David Lewis, “New Work for a Theory of Universals” The Problem of the One over the Many: Many different particulars can all have what appears to be the same nature. This appearance cannot be explained away, but must be accepted. (cf. argument at 213b) In other words, the appearance of oneness (sameness or similarity) suggests real oneness. Or, is it simply the case that there only particulars?

Universals and Properties There are two differences between universals and properties: 1)A universal is supposed to be wholly present wherever it is instantiated. A property is spread around. 2)Universals, in Armstrong’s view, are sparse. Properties are whatever can be meaningfully predicated of things. (210) Properties are so abundant that they can’t be counted upon to do work in scientific theories. (cf. 211a) But if we had an elite class of natural properties, the story would be different.

“Let us say that an adequate theory of properties is one that recognizes an objective difference between natural and unnatural properties; preferably, a difference that admits of degree. A combined theory of properties and universals is one sort of adequate theory of properties.” (211b) A nominalistic theory could work here, too. We need natural and unnatural properties to provide an adequate supply of semantic values for linguistic expressions. (cf. 212ab) “I also think that it is properties that we need in characterizing the content of our intentional attitudes.” (213a)

One over Many Not only does a theory of universals answer the problem of the one over the many, but an adequate nominalism does so as well. “An adequate Nominalism, of course, is a theory that takes Moorean facts of apparent sameness of type as primitive…” (214a)

Duplication, Supervenience, and Divergent Worlds Lewis’s aim is to distinguish natural and unnatural properties. Consider duplicates. (215-16) We analyze duplication in terms of shared properties. But to do this we need to distinguish between intrinsic and extrinsic properties. So, two things are duplicates iff they have precisely the same intrinsic properties. But how do we define intrinsicality? In terms of duplicates. Property P is intrinsic iff, for any two duplicate things, not necessarily from the same world, either both have P or neither does. Property P is extrinsic iff there is some such pair of duplicates of which one has P and the other lacks P. (216a) In other words, we have “a tight little circle of interdefinability.”

We ought to analyze duplication in terms of shared properties. Begin with natural properties. “On my analysis, all perfectly natural properties come out intrinsic.” But the converse is not true. (216b)

Two topics involving duplication: supervenience and divergence. Supervenience “To say that so-and-so supervenes on such-and-such is to say that there can be no difference in respect of so-and-so without a difference in respect of such-and-such.” (217a) Supervenience theses are reductionist. (217a) Supervenience theses usually involve the notion of qualitative duplication. (217b)

Divergent worlds Divergent worlds are useful in defining Determinism. 1)A system of laws of nature is Deterministic iff no two divergent worlds both conform perfectly to the laws of that system. 2) A world is Deterministic iff its laws comprise a Deterministic system. 3)Determinism is the thesis that our world is Deterministic.(218ab)

Minimal Materialism We can formulate the thesis of materialism as a supervenience thesis: no difference without a physical difference. Final formulation (M5): “Among worlds where no natural properties alien to our world are instantiated, no two differ without differing physically; any two such worlds that are exactly alike physically are duplicates.” The job of physics is not only to discover laws and causal relations but also to discover natural properties.

Laws and Causation We need natural properties to explain lawhood. Lewis favors a regularity analysis of causality (more later). Laws are regularities of natural properties. Just as the analysis of laws requires natural properties so does the analysis of causality. (Counterfactual analysis of causation (again more later).)