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Universals or properties are posited by philosophers to explain the similarity of numerically different things. When we say, for instance, that there are "two people driving the same car", it is common sense for most people that they are driving two different cars but those cars have shared properties - they are made by the same company, are the same model and year, are the same color, have the same engine and so on. In the language of this branch of metaphysics, the two cars are particulars, but those particular cars share properties, attributes or universals.

In discussion of universals, properties are usually distinguished from relations: a person may drive a red car, but they may be three inches taller than their brother. The former is a property, but the latter is a relation.

How do philosophers understand universals? The two ends of the spectrum of opinion are realism and nominalism. Realists hold that universals exist in some sense - that a red bus and a red book both have the property of red, and that this property is the same in both. Nominalists, on the other hand, deny this - stating instead that there are similarities between things, but that these can be explained by appeal to language, concepts, some shared resemblance between particulars, or classes with some primitive notion of naturalness.

The first philosopher to discuss properties that we know of is Plato in the Parmenides dialogue, and throughout the other dialogues as 'the Forms'. One problem with the notion of universals is whether it is possible for a universal to exist even if no particulars hold that universal. According to Plato, the Forms have a non-physical existence - that even if we were to destroy all the bottles in the world, the Form of the bottle would exist both before and after the particular individual bottles. Aristotle rejected the idea of universals existing outside of the particular instances. The Form of a bottle exists inside each individual bottle[1]. Realism has been held by modern philosophers including Bertrand Russell, J. P. Moreland[2] and D. M. Armstrong[3], while nominalism's contemporary advocates have included Willard Van Orman Quine, David Lewis and Gonzalo Rodriguez-Pereyra[4]. Trope theory is another response to the problem of universals, and is advocated by Chris Daly, D. C. Williams[5], G. F. Stout and J. Cook Wilson - the former two posit particulars and abstract particulars (tropes) while the latter says universals are tropes. D. M. Armstrong is critical of this latter view pointing out that "[o]nce one has accepted universals, the tropes seem to become redundant (or vice versa)".[6]

Forms of nominalism

There are a variety of ways to try and explain sameness of type without admitting a distinction between universals and particulars - these are forms of nominalism. Nominalists tend to say that we quite naturally talk about properties and relations between things, but we cannot infer the existence of universals from mere talk (any more than we could infer the existence of God or natural rights from the utterances of 'Thank God!' or 'You are breaching my rights.'). Why deny the existence of universals beyond the mere talk of universals? A fundamental desire of those in metaphysics is to follow Ockham's razor and reduce the number of things in existence to the minimum number we absolutely need to posit.

A simple form of nominalism is that of Predicate Nominalism. A Predicate Nominalist says that something is, say, green because the predicate 'is green' can be applied to it. D. M. Armstrong provides some good reasons for rejecting predicate nominalism. Predicate nominalists have transferred the explanation of a thing's greenness from the thing to the word that represents the property. This has only shifted the problem. What is it that makes it so that 'grass is green' is true and 'the stapler is green' is not? It also leads to some counter-intuitive results - few sensible people would deny that an atom is made up of protons, neutrons and electrons - and that the predicate 'contains electrons' has a truth value. They would agree that things have always been made up of protons, electrons and neutrons, even before we had any words to describe them. Even if no predicate existed to describe how the atom contains electrons, the property is still there. Armstrong states that the Predicate Nominalist has to give an account of this phenomena using the language of "possible predicates". Realism and other forms of nominalism dodge this difficulty.[7]

Class Nominalism is the view that for a thing to be of a certain type is to say that it exists within a particular class (strictly, in a particular set). Armstrong gives a very simple negation of this idea by pointing to empty classes. The class of all unicorns is empty and the class of, say, goblins is also empty. The nil class - that is, the class with no members - is the same. Thus, being a unicorn ultimately becomes the same as being a goblin. This seems counterintuitive for most people. Even if they grant that unicorns do not exist and goblins do not exist, if something were to appear in front of them, they could be reasonably sure of whether or not it is a unicorn. Even if a list of necessary and sufficient conditions could not be drawn up of what makes something a unicorn, enough conditions could be listed to state that something cannot be both a unicorn and a goblin.[8]

Class nominalist theories have to figure out a way of distinguishing those classes which are natural from other classes. The class of all red things is more natural in some sense than a all things which are either red or older than fifty years old. Anthony Quinton suggests that this notion of naturalness is primitive and not analyzable any further. Against Quinton, resemblance nominalists like H. H. Price suggests that we can determine natural classes on the basis how the things inside that class resemble each other.

Some nominalists have just refused to provide any expansion of their theories to explain some of the problems that realists see in them. Michael Devitt has coined the rather amusing term 'ostrich nominalist' to describe those who adopt a nominalist position whilst ignoring the One over Many argument (he also refers to those who accept realism solely on the basis of the One over Many argument to be 'mirage realists'[9]

Realist theories

There are a number of ways of dividing up those who subscribe to a realist view of universals: roughly, into Platonists and Aristotelians, and into those who accept a bundle of universals view of particulars and those who believe particulars are substances with attributes.

