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3 March 2016

Infinitesimals, Magnitudes and Definition in Frege

Here are two papers on mathematical concepts and definitions for a forthcoming book edited by Paolo Mancosu; These are first steps in the direction of making sense of the idea that some mathematical properties and definitions might be more ???natural??? than others. To conform to the format of the book, the first of these essays is meant to be survey-ish and introductory, so I just touch on some issues that need further development. In the first paper I use the definition of ???prime number??? and the introduction of the Legendre symbol in number theory as my core examples.

Here is a revised version of the ???Metatheory and Mathematical Practice in Frege??? paper ??? it has been edited and considerably shortened (at the request of the editors), for republication in the Reck-Beaney collection of papers on Frege. I???ve added a few new observations on more recent work, but for the most part I???ve tried to avoid extensive rewriting. The main result of the editing is that a paper that had been an inefficient hybrid of some details of the history of mathematics and some critical analysis of the ???no metatheory in Frege??? interpretation of Frege is now distilled into just a critical discussion of the ???no metatheory??? view. (The history of mathematics details will reappear elsewhere.) I???m told this version is much easier to read. (May 2005: further historical information, about ???transfer principles??? added at the editors request.) Link is to uncorrected page proofs.

A first attempt to make some sense of mathematical explanation and understanding, with special reference to visualization and unification ??? based accounts of understanding. Forthcoming in a volume on mathematical explanation, understanding and visualization edited by Paolo Mancosu and Klaus J??rensen. (uncorrected page proofs ??? so there may be typos, etc.) Comments most welcome. I hope that I will be allowed to immodestly claim that this contains the best account ever written of the philosophical significance of the 1905 Quebec Bridge collapse.

Proofstyle and Understanding in Mathematics I: Visualization, Unification and Axiom Choice

Here???s a link to the book in which the above article appears

Metatheory
and Mathematical Practice in Frege (appeared in **Philosophical
Topics** Fall 1997 issue [actually appeared in print 1998])

OOPS: the pdf file linked above is missing a page. Here is a copy of the missing page: Page 223

The
Liar and Sorites Paradoxes: Toward a Unified Treatment (appeared
in **Journal of Philosophy** Fall 1993; Reprinted in Delia Graff
and Tim Williamson???s collection *Vagueness* (Ashgate press))

Extending
Knowledge and ???Fruitful Concepts???: Fregean Themes in the
Philosophy of Mathematics (appeared in **Nous** Dec 1995
Reprinted in *Philosopher???s Annual* 1996; to be reprinted in a
collection on Frege edited by Erich Reck and Mike Beaney)

[PDF files ??? thanks to JSTOR]

Appeared in *Notre Dame Journal of Formal Logic* -
the file is an uncorrected galley proof

This one is an MS word file:

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?? My son Peter and I snowshoeing across frozen Lake Nipissing

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