity of indiscernibles such that if two bundles share all their qualities, then they are identical. Thus, ‘particulars’ are individuated only by reference to a difference in qualities. The elimination of particulars from Russell’s later metaphysical works, analysed away as complexes of qualities, is therefore, yet another application of logical atomism. Logical atomism (following Landini’s interpretation) should be understood as a philosophical method that consistently runs through Russell’s epistemological and metaphysical works and not as a combination of Russell’s metaphysical and epistemological views confined to a certain period of his academic career.

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Conclusion

One of Russell’s ontological aims was to give a parsimonious account of the ultimate kinds of reality. His earlier account of particulars admitted particulars as well as universals as the fundamental kinds of reality. The need to explain the unity and individuality of objects forced upon the early Russell the acceptance of particulars with substrata as immediate individuators, yet he could not reduce properties to particulars in accordance with the goal to economize his ontology because the relation of similarity resisted nominalistic explanation. So when he formulated the bundle theory he reached his goal. According to the bundle theory, there is one kind of ultimate reality, that of qualities, and the individuality of particulars can be explained as well as their generality, without having to admit substrata. I have argued that the early Russell (1903–14) held the substratum view of particulars. I provided textual evidence to the effect that the substrata served several roles. (1) They explained why it is logically possible that there may be two qualitatively alike ordinary or transient particulars. (2) They provided nonrecurring particulars for his construction of space–time series, on the relational theory of space and time. (3) They served as logical subjects in which predicates could inhere, without making all sentences which have the subject–predicate form analytic. The problem with this view was having to maintain that there is something which cannot be known, but which is merely supposed to exist to serve for explanatory purposes. A substratum, as Russell called it, was ‘a peg from which the predicates hang’. The bundle theory of particulars, in his later philosophy (as of 1940), helped him abandon the unknown substrata. The bundle theory takes qualities as ultimate. Qualities are universals, but they are immanent universals, that is, they are in space–time, not in some third realm waiting to be exemplified. Relations,

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according to Russell, are part of reality; they relate particulars (bundles). But he hesitated in recognizing their independent existence. Russell has famously argued against relations being reduced to properties of wholes or properties of the particulars that they relate. He maintains that relations need to exist independently of the particulars, or bundles in our case, that they relate. However, relations in the later period are immanent, not transcendent, as on a par with Russell’s immanent realism with respect to qualities. So Russell now has the problem of accounting for the existence of these entities, which for their existence depend on the existence of bundles of qualities. Relations are fundamental parts of reality, but they do not enjoy independent existence, as they did when they were transcendent. Now they are ontologically dependent on qualities. I argued that we can resolve this tension if, by appeal to Barnes, we abandon the traditional view that what is fundamental must also be ontologically independent. The separation of the fundamental from the ontologically independent helps us legitimize the existence of external, immanent, fundamental, yet dependent relations in the later Russell’s theory of particulars. In contrast to the literature on Russell’s bundle theory, I have shown that even though ordinary particulars are constructed, the same cannot be said of the transient particulars. They are inferred, not constructed. When we construct an entity, we construct a class or series to stand in place of the entity we wish to eliminate. Thus, we construct series of transient particulars to stand in place of ordinary particulars, and thereby eliminate ordinary particulars from the ontology. And constructions are of a different logical type than their constituents. But the later Russell’s transient particulars are complexes of qualities, and therefore the whole and its parts are of the same logical kind, that is, universal qualities. When Russell identifies transient particulars with complexes of qualities, this identification again results in the elimination of transient particulars. But we do not put classes of qualities in their place, and knowledge of a transient particular, that is, a quality-complex, is either through direct experience or through an inference, not by way of construction. At first sight it seems as if the bundle theory wipes out all the advantages of the substratum theory we mentioned above. For instance, now that a particular is merely a complex of compresent qualities, the logical possibility that two things that share all their properties, and yet be different particulars, seems to be left unexplained. But I pointed out, by appeal to O’Leary-Hawthorne and Russell himself, that the fact that two bundles of qualities may recur is merely a consequence of the bundle theory itself. Since the qualities forming a particular are such that they can occur at many places at different times, it logically follows

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that a bundle of them should have the same nature of multiple occurrence. It is highly unlikely for a complete complex of compresence to recur. But when it does, there will be one ‘particular’, not two. The logical subjects on the bundle theory are the bundles themselves as a whole. But this does not imply that all sentences which have the subject–predicate form will become analytic because the later Russell does not employ the notion of definition or meaning as analysis in the later period. That is, the meaning of the name of a particular does not require the analysis of the particular. Therefore, the predicate term will not be one of the analysans and thereby make the sentence analytic. However, I have explained that the later Russell’s own notion of meaning of proper names is not completely free of the analyticity charge either. According to his description theory of names, when we replace the name of a particular with a canonical definite description, if the predicate attributed to the particular happens to be in the description the sentence becomes analytic. Worse, it therefore becomes necessary. In order to avoid this consequence, I appealed to a more restricted version of the description theory of proper names, namely the nominal description theory. Another problem that the bundle theory seemed to face was in connection to the modal status of particulars (bundles). One charge was that the bundle theory implies that all particulars exist necessarily, since qualities out of which bundles are constituted exist necessarily. But this charge, we have seen, is easily evaded when one recognizes that the qualities of a bundle are bound by a relation of compresence, which is a contingent relation. Thus, the particular is not a necessary existent because such a group of qualities did not have to be compresent at that time or place; that was accidental. There is nothing in the theory that necessitates a specific group of qualities to be compresent. Another charge on modal grounds was that because the bundle theory maintains that it is necessarily true that a particular is composed of compresent qualities, the properties of a particular must be essential to it. I argued that this is not the case by showing that Russell eliminates particulars from his ontology. As Van Cleve pointed out, when particulars are eliminated, there is no particular which could have some or all of its qualities either essentially or contingently. I showed also that if Russell’s identification between particulars and bundles of qualities were a reductive one, then the qualities of a particular would indeed be essential to it because the identity relation between a particular, a, and a group of qualities, F, G and H, is a necessary relation. And throughout the changes on Russell’s views on the nature of particulars from the substratum theory to the bundle theory, in support of Landini’s

