Surf these sites: 19th Century Logic between Philosophy and Mathematics -- Online article by Volcker Peckhaus. CSHPM -- Canadian Society for History and Philosophy of Mathematics 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. 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. 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 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. Intuitionistic Logic -- A short entry in the Stanford Encyclopaedia of Philosophy by Joan R. Moschovakis. Nineteenth Century Geometry -- Philosophical-historical survey of the development of geometry in the 19th century. From the Stanford Encyclopedia, by Roberto Toretti. 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. Philosophia Mathematica -- Journal devoted specifically to philosophy of mathematics. Abstracts available online. Philosophy of Mathematics Class Notes -- Notes to a class by Carl Posy at Duke University, Fall 1992.
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