  We now describe a template of an argument for the existence of mathematical objects. Since the first philosopher who developed an argument of this general form was Frege, it will be referred to as the Fregean argument. But the template is general and abstracts away from most specific aspects of Frege’s own defense of the existence of mathematical objects, such as his view that arithmetic is reducible to logic. Fregean logicism is just one way in which this template can be developed; some other ways will be mentioned below.