Intuitionism (redirected from Intuitionism (philosophy of mathematics))

intuitionism

School of mathematical thought introduced by the Dutch mathematician Luitzen Egbertus Jan Brouwer (1881–1966). In contrast with mathematical Platonism, which holds that mathematical concepts exist independent of any human realization of them, intuitionism holds that only those mathematical concepts that can be demonstrated, or constructed, following a finite number of steps are legitimate. Few mathematicians have been willing to abandon the vast realms of mathematics built with nonconstructive proofs.

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intuitionism

In metaethics, a form of cognitivism that holds that moral statements can be known to be true or false immediately through a kind of rational intuition. In the 17th and 18th centuries, intuitionism was defended by Ralph Cudworth, Henry More (1614–87), Samuel Clarke (1675–1729), and Richard Price (1723–91); in the 20th century its supporters included H.A Prichard (1871–1947), G.E. Moore, and David Ross. Intuitionists have differed over the kinds of moral truths that are amenable to direct apprehension. For example, whereas Moore thought that it is self-evident that certain things are morally valuable, Ross thought that we know immediately that it is our duty to do acts of a certain type.

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intuitionism - intuitionistic logic

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Intuitionism 

the idealist movement in philosophy that considers intuition to be the sole reliable means of cognition. Although the intuitionist tendency is characteristic of many philosophers and philosophical trends of the past, intuitionism as a definite movement arose at the turn of the century. It is, in particular, a type of reaction to the spread of a rationalistic way of thought, which is based on the mechanistic and positivistic conception of scientific knowledge and on the limitation of experience exclusively to the sphere of sense perception. As a variety of irrationalism, intuitionism is opposed to the philosophy of dialectical materialism. Two forms of intuitionism can be distinguished. For the first, anti-intellectual form, the opposition of intuition and intellect is characteristic, as in H. Bergson (France) and the philosophy of life as a whole. The second form tries to unite intuition and intellect, as in the Russian philosophers N. O. Losskii, S. L. Frank, and E. N. Trubetskoi; the French neo-Thomists E. Gilson and J. Maritain; and, in part, E. Husserl and the phenomenological school—M. Scheler, N. Hartmann (Germany), and other philosophers.

Bergson contrasts intuition to discursive, logical thinking or logical knowledge. He interprets intuition as the immediate merging of subject and object, the overcoming of the opposition between them. In the biological versions of the philosophy of life (for example, in the German philosoher L. Klages) intuition verges on instinct, giving direct knowledge of an object without the aid of consciousness.

Representatives of the second tendency of intuitionism strive to go beyond the bounds of immediate sense experience and propose that philosophy base itself on a special kind of experience—mental (particularly “religious”) experience. Dialectical materialism, while criticizing the exaggerated role that intuitionism assigns to intuition in cognition, looks upon intuition as an organic moment in the cognitive process, acting in unison with discursive thinking.