Those who take a Platonic view of universals see them as transcendent of time and space, and are willing to accept that a universal may exist even though it has not been instantiated by a particular. J. P. Moreland defends the Platonic view of universals. The Aristotelian, immanent view of universals rejects any view which commits them to uninstantiated universals. D. M. Armstrong is a leading defender of this latter view:

Once you have uninstantiated universals you need somewhere special to put them, a "Platonic heaven," as philosophers often say. They are not to be found in the ordinary world of space and time. And since it seems that any instantiated universal might have been uninstantiated--for example, there might have been nothing past, present or future that had that property--then if uninstantiated universals are in a Platonic heaven, it will be natural to place all universals in that heaven.[10]

Armstrong suggests that the argument in Plato that one needs uninstantiated universals (or in Plato's language "Forms") can be understood in a number of different ways. Firstly, it can be understood as a thesis about meaning - that one needs a relationship with a transcendent Form in order to give backing to some sentences. This, Armstrong suggests, is unsatisfactory given the sort of work a theory of meaning has to do.

Secondly, Armstrong suggests that the defender of uninstantiated universals may appeal to a problem of "ideal limits" - that although there are not perfect circles in reality, there are imperfect circles, and it is possible to reason about perfect circles. Plato uses the ideal Forms as a way to back ethical statements with an objective ideal - even though the subject of those statements may only approximate them in the same way that a drawing of a circle can approximate the ideal Form of the circle. Armstrong says that you do not need to postulate universals for the problem ideal Forms attempt to solve: you can simply use predicates or concepts. Ideal limits, for Armstrong, are simply "conceptual devices used to classify actual instances by reference to the degree of divergence that therw ould be between the actual and the ideal instances if the latter were to exist".[11]

Armstrong rejects uninstantiated universals - and Platonic transcendent universals - because they are incompatible with his naturalistic project. But a similar appeal can be made as to the strangeness of Aristotelian universals. Take the synthetic element ununbium (Uub, aka. Copernicum - Cn). Before February 9, 1996, ununbium did not exist - it had never been synthesised. When the lab synthesized it in 1996, they apparently synthesised it and simultaneously synthesised the matching ununbium universal. A simple modal appeal changes this - if the lab had discovered it a month earlier, would the universal have been created then? If only one atom were synthesised, does the universal appear when the second atom gets synthesised? This kind of thought strikes some philosophers as rather queer.

The difference between the substance-attribute and bundle view of universals is simply this: the substance-attribute theorist believes that there is some core substance, and the instantiation of the universals provides attributes, while the bundle theorist sees the particular as no more than a collection of property instantiations. This distinction applies to both realist views and to tropes.

The substance-attribute view is adhered to by most of the philosophers who accept universals throughout history - Armstrong states that it is the "traditional" view of particulars. C. B. Martin accepts a substance-attribute view, but the attributes are tropes rather than universals. Armstrong holds to a substance-attribute view too. The traditional reason to be sceptical of the substance-attribute view is an epistemological one: you can come to know the attributes of a particular (you can see that the ball is red because you can see the ball), but we do not have any reasonable way to come to have knowledge of the substance.

The competing bundle view is held by Bertrand Russell in Human Knowledge, Its Scope and Limits, and is also held in trope form by G. F. Stout and by D. C. Williams. The bundle theorist denies the underlying substance. Leibniz's law of the Identity of Indiscernibles comes into play in this debate. Those subscribing to substance-attribute views can use the substance to individuate two particulars. Individuating bundles becomes more difficult. Any two particulars must differ in the universals they instantiate. If one wants to place limits on what is an acceptable universal, one may face more problems if one cannot fall back on substances to individuate. For instance, Armstrong limits his universals to those which are required by science (the "scientific realism" of the title Universals and Scientific Realism); others may wish to do so for other reasons. Armstrong also casts doubt on the state of relations for a bundle theorist.

Individuation is very simple for Stout and Williams' trope bundle theory. Each property is itself an individuated particular organised into resemblance classes. Therefore, as the properties are individuated, individuating particulars that instantiate the 'same' set of properties isn't a problem (because the properties aren't the same!).


  1. Of course, now we know that the Form of living things is in a sense contained inside each particular as DNA.
  2. J. P. Moreland, Universals, Central Problems of Philosophy series
  3. See Universals: An Opinionated Introduction, the two-volume Universals and Scientific Realism, and Stephen Mumford's David Armstrong.
  4. Rodriguez-Pereyra's book Resemblance Nominalism defends a resemblance nominalist view with an appeal to realist modal worlds
  5. D. C. Williams, "The Elements of Being" in D. C. Williams and Charles Thomas, The Principles of Empirical Realism
  6. D. M. Armstrong, Universals: An Opinionated Introduction, p. 17
  7. D. M. Armstrong, Universals: An Opinionated Introduction, p. 11.
  8. D. M. Armstrong, Universals: An Opinionated Introduction, p. 12.
  9. Michael Devitt, "'Ostrich Nominalism' or 'Mirage Realism'?", Pacific Philosophical Quarterly, 61 (1980) 433-9, and in D. H. Mellor and Alex Oliver's Properties (Oxford Readings in Philosophy).
  10. D. M. Armstrong, Universals: An Opinionated Introduction, p. 76
  11. D. M. Armstrong, Universals and Scientific Realism vol. 1 Nominalism and Realism - ch. 7 "Transcendent Universals".