The Finitism reference article from the English Wikipedia on 24-Jul-2004 (provided by Fixed Reference: snapshots of Wikipedia from wikipedia.org)

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 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.

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