Mathematics and Aspect-Seeing

I discuss the relevance of aspect-seeing to mathematics. Mathematical proofs, I argue, often involve re-descriptions, and typically give us new ways of seeing. They do that by leading us to a sort of reflective position, which is akin to the mental position from which we see aspects—see things anew, as we can re-see Jastrow’s duck-rabbit as a rabbit instead of a duck. From this position, we can examine our pre-mathematical, ‘primitive,’ sense of things, which, contingent as it is, guides the formation of mathematical practices and concepts and grounds them. I conclude by positioning my view between realism and antirealism in mathematics.