Frege's triangle and the existence of mathematical objects (Q2713189)

The triangle in question is a scheme representing Frege's classification of concept, meaning, and referent. The author examines a number of mathematical philosophies in the light of their interepretation of this triangle. For example, starting with a relabeling of the vertices as sign, meaning, and value, the author interprets the sign vertex as symbol (for formalism) and logical concept (for logicism); the meaning vertex is interpreted as algorithmic procedure for intuitionism and constructivism and mathematical activity in the sociocultural philosophy of mathematics; and the value vertex is interpreted as objects of the physical world for physicalism, realities for realism, eidos for platonism, and mathematical objects for mathematical platonism.