Platonism

Platonism is a philosophy of mathematics, which holds that mathematical concepts are objects ("forms"), existing independently of man's mind, that cannot be perceived through the senses.

Platonism is one of the ~three philosophies which dominate modern mathematics, the others being Intuitionism and Formalism/Logicism. However, few if any mathematicians adhere consistently to any of those three philosophies.

Platonism dates back to Plato and Socrates. The term "Platonism" is also sometimes used to refer to the philosophy of Plato generally.

Examples

In this section, I will show some examples of implicitly Platonic things written by working mathematicians.

The purpose of this section is to justify my claim that the premises of Platonism are widespread

modern mathematicians

saying things that implicit