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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.’

‘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.’

‘Historically, intuitionism has tended to be a kind of deontologism.’

‘Fortunately, the notion that intuitionalism and empiricism exhaust the alternatives no longer universally obtains.’

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.

‘This bibliography is intended as a reference guide to works dealing with mathematical intuitionism.’

‘The authors, breaking with the intuitionism that had dominated eighteenth-century French treatises, updated the logic of geometry manuals.’

‘A corresponding slogan for intuitionism would be that in mathematics, to exist is to be constructed.’

‘Connections with intuitionistic mathematics were noticed early on and toposes are still used to investigate models of various aspects of 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.’