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1The theory that primary truths and principles (especially those of ethics and metaphysics) are known directly by intuition.
- ‘This theory of intuitionism influenced later philosophers, in particular Rousseau and Bergson, but also the existentialists.’
- ‘Fortunately, the notion that intuitionalism and empiricism exhaust the alternatives no longer universally obtains.’
- ‘Historically, intuitionism has tended to be a kind of deontologism.’
- ‘Although Dummett's work on deduction has its roots in the debate over intuitionism, it does not necessarily follow that, in every case, the alternative logic advocated by a Dummett-style anti-realist would be intuitionistic logic.’
- ‘They both fail for open set logic, which is to say intuitionism, just as they both fail for its topological dual, closed set logic.’
- 1.1The theory that mathematical knowledge is based on intuition and mental construction, rejecting certain modes of reasoning and the notion of independent mathematical objects.
- ‘A corresponding slogan for intuitionism would be that in mathematics, to exist is to be constructed.’
- ‘The authors, breaking with the intuitionism that had dominated eighteenth-century French treatises, updated the logic of geometry manuals.’
- ‘Connections with intuitionistic mathematics were noticed early on and toposes are still used to investigate models of various aspects of intuitionism.’
- ‘This bibliography is intended as a reference guide to works dealing with mathematical intuitionism.’
- ‘Freudenthal studied the relation between axiomatic mathematics and reality, and this study led him to contribute to intuitionism, as well as to the application of mathematics to linguistics.’
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