Platonic idealism
Encyclopedia
Platonic idealism usually refers to Plato's
theory of forms
or doctrine of ideas,
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.
Plato
Plato , was a Classical Greek philosopher, mathematician, student of Socrates, writer of philosophical dialogues, and founder of the Academy in Athens, the first institution of higher learning in the Western world. Along with his mentor, Socrates, and his student, Aristotle, Plato helped to lay the...
theory of forms
Theory of Forms
Plato's theory of Forms or theory of Ideas asserts that non-material abstract forms , and not the material world of change known to us through sensation, possess the highest and most fundamental kind of reality. When used in this sense, the word form is often capitalized...
or doctrine of ideas,
Some commentators hold Plato argued that truth
Truth
Truth has a variety of meanings, such as the state of being in accord with fact or reality. It can also mean having fidelity to an original or to a standard or ideal. In a common usage, it also means constancy or sincerity in action or character...
is an abstraction. In other words, we are urged to believe that Plato
Plato
Plato , was a Classical Greek philosopher, mathematician, student of Socrates, writer of philosophical dialogues, and founder of the Academy in Athens, the first institution of higher learning in the Western world. Along with his mentor, Socrates, and his student, Aristotle, Plato helped to lay the...
's theory of ideas is an abstraction
Abstraction
Abstraction is a process by which higher concepts are derived from the usage and classification of literal concepts, first principles, or other methods....
, 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
Philosophy
Philosophy is the study of general and fundamental problems, such as those connected with existence, knowledge, values, reason, mind, and language. Philosophy is distinguished from other ways of addressing such problems by its critical, generally systematic approach and its reliance on rational...
, founded by Plato; at the beginning, this school had a physical existence at a site just outside the walls of Athens
History of Athens
Athens is one of the oldest named cities in the world, having been continuously inhabited for at least 7000 years. Situated in southern Europe, Athens became the leading city of Ancient Greece in the first millennium BCE and its cultural achievements during the 5th century BCE laid the foundations...
called the Academy
Academy
An academy is an institution of higher learning, research, or honorary membership.The name traces back to Plato's school of philosophy, founded approximately 385 BC at Akademia, a sanctuary of Athena, the goddess of wisdom and skill, north of Athens, Greece. In the western world academia is the...
, as well as the intellectual unity of a shared approach to philosophizing.
Platonism is usually divided into three periods:
- Early Platonism
- Middle PlatonismMiddle PlatonismMiddle Platonism is the modern name given to a stage in the development of Plato's philosophy, lasting from about 90 BC, when Antiochus of Ascalon rejected the scepticism of the New Academy, until the development of Neoplatonism under Plotinus in the 3rd century. Middle Platonism absorbed many...
- NeoplatonismNeoplatonismNeoplatonism , is the modern term for a school of religious and mystical philosophy that took shape in the 3rd century AD, based on the teachings of Plato and earlier Platonists, with its earliest contributor believed to be Plotinus, and his teacher Ammonius Saccas...
Plato's students used the hypomnemata
Hypomnemata
Hypomnema , also spelled hupomnema, is a Greek word with several translations into English including a reminder, a note, a public record, a commentary, a draft, a copy, and other variations on those terms.Michel Foucault uses the word in the sense of "note", but his translators use the word...
as the foundation to his philosophic approach to knowledge
Knowledge
Knowledge is a familiarity with someone or something unknown, which can include information, facts, descriptions, or skills acquired through experience or education. It can refer to the theoretical or practical understanding of a subject...
. 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
Philosophy of mathematics
The philosophy of mathematics is the branch of philosophy that studies the philosophical assumptions, foundations, and implications of mathematics. The aim of the philosophy of mathematics is to provide an account of the nature and methodology of mathematics and to understand the place of...
, especially regarding the foundations of mathematics
Foundations of mathematics
Foundations of mathematics is a term sometimes used for certain fields of mathematics, such as mathematical logic, axiomatic set theory, proof theory, model theory, type theory and recursion theory...
.
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
G. H. Hardy
Godfrey Harold “G. H.” Hardy FRS was a prominent English mathematician, known for his achievements in number theory and mathematical analysis....
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
Idealism
In philosophy, idealism is the family of views which assert that reality, or reality as we can know it, is fundamentally mental, mentally constructed, or otherwise immaterial. Epistemologically, idealism manifests as a skepticism about the possibility of knowing any mind-independent thing...
have some earlier origin, but Plato held Pythagoras
Pythagoras
Pythagoras of Samos was an Ionian Greek philosopher, mathematician, and founder of the religious movement called Pythagoreanism. Most of the information about Pythagoras was written down centuries after he lived, so very little reliable information is known about him...
in high regard, and Pythagoras as well as his followers in the movement known as Pythagoreanism
Pythagoreanism
Pythagoreanism was the system of esoteric and metaphysical beliefs held by Pythagoras and his followers, the Pythagoreans, who were considerably influenced by mathematics. Pythagoreanism originated in the 5th century BCE and greatly influenced Platonism...
claimed the world was literally built up from numbers, an abstract, absolute form.
See also
- Cambridge PlatonistsCambridge PlatonistsThe Cambridge Platonists were a group of philosophers at Cambridge University in the middle of the 17th century .- Programme :...
- GnosticismGnosticismGnosticism is a scholarly term for a set of religious beliefs and spiritual practices common to early Christianity, Hellenistic Judaism, Greco-Roman mystery religions, Zoroastrianism , and Neoplatonism.A common characteristic of some of these groups was the teaching that the realisation of Gnosis...
- IdealismIdealismIn philosophy, idealism is the family of views which assert that reality, or reality as we can know it, is fundamentally mental, mentally constructed, or otherwise immaterial. Epistemologically, idealism manifests as a skepticism about the possibility of knowing any mind-independent thing...
- PlatoPlatoPlato , was a Classical Greek philosopher, mathematician, student of Socrates, writer of philosophical dialogues, and founder of the Academy in Athens, the first institution of higher learning in the Western world. Along with his mentor, Socrates, and his student, Aristotle, Plato helped to lay the...
- Platonic epistemologyPlatonic epistemologyPlatonic epistemology holds that knowledge is innate, so that learning is the development of ideas buried deep in the soul, often under the midwife-like guidance of an interrogator. In several dialogues by Plato, Socrates presents the view that each soul existed before birth with "The Form of the...
- Platonic realismPlatonic realismPlatonic realism is a philosophical term usually used to refer to the idea of realism regarding the existence of universals or abstract objects after the Greek philosopher Plato , a student of Socrates. As universals were considered by Plato to be ideal forms, this stance is confusingly also called...
- Philosophy of mathematicsPhilosophy of mathematicsThe philosophy of mathematics is the branch of philosophy that studies the philosophical assumptions, foundations, and implications of mathematics. The aim of the philosophy of mathematics is to provide an account of the nature and methodology of mathematics and to understand the place of...