David Lewis,

1
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?

2
Universals and Properties

• There are two differences between universals and
  properties
• A universal is supposed to be wholly present
  wherever it is instantiated. A property is
  spread around.
• Universals, in Armstrongs view, are sparse.
  Properties are whatever can be meaningfully
  predicated of things. (210)
• Properties are so abundant that they cant 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.

3

• 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)

4
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)

5
Duplication, Supervenience, and Divergent Worlds

• Lewiss 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.

6

• 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)

7

• 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)

8

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

9
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.

10
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).)