I’ve just come back from a CMM discussion of Lewis on Quantities (built around John Hawthorne’s paper of that title).
One thing that came up was the issue of what you might call potentially “cross level” fundamental properties. These are properties that you might expect to find instantiated at the “bottommost” microphysical level, but also instantiated “further up”. For example, electrons have negative charge; but so do ions. But ions are composite entities, which (from what I remember of A-level chemistry) are charged in virtue of the charges of their parts.
Clearly in some sense, electrons and ions can have the same determinate property: e.g. “charge -1”. But, when giving e.g. a theory of universals, I’m wondering whether we have to say that they share the same Universal.
On Armstrong’s theory of quantities, it looks to me that we won’t say that the ion and the electron both instantiate the same Universal. The “charge -1” we find instantiated by the ion will be a structural universal, composed of the various charge Universals instantiated by the basic parts of the ion. The “charge -1” we find instantiated by an electron, on the other hand, looks like it’ll be a basic, non-structural universal. So, it seems to me, it’ll then be a challenge to Armstrong’s account to say why these two universals resemble each other in a tight enough way that we apply to them the same predicate. (To avoid confusion, let’s call the former “ur-charge -1” and leave “charge -1” as a predicate that applies to both ions and electrons, though not, on this view, in virtue of them instantiating the same Universal).
Let’s suppose we’re looking at a theory of universals (such as the one Lewis seems to contemplate at various points) which is just like Armstrong’s except for ditching all the structural universals. Electrons get to instantiate the Universal “ur-charge -1”. But ions, as actual-worldly complex objects, instantiate no Universals at all. Of course, again there’s the challenge to spell out exactly what the conditions are under which we’ll apply the predicate “charge -1” to things (roughly: when the various ur-charges instantiated by their parts “balance out”—though the details get tricksy).
What goes for charge can go for various other types of property. So we may find it useful to distinguish ur-mass 1kg (which will be a genuine basic universal) from the set of things “having mass 1kg”.
A last thought. What is the relation between mass properties and ur-masses? In particular, is it the case that things can only ever have masses when their basic parts have ur-masses? I don’t see any immediate reason to think so. Perhaps the actual world is one where things have mass in virtue of their parts having ur-mass. But why shouldn’t we think that “having parts that have ur-masses” is but one *realization* of mass: and that at other worlds quite different ur-properties may underlie mass (say, ur-mass-densities, rather than ur-masses). That’s potentially significant for discussions of modality and quantities: for two worlds that intially seem to be share the same stock of fundamental properties (spin, charge, mass, etc) may turn out to actual contain alien properties from each others point of view: if one contains ur-masses underlying the (non-fundamental) mass properties, while the other contains ur-mass-densities underlying those same properties.
(Thanks to all those at CMM for the discussion that led to this. This is x-posted at Metaphysical Values. And thanks to an anonymous commentator, who pointed out in an early version of this post that by “free radicals” I meant “ions”!)