Universals and Scientific Realism (Vol. 1: Nominalism and Realism)
Armstrong (David)
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Back Cover Blurb

  1. This is a study, in two volumes, of one of the longest-standing philosophical problems: the problem of universals1.
    1. In volume I David Armstrong surveys and criticizes the main approaches and solutions to the problems that have been canvassed, rejecting the various forms of nominalism and 'Platonic' realism.
    2. In volume II he develops an important theory of his own, an objective theory of universals2 based not on linguistic conventions, but on the actual and potential findings of natural science.
  2. He thus reconciles a realism about qualities and relations with an empiricist epistemology. The theory allows, too, for a convincing explanation of natural laws as relations between these universals3.


"Armstrong (David) - Introduction to Universals and Scientific Realism Vol. 1 (Nominalism and Realism)"

Source: Armstrong - Universals and Scientific Realism (Vol. 1: Nominalism and Realism), 1977

Full Text
  1. It is argued in this work,
    1. that there are universals1, both monadic and polyadic, that is, properties and relations, which exist independently of the classifying mind. Realism is thus accepted. Nominalism rejected.
    2. that no monadic universal is found except as a property of some particular, and no polyadic universal except as a relation holding between particulars. Transcendent or Platonic Realism is thus rejected.
    3. that what universals2 there are is not to be determined simply by considering what predicates can be applied to particulars. Instead, it is the task of total science, conceived of as total enquiry, to determine what universals3 there are.
    The view defended is therefore a scientific Realism about universals4. It might also be called a posteriori Realism. The working out of a scientific Realism about universals5 is intended to be the special contribution of these volumes.
  2. Contemporary philosophy recognizes two main lines of argument for the existence of objective universals6. The first is, or is a descendant of, Plato's One over Many argument. Its premiss is that many different particulars can all have what appears to be the same nature. In the terms used by Charles S. Peirce, different tokens may all be of the same type. The conclusion of the argument is simply that in general this appearance cannot be explained away, but must be accepted. There is such a thing as identity of nature.
  3. I take this argument to be sound. But the argument is sometimes presented as an argument from general words. It is asked how a general term can be applied to an indefinite multiplicity of particulars. It is answered that these particulars must be identical in some respect. There are two disadvantages in presenting the argument in this linguistic fashion.
    1. First, it obscures the fact that the same term may apply in virtue of different natures of the different particulars. As a result, where Realism is embraced, it is likely to be a priori rather than scientific Realism.
    2. Second, presenting the argument linguistically encourages confusion with an unsound argument to universals7 from meaning.
  4. This second argument moves from the existence of meaningful general words to the existence of universals8 which are the meanings of those words. Universals9 are postulated as the second term of the meaning relation. The argument from ideal cases, such as Plato's perfect circle, is perhaps a special case of this semantic argument to universals10,
  5. I regard this second line of argument as completely unsound. Furthermore, I believe that the identification of universals11 with meanings (connotations, intensions), which this argument presupposes, has been a disaster for the theory of universals12. A thoroughgoing separation of the theory of universals13 from the theory of the semantics of general terms is in fact required. Only if we first develop a satisfactory theory of universals14 can we expect to develop fruitfully the further topic of the semantics of general terms. Philosophers have all too often tried to proceed in the opposite way.
  6. In this first volume, Nominalism and Realism, I criticize at length and reject various versions of Nominalism, together with Platonic Realism. I also examine and reject the view that properties and relations are as particular as the objects which have properties and relations. I conclude that we must admit objective universals15 which, however, cannot exist independently of particulars. I go on to examine the notion of a particular and reject the view that we can give an account of particulars as "bundles of universals16". The conclusion drawn is that particularity and universality, irreducible to each other, are both involved in all existence. I end the first book by sketching a world-hypothesis which admits nothing but particulars having (universal) properties and relations.
  7. The position reached at that point, though contested by many, is, at least in general outline, familiar enough. But in the second volume a detailed attempt is made to work out a theory of universals17 which is based upon natural science. In making this attempt, I enter relatively unexplored temtory. For with the exception of a suggestive paper by Hilary Putnam ("Putnam (Hilary) - On Properties", 1970) contemporary philosophers, at least, have largely ignored the possibility of developing a theory of objective universals18, where the particular universals19 admitted are determined on the basis of scientific rather than semantic considerations. It might perhaps be argued that Plato in his later works, Aristotle and the Scholastic Realists were ahead of contemporary philosophy in this matter, although handicapped by the relative backwardness of the science and the scientific methodology of their day,
  8. My contention is that, by accepting this a posteriori Realism, the theory of universals20, arguably the central problem of ontology, can be placed on a securer and more intelligible foundation than anything previously available. In particular, such a doctrine makes possible the reconciliation of an empiricist epistemology, which I wish to retain, with ontological realism about universals21.
  9. Not all particulars are first-order particulars. Universals22 themselves fall under universals23. That is to say, universals24 have certain properties and stand in certain relations to each other. In the final part of the second book an attempt is made to work out a theory of higher-order universals25, but, again, one which is compatible virfth an empiricist epistemology. Of quite particular importance is the topic of relations between universals26. For this topic may hold the key to an account of the nature of causation27 and of nomic necessity. By this means, it may prove possible to answer Hume without sacrificing Empiricism.
  10. Finally, a word on the phrase "a posteriori Realism". The phrase may suggest that the theory advanced in this work is supposed to be supported by a posteriori reasonings of the sort with which natural science has made us familiar. This is far from being the case. The reasoning will have the characteristically a priori flavour which philosophical reasonings, especially when they concern first philosophy, seem inevitably, if distressingly, to have. What is maintained is the proposition that what universals28 there are is to be determined a posteriori. The status of this proposition is, however, a further question. It may have to be established, if it can be established, by a priori or relatively a priori reasoning.

