Office: 2228 Angell Hall

Department of
Philosophy

University of Michigan

Ann Arbor, MI 48109

Email:
tappen@umich.edu

Office Telephone: 734-764-2450

Last updated:
29 May 2008

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 Jørensen. (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:

**Personal:**

**Family Pictures:**

· My son Peter and I snowshoeing across frozen Lake Nipissing

· Peter at his grade 2 Halloween parade

· Andrea and Peter, shore of lake Nipissing in summer

· Michele and I in our favorite environment

· Michele and I in our second favorite – Lake Nipissing in winter

· Andrea, Peter and cousins Alex and Haley doing a snow dance – it worked!

My Parents' house from the ice on Lake Nipissing in winter

· Peter playing soccer: postgame , focus 1 , focus 2 , flying , safe hands , postgame 2