Browsing All Posts filed under »Philosophy of Math«

Teaching as a Grad Student: Guest Lecturing on Logicism

April 26, 2017 by

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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

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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. […]

Is the Universe Part of the World?

June 11, 2016 by

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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 […]

Grinworthy Quotes (10)

November 5, 2015 by

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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

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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 The following quote is at the very beginning of Paul Benacerraf’s unpublished PhD dissertation (Princeton, 1960) which I’m reading as part of my dissertation research.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

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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

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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 […]