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 Wittgenstein’s Tractatus Logico-Philosophicus.

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)

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, a’s being F is a state of affairs.

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.

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 can’t be so simple. Mustn’t 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?

Haecceities and Quiddities

Consider the following states of affairs:

I. Fa & GbII. Ga & FbIII. Fa & Ga & FbIV. Fa & Fb & GbV. Fa & Ga & GbVI. Ga & Fb & GbVII. Fa & Ga & Fb & Gb Are I and II, III and IV, V and VI the same worlds?

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.