"Armstrong (David) - Predicates"

Source: Armstrong - Universals and Scientific Realism (Vol. 1: Nominalism and Realism), 1977, Chapter 1

  1. Predicates as linguistic expressions – 1
  2. Identity-conditions for predicates – 6

"Armstrong (David) - Predicate Nominalism"

Source: Armstrong - Universals and Scientific Realism (Vol. 1: Nominalism and Realism), 1977, Chapter 2

  1. Nominalism versus Realism – 11
  2. Varieties of Nominalism – 12
  3. Can predicates determine properties? – 17
  4. Predicate Nominalism and two infinite regresses – 18
  5. Predicates and possible predicates – 21
  6. Predicate Nominalism and causality1 – 22

"Armstrong (David) - Concept Nominalism"

Source: Armstrong - Universals and Scientific Realism (Vol. 1: Nominalism and Realism), 1977, Chapter 3

"Armstrong (David) - Class Nominalism"

Source: Armstrong - Universals and Scientific Realism (Vol. 1: Nominalism and Realism), 1977, Chapter 4

  1. Class Nominalism is committed to an ontology of classes – 29
  2. Mereological Nominalism – 34
  3. Class Nominalism and co-extensive properties – 35
  4. Can class-membership determine properties? – 36
  5. An argument from the identity-conditions for classes – 37
  6. Only some classes are natural classes – 38
  7. Class Nominalism and two infinite regresses – 41
  8. Class Nominalism and causality1 – 42

"Armstrong (David) - Resemblance Nominalism"

Source: Armstrong - Universals and Scientific Realism (Vol. 1: Nominalism and Realism), 1977, Chapter 5

  1. The Resemblance analysis – 44
  2. Over-determination of the paradigms – 48
  3. The symmetry of resemblance – 49
  4. Can resemblance to paradigms determine properties? – 50
  5. The possible non-existence of paradigms – 51
  6. Resemblance Nominalism and two infinite regresses – 53
  7. Resemblance Nominalism and causality1 – 56

"Armstrong (David) - Arguments for Realism"

Source: Armstrong - Universals and Scientific Realism (Vol. 1: Nominalism and Realism), 1977, Chapter 6

