Purely Physical Explananda: Bistability in Perception

Abstract

Call an explanation of an empirical fact that appeals indispensably to mathematical facts: an extra-mathematical explanation. There has been a recent rush of attempts to establish the existence of such explanations. One of the challenges in doing so, however, is to find a case of explanation in which the explanandum is genuinely free of mathematics. In this chapter I first outline this challenge before drawing attention to an important class of explanations that seem to meet the challenge head on. The explanations in question are explanations that appeal to bistability: a situation in which the differential equations modelling a system have two roots, and thus the physical system has two stable states, but is unstable between them. I focus, in particular, on the case of perceptual bistability in which an ambiguous image of a duck-rabbit seems to ‘switch’ back and forth between the two disambiguations (duck and rabbit).