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Platonic idealism usually refers to Plato's theory of forms or doctrine of ideas.
Plato was an Athenian philosopher during the Classical period in Ancient Greece, founder of the Platonist school of thought, and the Academy, the first institution of higher learning in the Western world.
The theory of Forms or theory of Ideas is a philosophical theory, concept, or world-view, attributed to Plato, that the physical world is not as real or true as timeless, absolute, unchangeable ideas. According to this theory, ideas in this sense, often capitalized and translated as "Ideas" or "Forms", are the non-physical essences of all things, of which objects and matter in the physical world are merely imitations. Plato speaks of these entities only through the characters of his dialogues who sometimes suggest that these Forms are the only objects of study that can provide knowledge. The theory itself is contested from within Plato's dialogues, and it is a general point of controversy in philosophy. Whether the theory represents Plato's own views is held in doubt by modern scholarship. However, the theory is considered a classical solution to the problem of universals.
Some commentators hold that Plato argued that truth is an abstraction. In other words, we are urged to believe that Plato's theory of ideals is an abstraction, divorced from the so-called external world, of modern European philosophy, despite the fact Plato taught that ideals are ultimately real, and different from non-ideal things—indeed, he argued for a distinction between the ideal and non-ideal realm.
Truth is most often used to mean being in accord with fact or reality, or fidelity to an original or standard. Truth is also sometimes defined in modern contexts as an idea of "truth to self", or authenticity.
Abstraction in its main sense is a conceptual process where general rules and concepts are derived from the usage and classification of specific examples, literal signifiers, first principles, or other methods.
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 Goodis found, directing everything underneath.
Plato describes the "Form of the Good", or more literally "the idea of the good", in his dialogue the Republic (508e2–3), speaking through the character of Socrates. Plato introduces several forms in his works, but identifies the Form of the Good as the superlative. This form is the one that allows a philosopher-in-training to advance to a philosopher-king. It cannot be clearly seen or explained, but once it is recognized, it is the form that allows one to realize all the other forms.
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.
Philosophy is the study of general and fundamental questions about existence, knowledge, values, reason, mind, and language. Such questions are often posed as problems to be studied or resolved. The term was probably coined by Pythagoras. Philosophical methods include questioning, critical discussion, rational argument, and systematic presentation. Classic philosophical questions include: Is it possible to know anything and to prove it? What is most real? Philosophers also pose more practical and concrete questions such as: Is there a best way to live? Is it better to be just or unjust? Do humans have free will?
Athens is one of the oldest named cities in the world, having been continuously inhabited for at least 5000 years. Situated in southern Europe, Athens became the leading city of Ancient Greece in the first millennium BC, and its cultural achievements during the 5th century BC laid the foundations of western civilization.
The Academy was founded by Plato in c. 387 BC in Athens. Aristotle studied there for twenty years before founding his own school, the Lyceum. The Academy persisted throughout the Hellenistic period as a skeptical school, until coming to an end after the death of Philo of Larissa in 83 BC. The Platonic Academy was destroyed by the Roman dictator Sulla in 86 BC.
Platonism is usually divided into three periods:
Plato's students used the hypomnemata as the foundation to his philosophical 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 non-mathematical "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.
In analytic philosophy, anti-realism is an epistemological position first articulated by British philosopher Michael Dummett. The term was coined as an argument against a form of realism Dummett saw as 'colorless reductionism'.
Metaphysics is the branch of philosophy that examines the fundamental nature of reality, including the relationship between mind and matter, between substance and attribute, and between possibility and actuality. The word "metaphysics" comes from two Greek words that, together, literally mean "after or behind or among [the study of] the natural". It has been suggested that the term might have been coined by a first century CE editor who assembled various small selections of Aristotle’s works into the treatise we now know by the name Metaphysics.
In metaphysics, the problem of universals refers to the question of whether properties exist, and if so, what they are. Properties are qualities or relations that two or more entities have in common. The various kinds of properties, such as qualities and relations, are referred to as universals. For instance, one can imagine three cup holders on a table that have in common the quality of being circular or exemplifying circularity, or two daughters that have in common being the female offsprings of Frank. There are many such properties, such as being human, red, male or female, liquid, big or small, taller than, father of, etc. While philosophers agree that human beings talk and think about properties, they disagree on whether these universals exist in reality or merely in thought and speech.
Platonic 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. As universals were considered by Plato to be ideal forms, this stance is ambiguously also called Platonic idealism. This should not be confused with idealism as presented by philosophers such as George Berkeley: as Platonic abstractions are not spatial, temporal, or mental, they are not compatible with the later idealism's emphasis on mental existence. Plato's Forms include numbers and geometrical figures, making them a theory of mathematical realism; they also include the Form of the Good, making them in addition a theory of ethical realism.
In metaphysics, a universal is what particular things have in common, namely characteristics or qualities. In other words, universals are repeatable or recurrent entities that can be instantiated or exemplified by many particular things. For example, suppose there are two chairs in a room, each of which is green. These two chairs both share the quality of "chairness", as well as greenness or the quality of being green; in other words, they share a "universal". There are three major kinds of qualities or characteristics: types or kinds, properties, and relations. These are all different types of universals.
