19th Century Logic between Philosophy and Mathematics
Online article by Volker Peckhaus.
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'.…
Foundations: Philosophy of Mathematics
A study guide on the Philosophy of Mathematics provided by The Objectivist Center, including a study guide on the subject.
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 Sta…
Holistic Math
An enlarged paradigm of mathematical reality that includes psychology as an integral component.
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 whic…
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 ind…
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…
Nineteenth Century Geometry
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
A paper by Harold Ravitch, Los Angeles Valley College.
The Philosophical Implications of Mathematics
This weblog examines what we can learn about our humanness from the act of doing mathematics.
The Philosophy of Mathematics
Notes by R.B. Jones of foundations, problems, logicism and philosophers of mathematics.