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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.
http://plato.stanford.edu/entries/logic-intuitionistic/
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.
http://plato.stanford.edu/entries/mathphil-indis/
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.
http://plato.stanford.edu/entries/mathematics-constructive/
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.
http://plato.stanford.edu/entries/mathematics-inconsistent/
Philosophy of Mathematics Class Notes
Notes to a class by Carl Posy at Duke University, Fall 1992.
http://www.cs.washington.edu/homes/gjb/doc/philmath.htm
Nineteenth Century Geometry
Philosophical-historical survey of the development of geometry in the 19th century. From the Stanford Encyclopedia, by Roberto Toretti.
http://plato.stanford.edu/entries/geometry-19th/
19th Century Logic between Philosophy and Mathematics
Online article by Volker Peckhaus.
http://www.phil.uni-erlangen.de/~p1phil/personen/peckhaus/texte/logic_phil_math.html
Social Constructivism as a Philosophy of Mathematics
Article by Paul Ernest.
http://www.ex.ac.uk/~PErnest/soccon.htm
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.
http://www.ex.ac.uk/~PErnest/
PHILTAR - Philosophy of Mathematics
Links to pages on individual philosophers.
http://philtar.ucsm.ac.uk/philosophy_of_mathematics/individual_philosophers/
The Logical and Metaphysical Foundations of Classical Mathematics
Arché Research Project at the University of St Andrews. Description of the project, sponsors, researchers and publications.
http://www.st-andrews.ac.uk/academic/philosophy/arche/math.shtml
Mathematical Structures Group
Research topics include mathematical models and theories in the empirical sciences, models and theories in mathematics, category theory, and the use of mathematical structures in theoretical computer science. Bibliographic data.
http://www.mmsysgrp.com/mathstrc.htm
On Gödel's Philosophy of Mathematics
A paper by Harold Ravitch, Los Angeles Valley College.
http://www.friesian.com/goedel/
Foundations: Philosophy of Mathematics
A study guide on the Philosophy of Mathematics provided by The Objectivist Center, including a study guide on the subject.
http://ios.org/articles/foundations_phil-of-mathematics.asp
Canadian Society for History and Philosophy of Mathematics
Bulletin, members' pages, meetings.
http://home.adelphi.edu/~cshpm/
Structuralism, Category Theory and Philosophy of Mathematics
By Richard Stefanik (Washington: MSG Press,1994).
http://www.mmsysgrp.com/strctcat.htm
Holistic Math
An enlarged paradigm of mathematical reality that includes psychology as an integral component.
http://www.iol.ie/~peter/
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/
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