An approach to mathematics that, among other things,
makes no use of ExcludedMiddle.

*** http://www.andrew.cmu.edu/~cebrown/notes/intuitionism.html ( BrokenLink )

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To be able to include that in a mathematical epistemological context, we have to remember the great mathematical controversy of mathematical foundations in the beginning of the XXth century. The objective was to determine whether the mathematicians were discovering the "great absolute truth of the world" (position sustained of David Hilbert) or if they were just representing the world with equations (which was Poincaré's position).

During this memorable controversy, the question of mathematics to be intuitive or not (i.e. not governed only by intellectual inference such as in Turing's machines) was at the center of the diverging positions.

Years later, Brouwer reopened the debate with the objective of founding a logic based on pragmatic constructs of solutions (and not the fact that using the ExcludedMiddle principle, there can be a solution that cannot be determined). -- OlivierRey
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CategoryMath