Platonism: Platonism.
Platonism is the most influential mathematical philosophy in the history of mathematics. It originated from Plato in ancient Greece, and since then there has been an explicit or implicit Platonism concept in the field of western mathematics. In the19th century, it almost occupied the dominant position in the field of mathematics. At the beginning of the 20th century, the debate among the three schools of mathematics foundation just subsided, and Platonism became one of the hot topics of discussion.
The basic view of Platonism is that the object of mathematics is mathematical concepts such as numbers, quantities and functions, and mathematical concepts exist objectively as abstract generality or "* * *". Plato believed that they existed in a special world of ideas, and later Platonists did not accept the "theory of ideas", but they also believed that mathematical concepts were a special objective existence independent of the real world and an eternal existence independent of time, space and human thinking. Mathematicians get a new concept, not creation, but a description of this objective existence; New achievements in mathematics are not inventions, but discoveries. Correspondingly, Platonism believes that the truth of mathematical theory is objectively determined by the existence independent of the real world, and this truth is understood by "mental" experience and some kind of "mathematical intuition". Only through intuition can people reach the "mathematical world" independent of the real world.
Modern Platonism is also called "realism" because mathematical concepts are considered to be real. Platonism has a considerable influence in modern western mathematics, and some great mathematicians, such as G. Cantor, Russell, Godel and bourbaki, basically hold this view. It is generally believed that this is not accidental, but a philosophical reflection on the simple belief that mathematics reflects the objective world and mathematics has objective truth. Because of this, Platonism has a certain positive effect on the historical development of mathematics: it urges mathematicians to take an objective and scientific position in their own research, and when some highly abstract mathematical theories are doubted by people because they can't find realistic prototypes, it may also give people some faith. Although this belief is blind, it may also lead to mistakes.
The mistake of Platonism is obvious: taking the form of reflection as the object of understanding; Regard abstraction as concrete objective existence; It is of course an objective truth to think that a form of thinking itself is objective. Studying truth without human practice will inevitably lead to fallacy. Platonism is objective idealism in philosophy.
Plato's Philosophy: Philosophy of Objective Idealism
Platonic love: spiritual love, the desire to abandon the body.
Is Plato a freak with snake hair? No, that's Medusa.