Intuitionistic Logic Intuitionistic logic encompasses the principles of logical reasoning which were used by L. E. J. Brouwer in developing his intuitionistic mathematics, beginning in [1907]. Because these principles also underly Russian recursive analysis and the constru http://plato.stanford.edu/entries/logic-intuitionistic/ Top/Society/Philosophy/Philosophy_of_Science/Mathematics
Constructive Mathematics Constructive mathematics is distinguished from its traditional counterpart, classical mathematics, by the strict interpretation of the phrase `there exists' as `we can construct'. In order to work constructively, we need to re-interpret not only the exi http://plato.stanford.edu/entries/mathematics-constructive/ Top/Society/Philosophy/Philosophy_of_Science/Mathematics
Inconsistent Mathematics Inconsistent mathematics is the study of the mathematical theories that result when classical mathematical axioms are asserted within the framework of a (non-classical) logic which can tolerate the presence of a contradiction without turning every sent http://plato.stanford.edu/entries/mathematics-inconsistent/ Top/Society/Philosophy/Philosophy_of_Science/Mathematics
Hilbert's Program In 1921, David Hilbert made a proposal for a formalist foundation of mathematics, for which a finitary consistency proof should establish the security of mathematics. From the Stanford Encyclopedia, by Richard Zach. http://plato.stanford.edu/entries/hilbert-program/ Top/Society/Philosophy/Philosophy_of_Science/Mathematics
