Ch. 3: Simple Axiom

Sider writes:

Lewis denied laws as generalizations in the best system—the deductive system, cast in a language whose predicates express natural properties and relations, that best balances the virtues of simplicity and strength. The restriction on the language of the best system is essential; otherwise, as Lewis (1983b, p. 367) points out, a simple and maximally strong theory could be given with a single, simple axiom, ∀xFx, where F is a predicate true of all and only things in the actual world. All true generalizations would be counted as laws.

I’d like to get a bit more clear about just why this “simple axiom” would prove illicit by Lewis’s lights. The thought seems to be that this predicate does not express a perfectly natural property or relation. But why should this be? For illustration, assume supersubstantivalism. By assumption, every actual entity is simply a chunk of the spacetime manifold. Thus, F is guaranteed to apply to all actual entities just in case F expresses the property “is a portion of the spacetime manifold”. Doesn’t this seem to be a perfectly natural property?

The point may be more obvious if we ignore the supersubstantivalist assumption and just stipulate that the actual world is composed of all and only the material objects. Thus, so long as F has the value “is material,” it applies to every actual entity. But on superficial examination this seems to me entirely licit: isn’t “is material” a perfectly natural property, or at any rate as good a candidate as any we have?

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One thought on “Ch. 3: Simple Axiom

  1. This is very interesting topic! I have not though about this part of Lewis in the way Sider presents it before.

    I think I agree with Lewis that there is something wrong with allowing this simple axiom to determine laws. First, it seems to me that the predicate “is material” is not a natural property. In our world, materiality is grounded in the space time manifold, though in another world that resembles ours phenomenally, materiality may be grounded in corpuscles. The property of materiality can therefore be grounded in multiple properties, making it disjunctive and thus is not perfectly natural (Similar discussion about the property “heat” in Lewis 1983b, p. 369). Despite this, I think the “simple axiom” idea is still alright here because, as Sider says, the predicate must be true of only things in the actual world and the predicate “is material” is not.

    I think the biggest problem with accepting the simple axiom is that the predicate “is actual” applies generally to all and only things in the actual world, and thus would be considered a law. But the property of being actual is not a natural property; a perfect duplicate of the actual world would lack it. And more importantly, the property of actuality does not contribute anything to the world that bears it, it is about as extrinsic and non-natural as properties come. This seems to contradict the idea that laws should be intrinsic and fundamental, making the simple axiom too inclusive!

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