  1. Two statements about colours – 58
  2. Attribute variables – 62

"Armstrong (David) - Transcendent Universals"

Source: Armstrong - Universals and Scientific Realism (Vol. 1: Nominalism and Realism), 1977, Chapter 7

  1. The nature of the theory – 64
  2. What relation holds between particulars and Forms? – 66
  3. Can Forms determine properties? – 68
  4. The Forms and two infinite regresses – 69
  5. The Third Man – 71
  6. The Restricted Third Man – 72
  7. Transcendent universals1 and causality2 – 75
  8. Transcendent versus immanent universals3 – 75

"Armstrong (David) - Properties and Relations as Particulars"

Source: Armstrong - Universals and Scientific Realism (Vol. 1: Nominalism and Realism), 1977, Chapter 8

  1. Arguments for Particularism – 79
  2. Particularism and the Problem of Universals1 – 82
  3. The incoherence of Particularism – 86

"Armstrong (David) - Are Particulars Reducible to Universals"

Source: Armstrong - Universals and Scientific Realism (Vol. 1: Nominalism and Realism), 1977, Chapter 9

  1. The Identity of Indiscemibles – 91
  2. Another argument against the Bundle theory – 97
  3. Two further objections – 98

"Armstrong (David) - The Lockean Account of Particulars"

Source: Armstrong - Universals and Scientific Realism (Vol. 1: Nominalism and Realism), 1977, Chapter 10

  1. Unsound criticisms of the Lockean account – 103
  2. What is the relation between substratum and properties? – 104
  3. Another infinite regress – 106

"Armstrong (David) - Particulars and Universals"

Source: Armstrong - Universals and Scientific Realism (Vol. 1: Nominalism and Realism), 1977, Chapter 11

  1. The properties of a particular are not related to that particular – 108
  2. Are there two senses of the word "identity"? – 111
  3. States of affairs – 113
  4. Particularizing universals1 – 116
  5. Particularity and spatio-temporal position – 118
  6. Particularity and spatio-temporal position (continued) – 122

"Armstrong (David) - A World-Hypothesis"

Source: Armstrong - Universals and Scientific Realism (Vol. 1: Nominalism and Realism), 1977, Chapter 12

"Armstrong (David) - The Argument of Universals and Scientific Realism Vol. 2 (A Theory of Universals)"

Source: Armstrong - Universals and Scientific Realism (Vol. 1: Nominalism and Realism), 1977

