Consider three questions about the metaphysics of properties:
– What is the cardinality of the set of actually instantiated perfectly natural properties?
– What is the cardinality of the set of possible perfectly natural properties?
– Are any possible perfectly natural properties uninstantiated at the actual world?
Even if the answer to the first two questions is the same, this does not fix an answer to the third question. I’ll look at the first two questions in a future post, but for today I’ll concentrate on the third.
Call a world at which all possible perfectly natural properties are instantiated a maximal world. Although on some views of modality it might be that no worlds are maximal, it does seem to follow from the common Humean view that distinct perfectly natural properties are freely recombinable that some worlds are maximal (at least: size and shape of spacetime permitting). The question I’m interested in in this post is: what kinds of considerations might lead us to think that the actual world is or is not maximal?
Another way of putting the same question is: why should we believe in alien properties? This version of the question will of course be favoured by those who think there is no reason to believe in aliens, and who wish to shift the argumentative burden onto those who think the actual world is or might be non-maximal. The implied argument in this challenge is an argument from ideological parsimony. We can explain all of the phenomena with which we can have causal interaction without positing alien properties; so why posit them?
An interesting form of this parsimony argument appeals to the nature of reference. Here’s an initial stab:
1. We can only refer to contingently-instantiated properties if we have causal transaction with those properties.
2. We have no causal transaction with alien properties.
3. We cannot refer to alien properties.
4. We cannot grasp propositions which involve the existence of any entity to which we cannot refer.
5. We should not assign any credence to a proposition that we cannot grasp.
6. We should not assign any credence to the existence of alien properties.
This argument is not a very good one. If there are alien properties, then I have (plurally) referred to them in this very sentence. So 3) will be rejected by anyone who posits alien properties.
We might try to rescue this argument by explicitly restricting it to singular reference. But then we get a rather different conclusion:
1a. We can only refer to contingently-instantiated properties if we have causal transaction with those properties.
2a. We have no causal transaction with alien properties.
3a. For any property F, if F is alien then we cannot singularly refer to F.
4a. We cannot grasp propositions which are solely about entities to which we cannot singularly refer.
5a. We should not assign any credence to a proposition that we cannot grasp.
6a. For every property F, if F is alien then we should assign no credence to the proposition that something is possibly F.
The conclusion of the second argument is much weaker than the first. And it is not sufficient to support a prohibition on positing alien properties.
Consider an analogy from cosmology. We believe there are stars beyond the visible universe. We ourselves cannot have any causal interaction with them during our lifetimes, but light from them will reach our solar system in about one billion years time. Call any star which is more than one billion light-years beyond the edge of the currently-visible universe an alien star. We can formulate the following argument about them:
1b. We can only refer to contingently-instantiated objects if we have causal transaction with those properties.
2b. We have no causal transaction with alien stars.
3b. For cannot refer to alien stars.
4b. We cannot grasp propositions which are solely about entities to which we cannot singularly refer.
5b. We should not assign any credence to a proposition that we cannot grasp.
6b. For every object F, if F is an alien star then we should assign no credence to the proposition that F exists.
This argument calls for no revisions in cosmology. Obviously we cannot know anything at all about individual alien stars, but this presents no obstacle to an inference to the best explanation to their existence.
Of course, the analogy is not perfect. We inhabit a common spacetime with the alien stars, and so even if we can enter into no causal interactions with them, we can still be causally connected, as our future light cones overlap with theirs. And we arguably share a common cause with alien stars – the big bang. But it is hard to see why these disanalogies should make a difference. These sorts of causal relationships still aren’t sufficient to ground singular reference.
If these arguments are correct, then there is no obstacle to positing alien properties as part of a metaphysical inference to the best explanation. This was the line taken by David Lewis: a version of modal realism with alien properties came out, he thought, better in the overall cost-benefit analysis than a version of modal realism without alien properties. Here is the whole of his argument from On the Plurality of Worlds:
A world to which no … properties are alien would be an especially rich world. There is no reason to think we are privileged to inhabit such a world. Therefore any acceptable account of possibility must make provision for alien possibilities. (OPW p.92)
This argument is prima facie puzzling, in the light of methodological manuoevres that Lewis makes elsewhere. In responding to an argument that modal realism leads to inductive scepticism, as there are many more worlds in which induction is reliable than worlds where it is reliable, Lewis denies that we can formulate any preferred measure over the space of possibilities. The cardinality of worlds with alien properties is infinite, and so is the cardinality of worlds without.
Thus, by Lewis’ own lights, a belief in the existence alien properties cannot be based on the thought that if there were no alien properties, our world would be objectively special in virtue of being maximal. Even if our world is maximal and recombination holds, we can still find a measure over the space of worlds which makes the maximal worlds predominate over the non-maximal ones.
Of course, the thought that maximal worlds are special is a very natural one. It looks strange to say that the world could have lacked some properties, but that it could not have instantiated any extra properties. But it isn’t easy to make this vague thought more precise.
If we believed that the actual world contains only finitely many perfectly natural properties, then that might provide a route to denying property maximality. I’ll talk about this in a future post.