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Philosophers who affirm the existence of abstract objects are sometimes called Platonists; those who deny their existence are sometimes called nominalists. The terms "Platonism" and "nominalism" also have established senses in the history of philosophy. They denote positions that have little to do with the modern notion of an abstract object. [2]
Definitions is a list of 184 terms important in early Platonism together with one or more brief definitions. Though not in alphabetical or any other simple order, it is possible to discern some features of the organization of the collection. Definitions 1–20 consist chiefly of terms from natural philosophy.
Full-blooded Platonism is a modern variation of Platonism, which is in reaction to the fact that different sets of mathematical entities can be proven to exist depending on the axioms and inference rules employed (for instance, the law of the excluded middle, and the axiom of choice). It holds that all mathematical entities exist.
Mathematical Platonism is the metaphysical view that (a) there are abstract mathematical objects whose existence is independent of us, and (b) there are true mathematical sentences that provide true descriptions of such objects. The independence of the mathematical objects is such that they are non physical and do not exist in space or time.
The platonic Republic might be related to the idea of "a tightly organized community of like-minded thinkers", like the one established by Pythagoras in Croton. The idea that mathematics and, generally speaking, abstract thinking is a secure basis for philosophical thinking as well as "for substantial theses in science and morals ".
Platonic Forms were the first universals posited as such in philosophy. [7] Our term "universal" is due to the English translation of Aristotle's technical term katholou which he coined specially for the purpose of discussing the problem of universals. [8] Katholou is a contraction of the phrase kata holou, meaning "on the whole". [9]
Platonic love, a relationship that is not sexual in nature; Platonic forms, or the theory of forms, Plato's model of existence; Platonic idealism; Platonic solid, any of the five convex regular polyhedra; Platonic crystal, a periodic structure designed to guide wave energy through thin plates; Platonism, the philosophy of Plato (Classical period)
In philosophy and specifically metaphysics, the theory of Forms, theory of Ideas, [1] [2] [3] Platonic idealism, or Platonic realism is a theory widely credited to the Classical Greek philosopher Plato. The theory suggests that the physical world is not as real or true as "Forms".