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claim that Russell has consistently practised logical atomism as a method of philosophical inquiry, I showed that Russell did not abandon this philosophical research programme in his later metaphysical work, as we see that the final atoms of logical analysis are merely qualities in Inquiry and Human Knowledge. Neither did Russell abandon neutral monism, the metaphysical view that there is only one kind of substance which is neutral between mind and matter, in his later metaphysical work. I argued that in Human Knowledge, Russell in fact strengthens this metaphysical position by showing where the categories of the mental and the physical truly belong: in the realm of epistemology. I have also explained some of Russell’s epistemological views because they play important roles in the bundle theory of particulars. I have argued, for instance, that the postulates of scientific inferences are essential in the individuation of transient particulars. It is due to the structural postulate that we are able to reliably infer relations between qualities that we do not directly perceive. The postulates also ground the account of the persistence of ordinary particulars. It is due to the causal postulate and the law of quasi-permanence that we are able to collect certain quality-complexes together as belonging to one series, that is, as being spatio-temporal parts of one ordinary particular. The fundamental question for Russell in epistemology was what, if anything, can one know with certainty about the world external to her mind? In The Problems of Philosophy (1912), Russell has a view which is similar to his later views in Human Knowledge (1948), in the sense that in both works he maintains that we can know that there are material objects, that is, ordinary particulars, by inference. In his early work the argument is an inference to the best explanation of our experiences. In both works he admits that such knowledge comes in degrees of probability, except that in his later work he discusses theories of probability in detail and makes it central to his account of our knowledge of the external world. However, in Our Knowledge of the External World (1914) Russell attempted to get at certainty by means of logical construction of the objects of the external world out of phenomena (sense-data and sensibilia). But later on he recognized the limitations of this project. He saw that even if he accepts the validity of induction a priori, he is not able to ensure that inductive inferences will yield truths more often than falsehoods. He discovered the new problem of induction: Russell discovered that in order for an inductive inference to yield probable truth, we need to have some reason, before we make the inductive inference, to believe that the claim that we want to reach as the conclusion of an inductive inference has a good chance of being true. That is, the claim needs to have initial credibility. So, he articulated the principles which need to be true

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in order for our inductive generalizations to have that initial credibility. Thus, Russell specified five assumptions that we need to make about the world that would ground our inferences that we do make in common sense and science. But these assumptions themselves are only probably true; Russell does not put them forth as necessary truths about the world or as a necessity of thought. They ground our non-demonstrative inferences. One such postulate allows us to assume that there is a similarity between the structures of what we can observe and what we cannot, and this, along with other postulates, gives us grounds to justify our inferences from experiential data to what actually exists in the external world. Thus, Russell admits that whether things exist in the external world is not something we can experience or know about using deductive inferences which would give us certainty. Russell explains that ‘The belief in external objects is a learned reaction acquired in the first months of life, and it is the duty of a philosopher to treat it as an inference whose validity must be tested . . . logically, the inference cannot be demonstrative, but must be at best probable’ (An Outline 278). Therefore, we epistemically rely on non-demonstrative inferences, which give us knowledge about the external world which are probably true (HK 335). Thus, the later Russell’s bundle theory of particulars, combined with his emphasis on the role of non-demonstrative inference in acquiring knowledge about particulars, is a strong and consistent theory which should be given its due place in the contemporary literature on theories of particulars. I hope that my endeavour in this work to give a systematic account of his ontological and epistemological views has served this purpose. Unfortunately, I have to leave a proper comparison of Russell’s bundle theory to the contemporary bundle theories to another project. But the following are the main considerations I have in preferring a Russellian realist bundle theory of particulars over the alternatives. Given the goals of reducing kinds of ultimate entities to one and explaining the similarities and distinctnesses in our experience, the later Russell’s theory, where universal qualities bundled up in complexes of compresence stand in places of particulars, succeeds in both. Hochberg explains the reasons why philosophers might be inclined to posit universals and/or substrata. We experience similarities and account for this in ontology by positing universals. We experience two things as two, so we posit substrata to account for the numerical difference we experience (‘Universals’ 89). Then the question is, on the condition that we want to be economical, which posits could we do without, the substrata or the universals? As the later Russell

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shows, we can explain both similarities and numerical difference by positing merely universals. The recurrent characteristic of universal qualities explains the similarities we experience, whereas the numerical difference we experience is explained by the complexity of the qualities, including positional qualities, which are in a compresence relation. Thus, a Russellian bundle theory is able to account for both similarities and numerical differences that we experience. The main competitors to a realist bundle theory are resemblance nominalism, trope theory, substratum views. The substratum view has the disadvantage of positing something that cannot be experienced. It accepts the existence of an entity merely because it serves an explanatory role. Its existence presumably explains the unity of qualities and their numerical difference. But such a posit is not a better explanation of these phenomena than the one that the bundle theory provides, since the bundle theory is also able to account for numerical difference by appeal to the complexity of a bundle and the positional qualities that are allowed into the bundles, without having to posit an entity which cannot be experienced. Furthermore, accepting substrata along with a realist take on qualities and relations, that is, transcendent universals, leads to the problem of explaining the nature of the exemplification relation between a substratum and a universal relation. If it is a relation just like any other, on the assumption that all relations exist external to their terms, we are faced with Bradley’s vicious regress argument. Or else we hold that exemplification is a special kind of relation, which seems to be an ad hoc response to the problem. The later Russell’s bundle theory, admitting immanent universals and denying substrata, avoids this problem of exemplification all together. Nominalist theories, namely, resemblance nominalism and the trope theory, do not posit any entities which cannot be experienced. They also have the merit of reducing kinds of entities to one, that of particulars. However, they do not explain why some things seem to be similar. They assume similarity as a fundamental fact. But similarity is exactly what requires explanation. I hold with Russell that there is one reality existing independently of how we conceptualize it. Similarities and differences in reality exist independently of how we perceive the world. We recognize the similarities between things around us and we can remember them. In fact, this is what enables us to acquire knowledge of the external world, but more importantly, enables us to survive. It is highly unlikely that we come up with these categories even though there are no repetitions or similarities in reality. Thus, the fact that there are similarities and differences in reality demands an explanation. A realist bundle theory explains similarities by appeal to the fact that the same thing, namely a quality, recurs. It

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gives an explanation of similarities, as opposed to assuming that similarity is a fundamental fact about the world, as the nominalists do. In fact, similarity is not a fundamental fact about the world at all. It is derived from things having certain properties in common. When I assert this I do not think I am begging the question against the nominalists. Particulars are similar, not fundamentally, but with respect to a certain property or characteristic. If I build two houses and they are similar it is going to be because they are both triangular and green. They are similar because both are triangular and green, not the other way around: It is not the case that the houses are triangular and green because they are similar. Hence, similarity is not a fundamental relation, but a derivative one. Thus, it is not correct for nominalists to maintain that it is a fundamental relation and thereby evade the demand for an explanation. But the acceptance of the correspondence theory and the recognition that similarities need an explanation, even coupled with logical atomism, do not imply that qualities be universal, multiply occurring. Facts on such a Russellian view are complexes, which exist independently of our perceptions of them. The atoms of these complexes will need to correspond to parts of propositions that express them, if those propositions describe reality correctly. What makes the proposition that A is yellow true is the fact that A is yellow. This fact is a complex, and therefore has constituents. Still, a quality word or image may be held to refer to either a universal quality or a particular quality, that is, a trope. None of the above assumptions necessitate that the quality-complexes in reality be composed of universal qualities. But the numerical difference of tropes (particular qualities) on the trope theory is not explained satisfactorily. What accounts for the particularity of qualities might be the substratum, but if so, then there is the aforementioned objection that we are appealing to something which cannot be experienced. If a quality is particular in virtue of the particularity of the transient or ordinary particular it is part of, then the account is circular. And if the particularity of a quality is taken as primitive, it is left unexplained. The theory would leave both similarities and differences unexplained, by insisting that they are primitive. The remaining alternative is that they are particulars by virtue of the space–time points they occupy. But this alternative relies on the assumption that there are absolute points in space and moments in time. And given that the physical space–time is shown to be relative, this assumption is not correct. It is with these initial considerations that I leave the reader to consider how the later Russell’s bundle theory fares with other contemporary alternatives.

