Noah Schweber

The notion of computable function lies comfortably at the intersection of philosophy and mathematics – it describes something intuitively meaningful, and has a satisfying formalization which matches soundly with that intuition (this is Church’s thesis). However, this is true only in a restricted context, namely when we look at functions *of natural numbers*. When we try to generalize computability substantially, we run into both philosophical and mathematical problems. After saying a bit about why generalizing computability theory is something we should be interested in doing, I’ll present some approaches to generalized computability and where they run into problems (and hopefully some ideas for how to get around those problems).