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    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 constructive analysis of E. Bishop and his followers, intuitionistic logic may be considered the logical basis of constructive mathematics. From the Stanford Encyclopedia.

    Indispensability Arguments in the Philosophy of Mathematics - From the fact that mathematics is indispensable to science, some philosophers have drawn serious metaphysical conclusions. In particular, Quine and Putnam have argued that the indispensability of mathematics to empirical science gives us good reason to believe in the existence of mathematical entities. From the Stanford Encyclopedia.

    Philosophia Mathematica - Journal devoted specifically to philosophy of mathematics. Abstracts available online.

    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 existential quantifier but all the logical connectives and quantifiers as instructions on how to construct a proof of the statement involving these logical expressions. From the Stanford Encyclopedia.

    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 sentence into a theorem. By Chris Mortensen, from the Stanford Encyclopedia

    Paraconsistent Logic - The development of paraconsistent logic was initiated in order to challenge the logical principle that anything follows from contradictory premises, ex contradictione quodlibet. By Koji Tanaka, from the Stanford Encyclopedia.

    Dialetheism - A dialetheia is a true contradiction, a statement, A, such that both it and its negation, A, are true. Hence, dialeth(e)ism is the view that there are true contradictions. Dialetheism opposes the so-called Law of Non-Contradiction. By Graham Priest, from the Stanford Encyclopedia.

    Philosophy of Mathematics Class Notes - Notes to a class by Carl Posy at Duke University, Fall 1992.

    Nineteenth Century Geometry - Philosophical-historical survey of the development of geometry in the 19th century. From the Stanford Encyclopedia, by Roberto Toretti.

    19th Century Logic between Philosophy and Mathematics - Online article by Volker Peckhaus.

    Experimental Mathematics - A journal devoted to experimental aspects of mathematical research; now available electronically to subscribers. During the current open trial period you don't have to be a subscriber to access articles electronically. You can browse through the volumes and download most articles in Postscript form.

    Social Constructivism as a Philosophy of Mathematics - Article by Paul Ernest.

    Foundations: Philosophy of Mathematics - A study guide on the Philosophy of Mathematics provided by The Objectivist Center, including a study guide on the subject.

    Paul Ernest's Page - Based at School of Education, University of Exeter, United Kingdom, includes the text of back issues of the Philosophy of Mathematics Education Journal, and other papers on the philosophy of mathematics and related subjects.

    Philosophy of Science and Mathematics Events in Britain - University of Cambridge Department of History and Philosophy of Science. The stated purpose of this site is to help philosophers of science and mathematics in Britain to find each other in ordinary spacetime.

    Philosophical Biographies: Mathematics 1905-1933 - Short biographies of Frege, Schlick, Brouwer, Hilbert, Carnap, Gödel, and Turing from the Hegel by HypertText site.


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