Going further, my proposed convention also suggests that “Cartesian frames” should perhaps be renamed to “Cartesian factorizations”, which I think is a more immediately interpretable name for what they are. Then in your equation S=A×E, you can refer to A and E as “Cartesian factors”, satisfying your desire to treat A and E as interchangeable. And, you leave open the possibility that the factors are derivable from a “Cartesian partition” r=a⊔e of the world into the “Cartesian parts” a and e.
There is of course the problem that for some people “Cartesian” just means “factoring into coordinates” (e.g., “Cartesian plane”), in which case “Cartesian factorization” will sound a bit redundant, but for those people “Cartesian frame” is already not very elucidating.
My default plan is to not try to rename Cartesian frames, mostly because the benefit seems small, and I care more about building up the FFS ontology over the Cartesian frame one.
Going further, my proposed convention also suggests that “Cartesian frames” should perhaps be renamed to “Cartesian factorizations”, which I think is a more immediately interpretable name for what they are. Then in your equation S=A×E, you can refer to A and E as “Cartesian factors”, satisfying your desire to treat A and E as interchangeable. And, you leave open the possibility that the factors are derivable from a “Cartesian partition” r=a⊔e of the world into the “Cartesian parts” a and e.
There is of course the problem that for some people “Cartesian” just means “factoring into coordinates” (e.g., “Cartesian plane”), in which case “Cartesian factorization” will sound a bit redundant, but for those people “Cartesian frame” is already not very elucidating.
My default plan is to not try to rename Cartesian frames, mostly because the benefit seems small, and I care more about building up the FFS ontology over the Cartesian frame one.
I agree that “Factorization” is a good, erm, framing for Cartesian Frames