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Notes Introduction 1 However, this does not mean that nominalists cannot hold the correspondence theory of truth. We will see shortly that some nominalists hold that ‘redness’ in ‘Redness is a colour’ corresponds to all the red things, that is, ordinary particulars. Other nominalists maintain that ‘redness’ refers to the class of red ordinary particulars. Yet others may hold that ‘redness’ refers to the class of red tropes. 2 See Chapter 1 for more detail. 3 This and the next paragraph have appeared in my article, ‘Ramsey’s Influence on Russell’s Construction of Points’, in the summer 2012 issue of Russell. 4 However, Hochberg claims that the early Russell’s logical forms were exemplification patterns – monadic, dyadic, etc. Hence the logical forms were ontological ties for the early Russell (The Positivist 19). As far as I know, Russell never used this terminology of ‘nexus’ or ‘ontological tie’. And it is unlikely that he would accept an ontological tie if he thought that the infinite regress incurred was harmless. We should note, however, that Russell abandons the 1913 view that logical form is a constituent as early as 1914. Russell writes, ‘Thus form is not another constituent, but is the way the constituents are put together’ (OKEW 52). 5 Russell’s argument, against individual properties, which we will look into in Chapter 1, is the reason why retaining things or particulars does not allow us to dispense with properties.

Chapter 1 1 Only until 1940. After 1940, a term will stand for a bundle of universals. 2 Predicates and relations could be subjects until 1914. Russell in PLA (1918) says that his views changed after his discussions with Wittgenstein in 1914 (205). 3 ‘A proposition, unless it happens to be linguistic, does not itself contain words: it contains the entities indicated by words’ (Russell, POM §51). 4 The later Russell (as of 1940) will maintain that perceptual space, though not physical space, is absolute. See Chapter 2. 5 Despite their differences, McTaggart agrees with Russell on this point (‘Time’ 355). 6 My review of D. Bostock’s Russell’s Logical Atomism (2012) in Philosophy in Review, Vol. 33 (2013), no. 5.

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7 In the draft of Analysis of Mind (1919), Russell writes, ‘Sensations belong in equal measure to physics and to psychology: they are the intersection of mind and matter [cf. Mach, Analysis of Sensations]. They are not instances of knowledge: “they simply come and are” (James). There is no distinction of subject and object in sensation, nor is there any distinction between sensation and sense-datum’ (Essays 4).

Chapter 2 1 In this passage, Russell does not abide by the distinction between ‘property’ and ‘predicate’ he makes several pages later, that is, page 124, in MPD. For if he did, he should have used the word ‘predicate’ instead of ‘property’. Since he later claims that ‘property’ is wider than ‘predicate’, ‘being identical to x’ should be a property, and that property cannot be shared by two things. 2 Structural similarity will be further explained in Chapter 3. 3 I have been helped in this symbolization by Kinney’s dissertation Bertrand Russell’s Theory of Compresence (139–40) and private correspondence with D. Kaplan. Virtues are theirs; faults are mine. 4 There are also qualities which do not have any spatio-temporal location, such as being a prime number. 5 ‘You will not, I believe, admit an accident which is in two subjects at once. Thus, I hold, as regards relations, that paternity in David is one thing, and filiation in Solomon is another, but the relation common to both is a merely mental thing, of which the modifications of singulars are the foundation’ (Russell cites Leibniz (G.II. 486) in The Philosophy of Leibniz 206). 6 Russell makes the same point in ‘Logic and Ontology’: ‘It is quite clear that there are relational facts’ (128) and in MPD: ‘It is a fact that Alexander preceded Caesar, and this fact does not merely consist of Alexander and Caesar. Relation-words, it is clear, serve a purpose in enabling us to assert facts which would otherwise be unstatable. So far, I think, we are on firm ground. But I do not think that it follows that there is, in any sense whatever, a “thing” called “preceding”’ (175). 7 See Chapter 1. 8 This does not mean that there are two different kinds of universals for the phenomenal blue and the physical quality blue. The word ‘blue’ acquires a different meaning under the phenomenal and physical interpretations. 9 See my ‘Ramsey’s Influence on Russell’s Construction of Points’ (2012) for a detailed discussion of this problem. 10 P. Loptson and N. Griffin made this comment on an earlier draft.

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11 Van Cleve also points out that for Russell, a bundle is a whole with parts which are compresent with each other. Therefore, it is not just a sum of its parts. When the whole is a mere collection of parts, there is the problem that any grouping of properties would have to be a whole. But the later Russell would not face this problem because on his account a group of properties make a whole only if they are in a relation of compresence (123–4).

Chapter 3 1 Goodman’s solution was to maintain that we prefer the conclusion ‘All emeralds are green’ over the conclusion, ‘All emeralds are grue’ because it is ‘entrenched’ in practice. However, some philosophers, such as Aune, argued that the limitations Goodman brought with his ‘theory of entrenchment’ are not sufficient (132–3).

Chapter 4 1 See Chapter 5. 2 N. Griffin commented in conversation that Russell probably accepted identity as a relation when he discovered Peano in 1900. Russell takes identity as a primitive idea, that is, not defined in the system, in an article he wrote in French (1900–1) where he develops a logic of relations based on Peano’s logic. This article appeared in English as ‘The Logic of Relations’ in 1901. 3 As B. Linsky has commented on an earlier draft of this chapter, according to PM, one has to assume the axiom of reducibility in order for PIII to be true. Russell explains the need for this axiom as follows: ‘Suppose the common properties required for indiscernibility to be limited to predicates. Then the identity of indiscernibles will state that if x and y agree as to all their predicates, they are identical. This can be proved if we assume the axiom of reducibility. For in that case, every property belongs to the same collection of objects as is defined by some predicate. Hence there is some predicate common and peculiar to the objects which are identical with x. This predicate belongs to x, since x is identical with itself; hence it belongs to y, since y has all the predicates of x; hence y is identical with x. It follows that we may define x and y as identical when all the predicates of x belong to y’ (‘The Theory of Logical’ 243). 4 Hochberg notes that this problem was raised earlier, in 1947, by the Swedish philosopher I. Segelberg (The Positivist 45). 5 By ‘non-relational location properties’, Hochberg means positional qualities in perceptual space.

