Lewis is most famous for his work in metaphysics, philosophy of language and semantics, in which his books On the Plurality of Worlds (1986) and Counterfactuals (1973) are considered classics.

His works on the logic and semantics of counterfactual conditionals are broadly used by philosophers and linguists along with a competing account from Robert Stalnaker; together the Stalnaker–Lewis theory of counterfactuals has become perhaps the most pervasive and influential account of its type in the philosophical and linguistic literature.

His metaphysics incorporated seminal contributions to quantified modal logic, the development of counterpart theory, counterfactual causation, and the position called "Humean supervenience".

He went on to Swarthmore College and spent a year at Oxford University (1959–60), where he was tutored by Iris Murdoch and attended lectures by Gilbert Ryle, H. P. Grice, P. F. Strawson, and J. L. Austin.

Sometimes one of the solutions is "salient", a concept invented by the game-theorist and economist Thomas Schelling (by whom Lewis was much inspired).

(this particular state Lewis calls common knowledge, and it has since been a frequent topic of discussion among philosophers and game theorists), then they will easily solve the problem.

This treatment of counterfactuals is closely related to an independently discovered account of conditionals by Robert Stalnaker, and so this kind of analysis is called Stalnaker-Lewis theory.

Linguist Angelika Kratzer has developed a competing theory for counterfactual or subjunctive conditionals, "premise semantics", which aims to give a better heuristic for determining the truth of such statements in light of their often vague and context-sensitive meanings.

[12] What made Lewis's views about counterfactuals controversial is that whereas Stalnaker treated possible worlds as imaginary entities, "made up" for the sake of theoretical convenience, Lewis adopted a position his formal account of counterfactuals did not commit him to, namely modal realism.

Most often the idea that there exist infinitely many causally isolated universes, each as real as our own but different from it in some way, and that alluding to objects in this universe as necessary to explain what makes certain counterfactual statements true but not others, meets with what Lewis calls the "incredulous stare" (Lewis, On the Plurality of Worlds, 2005, pp. 135–137).

Lewis acknowledges that his theory is contrary to common sense, but believes its advantages far outweigh this disadvantage, and that therefore we should not be hesitant to pay this price.

[citation needed] Another criticism of the realist approach to possible worlds is that it has an inflated ontology—by extending the property of concreteness to more than the singular actual world it multiplies theoretical entities beyond what should be necessary to its explanatory aims, thereby violating the principle of parsimony, Occam's razor.

Among his prominent students were Robert Brandom, L. A. Paul, J. David Velleman, Peter Railton, Phillip Bricker, Cian Dorr, and Joshua Greene.

Lewis suffered from severe diabetes for much of his life, which eventually grew worse and led to kidney failure.

The transplant allowed him to work and travel for another year, before he died suddenly and unexpectedly from further complications of his diabetes, on October 14, 2001.

[15] Since his death a number of posthumous papers have been published, on topics ranging from truth and causation to philosophy of physics.

Lewis's monograph Parts of Classes (1991), on the foundations of mathematics, sketched a reduction of set theory and Peano arithmetic to mereology and plural quantification.