Nominalism

4. The twentieth century

Like ontological debates in earlier periods, ontological discussions in early analytic philosophy typically focused on the problem of universals. Thus, Frege, Moore and Russell were all anxious to undermine nominalistic theories that seek to analyse subject-predicate discourse without reference to nonlinguistic universals; and when the later Wittgenstein attacks the view that the use of a general term like ‘game’ is grounded in the antecedent recognition of a property or set of properties common to all the items to which the term applies, he is, among other things, challenging their Platonistic accounts of subject-predicate discourse (see Wittgenstein, L. §10). Although concern with universals has continued throughout the twentieth century, the investigations of recent nominalists bear on a wider range of issues than those of their medieval and classical modern forbears. In addition to concern with universals, contemporary nominalists attempt to provide reductive accounts of things as diverse as the mathematician’s sets, propositions, states of affairs, events and possible worlds, and philosophers of a nominalistic spirit take different attitudes towards different items on this list. Some, for example, are nominalists with regard to the traditional universals while insisting on a Platonistic account of sets; others insist on the irreducibility of events while providing reductive accounts of discourse apparently about propositions, states of affairs and universals. Indeed, few philosophers have been willing to defend a nominalistic approach to all of the so-called abstract entities. One exception is Wilfred Sellars (see Sellars, W. §2).

The account given by Sellars is an elaboration of Ockham’s suggestion that talk about abstract entities is metalinguistic discourse. This suggestion had previously been elaborated in a proposal by Rudolf Carnap The Logical Syntax of Language that we construe talk about abstract entities as pseudo-material mode discourse, discourse apparently, but not really about nonlinguistic objects (see Carnap, R. §3). Carnap’s concern is with sentences of the following sort:

His proposal is that we treat these sentences as disguised ways of making claims about the syntax of certain linguistic expressions. Thus, (1)-(4) become:

The difficulty with this proposal is that (1)-(4) turn out to be claims about English expressions. The proposal forces us to take the Spanish counterparts of (1)-(4), for example, to be claims about Spanish words, so that (1)-(4) and what are supposed to be their Spanish translations do not even agree in reference. Sellars responds to this problem by introducing a kind of quotation that cuts across languages, called dot quotation. Whereas standard quotation of the sort we meet in (1′)-(4′) creates metalinguistic expressions that apply exclusively to words in the quoting language, the application of Sellars’ dot quotation to an expression creates a metalinguistic common noun that is true of all those expressions, regardless of language, which play the same linguistic role that the quoted expression plays in the base language. Thus, ‘ $\cdot \mathrm{man}\cdot$ ’ is a common noun true of ‘hombre’, ‘homme’, and ‘Mensch’. In their respective languages, these terms play the same role that ‘man’ plays in English; they are all ‘ $\cdot \mathrm{man}\cdot$ ‘s. Now, Sellars wants to claim that using the machinery of dot quotation, we can provide a satisfactory reconstruction of (1)-(4) as:

As Sellars understands them, (1′′)-(4′′) represent claims about linguistic expressions construed as tokens rather than types; and talk of linguistic tokens can be recast as talk about speakers and inscribers. Even the apparent Platonism involved in talk about linguistic roles is illusory since talk about linguistic roles can be eliminated by reference to talk about the linguistic rules that govern the use of terms. Accordingly, talk apparently about abstract entities is consistent with the most austere nominalism; it is merely metalinguistic discourse that cuts across languages.

Sellars believes that the sort of account he proposes for (1)-(4) can be extended to handle all discourse involving the so-called abstract entities. A slightly less radical form of nominalism is found in the writings of W.V. Quine (see Quine, W.V. §6). Early in his career, Quine espoused a nominalism as austere as that developed by Sellars, but by the time he wrote Word & Object (1960), he had concluded that there is one kind of abstract entity whose existence we have to acknowledge, the mathematician’s set or class. Quine remains unwilling to recognize things like properties, relations, kinds, and propositions, however. Unlike sets, these alleged entities lack clear-cut identity conditions and should play no role in our ontology.

Most contemporary philosophers agree with Quine that we must endorse an ontology of sets. This view provides the backdrop for the reductive approach to universals defended by G.F. Stout and D.C. Williams. They hold that there are particular as opposed to general qualities or properties, things like the whiteness of this piece of paper. So there are abstract entities besides sets; but they are one and all particulars. Williams calls these abstract particulars tropes and he tells us that they constitute ‘the alphabet of being’. Tropes are ontologically primitive, and items from other categories are constructions out of them. Thus, the universal of the Platonist is a set of resembling tropes; and familiar concrete objects are bundles of tropes that contingently enter into a relation of ‘collocation’.

Although Williams’ trope-theoretic nominalism continues to enjoy some popularity, the most prominent form of nominalism in the contemporary arena is that influenced by developments in the semantics of modal logic, where we meet the idea that the actual world is just one of infinitely many possible worlds and that the totality of possible worlds constitutes the subject matter for talk about necessity and possibility (see Possible worlds). Contemporary nominalists claim that the framework of possible worlds provides the resources for a genuinely reductive account of things like properties and propositions. These philosophers propose that we take possible worlds as primitive. Each such world, they claim, can be characterized in nominalist terms as a totality of concrete particulars, and they argue that we can provide a nominalist treatment of things like properties and propositions by identifying them with set-theoretical entities of a transworld sort. We can identify properties with functions from worlds to sets of objects, relations with functions from worlds to sets of ordered n-tuples and propositions with sets of worlds or functions from worlds to the truth values. The most prominent proponent of this sort of view is David Lewis (see Lewis, D. §3). He has invoked the framework of possible worlds not simply to provide an account of properties and propositions, but to clarify the concept of meaning, to state truth conditions for counterfactuals, and to provide an analysis of causation (1986).