form

form

[fawrm]

In the philosophy of Plato and Aristotle the active, determining principle of a thing. The term was traditionally used to translate Plato's eidos, by which he meant the permanent reality that makes a thing what it is, in contrast to the particulars that are finite and subject to change. Each form is the pattern of a particular category of thing in the world; thus, there are forms of human, stone, shape, colour, beauty, and justice. Whereas the physical world, perceived with the senses, is in constant flux and knowledge derived from it restricted and variable, the realm of forms, apprehensible only by the mind, is eternal and changeless. Particular things derive what reality they have by “participating” in, or imperfectly copying, the forms. Aristotle rejected the abstract Platonic notion of form and argued that every sensible object consists of both matter and form, neither of which can exist without the other. For Aristotle, the matter of a thing consists of those of its elements which, when the thing has come into being, may be said to have “become” it; the form of a thing is the arrangement or organization through which such elements have become the thing in question. Thus a certain lump of bronze is the matter that, given a certain form, becomes a statue or, given another, becomes a sword. The Aristotelian concept of form was adapted and developed by St. Thomas Aquinas and other scholastic philosophers. The Enlightenment philosopher Immanuel Kant used the notion of form to describe the mentally imposed conditions of sensible experience, namely space and time.

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Form may mean:

In martial arts

  • Kata (martial arts) (型 or 形), the detailed pattern of defence-and-attack
  • Taeguk (Taekwondo) (형), the "forms" used to create a foundation for the teaching of Taekwondo
  • Taolu (套路), forms used in Chinese martial arts and sport wushu

In mathematics

  • Quadratic form, a homogeneous polynomial of degree two in a number of variables
  • Algebraic form, which generalises quadratic forms to degrees 3 and more, also known as quantics or simply forms
  • Bilinear form, on a vector space V over a field F is a mapping V × VF that is linear in both arguments
  • Multilinear form, which generalises bilinear forms to mappings VNF
  • Differential form, a concept from differential topology that combines multilinear forms and smooth functions
  • Modular form, a (complex) analytic function on the upper half plane satisfying a certain kind of functional equation and growth condition
  • Indeterminate form, an algebraic expression that cannot be used to evaluate a limit

In biology

In computing

See also

  • Sixth form, a British term for the final two years of secondary school

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