Wolfgang Schwarz

Some Thoughts on Fundamental Structural Properties

Fundamental (or 'perfectly natural') properties are properties on whose distribution in a world all qualitative truths about that world supervene. That is, whenever two worlds are not perfect qualitative duplicates, they differ in the distribution of fundamental properties.

This is not the only job discription for fundamental properties. If it were, far too many classes of properties could play that role. For instance, all qualtiative truths trivially supervene on the distribution of all properties, or on the distribution of all intrinisic properties, or (for what it's worth) on the distribution of all extrinsic properties. (That's because no two things, whether duplicates or not, ever agree in all extrinsic properties.)

One of Lewis' further constraints is that the fundamental properties should all be intrinsic. Another is that they should provide a minimal basis for qualitative difference: the qualitative truths should, if possible, not be completely determined by a proper subset of the fundamental properties.

As the distribution of structural properties is determined by the distribution of simpler properties over smaller things, one might expect that no structural property is fundamental. Lewis disagrees (except in "Ramseyan Humility", where he switches terminology and uses "fundamental" for "simple and fundamental"):

I am following Armstrong, mutatis mutandis, in declining to rule out perfectly natural properties that are conjunctive or structurally complex. ("New Work", p.37)

The reason he gives (both here and in "Against Structural Universals", and in "Ramseyan Humility", where the fundamental properties are called "near-enough fundamental") is that the world might be infinitely complex, with 'structures all the way down'.

However, from the existence of such worlds it does not follow that no simple, non-structural properties are instantiated there. Complex objects can instantiate simple properties. It might even turn out that all truths about such worlds are determined by their distribution of simple properties. So a further argument is needed, but I cannot find one in Lewis or Armstrong.

(Perhaps Lewis was aware of the missing step. On p.12 of "New Work" he writes: "If the world were infinitely complex, there might be no way to cut down to a minimal basis". Similarly in Fn.4 of "Ramseyan Humility". If he believed that infinite complexity entails lack of simple properties I guess he should have used "would" instead of "might".)

Here is an argument for the opposite thesis, that structural properties are always redundant.

1. Assumption: Worlds W1 and W2 differ in the distribution of structural properties (and thereby fail to be duplicates).

2. Definitions: Let A be an arbitrary mereological atom; let S be the set of all A-duplicates together with all duplicates of W1; let Q be the property being a member of S.

Consequences:

3. W1 and W2 are not both atoms. (By 1., they differ in the distribution of a structural property, and atoms can't do that.)

4. Q is intrinsic. (It is a disjunction of intrinsic properties.)

5. Q is simple. (Structural properties never belong to atoms.)

6. Either W2 is an atom or W1 and W2 differ in the distribution of Q. (For by 1., W2 is not a duplicate of W1.)

7. If W2 is an atom, W1 and W2 differ in the distribution of the simple intrinsic property being an atom. (From 3.)

8. If W2 is not an atom, W1 and W2 differ in the distribution of the simple intrinsic property Q. (From 4., 5. and 6.)

9. W1 and W2 differ in the distribution of simple intrinsic properties. (From 7. and 8.)

So the assumption that two infinitely complex worlds could differ in the distribution of structural properties without differing in the distribution of simple intrinsic properties is inconsistent.

That is, if our job description for fundamental properties is that a) they are all simple, b) they are all intrinsic and c) they account for all qualitative truths and differences, infinitely complex worlds provide no reason to worry that the description may be unsatisfied.

Lewis endorsed (b) and (c) but not (a). Why? Was it because he thought by endorsing (b) and (c) he did enough to give "fundamental" a determinate meaning that rules out (a), perhaps because a specific class of properties satisfying (b) and (c) but not (a) is a very powerful reference magnet? Perhaps. More likely, he rejected (a) because he added further descriptive conditions besides (b) and (c), conditions that undermine (a). Particularly relevant in this respect seems the condition that sharing of a natural property should always make for intuitive resemblance: my Q hardly satisfies that.

But suppose there was another philosopher who agreed with Lewis that a primitive distinction between fundamental and other properties is needed, for instance in a theory of laws or a theory of content, but who added that all these properties must be simple, even if that makes them less directly relevant for intuitive resemblance. Could we find out who is right? I don't know how we could. Then how can we trust that Lewis's job description for fundamental properties is the right one?

When philosophers give different job descriptions for something, that doesn't necessarily mean that they really disagree. It often only means that they use the relevant term in different ways. But the situation I have in mind is not of this kind. For instance, both parties claim that what they call "fundamental properties" figure in laws of nature, not the less fundamental properties their opponent calls "fundamental properties". They cannot both be right.