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 Treeness. A Tree is the ideal that each of us holds that allows us to identify the imperfect reflections of trees all around us. This article is primarily concerned with truth as it is used in the evaluation of propositions, sentences, and similar items. ...
Statue of a philosopher, presumely Plato, in Delphi. ...
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. Plato, in The Republic Book VI (509d513e), uses the literary device of a divided line to teach his basic views about four levels of existence (especially the intelligible world of the forms, universals, and the visible world we see around us) and the corresponding ways we come to know...
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; 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. An academy is an institution for the study of higher learning. ...
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. Middle Platonism refers to the development of certain philosophical doctrines associated with Plato during the first and second centuries A.D. One of the outstanding thinkers of Middle Platonism was Philo Judeaus (Philo the Jew) who synthesized Platos philosophy with Jewish scripture largely through allegorical interpretation of the later. ...
Neoplatonism (also NeoPlatonism) is an ancient school of philosophy beginning in the 3rd century A.D. It was based on the teachings of Plato and Platonists; but it interpreted Plato in many new ways, such that Neoplatonism was quite different from what Plato taught, though not many Neoplatonists would...
Philosophy of mathematics is that branch of philosophy which attempts to answer questions such as: why is mathematics useful in describing nature?, in which sense, if any, do mathematical entities such as numbers exist? and why and how are mathematical statements true?. Various approaches to answering these questions will be...
The term foundations of mathematics is sometimes used for certain fields of mathematics itself, namely for mathematical logic, axiomatic set theory, proof theory, model theory, and recursion theory. ...
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. G. H. Hardy Godfrey Harold Hardy (February 7, 1877 – December 1, 1947) was a prominent British mathematician, known for his achievements in number theory and mathematical analysis. ...
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. Friedrich Nietzsche, 1882 Friedrich Wilhelm Nietzsche (October 15, 1844  August 25, 1900) was a highly influential German philosopher. ...
See also
