Skip to main content Accessibility help
×
Hostname: page-component-8448b6f56d-dnltx Total loading time: 0 Render date: 2024-04-18T22:50:44.524Z Has data issue: false hasContentIssue false

5 - Improvements in the new edition

Published online by Cambridge University Press:  05 August 2011

Bernard Linsky
Affiliation:
University of Alberta
Get access

Summary

Russell begins the Introduction to the second edition by writing that the body of the text has not been changed for the new edition because any new propositions would disrupt the elaborate system of numbered theorems. Changes, he says, will be proposed in the Introduction, but not worked into the system. Appendix A does have a number (✻8), and numbered theorems, but the other changes are not formulated so technically. Thus even the definitions of the standard connectives in terms of the Sheffer stroke remain unnumbered. More serious for the reader, however, is the lack of precision in the discussion of extensionality and the abandonment of the axiom of reducibility. The informal approach to the discussion of the changes leaves it unclear which are minor, and which central, and for all, exactly what is being proposed. Following the opening excuse for not modifying the technical body of the work, Russell goes on to present a seemingly disjointed list of changes which are “desirable”, beginning with what he describes as “the most definite improvement resulting from work in mathematical logic during the past fourteen years…”. This improvement turns out to be the reduction of the propositional connectives to one, the Sheffer stroke “p|q” for “not both p and q.” It is true that the foundation for the logic circuits of contemporary computer chips is the thousands of connections executing operations on current that model this very stroke, now called the “nand” connective, so, in a way, this use of the Sheffer stroke in “logic” is the greatest legacy of the second edition of PM.

Type
Chapter
Information
The Evolution of Principia Mathematica
Bertrand Russell's Manuscripts and Notes for the Second Edition
, pp. 108 - 137
Publisher: Cambridge University Press
Print publication year: 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×