In psychology, as in physics, principles approach universality only if formulated at a sufficiently abstract level. Among the most fundamental principles are those of generalization and inductive inference and those of perceptual and mental transformation. With respect to their appropriate abstract representational space, the former principles are well formulated as (Bayesian) integration over suitable (e.g., connected) subsets of points in the space, and the latter as geodesic (hence, least-time) paths between points in the space. Critics sometimes insufficiently appreciate the following: (a) Generality requires such abstraction. (b) Perceptual principles are not themselves given in sensory input. (c) Principles of learning are not themselves learned. (d) Though all such principles are somehow instantiated in the brain, their ultimate, nonarbitrary source must be sought in the regularities of the world – including those reflecting abstract mathematical principles (e.g., of group theory and symmetry). New light may thus be shed on the cognitive grounds of science and ethics.