Reading Natural Philosophy: Essays in the History and Philosophy of Science and Mathematics

By David B. Malament | Go to book overview

13
Maximality vs. Extendability:
Reflections on Structuralism and
Set Theory

GEOFFREY HELLMAN


1. Introduction

In a recent paper, while discussing the role of the notion of analyticity in Carnap's thought, Howard Stein wrote:

The primitive view--surely that of Kant — was that whatever is trivial is obvious.
We know that this is wrong; and 1 would put it that the nature of mathemati-
cal knowledge appears more deeply mysterious today than it ever did in earlier
centuries—that one of the advances we have made in philosophy has been to
come to an understanding of just how deeply puzzling the epistemology of
mathematics really is. (1993, 283)

Although our principal concern here is not with analyticity but rather with competing visions of the very subject matter of mathematics, the present essay can certainly be read as an extended illustration of this poignant remark.1

There is a recurring emphasis in Stein's writing on the importance of theoretical insights of our leading intellectual forebears in science and mathematics for the healthy practice of philosophy. In this spirit, I can think of no better way to introduce the subject of this essay than by quoting from the concluding remarks of Zermelo's great, yet underappreciated, 1930 paper, “Über Grenzzablen und Mengenbereiche.” Having formulated

I am grateful to audiences at the Steinfest. University of Chicago, May 21–23, 1999,
and at the Philosophy of Mathematics Conference at the University of California,
Santa Barbara, Feb. 4–6, 2000, and especially to Stewart Shapiro and Tony Anderson,
for helpful comments on earlier drafts of this paper.

-335-

Notes for this page

Add a new note
If you are trying to select text to create highlights or citations, remember that you must now click or tap on the first word, and then click or tap on the last word.
One moment ...
Default project is now your active project.
Project items

Items saved from this book

This book has been saved
Highlights (0)
Some of your highlights are legacy items.

Highlights saved before July 30, 2012 will not be displayed on their respective source pages.

You can easily re-create the highlights by opening the book page or article, selecting the text, and clicking “Highlight.”

Citations (0)
Some of your citations are legacy items.

Any citation created before July 30, 2012 will labeled as a “Cited page.” New citations will be saved as cited passages, pages or articles.

We also added the ability to view new citations from your projects or the book or article where you created them.

Notes (0)
Bookmarks (0)

You have no saved items from this book

Project items include:
  • Saved book/article
  • Highlights
  • Quotes/citations
  • Notes
  • Bookmarks
Notes
Cite this page

Cited page

Style
Citations are available only to our active members.
Sign up now to cite pages or passages in MLA, APA and Chicago citation styles.

(Einhorn, 1992, p. 25)

(Einhorn 25)

1

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

Cited page

Bookmark this page
Reading Natural Philosophy: Essays in the History and Philosophy of Science and Mathematics
Table of contents

Table of contents

Settings

Settings

Typeface
Text size Smaller Larger Reset View mode
Search within

Search within this book

Look up

Look up a word

  • Dictionary
  • Thesaurus
Please submit a word or phrase above.
Print this page

Print this page

Why can't I print more than one page at a time?

Full screen
/ 429

matching results for page

Cited passage

Style
Citations are available only to our active members.
Sign up now to cite pages or passages in MLA, APA and Chicago citation styles.

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn, 1992, p. 25).

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences."1

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

Cited passage

Welcome to the new Questia Reader

The Questia Reader has been updated to provide you with an even better online reading experience.  It is now 100% Responsive, which means you can read our books and articles on any sized device you wish.  All of your favorite tools like notes, highlights, and citations are still here, but the way you select text has been updated to be easier to use, especially on touchscreen devices.  Here's how:

1. Click or tap the first word you want to select.
2. Click or tap the last word you want to select.

OK, got it!

Thanks for trying Questia!

Please continue trying out our research tools, but please note, full functionality is available only to our active members.

Your work will be lost once you leave this Web page.

For full access in an ad-free environment, sign up now for a FREE, 1-day trial.

Already a member? Log in now.