Neuroscience Perspective on the Foundations of Mathematics

Patrick Suppes (Stanford) gives a talk at the Workshop on Groundedness (26-27 October, 2012) titled "Neuroscience Perspective on the Foundations of Mathematics". Abstract: I mainly ask and partially answer three questions. First, what is a number? Second, how does the brain process numbers? Third, what are the brain processes by which mathematicians discover new theorems about numbers? Of course, these three questions generalize immediately to mathematical objects and processes of a more general nature. Typical examples are abstract groups, high dimensional spaces or probability structures. But my emphasis is not on these mathematical structures as such, but how we think about them. For the grounding of mathematics, I argue that understanding how we think about mathematics and discover new results is as important as foundations of mathematics in the traditional sense.