Socrates first discovered the concept, or eidos as the relation between the particular and the general and as a germ of a new meaning of the general question concerning being. This meaning emerged in its full purity when the Socratic eidos went on to unfold into the (transcendental) Platonic "Idea." (see also essence) The eidos is absolutely and eternally real, but in respect to each single realization, it is the possible, its potentiality.
Plato and Euclid developed an indissoluble partnership between geometrical and philosophical ideas of truth. The Platonic concept of the theory of ideas was possible only because Plato had continually in mind the static shapes discovered by Greek mathematics.(see form.) Euclid's geometry was based on figures that are radically removed from experience. Not only the idealizations of point, line, and plane, but the idea of similar triangles, whose differences are considered inconsequential or fortuitous, and that become identified as "the same," mark an immense step away form ordinary perception. On the other hand, Greek geometry did not achieve completion as a real system until it adopted Plato's manner of thinking, in which truth was understood as a correspondence with the world of forms. (see Ernst Cassirer, The Problem of Knowledge.) The concepts and propositions that Euclid placed at the apex of his system were a prototype and pattern for what Plato called the process of synopsis in idea. What is grasped in such synopsis is not the peculiar, fortuitous, or unstable; it possesses universal necessary and eternal truth.
For Aristotle, the problem of the concept is transformed into the problem of teleology. Amid all the multiplicity and particularization of empirical becoming, there emerges something universal and typical, which gives this becoming its direction. The world of "Forms" does not stand beyond phenomena as something prior to and separate from them, but is immanent in the phenomena as a whole of teleological forces, which rule and guide the consummation of purely material events. For Aristotle, the eidos of an identity or process is its organizing principle. Form in nature is not a separate, self-subsistent absolute. It exists only in that which it informs. (see also organicism )
In the tenth book of the Republic, Socrates differentiates the maker of an object, such as a bed, made in accordance with the Idea of the thing (this is its eidos or form) , from the artist, proceeding in a quick and easy fashion, as if using a mirror.
In articulating the aesthetic of the transcendental ideal, Plotinus used Plato's framework to enhance the importance of art rather than to reduce it. Now art could reflect the ideal more accurately than imperfect nature itself. The arts "go back to the Ideas from which Nature itself derives,...and add where nature is lacking." (Enneads) Post-Platonic theorists tended to assign a double residence to the Ideas: both within a transcendental space and in the mind. (see Abrams, Mirror and Lamp, p. 43) The latter possibility, the intuitive ideal, allowed art to conform to a vision both personal and subjective. (see Panofsky, Idea)
In the Critique of Judgement, Kant describes aesthetical ideas as "representations of the imagination which occasion much thought, without however any definite thought, i.e. any concept being capable of being adequate to them. An aesthetic idea, which cannot be completely compassed and made intelligible by language, is the counterpart of a rational idea of the understanding, to which no intuition (or representation of the imagination) is adequate. (p. 157)
“My dialectical method is, in its foundations, not only different from the Hegelian, but exactly opposite to it. For Hegel, the process of thinking, which he even transforms into an independent subject, under the name of 'the idea', is the creator of the real world, and the real world is only the external appearance of the idea. With me, the reverse is true: the ideal is nothing but the material world reflected in the mind of man, and translated into forms of thought." Karl Marx, Capital, vol. 1,Preface to the Second Edition. (p.102) (see ideal / real )
Sigmund Freud approached ideas in relation to their affective force. For Freud, repression severs the connection between idea and affect. One by-product of this seperation is anxiety.
For Gilles Deleuze the affective force, level of intensity, desire, or affirmation conveys ideas and ultimately govern their truth-value