Reality is the sum or aggregate of all that is real or existent, as opposed to that which is merely imaginary. The term is also used to refer to the ontological status of things, indicating their existence. In physical terms, reality is the totality of the universe, known and unknown. Philosophical questions about the nature of reality or existence or being are considered under the rubric of ontology, which is a major branch of metaphysics in the Western philosophical tradition. Ontological questions also feature in diverse branches of philosophy, including the philosophy of science, philosophy of religion, philosophy of mathematics, and philosophical logic. These include questions about whether only physical objects are real, whether reality is fundamentally immaterial, whether hypothetical unobservable entities posited by scientific theories exist, whether God exists, whether numbers and other abstract objects exist, and whether possible worlds exist.
The philosophy of mathematics is the branch of philosophy that studies the assumptions, foundations, and implications of mathematics, and purports to provide a viewpoint of the nature and methodology of mathematics, and to understand the place of mathematics in people's lives. The logical and structural nature of mathematics itself makes this study both broad and unique among its philosophical counterparts.
In philosophy, rationalism is the epistemological view that "regards reason as the chief source and test of knowledge" or "any view appealing to reason as a source of knowledge or justification". More formally, rationalism is defined as a methodology or a theory "in which the criterion of the truth is not sensory but intellectual and deductive".
Foundations of mathematics is the study of the philosophical and logical and/or algorithmic basis of mathematics, or, in a broader sense, the mathematical investigation of what underlies the philosophical theories concerning the nature of mathematics. In this latter sense, the distinction between foundations of mathematics and philosophy of mathematics turns out to be quite vague. Foundations of mathematics can be conceived as the study of the basic mathematical concepts and how they form hierarchies of more complex structures and concepts, especially the fundamentally important structures that form the language of mathematics also called metamathematical concepts, with an eye to the philosophical aspects and the unity of mathematics. The search for foundations of mathematics is a central question of the philosophy of mathematics; the abstract nature of mathematical objects presents special philosophical challenges.
Pure mathematics is the study of mathematical concepts independently of any application outside mathematics. These concepts may originate in real-world concerns, and the results obtained may later turn out to be useful for practical applications, but the pure mathematicians are not primarily motivated by such applications. Instead, the appeal is attributed to the intellectual challenge and aesthetic beauty of working out the logical consequences of basic principles.
Actual idealism was a form of idealism, developed by Giovanni Gentile, that grew into a 'grounded' idealism, contrasting the transcendental idealism of Immanuel Kant, and the absolute idealism of G. W. F. Hegel. To Gentile, who considered himself the "philosopher of Fascism," actualism was the sole remedy to philosophically preserving free agency, by making the act of thinking self-creative and, therefore, without any contingency and not in the potency of any other fact.
Christianity and Hellenistic philosophies experienced complex interactions during the first to the fourth centuries.
In metaphysics, realism about a given object is the view that this object exists in reality independently of our conceptual scheme. In philosophical terms, these objects are ontologically independent of someone's conceptual scheme, perceptions, linguistic practices, beliefs, etc.
Platonism, rendered as a proper noun, is the philosophy of Plato or the name of other philosophical systems considered closely derived from it. In narrower usage, platonism, rendered as a common noun, refers to the philosophy that affirms the existence of abstract objects, which are asserted to "exist" in a "third realm" distinct both from the sensible external world and from the internal world of consciousness, and is the opposite of nominalism. Lower case "platonists" need not accept any of the doctrines of Plato.
Metaphysics is the branch of philosophy that investigates principles of reality transcending those of any particular science. Cosmology and ontology are traditional branches of metaphysics. It is concerned with explaining the fundamental nature of being and the world. Someone who studies metaphysics can be called either a "metaphysician" or a "metaphysicist".
The following outline is provided as an overview of and topical guide to metaphysics:
Objectivity is a philosophical concept of being true independently from individual subjectivity caused by perception, emotions, or imagination. A proposition is considered to have objective truth when its truth conditions are met without bias caused by a sentient subject. Scientific objectivity refers to the ability to judge without partiality or external influence, sometimes used synonymously with neutrality.
Structuralism is a theory in the philosophy of mathematics that holds that mathematical theories describe structures of mathematical objects. Mathematical objects are exhaustively defined by their place in such structures. Consequently, structuralism maintains that mathematical objects do not possess any intrinsic properties but are defined by their external relations in a system. For instance, structuralism holds that the integer 1 is exhaustively defined by being the successor of 0 in the structure of the theory of natural numbers. By generalization of this example, any integer is defined by their respective place in this structure of the number line. Other examples of mathematical objects might include lines and planes in geometry, or elements and operations in abstract algebra.
Mathematicism is any opinion, viewpoint, school of thought, or philosophy that states that everything can be described/defined/modelled ultimately by mathematics, or that the universe and reality are fundamentally/fully/only mathematical, i.e. that 'everything is mathematics' necessitating the ideas of logic, reason, mind, and spirit.