Platonic idealism usually refers to Plato's theory of forms or doctrine of ideas, the exact philosophical meaning of which is perhaps one of the most disputed questions in higher academic philosophy. At least one may say, with some degree of certitude, that Plato held the realm of ideas to be absolute reality. As for the exact relationship between the ideal and non-ideal world, the platonic corpus is silent, insofar as interpretation must rely upon literary device, metaphor, and amphibology. Some commentators hold Plato argued that truth is an abstraction. In other words, we are urged to believe that Plato's theory of ideas is an abstraction, divorced from the so-called external world, of modern European philosophy, despite the fact Plato taught that ideas are ultimately real, and different from non-ideal things--indeed, he argued for a distinction between the ideal and non-ideal realm.
These commentators speak thus: For example, a particular tree, with a branch or two missing, possibly alive, possibly dead, and with the initials of two lovers carved into its bark, is distinct from the abstract form of Tree-ness. A Tree is the ideal that each of us holds that allows us to identify the imperfect reflections of trees all around us.
Plato gives the divided line as an outline of this theory. At the top of the line, the Form of the Good is found, directing everything underneath.
Some contemporary linguistic philosophers construe "Platonism" to mean the proposition that universals exist independently of particulars (a universal is anything that can be predicated of a particular).
Platonism is an ancient school of philosophy, founded by Plato; at the beginning, this school had a physical existence at a site just outside the walls of Athens called the Academy, as well as the intellectual unity of a shared approach to philosophizing.
Platonism is usually divided into three periods:
Plato's students used the hypomnemata as the foundation to his philosophic approach to knowledge. The hypomnemata constituted a material memory of things read, heard, or thought, thus offering these as an accumulated treasure for rereading and later meditation. For the Neoplatonist they also formed a raw material for the writing of more systematic treatises in which were given arguments and means by which to struggle against some defect (such as anger, envy, gossip, flattery) or to overcome some difficult circumstance (such as a mourning, an exile, downfall, disgrace).
Platonism is considered to be, in mathematics departments the world over, the predominant philosophy of mathematics, especially regarding the foundations of mathematics.
One statement of this philosophy is the thesis that mathematics is not created but discovered. A lucid statement of this is found in an essay written by the British mathematician G. H. Hardy in defense of pure mathematics.
The absence in this thesis of clear distinction between mathematical and nonmathematical "creation" leaves open the inference that it applies to allegedly creative endeavors in art, music, and literature.
It is unknown if Plato's ideas of idealism have some earlier origin, but Plato held Pythagoras in high regard, and Pythagoras as well as his followers in the movement known as Pythagoreanism claimed the world was literally built up from numbers, an abstract, absolute form.
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