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Platonic idealism is the theory that the substantive reality around us is only a reflection of a higher truth. That truth, Plato argues, is the abstraction. A particular tree, with a branch or two missing, possibly alive, possibly dead, and initials of two lovers carved into its bark, is distinct from the 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.
Some people 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; this school had an actual, 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 generally divided into three periods:
- Early Platonism
- Middle Platonism
- Neoplatonism
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 in some undescribed realm. 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.
Nietzsche was highly critical of Plato and his influence on Western philosophical thought.
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