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6 Russell explains that on the scenario that x is completely surrounded by red, and supposing that a y which is qualitatively identical to x is completely surrounded by black, then x and y will be distinguished by having different relations because one will be surrounded by black and the other by red. But Russell’s answer to this is that we will need to know that something cannot be surrounded by red and black at the same time and this, according to Russell, presupposes the numerical diversity of x and y (‘On the Relation’ 117).

Chapter 5 1 Russell took classes to be aggregates, but today ‘aggregate’ is regarded as a non-class, something not abstract. K. Fine, for instance, takes ‘aggregation’ to be a form of nonstructural composition, as in a quantity of sand of its grains (‘Compounds’). 2 See Chapter 4. 3 Russell maintains the same view earlier (1912–13) in ‘On the Notion of Cause’ (172–3). 4 Propositional functions are ‘expressions in which there are one or more variables and which are such that, when values are assigned to the variables, the result is a proposition’ (MPD 124). 5 Russell keeps to this view of modality as only applying properly to propositional functions in his later work, as we see in ‘Philosophy of Logical Atomism’ (231) and AMa (169–70). 6 ‘Chtw (−) =1’ reads as ‘The chance of a proposition at time t in world w is equal to 1’, that is, the proposition is necessary. ‘Chtw (−) > 0’ reads as ‘The chance of a proposition at time t in world w is greater than 0’, that is, the proposition is possible.

Chapter 6 1 But both the early and the later Russell accept that genus-species-type propositions are of the subject–predicate proposition. 2 Russell, in PM (1910), writes, ‘A definition is, strictly speaking, no part of the subject in which it occurs. For a definition is concerned wholly with the symbols, not with what they symbolize. Moreover, it is not true or false, being the expression of volition, not of a proposition’ (11). 3 Russell makes the same point in IMT: ‘We do not have to grasp all the constituents of a bundle in order to understand what the name refers to. When we name a bundle as “W”, we do not necessarily know all its parts; therefore the judgment is not analytic.’ Russell claims that his theory implies that ‘we cannot express our

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knowledge without names for complex wholes, and that we can be acquainted with complex wholes without knowing of what constituents they consist’ (128–9).

Chapter 8 1 And on the monadistic view (Leibniz) ‘a is bigger than b’ will be expressed in the subject–predicate form, ‘a has the property of being bigger than b.’ But argues Russell, this predicate, ‘bigger than b’, is derived from the relation of a to b, so a has to intrinsically differ from b. But, says Russell, analysis of a does not reveal anything to differentiate it from b (§214). What he means is that if they happen to be the same with respect to their intrinsic qualities they will not be different to begin with. 2 R. M. Marsh, the editor of Russell’s Logic and Knowledge, notes that this theory was not original to Russell. It dates back to St Augustine’s De Magistro (Marsh 125). 3 ‘In every proposition that we can apprehend all the constituents are really entities with which we have immediate acquaintance’ (Russell, ‘On Denoting’ 56). 4 ‘A particular number is not identical with any collection of terms having that number: the number 3 is not identical with the trio consisting of Brown, Jones, and Robinson. The number 3 is something which all trios have in common, and which distinguishes them from other collections’ (Russell, Introduction 11–12). 5 Bostock argues that Russell should have abandoned this theory even earlier (130), so he does not think this theory is an essential component of logical atomism either. 6 I must note that I disagree with Landini when he takes Russell to hold that only particulars are the atoms of logical analysis in PLA lectures. Landini appeals to p. 199 of PLA to support this interpretation; but all that Russell says is that particulars are terms of relations in atomic facts, which does not preclude qualities or relations themselves from being logical simples. In fact, earlier on p. 179 of PLA, Russell writes that the logical atoms are either particulars (such as little patches of colour, momentary sounds) or predicates or relations.

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Bibliography Adams, Robert M. ‘Primitive Thisness and Primitive Identity’. The Journal of Philosophy 76.1 (1979): 5–26. Allaire, Edwin. ‘Bare Particulars’. Universals and Particulars. Ed. Michael J. Loux. New York: Anchor Books, 1970 [1963]. Armstrong, David. Universals and Scientific Realism. Nominalism and Realism. Vol. 1 and Vol. 2. Cambridge: Cambridge University Press, 1978. Aune, Bruce. ‘The Paradox of Empiricism’. Metaphilosophy 1 (1970): 128–38. Ayer, A. J. Philosophical Essays. London: Macmillan & Co Ltd, 1954. Bach, Kent. ‘What’s in a Name’. Australasian Journal of Philosophy 59.4 (1981): 371–86. Barcan-Marcus, Ruth. ‘The Identity of Individuals in a Strict Functional Calculus of Second Order’. The Journal of Symbolic Logic 12.1 (1947): 12–15. Barnes, Elisabeth. ‘Emergence and Fundamentality’. Mind 121.484 (2012): 873–901. Bergmann, Gustav. Realism: A Critique of Brentano and Meinong. Wisconsin: University of Wisconsin Press, 1967. Berkeley, Bishop. A Treatise Concerning the Principles of Human Knowledge. Oxford: Oxford University Press, 1998 [1710]. Bigelow, John, John Collins and Robert Pargetter. ‘The Big Bad Bug: What Are the Humean’s Chances?’ British Journal of Philosophy of Science 44 (1993): 443–62. Black, Max. ‘The Identity of Indiscernibles’. Mind. New Series 61.242 (1952): 153–64. Blanshard, Brand. Reason and Analysis. London: Allen & Unwin, 1962. Bostock, David. Russell’s Logical Atomism. Oxford: Oxford University Press, 2012. Bradley, Francis Herbert. Appearance and Reality. Oxford: Oxford University Press, 1962 [1893]. Campbell, Keith. Abstract Particulars. Oxford: Blackwell, 1990. Carnap, Rudolf. The Logical Structure of the World. Trans. Rolf A. George. Berkeley: University of California Press, 1967. Castañeda, H. N. ‘Thinking and the Structure of the World’. Philosophia: Philosophical Quarterly of Israel 4 (1974): 3–40. Casullo, Albert. ‘The Contingent Identity of Particulars and Universals’. Mind. New Series 93.372 (October 1984): 527–41. —. ‘A Fourth Version of the Bundle Theory’. Philosophical Studies 54 (1988): 125–39. Chisholm, Roderick M. On Metaphysics. Minneapolis: University of Minnesota Press, 1989. Dainton, Barry. Time and Space. Montreal: McGill-Queen’s University Press, 2001.

