Getting More from External Relations

A speculative post. Consider two cases where it has been thought that substantive new metaphysics would be needed:

  • ‘Strong’ emergence, to allow for the apparent conceptual possibilities of wholes whose properties don’t supervene on the properties of their parts.
  • Haecceities, to ground identity and distinctness for individuals in the light of mirror worlds.

In each case, more familiar metaphysics turns out to be able to do the job for us. We just need to appeal to the right perfectly natural external relations (PNERs):

  • ‘Weak’ emergence: emergent properties are the result of perfectly-natural-external-relation(-non-spatio-temporal) (PNERNSTs) holding between the elements. The correct supervenience thesis is not supervenience of whole on parts, but supervenience of whole on parts plus the PNERs they stand in to one another. (Consider two spatiotemporally isolated spheres, and contrast with two adjacent spheres. The wholes composed by the pairs are not intrinsically similar.)
  • Anti-haecceitism: Individuals can be ‘weakly discerned’ by their place in a network of irreflexive PNERs. No two worlds differ merely by a permutation of individuals.

It’s tempting to try to extend this strategy from haecceities to quiddities, given the close similarity between these two kinds of mysterious entity. Instead of positing:

  • Quiddities, to ground identity and distinctness for properties in the light of mirror worlds;

we can appeal to PNERs between properties:

  • Anti-quidditism: Properties can be ‘weakly discerned’ by their place in a network of irreflexive PNERs. No two worlds differ merely by a permutation of properties.

The PNERs that hold between properties are not of the same kind as the PNERs that hold between individuals, of course. The former are nomic relations, such as are expressed directly in the equations that figure in the fundamental laws of nature. The latter we might call configuration relations: they’re usually taken to be spatio-temporal relations and entanglement relations and possibly more.

All sides agree that configuration relations are recombinable, at least to a limited degree: many patterns of configuration relations are possible. But necessitarians deny that nomic relations are recombinable. In fact, it is open to the necessitarian to draw the distinction between nomic relations and configuration relations in this modal way: configuration relations are whichever PNERs admit of some recombination. That in turn promises a novel-looking necessitarian account of the difference between individuals and properties: individuals are those things which only stand in configuration PNERs, while properties are those things which only stand in nomic PNERs.

What of the other cases – things that stand in no PNERs, and things that stand in both kinds of PNER? I think the former kind of thing is otiose: what possible grounds could we ever have to posit them? The latter kind of thing might conceivably be wanted, though; perhaps tropes would fit the bill, or some located entity which featured directly in the laws of nature (God? The Universe?).

Getting More from External Relations