Universals

The concept of universals arises very naturally from the observation that things are similar to one another and that thanks to these similarities they can be grouped in various categories. Classification of objects is the foundation of all knowledge, and without it we wouldn’t be able to discover and describe any regularities. Most probably even the language that we speak would not be possible without things being similar in different respects. A natural metaphysical explanation of the fact that two things of a given kind (trees, chairs, electrons) have “something in common” is that there exists a certain object that stands in a particular relation to those things. For instance, two red flowers can be said to resemble one another because there is a third object, redness, that is somehow present in both flowers.

Thus the notion of a general object – a universal – is born. The fundamental relation that is supposed to hold between ordinary things (which we will now refer to as “particulars”) and universals can be called “instantiation” or “exemplification”. The colour red is instantiated, or exemplified, by various red objects. Hence we can broadly characterize universals as entities that are exemplified (more formally: u is a universal if and only if there is an x such that x exemplifies u), while particulars can exemplify but are never exemplified themselves. We can distinguish two categories of universals: monadic and polyadic. Monadic universals are instantiated by individual objects, while polyadic universals are exemplified by pairs, or more generally n-tuples of objects. Monadic universals are primarily properties, although some insist to identify a separate category of monadic universals, namely kinds. Polyadic universals, on the other hand, comprise relations of many arguments (such as being the father of, or being a child of two parents). We can also distinguish universals of the first order, which are instantiated by particulars only, and universals of higher orders, instantiated by other universals.

Postulating the existence of universals helps us analyzing some semantic features of basic subject-predicate statements of the natural language. If we consider the statement “Socrates is courageous”, it can be said to be true when the object described as “Socrates” exemplifies the property represented by the predicate “is courageous” (i.e. courage). However, the predicate “is courageous” cannot be said to refer to (to be the name of) the property of being courageous. Two different semantic functions have to be distinguished: that of denoting (referring, naming) and that of connoting. The predicate “is courageous” denotes all courageous people, but connotes courage. On the other hand, the name “Socrates” denotes an individual, but connotes nothing (there is no property with respect to which we call an individual “Socrates”). Thus, the semantic analysis of statements of the form “a is P” is as follows: this statement is true if the object denoted by “a” exemplifies the universal connoted by “P”.

The assumption of the existence of universals can also account for the phenomenon of abstract reference of natural language. Abstract reference is visible in sentences of the following sort: “Redness is a colour”, “Courage is a moral virtue”, “This rose and this tulip have the same colour”, “Each object has a property that no one will ever know”, “The relation of being an ancestor is the smallest relation satisfying the following conditions: if x is a parent of y, x is an ancestor of y, and if x is an ancestor of y and y is an ancestor of z, then x is an ancestor of z”. The terms “redness”, “courage”, “colour”, “moral virtue”, “property”, “the relation of being an ancestor”, can be naturally interpreted as denoting (not connoting!) universals. (Exercise: read all the past lectures and find sentences containing abstract reference there.)

The ontological position accepting the existence of universals is called metaphysical realism (realism in short), and its negation is referred to as nominalism. The unrestricted version of realism maintains that for every meaningful predicate of natural language there is a universal connoted by it. But it is highly unlikely that this version of realism could be true. Let us consider the following example: the predicate “has inertial mass m or electric charge q”. While it is natural to expect that the separate predicates “has mass m” and “has charge q” indeed connote some properties, the disjunctive predicate is unlikely to pick a new property. After all, it is unintuitive to assume that an object that has mass m and no electric charge, and another object that has a different mass m’ but electric charge q”, have something in common by virtue of this very fact. Moreover, disjunctive properties typically do not figure in causal explanations or laws of nature.

There is a more formal argument that can be made against the unrestrained version of realism. Let us consider the predicate “is not exemplified by itself”. If this predicate connotes a property, then a contradiction ensues, for it will be true that this property exemplifies itself if and only if it does not exemplify itself. This argument is a version of Russell’s famous paradox of the class of all classes that are not their own elements.

This lecture is based on Chapter 1 "The Problem of Universals I" of Michael Loux's book Metaphysics: A Contemporary Introduction. You are advised to read the entire chapter.