9781472512666_Biblio_Final_txt_print.indd 161

1/14/2003 2:06:41 PM

162

Bibliography

Demopolous, William and Michael Friedman. ‘Bertrand Russell’s The Analysis of Matter: Its Historical Context and Contemporary Interest’. Philosophy of Science 52 (1985): 621–39. Fine, Kit. ‘Compounds and Aggregates’. Nous 2 (June 1994): 137–58. Fodor, Jerry A. ‘The Mind-Body Problem’. Scientific American 244.1 (January 1981): 114–23. French, Steven. ‘Why the Principle of the Identity of Indiscernibles Is Not Contingently True Either?’ Synthese 78 (1989): 141–66. Garvin, Ned S. ‘Russell’s Naturalistic Turn’. Russell: The Journal of Bertrand Russell Studies 11.1 (1991): 36–51. Goodman, Nelson. Fact, Fiction and Forecast. Indianapolis: Bobbs-Merrill Company Inc., 1973 [1955]. —. The Structure of Appearance. Ed. Geoffrey Hellman. Dordrecht: Reidel, 1977 [1951]. Griffin, Nicholas J. ‘Introduction’. The Cambridge Companion to Russell. Ed. Nicholas Griffin. New York: Cambridge University Press, 2003. —. ‘Some Remarks on Russell’s Early Decompositional Style of Analysis’. The Analytic Turn: Analysis in Early Analytic Philosophy and Phenomenology. Ed. Michael Beaney. London: Routledge, 2007. Griffin, Nicholas and Gad Zak. ‘Russell on Specific and Universal Relations: The Principles of Mathematics, §55’. History and Philosophy of Logic 3 (1982): 55–67. Hacking, Ian. ‘The Identity of Indiscernibles’. Journal of Philosophy 72.9 (1975): 249–56. Hochberg, Herbert. The Positivist and the Ontologist: Bergmann, Carnap, and Logical Realism. Atlanta: Rodopi, 2001. —. ‘Things and Descriptions’. Essays on Bertrand Russell. Ed. E. D. Klemke. Urbana: University of Illinois Press, 1971 [1970]. —. ‘Things and Qualities’. Metaphysics and Explanation. Ed. W. Capitan and D. Merill. Pittsburgh: University of Pittsburgh Press, 1964. —. ‘Universals, Particulars, and Predication’. The Review of Metaphysics 19.1 (September 1965): 87–102. Hoy, Ronald C. ‘Inquiry, Intrinsic Properties, and the Identity of Indiscernibles’. Synthese 61 (1984): 275–97. Hume, David. ‘An Abstract of a Treatise of Human Nature’. An Enquiry Concerning Human Understanding. Ed. Charles William Hendel. Indianapolis: Bobbs-Merrill Company, Inc., 1955 [1748]. Jourdain, Philip E. B. ‘The Logical Significance of Ockham’s Razor’. The Monist 29.3 (July 1919): 450–1. Kalish, Montague and Mar. Logic: Techniques of Formal Reasoning. Oxford: Oxford University Press, 1980 [1964]. Keynes, Maynard. A Treatise on Probability. The Collected Writings of John Maynard Keynes Vol. 8. New York: St. Martin’s Press, 1973 [1921]. Kim, Jaegwon. ‘Making Sense of Emergence’. Philosophical Studies 95 (1999): 3–36.

9781472512666_Biblio_Final_txt_print.indd 162

1/14/2003 2:06:42 PM

Bibliography

163

Kinney, Laurence Forman. ‘Bertrand Russell’s Theory of Compresence’. PhD Diss. Syracuse University, 1976. Kneale, William. ‘Modality, De Dicto, and De Re’. Logic, Methodology and the Philosophy of Science: Proceedings of the 1960 International Congress. Ed. Ernest Nagel, Patrick Suppes and A. Tarski. Stanford: Stanford University Press, 1962. Koç Maclean, Gülberk. ‘Ramsey’s Influence on Russell’s Construction of Points’. Russell: The Journal of Bertrand Russell Studies. New Series 32.1 (Summer 2012): 42–54. Kripke, Saul A. ‘Identity and Necessity’. Identity and Individuation. Ed. Milton K. Munitz. New York: New York University Press, 1971. —. Naming and Necessity. Cambridge: Harvard University Press, 1980 [1972]. Landini, Gregory. ‘Russell On What There Isn’t’. Giornale de Filosofia. Giugno [June] (2009): 1–34. —. Wittgenstein’s Apprenticeship with Russell. Cambridge: Cambridge University Press, 2007. Landini, Gregory and Thomas R. Foster. ‘The Persistence of Counterexample: Re-examining the Debate Over Leibniz Law’. Nous 25.1 (1991): 43–61. Loar, Brian. ‘The Semantics of Singular Terms’. Philosophical Studies 30 (1976): 353–77. Locke, John. An Essay Concerning Human Understanding. Ed. Roger Woolhouse. London: Penguin Books, 1997 [1690]. Loux, Michael J. Metaphysics: A Contemporary Introduction. London: Routledge, 1998. —. Substance and Attribute. Dordrecht: Reidel, 1978. Lowe, E. J. A Survey of Metaphysics. Oxford: Oxford University Press, 2002. McTaggart, John M. Ellis. ‘Time’ (1921). Metaphysics; Contemporary Readings. Ed. Michael J. Loux. New York: Routledge, 2008 [2001]. Miles, Murray. Inroads: Paths in Ancient and Modern Western Philosophy. Toronto: University of Toronto Press, 2003. Newman, M. H. A. ‘Mr. Russell’s Causal Theory of Perception’. Mind, New Series 37.146 (1928): 137–48. Nolan, David. ‘Quantitative Parsimony’. The British Journal for the Philosophy of Science 48.3 (1997): 329–44. O’Leary-Hawthorne, John. ‘The Bundle Theory of Substance and the Identity of Indiscernibles’. Analysis 55.3 (1995): 191–6. Pears, David. The False Prison. Vol. 1. Oxford: Oxford University Press, 1987. Plato. ‘Phaedo’. Complete Works. Ed. John M. Cooper. Indiana: Hackett Publishing Company, Inc., 1997. —. ‘Parmenides’. Complete Works. Ed. John M. Cooper. Indiana: Hackett Publishing Company, Inc., 1997. Putnam, Hilary. ‘On Properties’. Essays in Honor of Carl G. Hempel. Ed. Nicholas Rescher et al. Dordrecht: Reidel, 1969. Quine, W. V. O. ‘Identity, Ostension, and Hypostasis’. From a Logical Point of View. Revised 2nd ed. Cambridge: Harvard University Press, 1996 [1953].

