Review: David Lewis, Counterfactuals

A nightmarishly difficult account of modal logic. The general idea is simple, though. What is a counterfactual? Df. = strict conditionals corresponding to an accessibility assignment determined by similarity of worlds–overall similarity, with respects of difference balanced off somehow against respects of similarity (Lewis 9). Lewis argues that the following modal operators obtain:

⃣ → means “if it were the case that x, then it would be the case…”
◇→ means “if it were the case that x, then it might be the case…”

The following two counterfactuals are interdefinable

Ф ◇→ ⃣ =

1.2 Strict Conditionals
⃣ (Ф ⊃ψ)

Accessible worlds:

⃣ (Ф ⊃ψ) is true at i iff ψ is true at every accessible Ф world.

Propositions

Entities that can be true or false at worlds, and (2) there are enough of them (46).

Sets of worlds are propositions. Lewis: A proposition P is true at a world i iff i belongs to the proposition–the set–P. (What if a person can also be defined as a possible world? In which case we have the following: A proposition (or maybe its set) = a Possible World = a person. Thus, a proposition (or its set) = a person. Gordon Clark?)

An impossible proposition is an empty set (47).

Section 4 is his famous chapter on Possible Worlds. The gist of it is quite similar (even if the particulars are not!). A possible world is simply the way things could have been. Lewis, however, seems committed to the idea that there are things that exist which aren’t actual, but he tries to shore up this problem by saying that actual worlds are indexical (here, now, I). See his discussion on realism on p. 87.

All maximal consistent sets are indices (125)

Harassing the Hobgoblins: Intro to Analytic Theology

I am not an expert in analytic theology, and I have been critical of analytic philosophy in the past.  Nonetheless, it can be useful in clarifying concepts.  One problem is that people jump into the deeper waters, reading countless computer symbols and the analytic guys never bother to clarify what’s going on.  I’ll try.

Beginner

McCall, Thomas.  Introduction to Analytic Theology.  It is what the title says. He introduces some key concepts but doesn’t really get beyond Leibniz’s Law.  Still, anything McCall writes is worth getting.

Moreland, JP.  Love Your God with all your Mind.  What would it look like if you applied analytic reasoning to the development of the soul?

Morris, Thomas V.  Our Idea of God.  He doesn’t call it analytic theology, but it is an early essay into how it is done.  Wonderfully accessible.

Nash, Ronald.  The Concept of God.  Kind of a simplified version of Plantinga’s Does God have a Nature?  Some great responses to open theism.

Clark, Kelly.  Return to Reason.  This is the unsung volume in apologetics.

Intermediate

McCall, Thomas.  Which Trinity? Whose Monotheism?  Not primarily analytic theology, per se, but it is a great application of analytic theology.

Crisp and Rea, Analytic Theology: New Essays.  Some outstanding essays, some bleh.  Sadly, Rea, Wolterstorff, and possibly stump have surrendered the field on sexual ethics.

Craig and Moreland, Philosophical Foundations for a Christian Worldview.  Somewhat technical, but simply grand.

Moreland and Rae, Body and Soul.  Outstanding defense of substance dualism.  Moreland writes with Kingdom Power.

Moreland, JP.  Kingdom Triangle.  Triangulates (sorry) analytic theology with continuationist theology.

Morris, Thomas V. Logic of God Incarnate.  Rescues Christology from the contradiction charge.  Several very important concepts introduced.

Plantinga and Wolterstorff.  Faith and Rationality.  Almost as important historically as it is philosophically.

Richards, Jay Wesley. The Untamed God.  Introduces modal concepts and show where they advance beyond Aristotle.

Advanced

Kripke, Saul.  Naming and Necessity.  Some technical chapters, but a mostly accessible work on language and possible worlds.

Lewis, David.  Counterfactuals.  Very difficult, but Lewis does walk you through his method, so it is readable.

Plantinga, Alvin. Nature of Necessity.  One of the most important philosophy works in the last century.  Possible Worlds matter.

———–.  Does God Have a Nature? Plantinga got accused of denying simplicity in this book.  I never saw where he did so.  Great primer on how to do analytic theology.

———–.  Warrant and Proper Function.   Clears up a lot of (perhaps deliberate) misunderstanding on what Plantinga means by “warrant.

———.  Warranted Christian Belief.  Application of his previous two books.

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.