Armstrong,

1
Armstrong, The Nature of Possibility

• Armstrong advocates a combinatorial theory of
  possibility a combination of given, actual,
  elements.
• What does that mean? There are things in this
  world with their properties, and we generate a
  possible world by combining given, known,
  properties in different ways.
• This view also appeals to Wittgensteins
  Tractatus Logico-Philosophicus.

2

• Naturalism and Realism
• My central metaphysical hypothesis is that all
  there is, is the world of space and time. It is
  this world which is to supply the actual elements
  for the totality of combinations. So what is
  proposed is a naturalistic form of a
  combinatorial theory. (184a)
• Naturalism the space-time world is all there
  is. (186b)

3

• For Armstrong, the world contains
• Individuals a, b, And individuals will have
  spatial and temporal parts. (To be an individual,
  a thing must fall under a concept. (185b))
• Properties F, G, These are simple
  properties, to be conceived of as universals.
  I.e. a property may be possessed by more than one
  individual.
• Relations R, S, Like properties they are
  universals.
• What universals there are is to be determined a
  posteriori by natural science.
• States of affairs (or facts) According to
  Armstrong the existence of individual a and
  property F does not suffice to show that a is F.
  Rather, as being F is a state of affairs.

4
An argument for states of affairs

1. If something is to be an individual, then it must
   be one thing.
2. But, to be one thing, it must fall under a
   concept.
3. For something to fall under a concept is for it
   to have a predicate or property or stand in
   relation to some other thing or property. (I.e.,
   one must be able to formulate the proposition, a
   is F)
4. For any proposition, there must be some state of
   affairs that is its truth-maker.
5. Therefore, states of affairs are at the bedrock
   of our ontology.

5
Wittgenstein worlds

• Take an individual a and two properties F and G.
  There are two statements a is F and a is G.
  The former is true i.e., there is a state of
  affairs that is the truth-maker of that
  proposition. But a is G has the same form as
  the atomic proposition a is F. Therefore, it
  describes a (merely) possible state of affairs.
• But note this cant be so simple. Mustnt we
  also say that F and G have to be properties of
  some appropriate kind? E.g., let a ball, F
  red, and G B-flat Major. So the ball is red
  and the ball is (in) B-flat Major are
  comparable propositions and the latter is
  (merely) possible?

6
Haecceities and Quiddities

• Consider the following states of affairs
• Fa Gb
• Ga Fb
• Fa Ga Fb
• Fa Fb Gb
• Fa Ga Gb
• Ga Fb Gb
• Fa Ga Fb Gb
• Are I and II, III and IV, V and VI the same
  worlds?

7

• The haecceitist holds that these sets of worlds
  differ the anti-haecceitist denies it.
• Strong and weak anti-haecceitism a strong
  anti-haecceitism denies that individuals are
  anything more than the bundles of their
  properties. (p. 59) For the strong
  anti-haecceitist world VII collapses into a one
  individual world. The weak anti-haecceitist does
  not collapse world VII into the single individual
  world.
• Armstrong rejects strong anti-haecceitism, says
  choice is between weak anti-haecceitism and
  haecceitism.