9781472512666_Biblio_Final_txt_print.indd 163

1/14/2003 2:06:42 PM

164

Bibliography

—. ‘On What There Is’. From a Logical Point of View. Revised 2nd ed. Cambridge: Harvard University Press, 1996 [1953]. Ramsey, F. P. Letter dated 29 October 1927. Box 5.38 Bertrand Russell Archives, McMaster University. Rodriguez-Pereyra, Gonzalo. Resemblance Nominalism. Oxford: Clarendon Press, 2002. Russell, Bertrand. ABC of Relativity. London: Unwin Hyman Ltd, 1985 [1925]. —. The Analysis of Matter. London: Routledge, 2001 [1927]. —. The Analysis of Mind. London: Routledge, 1997 [1921]. —. Appendix to Human Knowledge. (1958) Box 3.25 Bertrand Russell Archives, McMaster University. —. ‘The Axioms of Geometry’ (1899). The Collected Papers Vol. 2. Ed. Nicholas Griffin, Albert C. Lewis and W. G. Stratton. London: Unwin Hyman Ltd, 1990. —. ‘The Classification of Relations’ (1899). Bertrand Russell: His Works Collected Papers Vol 2. Ed. Nicholas Griffin and Albert C. Lewis. London: Unwin Hyman Ltd, 1990. —. An Essay on the Foundations of Geometry. London: Routledge, 1897. — . Essays on Language, Mind and Matter 1919–26. The Collected Papers of Bertrand Russell 9. Ed. John Greer Slater and Brend Frohmann. London: Unwin Hyman Ltd, 1988. —. ‘The Existential Import of Propositions’ (1905). Essays in Analysis. Ed. Douglas Lackey. New York: George Braziller, Inc., 1973. —. A History of Western Philosophy. New York: Simon & Schuster, 1945. —. Human Knowledge: Its Scope and Limits. New York: Touchstone Books, 1948. —. An Inquiry into Meaning and Truth. London: Routledge, 1995 [1940]. —. Introduction to Mathematical Philosophy. London: Allen & Unwin, 1948 [1919]. —. ‘Knowledge by Acquaintance and Knowledge by Description’ (1910–11). Mysticism and Logic. Melbourne: Penguin Books, 1953 [1918]. —. Letter to Newman. 24 May 1928. RA1 7.10: 5.34. Bertrand Russell Archives, McMaster University. [Printed in The Autobiography of Bertrand Russell. London: Unwin Paperbacks, 1978 [1971], pp. 413–14.] —. Letter to R. S. Hartman. 17 May 1953. RA 750; 11.13. Bertrand Russell Archives, McMaster University. —. ‘Logic and Ontology’. My Philosophical Development. London: Routledge, 1985 [1959]. —. ‘The Logic of Relations’ (1901). Bertrand Russell. Logic and Knowledge. Ed. Robert Charles Marsh. London: Routledge, 1997 [1956]. —. ‘Logical Atomism’ (1924). Bertrand Russell: Logic and Knowledge. Ed. Robert Charles Marsh. London: Routledge, 1997 [1956]. —. My Philosophical Development. London: Routledge, 1985 [1959]. —. ‘Necessity and Possibility’ (1905). Foundations of Logic 1903–1905. The Collected Papers Vol.4. Ed. Alasdair Urquhart. London: Routledge, 1994.

9781472512666_Biblio_Final_txt_print.indd 164

1/14/2003 2:06:42 PM

Bibliography

165

—. ‘Non-Deductive Inference’ (1945?). Last Philosophical Testament 1943–68. The Collected Papers of Bertrand Russell Vol. 11. Ed. John G. Slater with the assistance of Peter Köllner. London: Routledge, 1997. —. ‘Note on Non-Demonstrative Inference and Induction’ (1959). Last Philosophical Testament 1943–68. The Collected Papers of Bertrand Russell Vol. 11. Ed. John G. Slater with the assistance of Peter Köllner. London: Routledge, 1997. —. ‘On Denoting’. Bertrand Russell: Logic and Knowledge. Ed. Robert Charles Marsh. London: Routledge, 1997. —. ‘On the Nature of Acquaintance’ (1914). Bertrand Russell: Logic and Knowledge. Ed. Robert Charles Marsh. London: Routledge, 1997 [1956]. —. ‘On the Notion of Cause’ (1912–13). Mysticism and Logic. Melbourne: Penguin Books, 1953 [1918]. —. ‘On Propositions: On What They Are and How They Mean’ (1919). Bertrand Russell: Logic and Knowledge. Ed. Robert Charles Marsh. London: Routledge, 1997 [1956]. —. ‘On the Relation of Universals and Particulars’ (1911). Bertrand Russell: Logic and Knowledge. Ed. Robert Charles Marsh. London: Routledge, 1997 [1956]. —. ‘On Scientific Method in Philosophy’ (1914). Mysticism and Logic. Melbourne: Penguin Books, 1953 [1918]. —. ‘On Sensations and Ideas’. The Philosophy of Logical Atomism and Other Essays 1914–1919. The Collected Papers of Bertrand Russell 8. Ed. John G. Slater. London: Allen & Unwin, 1986. —. Our Knowledge of the External World. London: Routledge, 1995 [1914]. —. An Outline of Philosophy. London: Allen & Unwin, 1927. —. The Philosophy of Leibniz. London: Routledge, 1997 [1900]. —. ‘The Philosophy of Logical Atomism’ (1918). Bertrand Russell: Logic and Knowledge. Ed. Robert Charles Marsh. London: Routledge, 1997 [1956]. —. Principia Mathematica to *56. A. N. Whitehead and B. Russell. Cambridge: Cambridge University Press, 1997 [1910]. —. The Principles of Mathematics (1903). 2nd ed. New York: W.W. Norton, 1938. —. ‘The Problem of Universals’ (1946). Last Philosophical Testament 1943–68. The Collected Papers of Bertrand Russell Vol. 11. Ed. John G. Slater with the assistance of Peter Köllner. London: Routledge, 1997. —. The Problems of Philosophy. Oxford: Oxford University Press, 1989 [1912]. —. ‘The Relation of Sense-data to Physics’ (1914). Mysticism and Logic. Melbourne: Penguin Books, 1953 [1918]. —. Theory of Knowledge. The 1913 Manuscript. The Collected Papers of Bertrand Russell 7. Ed. Elisabeth Ramsden Eames with Kenneth Blackwell. London: Routledge, 1992 [1984]. —. ‘The Theory of Logical Types’ (1910). Essays in Analysis. Ed. Douglas Lackey. New York: George Braziller, Inc., 1973.

