Fri Dec 1, 2017
Marianna Antonutti (LMU Munich)
What is ordinary mathematics?
The term “ordinary mathematics” is used to denote a collection of areas that are, in some sense, central to the practice of most working mathematicians, typically taken to contain such fields as number theory, real and complex analysis, geometry, and algebra. This notion has been taken for granted by both philosophers and logicians; for example, reverse mathematics is often described as the study of what set existence axioms are necessary to prove theorems of ordinary mathematics, and the ability to recover ordinary mathematics has been considered a key measure of the success of a foundational framework at least since Russell. However, the precise extent of this notion has not been explicitly discussed. This talk will propose two ways in which this notion can be made more precise. According to the first, ordinary mathematics is that part of mathematics that concerns countable or countably representable objects. According to the second, ordinary mathematics is that part of mathematics that does not make essential use of intrinsically set theoretic methods or concepts. I will discuss potential counterexamples to both views, and assess the prospects for formulating a precise account of the notion of ordinary mathematics.
This is joint work with Benedict Eastaugh.