# Finitism

In the

philosophy of mathematics,

**finitism** is an extreme form of

constructivism, according to which a mathematical object does not exist unless it can be constructed from

natural numbers in a

finite number of steps.
(Most constructivists, in contrast, allow a

countably infinite number of steps.)
The most famous proponent of finitism was

Leopold Kronecker, who said:

- "God created the integers, all else is the work of man."

Although most modern constructivists don't take such a strong view, they can trace the origins of constructivism back to Kronecker's finitist work.

Even stronger than finitism is the *ultraintuitionism* (or *ultrafinitism* as it is now more commonly known) of A. S. Esenin-Vol'pin.