The concept of group and the theory of perception

Prompted by the title of Ernst Cassirer's 1944 essay, the origin of the idea of a Group theoretical approach, in the mathematical sense, in vision science is here explored, as well as the several ways in which its implementation had been attempted. That object recognition might proceed by a more generative approach rather than by separate individual cataloging had already been argued by Kant, and Cassirer examined how mathematical group theory might be called on for this purpose, in view of the success of its use in geometry and in the physical sciences. However, such a promise appears unlikely in view of the categorical differences between analysis of mental phenomena and of the physical world.