A group of bloggers discussing philosophical ideas as well as the profession of philosophy

*October 8, 2018*
by *Aaron Thomas-Bolduc*

Comments Off on Grinworthy Quotes (16): Self-promotion Edition

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 […]

*February 21, 2018*
by *Aaron Thomas-Bolduc*

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 […]

*February 16, 2018*
by *Aaron Thomas-Bolduc*

Comments Off on Grinworthy Quotes (15)

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 […]

*January 18, 2018*
by *Aaron Thomas-Bolduc*

Comments Off on Grinworthy Quotes 14

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.

*September 27, 2017*
by *Aaron Thomas-Bolduc*

Comments Off on The Further Adventures of Hero and Hera.

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 […]

*April 26, 2017*
by *Aaron Thomas-Bolduc*

Comments Off on Teaching as a Grad Student: Guest Lecturing on Logicism

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 […]

*February 28, 2017*
by *Aaron Thomas-Bolduc*

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. […]

*November 5, 2015*
by *Aaron Thomas-Bolduc*

Comments Off on Grinworthy Quotes (10)

Here’s other amusing line from Paul Benacerraf’s dissertation (Princeton, 1960, p. 182): It was in fact through [Cantor’s] interest in the infinite and in infinite numbers that he developed the theory of sets. The purpose was to make an honest woman of the infinite, a task held by most mathematicians of his time to be […]

*October 8, 2015*
by *Aaron Thomas-Bolduc*

Comments Off on Grinworthy Quotes (9)

I know it’s been a while since I’ve posted one of these — I’ve been reading some fairly dry material recently. The following quote is at the very beginning of Paul Benacerraf’s unpublished PhD dissertation (Princeton, 1960) which I’m reading as part of my dissertation research. The quote is attributed to an unnamed undergraduate student. […]

*June 5, 2015*
by *Aaron Thomas-Bolduc*

Comments Off on Grinworthy Quotes (8)

Here is another quote from John Burgess, this time from his book Fixing Frege (Princeton University Press: 2005). Anyone who reads logic/mathematics/philosophy of mathematics will have come across the phenomenon he’s talking about. Now it is a common mathematical practice, called “abuse of language,” to omit to distinguish notationally between items that are distinct notionally, […]

*April 26, 2015*
by *Aaron Thomas-Bolduc*

Comments Off on Hashtag_Octothorpe

A while back I was reading a paper by Bob Hale and Crispin Wright, first published in 2000 [1], in which they use the symbol “#” to denote an arbitrary matrix sentence. That was over half a decade before twitter went live. That symbol, variously known as the hash sign/symbol, the number sign, or octothorpe […]

*March 14, 2015*
by *Aaron Thomas-Bolduc*

Comments Off on Grinworthy Quotes (7)

Here is John Burgess’s amusing description of Quine’s view of mathematical ontology as motivated by the indispensability argument, from “Mathematics and the Bleak House” (Phil. Math. 12, 2004). Quine…urged a very different sort of reason for accepting the existence of numbers (or other abstract mathematical entities to which numbers could be “reduced”). According to Quine, […]

*October 1, 2014*
by *Aaron Thomas-Bolduc*

Justin Caouette suggested to me that I start posting some of the amusing, and sometimes shocking philosophical quotations that I come across, and often share with him. This will be an on going series, though it is a matter of what I happen to be reading at any given time. The reason I have been […]

*July 23, 2014*
by *Aaron Thomas-Bolduc*

Comments Off on Bleg: Philosophy survey for mathematicians (From Logblog)

There’s a new survey about the intuitions of mathematicians which will be very helpful for philosophers of mathematics (like me). Here is Richard Zach’s original post: A group of researchers in philosophy, psychology and mathematics are requesting the assistance of the mathematical community by participating in a survey about mathematicians’ philosophical intuitions. The survey is […]

*June 23, 2014*
by *Aaron Thomas-Bolduc*

I work primarily in the philosophy and history of mathematics which has naturally led to discussion about the philosophy of mathematics with people outside my field, and outside of philosophy. In this post I will try to address, in a loose and (mostly) non-technical way, some of the questions that often arise in such discussions. […]

December 6, 2018byAaron Thomas-Bolduc3