Tuesday, May 3, 2016

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.

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