Browsing All Posts filed under »Philosophy of Math«

Discovery and Invention Part I: Distinctions and Notations

December 6, 2018 by

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In this three part (probably) series, I’m going to look at the notions of invention and discovery as they relate to how we think about mathematics and logic. In this first post, I’m going to set up the distinction between discovery and invention as I see it, and then talk about whether systems of notation for […]

Grinworthy Quotes (16): Self-promotion Edition

October 8, 2018 by

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I just had a co-authored (with Eamon Darnell) paper that’s based on a chapter of my dissertation (both titled “Is Hume’s Principle Analytic?” — link to preprint of the paper) accepted for publication (yay!). Near the end of the paper, we raise an issue that seems (to me at least) to have been under the surface […]

Frege and Hume at Thanksgiving

October 2, 2018 by

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It’s almost Thanksgiving here in Canada, so here’s a thanksgiving themed post about concepts from Frege and Neo-logicism. In his Grundlagen (1884), Frege proposes that the number that belongs to two concepts is the same just in case the objects falling under those concepts can be correlated one-to-one (i.e. they’re equinumerous). The formalization of that claim is […]

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

February 21, 2018 by

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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

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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

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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

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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 […]