## Monday, February 6, 2023

### Eliminating contingent relations

Here’s a Pythagorean way to eliminate contingent relations from a theory. Let’s say that we want to eliminate the relation of love from a theory of persons. We suppose instead that each person has two fundamental contingent numerical determinables: personal number and love number, both of which are positive integers, with each individual’s personal number being prime and an essential property of theirs. Then we say that x loves y iff x’s love number is divisible by y’s personal number. For instance suppose we have three people: Alice, Bob and Carl, and Alice loves herself and Carl, Bob loves himself and Alice, and Carl loves no one. This can be made true by the following setup:

Alice Bob Carl
Personal number 2 3 5
Love number 10 6 1

While of course my illustration of this in terms of love is unserious, and only really works assuming love-finitism (each person can only love finitely many people), the point generalizes: we can replace non-mathematical relations with mathematizable determinables and mathematical relations. For instance, spatial relations can be analyzed by supposing that objects have a location determinable whose possible values are regions of a mathematical manifold.

This requires two kinds of non-contingent relations: mathematical relations between the values and the determinable–determinate relation. One may worry that these are just as puzzling as the contingent ones. I don't know. I've always found contingent relations really puzzling.