Possible Worlds Semantics

Loux gives a great discussion on the topic of “possible worlds.”  This might seem irrelevant and arcane, but it is a powerful tool that helps us in discussions on the problem of evil, ontological argument, God’s foreknowledge, and human nature.  And it helps us understand Plantinga.

Modal notions: notions of necessity, possible, impossible, and contingent.

The empirical and nominalist traditions view modalities with suspicion (177).

  1. Leibnizian idea of possible worlds.
    1. To say that a proposition is true is to say that it is true in that possible world that is the actual world (181).
    2. Possible World (PW): the way the world might have been.
      1. De dicto: necessity or possibility applied to a proposition taken as a whole. A proposition has a certain property, the property of being necessarily true.
      2. De re: modal exemplification.  It is not talking about propositions, but about a property’s modal status (184).
      3. As propositions can be true or false in possible worlds, so can objects exist or fail to exist.
      4. To say that an object, x, has a property, P, necessarily or essentially is to
  2. Possible Worlds Nominalism
    1. David Lewis. Other possible worlds are “more things of that sort.”
      1. They are just further concrete objeccts.
      2. No causal relations tying objects from distinct worlds.  Hence, no transworld individuals.
      3. World-indexed property: a property a thing has just in case it has some other property in a particular possible world.
        1. Only world-bound individuals.
        2. It’s nonsensical to say, “That could have been me, had this happened” (as usual, nominalism goes against all prephilosophical notions).
  3. Possible Worlds Actualism: Alvin Plantinga
    1. A PW is part of the network of modal concepts and it can be understood only in terms of that network.
    2. We need concepts like de re and de dicto.
      1. Propositions are the subjects of de dicto modality.
    3. We must distinguish the existence of a property from its being exemplified.  We must distinguish the existence of a state of affairs from its obtaining (203).
      1. PWs are just states of affairs (SoA) of a certain kind.
      2. All SoA are necessary beings, so the PWs for them actually exist.  Not all of the PWs, however, obtain.
    4. A PW is a very comprehensive–maximally comprehensive SoA.
      1. One SoA may include or preclude another.
      2. PWs are SoA with a maximality property.
        1. The various PWs are abstract entities.
        2. It could have failed to obtain, but not failed to exist.
    5. Propositions have a property that no SoA does–that of being true of false (206).
      1. To say that a thing exists in a PW is not to say that it is physically contained or literally present in the world.  
      2. It is merely to make the counterfactual claim that had the world been actual, the thing would have existed.
    6. All of this is just another way of saying, “Things could have gone otherwise.”
    7. Leibnizian Essentialism: there are individual essences.
      1. A thing’s essence: the property such that the thing has it essentially and necessarily that nothing other than the thing has it.
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Some brief notes on nominalism

Nominalism seeks the simplest explanation in ontology.  One of their confusions regarding realism, though, is that they think universals have spatial location.  But as B. Russell pointed out, the universal “being north of” is not spatial.

The austere nominalist is committed to just one ontological category, particulars.  Austere nominalism runs into problems when it gets to the category of abstract particulars, such as “courage is a virtue.”

Metalinguistic Nominalism

Not universals; just linguistic expressions about nonlinguistic objects.  One of the difficulties, though, is it is forced to rely on type/token distinctions, which start to look like universals. It’s not hard to see connections with postmodernism.

Trope Theory

By far the most interesting.  Concrete particulars have colors, etc., but those attributes are just particulars.  So, if two objects have the color “red,” does that mean they share the universal “redness”?  Not necessarily.  Rather, they have the set of resembling trope red.  But isn’t a set a universal?  Not exactly.  Sets have clear-cut identity conditions.  Universals do not.  Sets are identical just in case all members are identical.  Set, α, is identical with set ,β , when the members of each set are identical with one another.

So this appears to give the trope nominalist an edge over the realist, except for one problem.  Take the referents

“Being a unicorn”

And

“Being a griffin.”

Since there are no such things as unicorns or griffins, they must belong to the set, null.  As Loux points out, “given the identity conditions for sets, there is just one null set,” which would mean both propositions are in fact identical.  But this is clearly false (91-92), as any schoolchild knows.

Other problems with trope nominalism (cf Moreland):

  • membership in a set of tropes is arbitrary (Moreland doesn’t expound)
  • Two red balls (A and B) resemble each other because they have red₁ and red₂ constituents.
    • The copula “is” in question is neither of predication or identity, but set membership.
    • Rejoinder:  why red and not green?  Red tropes resemble each other in a different way than green tropes?  Why?
  • If two tropes, Red and Sweet, are in the same location, how are they not identical on the Trope Nominalist view.