Banishing Infinity
The Ultrafinitist Gambit Let’s start with a confession. I love mathematics, but I’m allergic to grand metaphysical claims. Infinity sits right at the center of those claims like a peacock in a library. Gorgeous. Loud. A little absurd in the wrong aisle. Enter the ultrafinitists . They walk in with scissors and start clipping the peacock’s tail. They argue that infinity isn’t just suspicious. It’s unnecessary. Worse, it’s misleading. If you can’t build it, compute it, or even name it without cheating, why are we treating it like a citizen of mathematics? That’s the vibe. It’s bolder than classic finitism and pricklier than intuitionism . It says: cut the drama. Keep the numbers you can actually touch. Maybe also the ones you can plausibly reach. The rest is costume jewelry. This isn’t a purely armchair rebellion. In April 2025, Columbia University hosted a conference. Ultrafinitism: Physics, Mathematics, & Philosophy. The roster was serious. Set theorist Joel David Hamki...