David Lewis has written on several areas of philosophy (metaphysics, mind, logic, language), but is best known for his work on counterfactuals (conditionals such as ‘If kangaroos had no tails, they would topple over’). Lewis analyses such conditionals in terms of possible worlds, and in so doing espouses ‘extreme modal realism’—see Robert Stalnaker’s article in Loux 1979. Extreme modal realism—as it emerges from Lewis’s Counterfactuals (1973) On the Plurality of Worlds (1986) and articles in the Philosophical Papers—is ‘the thesis that the world we are part of is but one of a plurality of worlds, and that we who inhabit thisi world are only a few out of all the inhabitants of all the worlds’ (1986, p. vii). Moreover, the claim that there is a plurality of worlds is, Lewis maintains, an existential one.

The notion of similarity between worlds functions here as a primitive and raises issues concerning, for instance, identity across worlds (Lewis’s position on which has been criticized by Saul Kripke in ‘Identity and necessity’: see Moore 1993 below), but it offers Lewis a standpoint from which to treat other matters. Modality on his analysis becomes quantification (what is possible is what is the case at some world, what is necessary is what is the case at all worlds, and so on for ‘the impossible’ and ‘the contingent’). Similarly, the articles ‘Causation’ and ‘Events’ (in 1987) analyse both phenomena in terms of counterfactuals as Lewis conceives them. Lewis’s version of modal realism has, however, been criticized by, among others, P.Forrest and D.M.Armstrong (Australasian Journal of Philosophy 62 (1984):164–8), and moderate modal realists such as Robert Stalnaker (see his contribution in Loux) have instead attempted to interpret ‘possible worlds’ in terms of states of affairs or possible histories of the world (Lewis rejects ‘ersatz modal realism’, as he calls this position, in chapter 3 of 1986, and replies to other criticisms in chapter 2).

In the introduction to volume 2 of Philosophical Papers (1987) Lewis writes that much of his work seems to advance the thesis of ‘Humean supervenience…the doctrine that all there is to the world is a vast mosaic of local matters of particular fact’ (p. ix): the world is the sum of all space-time points and qualities at them—‘all else supervenes on that’. Lewis’s materialism motivates his contributions to the philosophy of mind (see the articles collected under that heading in volume 1 of Philosophical Papers, 1983), in which he has developed ‘a broadly functionalist theory of mind, according to which mental states qua mental are realizers of roles specified in commonsense psychology’ (p. xi).

Lewis’s more recent concern has been with the philosophy of mathematics. In Parts of Classes (1991) he attempts a mereological reduction of set theory: parts of classes are subclasses (the null set not being a genuine class), and singletons (unit classes) are their mereological atoms; Lewis’s axiomatization of set theory makes singletons the primitives of his theory. If, as Lewis believes, ‘most of mathematics is into set theory up to its ears’ (p. 58), then his structuralist treatment of set theory results in the nominalization of mathematics.

Sources: A.W.Moore (ed.) (1993) Meaning and Reference, Oxford; AJP 62, 1984; IWW; WW(Am); DAS; Burkhardt.