9781472512666_Biblio_Final_txt_print.indd 165

1/14/2003 2:06:42 PM

166

Bibliography

Sainsbury, R. Mark. Russell. London: Routledge & Kegan Paul Ltd., 1979. Schilpp, Arthur. Ed. The Philosophy of Bertrand Russell. New York: Tudor Publishing Company, 1951 [1944]. Searle, John R. ‘Proper Names’. Mind 67 (1958): 166–73. Stace, Walter Terence. ‘Russell’s Neutral Monism’. The Philosophy of Bertrand Russell. Ed. Paul Arthur Schilpp. New York: Tudor Publishing Company, 1951 [1944]. Van Cleve, James. ‘Three Versions of the Bundle Theory’. Philosophical Studies 47 (1985): 95–107. —. ‘Why Coherence Is Not Enough: A Defense of Moderate Foundationalism’. Contemporary Debates in Epistemology. Ed. M. Steup and E. Sosa. Oxford: Blackwell, 2005. Weitz, Morris. ‘Analysis and Unity of Russell’s Philosophy’. The Philosophy of Bertrand Russell. Ed. Paul Arthur Schilpp. New York: Tudor Publishing Company, (1951) [1944]. Williams, Donald C. ‘On the Elements of Being: I’. The Review of Metaphysics 7 (1953): 3–18. Wittgenstein, Ludwig. Tractatus Logico-Philosophicus. Trans. C. K. Ogden. London: Routledge, 1996 [1922]. Wolterstorff, Nicholas. ‘On the Nature of Universals’. Universals and Particulars. Ed. Michael. J. Loux. New York: Anchor Books, 1970. —. ‘Qualities’. Universals and Particulars. Ed. Michael J. Loux. New York: Anchor Books, 1970. Zimmerman, Dean W. ‘Distinct Indiscernibles and the Bundle Theory’. Mind 106.422 (1997): 305–9.

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Index a priori 70–3, 76–8, 80, 82, 106, 131, 138, 150 absolute monism 136–7 absolute theory of space and time 22–3, 26, 42–3, 48–9, 62, 91, 153, 155 abstract entities 3, 7–8, 48, 63, 137 abstract particulars 9 abstract reference 4, 7–8, 10, 47 accidental qualities or properties 2, 12 accidental predication 101, 103, 106 acquaintance 7, 13, 24, 25, 27, 39, 67, 135, 137–8, 141–2, 149–50, 159 Adams, R. M. 93 Allaire, E. 11–14 analogy 69, 72, 81 analysis 2–3, 11, 15, 27, 34, 46, 53, 56, 91, 101, 104, 110–14, 116–17, 133–43, 149–50, 159 analytic, analyticity 11, 18, 41, 106, 109–17, 147, 149, 158 Aristotelian 6–7, 11–12, 50, 75–6, 121, 136 Armstrong, D. 45, 47, 85–6, 104 attribute agreement 7, 8, 10 attribute ascription 12–13, 16, 18, 99, 108–12, 115–17, 149 Ayer, A. J. 16, 87, 91 Bach, K. 115 Barcan-Marcus, R. 104 bare particular 12–13, 19, 111–12, 121 Barnes, E. 54–5, 57–8, 148 Bergmann, G. 11, 14–15 Berkeley, B. 16 Bigelow, J. 107 Black, M. 42, 83, 89–97 Blanshard, B. 91 Bonjour, L. 77 Bostock, D. 29, 32, 38, 63–4, 66, 72, 119, 123, 126–8, 133, 139–40, 143, 155, 159 Bradley, F. H. 14–15, 51, 136, 152 Broad, C. D. 56 bundle 1–3, 6–7, 11, 12, 16–18, 39, 41–69, 83–6, 88–91, 93–7, 99–105, 108–11,

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114, 116, 133–4, 141, 143, 145, 147–53, 155, 157–8 Carnap, R. 8–9, 115 Castañeda, H. N. 16 Casullo, A. 85–6, 91–4 causation 25, 35, 37, 44, 57, 59, 65, 67–73, 77–82, 84, 101, 120–31, 143, 150 certainty 67, 71–4, 82, 150–1 Chisholm, R. M. 100 class 1–4, 7–10, 17, 19, 23–4, 26, 29–31, 33–7, 39, 46–7, 53, 63–5, 66, 69, 74, 81, 100–2, 106, 122–3, 125–6, 135, 139–40, 143–4, 148, 155, 158 coherence 76–7, 124 Collins, J. 107 common sense 5–6, 69, 81, 151 companionship difficulty 9–10 complex 1, 8, 32, 39, 42–8, 50, 53, 56–63, 65–8, 79–80, 83–5, 88, 90, 92, 95–7, 99–106, 108–9, 114, 116, 129, 131, 133, 135, 138, 141, 143–5, 148–53, 159 compresence 16, 26–7, 36, 43–8, 50, 54, 57–63, 65, 79, 84–5, 96, 99, 101, 109, 130, 144, 149, 151–2, 157 conceivability 91–2 construction 8–9, 23, 25–6, 34, 36, 43–4, 57, 59–60, 62–4, 66, 69, 72, 78–9, 84, 122–4, 127, 134–5, 139–44, 147–8, 150 contingent 10, 16, 18, 77–8, 85, 99–104, 106, 108, 110, 149 contingency 102, 108 continuity 35, 79–80, 82, 130 coordinate qualities 49, 97 correspondence 4, 32, 53, 153, 155 deductive inference 68, 71, 78, 151 definition, philosophical 111–13 mathematical (denotational) definition 112–13

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demonstratives 134 Demopolous, W. 130 denoting 113 derivative predicate 4 beliefs 142 contingency 108 entity 54–5, 57, 153 fact 33 necessity 104–5 Descartes, R. 78, 120–1, 125–6, 142 description 6, 64, 67, 92–5, 113, 149 definite description 93, 104–5, 110, 112–17, 134–5, 140 knowledge by description 141–2 nominal description 116, 149 diversity, numerical 12–3, 22–3, 35, 41–3, 86, 96, 158 egocentric 25, 44 Einstein, A. 27 elimination 8, 56, 66, 75, 96, 101, 106, 108, 140, 145, 148 emergent entity or property 55–7, 92 empiricism 4, 7, 13, 16, 121 endurantism 1–2, 19, 44 epistemology 63, 68, 69, 123, 128, 138, 141–2, 150 essence 11–12, 21, 110, 113 essential qualities or properties 2, 12, 17–8, 100–3, 121, 149 events 2–3, 19, 23–4, 26–7, 35–8, 43–4, 57, 59–60, 64, 70–3, 78–81, 114, 121–4, 126–31, 135, 140, 143–4 facts 7–8, 10, 24, 29, 31–3, 39, 52, 54, 76–8, 82, 109, 114–15, 136–8, 142, 152–3, 156, 159 Fodor, J. 124 Foster, T. R. 93 foundationalism 68, 77, 132 French, S. 92 Friedman, M. 130 functionalism 124 fundamental 1, 5, 8, 10–1, 13, 29, 32–3, 45, 54–8, 75, 135, 145, 147–8, 152–3 Garvin, N. S. 67 Goodman, N. 8–9, 17, 73–4, 157 Griffin, N. 29, 157

