Philosophy of Science: Mathematics

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	Home: Philosophy of Science: Mathematics CATEGORIES:   Brown, George Spencer (5)   Conferences (9)   Journals (3) LINKS: 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. 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. 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. 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. Philosophy of Mathematics Class Notes http://www.cs.washington.edu/homes/gjb/doc/philmath.htm Notes to a class by Carl Posy at Duke University, Fall 1992. 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. Social Constructivism as a Philosophy of Mathematics http://www.ex.ac.uk/~PErnest/soccon.htm Article by Paul Ernest. Paul Ernest's Page http://www.ex.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. PHILTAR - Philosophy of Mathematics http://philtar.ucsm.ac.uk/philosophy_of_mathematics/individual_philosophers/ Links to pages on individual philosophers. The Logical and Metaphysical Foundations of Classical Mathematics http://www.st-andrews.ac.uk/academic/philosophy/arche/math.shtml Arché Research Project at the University of St Andrews. Description of the project, sponsors, researchers and publications. Mathematical Structures Group http://www.mmsysgrp.com/mathstrc.htm 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. On Gödel's Philosophy of Mathematics http://www.friesian.com/goedel/ A paper by Harold Ravitch, Los Angeles Valley College. Foundations: Philosophy of Mathematics http://ios.org/articles/foundations_phil-of-mathematics.asp A study guide on the Philosophy of Mathematics provided by The Objectivist Center, including a study guide on the subject. Canadian Society for History and Philosophy of Mathematics http://home.adelphi.edu/~cshpm/ Bulletin, members' pages, meetings. Structuralism, Category Theory and Philosophy of Mathematics http://www.mmsysgrp.com/strctcat.htm By Richard Stefanik (Washington: MSG Press,1994). Holistic Math http://www.iol.ie/~peter/ An enlarged paradigm of mathematical reality that includes psychology as an integral component. 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. 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. 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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