finitism

In the philosophy of mathematics, the view that the only legitimate numbers are finite: ‘God created the integers, the rest is the work of man’ (L. Kronecker). In mathematics the restriction to finitary methods was advocated by David Hilbert. It shares with constructivism the view that one cannot assert the existence of a mathematical object without indicating how to construct it. It adds the principle that one should never deal with the set of all the objects of an infinite totality. That a theorem holds for all members of such a set simply means that for any particular member of the set one can repeat the argument.