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Hacking, I. 92–7 Hartman, R. S. 113 Hochberg, H. 8, 16, 19, 50, 91, 93, 151, 155 Hoy, R. C. 93 Hume, D. 16–17, 67, 71 identity 8, 11, 18, 21, 28, 65–6, 79–80, 84–90, 99–105, 149, 157 identity of indiscernibles 17, 42, 83–9, 93–6, 110, 145, 157 images 36, 38, 123–4, 140 immanent qualities (universals) 3, 6, 15, 38, 45, 47–8, 50, 57, 94–5, 97, 147, 152 immanent realism 6–7, 148 immanent relations 148 imperfect community problem 8–10 individuation 2, 13, 17, 21, 42, 62, 83–4, 91, 97, 103, 144, 145, 150 induction 67, 69, 71–4, 76–7, 80, 150 instantiation 2–4, 12, 27–8, 33, 38, 57 Jourdain, P. 119–20 Kant, I. 70, 82, 110 Keynes, J. M. 75–6, 107 Kinney, L. F. 48, 156 Kneale, W. 115 Kripke, S. 104–5, 115–17 Landini, G. 39, 66, 93, 133, 138, 141, 145, 149, 159 laws 34–5, 37, 59, 70–3, 78–9, 94, 106, 120–5, 127–8 Leibniz, G. 51, 89, 110–11, 136, 159 Leibniz’s law 86 Loar, B. 115 Locke, J. 11, 13 logical atomism 56, 133–43, 145, 150, 153, 159 Loux, M. J. 1, 4–6, 13, 19 Lowe, E. J. 105 material substance 33–4, 139–40 McTaggart, J. M. E. 155 meaning 16, 18, 109–17, 119, 149 referential theory of 4, 32, 134–6 memory 24–5, 37, 76, 137 mental substance 36–8, 81, 120–1, 126, 140–1 mereological essentialism 99–100, 102, 106

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Index metaphysics 5, 35, 85, 129, 136, 144 Mill, J. S. 71, 105 mind 16, 25, 36, 39, 55, 65, 72, 81, 124–5, 127, 138, 140, 150 mind and matter 2, 16, 61, 121–2, 126, 131, 135, 150, 156 modality 86, 105–8, 158 multiple occurrence 3, 15–6, 47–8, 57, 60, 149, 153 name 4, 20, 38, 44–7, 49–50, 85, 87–8, 90, 103–5, 109–17, 128, 134, 149, 158–9 naturalized epistemology 68 necessary 18, 44, 64, 76, 82–7, 89, 99–108, 114–15, 126, 130, 138, 149, 151, 158 necessity 3, 70, 75, 99–100, 103–8, 151 neutral monism 37, 39, 61, 119–28, 138, 150 Newman, M. H. A. 130 Nicod, J. 76 nominalism 3, 7, 10, 29–31, 152 non-demonstrative inference 62, 67–9, 74–6, 78, 151 Ockham’s principle 7, 35, 119–20 O’Leary-Hawthorne, J. 85, 94–5, 97, 148 ontology 1, 18, 20, 39, 57, 63, 66, 122, 126, 134, 143, 147–9, 151 ostensive definition 58, 60 Pargetter, R. 107 Pears, D. 101, 137–8 perceptual space and/or time 20, 22, 35, 42, 48–9, 58, 61–2, 91, 97, 155, 157 perdurance 1–3, 19, 33, 44 permanence 78–9 persistence 2, 19, 27, 34, 44, 68–9, 74, 78–80, 83, 109, 139–40, 144, 150 phenomenalism 38, 69, 72–3 physical space and/or time 6, 35, 43, 48, 58, 61–2, 153, 155 Plato 5–7, 14, 38, 49–50 points or instants 22–3, 25–7, 35, 43, 59–61, 64–5, 112, 140 point-instant 6, 23, 35, 41, 43–4, 48, 59–62, 65, 83–5, 143–4, 153 positional qualities 42, 44, 48, 62, 88, 90–1, 95, 152, 157

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169

postulates 62, 73, 75–82, 129–31, 150–1 primitive 4–6, 58, 120, 153, 157 probability 73–6, 78, 80, 82, 107–8, 150 propositional function 86, 103, 105–8, 158 quality-complex 44, 56, 67, 84, 88, 96, 102–3, 105, 109, 114, 131, 133, 148, 150, 153 quasi-permanence 78–9, 82, 150 Quine, W. V. O. 7, 17, 68 realism 1, 3–7, 11, 13–14, 16–18, 31, 33, 49, 52–3, 83, 85–6, 89, 94–6, 99, 110–11, 116, 148, 151–2 reduction 2, 4–5, 7, 8, 11–12, 16, 20, 22, 50–1, 53–5, 65–6, 85, 99–103, 105–6, 110, 113, 122, 147, 149, 152 reference, abstract 4, 7–8, 10, 47 theory of 114–15 regress 7, 14–15, 30–2, 53, 58, 152, 155 relational facts 24, 52–3, 156 resemblance 7, 10, 30–3, 53, 152 structural 125 Rodriguez-Pereyra 7, 31–2 Sainsbury, R. M. 119, 128 Searle, J. R. 115 sensations 2–3, 20, 24–5, 27, 34–8, 49, 64, 120–1, 123–4, 128, 134, 137, 140, 156 sense-data 2, 7, 19, 23, 25–8, 33–7, 72, 120–1, 134, 138, 150, 156 series 2, 6, 23–4, 26, 35, 37–8, 41, 43–4, 59, 61–2, 66, 68–9, 78, 79, 82–4, 101–3, 122, 127, 129, 135, 140, 143–4, 147–8, 150 solipsism 78–9 Stace, W. T. 19, 35, 119, 121–5, 127–8 structure 1–2, 8, 39, 56, 63–4, 68, 77, 79–82, 125–6, 128–31, 134–6, 144, 151 substratum 1–3, 7, 11–14, 16–19, 21–5, 27–8, 33–5, 39, 41–4, 47, 49, 57, 61, 67, 79, 85, 87–8, 90, 95, 101, 109, 111–14, 121–2, 143, 147–9, 151–3 synthetic 77, 82, 111, 114 tense 24–5, 57 transcendent 2–3, 14, 27, 33, 38, 45, 47–8, 50, 57, 148, 152

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tropes 1–2, 9–11, 16–17, 27–8, 30, 33, 54, 152–3, 155 truth-maker 8, 24, 31, 39, 53–4 truth-value 8, 18, 32, 135 universals 1–12, 14–20, 23, 27–33, 38–9, 42, 44–5, 47–54, 57–8, 65–6, 68, 85–7, 94–5, 99, 133–4, 137–8, 141–4, 147–8, 151–3, 155–6 Van Cleve, J. 99–102, 149, 157

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Weitz, M. 27–8, 48–9 Whitehead, A. N. 86, 120 wholes 17, 45–6, 51, 53, 55–7, 92, 99–101, 109, 111, 114, 137, 144, 148–9, 157, 159 Williams, D. C. 9, 16–7 Wittgenstein, L. 42, 87, 155 Wolterstorff, N. 9–10 Zak, G. 29 Zimmerman, D. W. 95

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