Abstract

Throughout mathematics there are constructions where an object is obtained as a limit of an infinite sequence. Typically, the objects in the sequence improve as the sequence progresses, and the ideal is reached at the limit.

I introduce a view that understands this as a process by which a single dynamic mathematical object develops toward a goal. This view is analogous to the endurantist position in the metaphysics of time, although it does not involve time; rather, it highlights a commonality between the temporal trajectory of an object and this type of mathematical construction.

For example, just as a plant starts as a seed and then develops by adding and removing cells through time, so too does the approximation to pi obtained from the Leibniz series develop, starting at 4, then subtracting 4/3, adding 4/5, subtracting 4/7, and so on. In both cases, there is a strong intuition that we are dealing with a single object that maintains its identity throughout the process, because each change is naturally viewed as a modification of a single object, rather than the creation of an entirely new object.

This view is supported by a general philosophical discussion, by a formal framework for dynamic mathematical objects that develop through processes, and by applications to a variety of mathematical processes where it has significant advantages, including the revision semantics of truth.