Browsing All posts tagged under »Frege«

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 […]

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. […]

Grinworthy Quotes (12)

July 24, 2016 by

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Here’s W. V. O. Quine discussing the fact that Frege didn’t adopt a type theoretic approach (like Russell and Whitehead’s) when faced with Russell’s paradox. Actually, it is not to be wondered that Frege did not think of this course, or, thinking of it, adopt it. It was by having all his classes at ground […]

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. […]