intuitionism

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