I have started to notice a common theme in the things in which I am interested lately. That is conventionality. Perhaps this is something I should pay more attention to.

In terms of general philosophy, Carnap has been quite intriguing. This started with an (admitted) caricature of Carnap in Penelope Maddy's recent books. The major point was something like mathematics is conventional in that at some point, some people agreed on rules of inference and stating that things existed and changes to that system have only developed on pragmatic grounds of the goals of the social activity.

In less of a caricature, Carnap really had something called language-planning more in mind. That is, the purpose of a logician of science was to come up with myriad formal systems of logic and math such that the natural scientist can figure out which is the most useful for their activities.

Strangely, Carnap still maintains that there is bifurcation of geometry into mathematical geometry and physical geometry. This is based on the idea that there is a correct (true) geometry of space. This seems rather strange to me, and I am planning on writing about it before the end of the quarter.

In my (mostly naive) view, the mathematics used in physics is just a model that has proved useful for accounting for empirical data in a "good" way. That is, idealising space as a Riemannian manifold is better than as a Euclidean manifold, not because the Riemannian model is more correct, but rather that it is just more useful, perhaps on account of its simplicity.

Back to convention, however, Quine talks about the (conceptual) impossibility of the development of logic by convention, and this view is rightly doubted by Skyrms based on intuition from evolutionary game-theoretic models of the evolution of conventional meaning in Lewis signalling games. I think it would be quite interesting to see something resembling logical inference develop in a game-theoretic population model, but being able to do that myself is still a bit of a ways off.