Aside:

Essentially, the STV is an argument that much of the apparent complexity of emotional valence is evolutionarily contingent, and if we consider a mathematical object isomorphic to a phenomenological experience, the mathematical property which corresponds to how pleasant it is to be that experience is the object’s symmetry.

I don't see how this can work given (I think) isomorphism is transitive and there are lots of isomorphisms between sets of mathematical objects which will not preserve symmetry.

Toy example. Say we can map the set of all phenomenological states (P) onto 2D shapes (S), and we hypothesize their valence corresponds to their symmetry along the y=0 plane. Now suppose an arbitrary shear transformation applied to every member of S, giving S!. P (we grant) is isomorphic to S. Yet S! is isomorphic to S, and therefore also isomorphic to P; and the members of S and S! which are symmetrical differ. So which set of shapes should we use?

Trivial objection, but the y=0 axis also gets transformed so the symmetries are preserved. In maths, symmetries aren't usually thought of as depending on some specific axis. E.g. the symmetry group of a cube is the same as the symmetry group of a rotated version of the cube.

*0 points [-]Mea culpa. I was naively thinking of super-imposing the 'previous' axes. I hope the underlying worry still stands given the arbitrarily many sets of mathematical objects which could be reversibly mapped onto phenomenological states, but perhaps this betrays a deeper misunderstanding.