the stuff of proof: interview with Penelope Maddy

Richard Marshall in 3:AM Magazine:

Penelope Maddy is the candy-store kid of metaphilosophical logic and maths. She’s stocked up with groovy thoughts about the axioms of mathematics, about what might count as a good reason to adopt one, about mathematical realism, about Gödel’s intuitions, naturalism, second philosophy, Hume and Quine, world-word connections, about where mathematical objectivity comes from, about the limitations of drawing analogies, about depth, about Wittgenstein and the logical must, about the Kantianism of the Tractatus and about the relationship between science and philosophy. Suck it and see, this one has a fizz …

3:AM: What made you become a philosopher? Are you a lone brooder or prefer to think and argue aloud with others?

Penelope Maddy: I started out in mathematics and was moved from there to philosophy by others, oddly enough, without really understanding what was going on. Foundational questions captured my interest early on: one of my most cherished memories is the sudden realization that the number 1 could be defined in naive set theory! Poking around in my great high school math teacher’s secret book closet, I soon came to understand that 2+2=4 and the rest of classical mathematics could be proved from the standard assumptions of axiomatic set theory, but that one of the first and most natural questions about infinite sets, the Continuum Hypothesis (CH), couldn’t be settled one way or the other on the basis of those same axioms. What could a solution to such an open question even look like?!

At the time, UC Berkeley was the place to go to study set theory: forcing was new, and larger and larger large cardinal axioms were being proposed in turn. Another vivid memory is watching in awe as one of my professors showed us the proof that if there’s a measurable cardinal, then one of the open questions (not CH, alas) has an answer (there are sets outside Gödel’s minimal universe). This was just the answer one would want and expect, but why in the world would one think that this candidate for a new axiom — ‘there are measurable cardinals’ — is true?! Perhaps there could be new axioms even to settle CH, but what counts as a proper argument for or against a proposed axiom?

Without realizing it, I’d slipped into philosophy. When I applied to the Princeton math department for graduate school, they admitted me instead into the program in history and philosophy of science on the basis of my statement of interests. Being from Berkeley, I figured this must be a program like their Logic and Methodology, but when I arrived, it turned out I was pretty much just in the philosophy department. The transition took some fierce adjustments and teetered on disaster at times, but I eventually came to see the wisdom of those admissions officers.

More here.