Encyclopedia > Finitism

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

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