Abstract

Mathematical objects, according to intuitionists, exist only in the mind of the mathematician. Such objects are, in reality, structures which are created by the mathematician. Creation of such structures is limited by the capability of the mind to generate sequences of objects. Knowledge of mathematical objects or structures is possible through the mind’s capability to survey or inspect the structures that it has created. The platonist, contrary to the intuitionist, maintains that mathematical objects have an existence which is not causally dependent on the mind of the mathematician. Such objects, he believes, are not created through the mind’s activity. Both platonists and intuitionists agree that there are mathematical objects; they disagree with respect to the causal origin of such objects.