Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Home
Hostname: page-component-55597f9d44-2qt69 Total loading time: 0.559 Render date: 2022-08-17T09:51:44.082Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "useNewApi": true } hasContentIssue true
  • English
Philosophy Philosophy

Article contents

Lucas against Mechanism

Published online by Cambridge University Press:  25 February 2009

David Lewis
David Lewis
Affiliation:
University of California at Los Angeles.
Rights & Permissions[Opens in a new window]

Extract

HTML view is not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

J. R. Lucas argues in “Minds, Machines, and Gödel”, that his potential output of truths of arithmetic cannot be duplicated by any Turing machine, and a fortiori cannot be duplicated by any machine. Given any Turing machine that generates a sequence of truths of arithmetic, Lucas can produce as true some sentence of arithmetic that the machine will never generate. Therefore Lucas is no machine.

Type
Discussion
Information
Philosophy , Volume 44 , Issue 169 , July 1969 , pp. 231 - 233
Copyright
Copyright © The Royal Institute of Philosophy 1969

References

1 Philosophy, 36 (1961): 112–127.Google Scholar

2 Lucas arithmetic belongs to a class of extensions of Peano arithmetic studied by Turing, A. M. in “Systems of Logic Based on Ordinals”, Proceedings of the London Mathematical Society, sec. 2, 45 (1939): 161–228CrossRefGoogle Scholar, and by Feferman, S. in “Transfinite Recursive Progressions of Axiomatic Theories”, Journal of Symbolic Logic, 27 (1962): 259–316.CrossRefGoogle Scholar

3 I am indebted to George Boolos and Wilfrid Hodges for valuable criticisms of an earlier version of this paper.

You have Access
46
Cited by

Save article to Kindle

To save this article 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.

Lucas against Mechanism
Available formats
×

Save article to Dropbox

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

Lucas against Mechanism
Available formats
×

Save article to Google Drive

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

Lucas against Mechanism
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *