Determinates vs. values

Spot has a mass of 10kg, while Felix has a mass of 8kg. The standard Platonic way to model the facts expressed by this is to say that Spot and Felix both have the determinable property of mass and they also have the determinate properties mass-of-10kg and mass-of-8kg, respectively. But there is another Platonic way to model these facts. Rephrase the beginning statement as: "Spot masses 10kg while Felix masses 8kg." The natural First Order Logic rendering of the English is now: Masses(spot, 10kg) and Masses(felix, 8kg). In other words, there is a relation between Spot and Felix, on the one hand, and the two respective values of 10kg and 8kg, on the other.

The determinate property approach multiplies properties: for each possible mass value, it requires a property of having mass of that value. The value approach, on the other hand, introduces a new class of entities, mass-values. So far, it looks like Ockham's razor favors the standard determinate property approach, since we don't want to multiply classes of entities.

However, the determinate property approach has some further ideology. It requires a determinable-determinate relation, which holds between having mass and having mass m. The mass-value approach doesn't require that. We can define having mass in terms of quantification: to have mass is to mass something (∃x Masses(spot, x)). Moreover, the value approach might be able to greatly reduce the number of values it posits. For instance, mass, length and charge values could all simply be real numbers in a natural unit system like Planck units. If one thinks that the Platonist needs mathematical objects like numbers anyway, the additional commitment to values comes for free. Further, the determinate property approach requires positing either a privileged bijection relation (or set of bijection relations) between mass values and non-negative real numbers or enough mathematical-type relations between mass determinates (e.g., a relation of one mass determinate being the sum of two or more mass determinates) to make sense of the mathematics in laws of physics like F=Gmm'/r².

There is also a potential major epistemological bonus for the value approach if the values are real numbers. Standing in a mass relation to a particular real number will be causally relevant. Thus, real numbers lose the inertness, the lack of connection to concrete beings like us, that is at the heart of the epistemological problems for mathematical Platonism.

All that said, I'm not enough of a Platonist to like the story. Is there a non-Platonic version of the story? Maybe. Here's one wacky possibility after all: Values are non-spatiotemporal contingent and concrete beings. They may even be numbers, contingent and concrete nonetheless.

Spacetime: Beyond substantivalism and relationalism

According to substantivalism, spacetime or its points or regions is a substance, and location is a relation between material things and spacetime or its points or regions. According to relationalism, location is constituted by relations between material things. Often, the two views are treated as an exhaustive division of the territory.

But they're not. Lately, I've found myself attracted to a tertium quid which I know is not original (it's a story other people, too, have come to by thinking about the analogy between location and physical qualities like charge or mass). On a simplified version of this view, being located is a determinable unary property. Locations are simply determinates of being located. This picture is natural for other physical qualities like charge. Having charge of 7 coulombs is not a matter of being related to some other substances--whether other charged substances or some kind of substantial "chargespace" or its points or regions. It's just a determinate of the determinable having charge.

This determinate-property view is more like the absolutism of substantivalism, but differs from substantivalism by not positing any "spacetime substance", or by making the locations into substances. Locations are determinates of a property, and hence are properties rather than substances. If nominalism is tenable for things like charge or mass, the theory won't even require realism about locations.

Becoming charged

Suppose I become negatively electrically charged. I then acquire a bunch of dispositional properties, such as the property of repelling electrons and attracting positrons. But have I gained any basic dispositional properties?

One could take one of two views here:

1. In becoming charged, I took on new basic dispositional properties characteristic of charge.
2. Prior to being charged, I already had the dispositional property of being such as to repel electrons and attract positrons when negatively charged.

On the first view, charge is a dispositional property. On the second view, charge is not a dispositional property per se, but a triggering condition for a dispositional property I already had. An advantage of the first view is that it helps explain why it is that charge makes anything that has it be ceteris paribus attractive to electrons and repellent to positrons. On the second view, it is just a coincidence or a matter of divine arrangement that all the material things there are have the dispositional property stated in (2). On the other hand, the second view is slightly neater in a different way, because it allows one to say that all dispositional properties are grounded in the essences of things. I suspect that only a generalization of the first view lets one preserve the Catholic view that pursuit of the supernatural end of human life is something graciously superadded on top of our nature.