philosophy of mathematics | A Philosopher's Take

Browsing All posts tagged under »philosophy of mathematics«

Discovery and Invention Part I: Distinctions and Notations

December 6, 2018 by Aaron Thomas-Bolduc

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 […]

Frege and Hume at Thanksgiving

October 2, 2018 by Aaron Thomas-Bolduc

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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 […]

The Further Adventures of Hero and Hera.

September 27, 2017 by Aaron Thomas-Bolduc

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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 […]

Goldilocks, Bad Company and some Slippery Fish

February 28, 2017 by Aaron Thomas-Bolduc

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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. […]

Call for Applications: Summer School on Mathematical Philosophy for Female Students

December 23, 2016 by Aaron Thomas-Bolduc

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I was reminded by Alison’s post yesterday, that the Munich Center for Mathematical Philosophy (MCMP) has recently put out their call for applications for their summer school for women. It is the fourth iteration of this summer school, and this year’s lecturers are a veritable who’s who of mathematical philosophy. Applications are due March 5th, […]

Grinworthy Quotes (10)

November 5, 2015 by Aaron Thomas-Bolduc

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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 […]

Grinworthy Quotes (9)

October 8, 2015 by Aaron Thomas-Bolduc

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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. […]

Grinworthy Quotes (8)

June 5, 2015 by Aaron Thomas-Bolduc

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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, […]

Hashtag_Octothorpe

April 26, 2015 by Aaron Thomas-Bolduc

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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 […]

Grinworthy Quotes (7)

March 14, 2015 by Aaron Thomas-Bolduc

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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, […]