Directory of Mathematics Resources

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• 19th Century Logic between Philosophy and Mathematics

http://www.meta-religion.com/Mathematics/Philosophy_of_mathematics/19_century_logic.htm
Online article by Volker Peckhaus.

• Canadian Society for History and Philosophy of Mathematics

http://www.cshpm.org/
Bulletin, members' pages, meetings.

• Constructive Mathematics

http://plato.stanford.edu/entries/mathematics-constructive/
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.

• Hilbert's Program

http://plato.stanford.edu/entries/hilbert-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.

• Holistic Math

http://www.iol.ie/~peter/
An enlarged paradigm of mathematical reality that includes psychology as an integral component.

• Inconsistent Mathematics

http://plato.stanford.edu/entries/mathematics-inconsistent/
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.

• Indispensability Arguments in the Philosophy of Mathematics

http://plato.stanford.edu/entries/mathphil-indis/
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.

• Intuitionistic Logic

http://plato.stanford.edu/entries/logic-intuitionistic/
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.

• Nineteenth Century Geometry

http://plato.stanford.edu/entries/geometry-19th/
Philosophical-historical survey of the development of geometry in the 19th century. From the Stanford Encyclopedia, by Roberto Toretti.

• On Gödel's Philosophy of Mathematics

http://www.friesian.com/goedel/
A paper by Harold Ravitch, Los Angeles Valley College.

• Paul Ernest's Page

http://people.exeter.ac.uk/PErnest/
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 Mathematics Class Notes

Notes to a class by Carl Posy at Duke University, Fall 1992.

• Social Constructivism as a Philosophy of Mathematics

http://people.exeter.ac.uk/PErnest/soccon.htm
Article by Paul Ernest.

• The Logical and Metaphysical Foundations of Classical Mathematics

http://www.st-andrews.ac.uk/~arche/projects/maths/
Arché Research Project at the University of St Andrews. Description of the project, sponsors, researchers and publications.

• The Philosophical Implications of Mathematics

http://meaningofmath.blogspot.com/
This weblog examines what we can learn about our humanness from the act of doing mathematics.

• The Philosophy of Mathematics

http://www.rbjones.com/rbjpub/philos/maths/
Notes by R.B. Jones of foundations, problems, logicism and philosophers of mathematics.

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