Finitism: a radical position in the philosophy of mathematics according to which a mathematical object exists only if can be derived from ►natural numbers in a finite sequence of steps. Thus, finitists reject all irrational and real numbers, ►set theory, and infinitude in any form or shape. Their most famous representative was the German mathematician Leopold Kronecker, who in the 19th century led a relentless crusade against the infinite sets postulated by his former disciple ►Georg Cantor. He is credited with the famous saying, "God made the natural numbers; all else is the work of man." However, since finitism by its very nature dismisses various broad and useful areas of mathematics, it has few remaining supporters.
