Browsing All Posts filed under »Philosophy of Math«

It’s a Small World: The Leśniewski-Sobociński Theorem.

February 21, 2018 by


The other day I was reading M. Resnik’s Frege and the Philosophy of Mathematics (1980). In discussing `Frege’s way out’, he mentions a proof by Leśniewski showing that Frege’s attempted fix to the system of the Grundgesetze is inconsistent, but gives a reference to a paper published by Sobociński in 1949. This intrigued me, as […]

Grinworthy Quotes 15

February 16, 2018 by


Frege on Euclidean geometry and axioms, but also astrology and alchemy. From his Nachlass*. Now the question is whether to strike Euclidean or non-Euclidean geometry from the ranks of science and to put it alongside of Alchemy and Astrology as mummies. Where one only let himself toy with ideas, he need not take things so […]

Grinworthy Quotes 14

January 18, 2018 by


In discussing the possibility of adopting category theory as a (the) foundations for mathematics, Jean-Pierre Marquis has this to say in his Stanford Encyclopedia article (2015): To use a well-known metaphor: from a categorical point of view, Neurath’s ship has become a spaceship. I hope there is a literature developing about Neurath’s spaceship.

The Further Adventures of Hero and Hera.

September 27, 2017 by


Those familiar with the neo-logicism literature, may also be familiar with the characters Hero and Hera. Hero was introduced by Crispin Wright in the late `90s, and the story Hero and his sister Hera was fleshed out by Philip Ebert and Marcus Rossberg in 2007*. In that paper, we learn that Hero and Hera both […]

Teaching as a Grad Student: Guest Lecturing on Logicism

April 26, 2017 by


I was recently given the opportunity to give a lecture on Frege’s logicism and related topics for our Logic III course (cross-listed as an undergraduate and a graduate course). That class had gotten up to the point of looking at second-order Peano Arithmetic, which is a natural jumping off point for looking at the logic […]

Goldilocks, Bad Company and some Slippery Fish

February 28, 2017 by

Comments Off on Goldilocks, Bad Company and some Slippery Fish

No this isn’t a terrible (amazing?) fairy tale. And no, the title isn’t (just) badly thought out clickbait. The Bad Company problem, the Goldilocks problem and the Problem of Fishiness are all problems I’m writing about in my dissertation. More specifically, the overarching idea is to look at ways of solving the Bad Company problem. […]

Is the Universe Part of the World?

June 11, 2016 by

Comments Off on Is the Universe Part of the World?

First let me head off the suspicion that I’ll be discussing some sort of weird idealist/massively subjectivist/etc metaphysics. I’m concerned with ‘world’ and ‘universe’ as they’re used by analytic metaphysicians, logicians, and philosophers of mathematics. In particular I’m concerned about the cardinalities of the domains of discourse assumed by some philosophers when dealing with, in […]