INDEX

Jamie Tappenden

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: 3 March 2016

Curriculum Vitae

Some Online Papers:

Here is a paper dealing with Frege on the concept of object and the connection to sharp definition. His definition of infinitesimal is an orienting case study. The paper draws on his discussion of Riemann's definition of the Riemann integral, which Frege puts forward as a model correct definition. The paper also contains some discussion of Clebsch-Aronhold symbolic notation in the study of algebraic invariants.

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.

Mathematical Concepts and Definitions

Mathematical Concepts: Fruitfulness and Naturalness

The first half of my forthcoming book is a study of Frege and his nineteenth century mathematical environment, as well as a glimpse into some of these independently exciting and philosophically interesting mid-nineteenth century developments, exemplified by the contrast in styles of Riemann and Weierstrass. There are a lot of details; an overview of the historical background, and an overview of the connection to Frege, appears in this article "The Riemannian Background to Frege's Philosophy". The link is to uncorrected page proofs: the article appears in The Architecture of Modern Mathematics (OUP 2006) edited by Jeremy Gray and Jose Ferreir??s:

The Riemannian Background to Frege???s Philosophy

One of my current research objectives is to chart out the details and philosophical interest of Riemann???s idea (picked up by Dedekind and others) that proper mathematical method involves defining concepts by ???essential characteristics???. Among the criteria for recognizing when a function has been properly defined by essential characteristics is fruitfulness in supporting easy arguments for problems that had previously required ???tiresome computations???. A first step toward working out these details is this paper, which recently appeared in Dialectica. It takes as its organizing focus Frege???s ???Julius Caesar Problem???. The link is to uncorrected page proofs:

The Caesar Problem in its Historical Context: Mathematical Background

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.

Metatheory and Mathematical Practice in Frege (significantly shortened and slightly updated with new material)

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]