Full Text
  1. Volume II is divided into four Parts. In the first Part, Predicates and Universals1, it is argued that predicates (predicate-types) are correlated with universals2 in a many-many rather than a one-one manner. Given a predicate applying to certain particulars, it may apply in virtue of many, one or no universals3. Given a universal there may be many, one or no predicates corresponding to it. It is the mistaken identification of universals4 with meanings, the meanings of predicates, which has prevented the realization that no simple correlation of predicates and universals5 can be found.
  2. It is argued in particular that if 'P' and 'Q' are distinct predicates, each applying in virtue of genuine universals6, then 'P v Q', '~P' and '~Q' do not so apply. There are no disjunctive or negative universals7. It is argued, however, that provided there is a particular to which both 'P' and 'Q' apply, then there is a universal, P&Q. There are conjunctive universals8. P and Q are proper parts of this conjunctive universal.
  3. But how is it determined when we have arrived at genuine generic identities, genuine universals9? It is argued that we have nowhere to begin but with the classifications which we naturally make. Natural science may then take us beyond these classifications to more deeply hidden classings and sortings which, it is our hope, approach more closely to an isolation of genuine universals10. Formal identity criteria for universals11 may be given. They are identical if and only if they bestow identical causal powers upon the particulars which fall under them. But the identification of universals12 must be a posteriori.
  4. In the final chapter of the first Part, it is argued that non-synonymous predicates may apply to the very same particulars in virtue of the very same universals13. Such predicates may stand to such universals14 in different fashions. Predicates may be said to "name", to "analyse" or else to be "external" to the universals15. All this casts light upon the nature of the so-called "contingent identification of properties", for example, colour with light-waves and mental states with physical states of the brain.
  5. The second Part of the volume, Properties and Relations, tries to advance first the theory of properties, and then the theory of relations, in a more direct manner. In the chapter on properties it is denied, pace Aristotle, that we need to recognize special sorts of monadic universals16 associated with stuffs and kinds (being gold and being an electron). An account of such universals17 can be given in terms of instantiated conjunctions of properties, and an instantiated conjunction of properties is a property.
  6. A classification of various categories of property is then made, including the important category of structural property. The properties (and relations) which go to make up a structural property do not qualify the very same particular which the structural property qualifies, but, rather, proper parts of that particular. In ch. 18 §v18 it is suggested that the "foundation in things" for the notion of number lies in non-relationally structural properties possessed by the particular which is the aggregate (not the class) of the things numbered.
  7. In ch. 19 ("Armstrong (David) - Relations") it is first argued that we do not need to recognize relational properties as anything over and above (non-relational) properties and relations. The question is then taken up whether all properties may not dissolve ad infinitum into structures of propertied-things-in-relation, so that there are no irreducible properties. It is concluded that this is possible, although it does not have to be so. The familiar distinction between internal and external relations is then drawn. It is argued that internal relations are reducible to properties of the "related" things. It is then tentatively suggested that all genuine (i.e. external) relations holding between first-order particulars are spatio-temporal relations. Finally, it is argued that particulars are never reflexively related. Any relation must relate at least two distinct particulars.
  8. The third Part of volume II, The Analysis of Resemblance, tries to give an account of various sorts of resemblance. The resemblance of particulars involves no especial difficulties. It is a matter of the resembling things' having certain properties. But certain cases of the "resemblance of universals19", for example that of the lengths among themselves and the colours among themselves, raise great difficulties. Difficulties are found in various projects:
    • to reduce such resemblances to the resemblance of (first-order) particulars;
    • to account for the resemblances in terms of common properties or relations of the universals20 involved (second-order properties and relations);
    • to account for the resemblances by drawing the distinction between determinable and determinate properties; and, finally,
    • in the attempt to give a subjectivist account of such resemblances.
  9. It is then argued that there are no determinable universals21, only determinates. The problem arises, what unifies classes of universals22 such as the determinate lengths or the determinate shades of colour. It is suggested that the unifying factor is a series of partial identities holding between different members of the class in question. The conjunctive properties P&Q and Q&R are partially identical. But in the case of the lengths, colours, etc., it is argued that the properties involved are structural properties. Hence the partial identities concerned are identities of parts of such structures. This solution can be rather easily applied to the case of the lengths. But it meets epistemological difficulties in the case of the colours, which appear to be simple and unstructured. It is suggested that the colours are in fact structural properties, although we are unable to perceive this structure.
  10. In the fourth and final Part of volume II, Higher-order Universals23, it is argued that there are second-order (and perhaps higher-order) universals24: properties and relations of properties and relations. But a thesis of Formalism is upheld. It is suggested that higher-order universals25 are restricted to formal or topic-neutral universals26, such universals27 as being complex as opposed to being a colour,
  11. The investigation of higher-order properties is of rather a tentative sort. In the case of higher-order relations, it is suggested that these are restricted to the relations between universals28 of (non-logical) necessitation, probabilification and exclusion. It is further suggested that these relations constitute the laws of nature. A law of nature, on this view, is something more than a mere uniformity in nature. It is a uniformity springing from a relation holding berween the universals29 involved. In this way, it is suggested, a Realism about universals30 is able to give a non-sceptical answer to the problem of what constitutes a law of nature. Causal connection is seen as a particular case of nomic connection.

In-Page Footnotes ("Armstrong (David) - The Argument of Universals and Scientific Realism Vol. 2 (A Theory of Universals)")

Footnote 18: "Armstrong (David) - Properties", Section “Numbers and Properties”.

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