# Online Encyclopedia

# 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 natural numbers, all else is the work of man."

Although most modern constructivists take a weaker view, they can trace the origins of constructivism back to Kronecker's finitist work.

Even stronger than finitism is *ultrafinitism* (also known as *ultraintuitionism*), associated primarily with Alexander Esenin-Volpin .

Last updated: 10-24-2004 05:10:45