Skip to main content Accessibility help
×
Home
Hostname: page-component-99c86f546-qdp55 Total loading time: 0.347 Render date: 2021-11-29T09:20:59.147Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true, "newUsageEvents": true }

2 - The consequences of analysis

Published online by Cambridge University Press:  22 September 2009

Marcus Tomalin
Affiliation:
University of Cambridge
Get access

Summary

Chapter overview

The purpose of this chapter is to summarise some of the movements within the formal sciences that occurred during the nineteenth and twentieth centuries, and which were ultimately to exert a profound ifluence over the development of TGG. Since the origins of TGG are the main focus of the following chapters, and since any search for origins necessarily entails an infinite regress if taken to an extreme, an arbitrary beginning is required, and the starting point chosen for this discussion is the emergence of the calculus as an identifiable set of algorithmic procedures in the late seventeenth century. Accordingly, the advent of the calculus is discussed in section 2.2 and some of the disputes associated with its appearance are reviewed, along with the main subsequent advances that led to the creation of the branch of mathematics known as ‘analysis’. In section 2.3 various attempts to provide a more secure foundation for analysis are briefly assessed, with particular attention being given to the endeavour to derive the calculus from the rudiments of number theory. The development of set theory, which grew out of the need to secure the basis of arithmetic, is summarised in section 2.4, and some of the resultant paradoxes are explored. The remaining sections of the chapter discuss the three main theories that emerged at the end of the nineteenth century and the beginning of the twentieth century in direct response to the foundations crisis prompted by set theory.

Type
Chapter
Information
Linguistics and the Formal Sciences
The Origins of Generative Grammar
, pp. 21 - 53
Publisher: Cambridge University Press
Print publication year: 2006

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.)

Send book to Kindle

To send this book to your Kindle, first ensure no-reply@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 sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent 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
×

Send book to Dropbox

To send 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 sending content to Dropbox.

Available formats
×

Send book to Google Drive

To send 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 sending content to Google Drive.

Available formats
×