David Armstrong on the Metaphysics of Mathematics

This paper has two components. The first, longer component (sec. 1-6) is a critical exposition of Armstrong’s views about the metaphysics of mathematics, as they are presented in Truth and Truthmakers and Sketch for a Systematic Metaphysics. In particular, I discuss Armstrong’s views about the nature of the cardinal numbers, and his account of how modal truths are made true. In the second component of the paper (sec. 7), which is shorter and more tentative, I sketch an alternative account of the metaphysics of mathematics. I suggest we insist that mathematical truths have physical truthmakers, without insisting that mathematical objects themselves are part of the physical world.