“The point of philosophy is to start with something so simple as not to seem worth stating, and to end with something so paradoxical that no one will believe it.”–Bertrand Russell

Mathematics is nearly always referred to as the foundation of science. It is imagined to be a type of bedrock upon which the rest of our knowledge is built. It is common to hear people talk of mathematics being “everywhere” and in “everything”.

But, is this justified? Is mathematics really IN everything. Or does it simply give one hell of a good approximation of (nearly) everything. Is mathematics real at all? Or is it simply a highly workable form of Logic? These are some (though, not nearly all) of the questions that Philosophers of Mathematics find themselves asking. And I’ve compiled a short list of links to get the ball rolling if you find yourself interested in the topic (Categorized by Essays, General websites, and People).

Essays:

The Unreasonable Effectiveness of Mathematics in the Natural Sciences by Eugene Wigner. This is a fantastic essay on exactly what the title says. Though it seems strange to call the effectiveness of Math in the Natural Sciences Unreasonable, it may very well be. I’d start here for a good read.

The Axiom of Choice by Eric Schechter, This one’s a bit Mathy, but if you have the back ground it’s quite interesting.

General Websites:

The Philosophy of Mathematics website. A web page with a comprehensive selection of material.

Stanford Encyclopedia of Philosophy. There are some links here to the Philosophy of Mathematics along with a huge amount on Philosophy in general.

The Canadian Society for the History and Philosophy of Mathematics

Philosophy of Real Mathematics. This is a blog that seems to be dying out. But the archives are a treasure trove (did I spell that right?)

The n-Category Cafe. Another Blog, mostly about Math proper, but Philosophy and physics are both thrown in.

People:

Wittgenstein at the Stanford Encyclopedia

The Bertrand Russell Society Quarterly

Leibniz translations A page with many translations of Leibniz’s work, including writings on Metaphysics, Ethics, Etc.

Aristotle at MIT, a compendium of his writing. Our concern is with his logic writing which comes from a collection know together as, “The Organon.” This consists of “The Categories”, “Topics”, “The Prior Analytic”, On Interpretation”, and “The Posterior Analytic”

Godel’s Philosophy of Mathematics, by Harold Ravitch, PhD

Frege. He is generally considered the founder of modern Logic, and pushed the idea of Logicism (ie. Math=logic).