Platonism or realism of ideas is a philosophical theory inspired more or less directly by the theory of forms of Plato, theory according to which there are intelligible entities in oneself, whose content is independent of the contingency of the sensitive experience. These entities, depending on the version of Platonism we are talking about, can be concepts (Ideas in general, as in Plotinus or Augustine), numbers (mathematical Platonism of Pythagorean inspiration, as in Jamblique or Lautman), or even logic values (Frege logicism for example). This theory is one of the possible responses, along with nominalism (William of Ockham) and conceptualism (Pierre Abélard), to the question of the ontological status of cognitive concepts (ideas, numbers or propositional contents).
History of Platonism
Platonism in Antiquity
According to Theophrastus, Plato devoted himself to the study of phenomena and he was attached to the descriptive knowledge of nature, in which he wants to bring into play two principles: one which is subject and acts as matter, to which he gives the name of “universal receptacle”, the other which acts as cause and motor and which it attaches to divine power and to good. The first form of Platonism was defended by Plato within the framework of the theory of ideas, but it must be seen that this theory was never explicitly stated by Plato but that it underpins a large part of Platonic thought: the texts the most important for knowing the theory of ideas are The Republic, the Phaedo, the Symposium and the Parmenides, as well as to a certain extent the Socratic dialogues. The later Plato, increasingly influenced by Pythagorean thought, tended to identify Ideas and Numbers, which was not the case in his earlier writings. In The Republic, the supreme Idea was the Good, in the sense of propriety, not moral goodness. In Symposium, the supreme Idea was Beauty. For the Neoplatonists, the domain of Ideas will become the Intellect, and the Supreme Form will become the One.
Platonism in the Middle Ages
The Middle Ages were undoubtedly the period during which Platonism was the most discussed but also defended with the most vigorous arguments against nominalism. The quarrel between these two theories was called the quarrel of universals and is one of the founding moments of medieval philosophy and epistemology.
Platonism in contemporary times
The most important defenders of Platonism in contemporary times are the analytical philosophers Frege and Russell, who postulate the existence of a realm in which the meanings of logical and mathematical propositions exist autonomously. This Platonism is criticized in Ludwig Wittgenstein’s Tractatus logico-philosophicus, which revives a certain form of nominalism.
Kurt Gödel also asserted himself resolutely Platonic unlike his friend Albert Einstein, who called himself a Spinozist.
The mathematician and physicist Roger Penrose grants a mathematical ontology to the laws of physics in all his works, and more especially in his latest book The Road to Reality: A Complete Guide to the Laws of the Universe. The thesis of Platonism was vigorously questioned by Willard van Orman Quine.
Platonism and realism
It would be more correct to qualify the so-called “Platonic” mathematicians of “realist” mathematicians, because realism in mathematics takes up the idea that the nature of mathematical objects is real in the sense that it is independent of the intellect of the human being, but it does not necessarily take all the attributes of Plato’s world of ideas. However, this terminology is often used by mathematicians themselves.