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The Philosophical Implications of Mathematics -
This weblog examines what we can learn about our humanness from the act of doing mathematics.
http://meaningofmath.blogspot.com Social Constructivism as a Philosophy of Mathematics -
Article by Paul Ernest.
http://www.ex.ac.uk/~PErnest/soccon.htm 19th Century Logic between Philosophy and Mathematics -
Online article by Volker Peckhaus.
http://www.meta-religion.com/Mathematics/Philosophy_of_mathematics/19_century_logic.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/ 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/~arche/projects/maths/ 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/ The Philosophy of Mathematics -
Notes by R.B. Jones of foundations, problems, logicism and philosophers of mathematics.
http://www.rbjones.com/rbjpub/philos/maths/ 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/ PHILTAR - Philosophy of Mathematics -
Links to pages on individual philosophers.
http://philtar.ucsm.ac.uk/philosophy_of_mathematics/individual_philosophers/ 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/ Canadian Society for History and Philosophy of Mathematics -
Bulletin, members' pages, meetings.
http://home.adelphi.edu/~cshpm/ 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/ Holistic Math -
An enlarged paradigm of mathematical reality that includes psychology as an integral component.
http://www.iol.ie/~peter/ 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 On Gödel's Philosophy of Mathematics -
A paper by Harold Ravitch, Los Angeles Valley College.
http://www.friesian.com/goedel/ Philosophy of Mathematics Class Notes -
Notes to a class by Carl Posy at Duke University, Fall 1992.
http://www.badros.com/greg/doc/philmath.htm 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 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/ Structuralism, Category Theory and Philosophy of Mathematics -
By Richard Stefanik (Washington: MSG Press,1994).
http://www.mmsysgrp.com/strctcat.htm
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