Skip to main content Accessibility help
×
Home
Hostname: page-component-5f95dd588d-zfpxq Total loading time: 0.181 Render date: 2021-10-28T21:56:13.093Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true, "newUsageEvents": true }

I - Basic Logic

Published online by Cambridge University Press:  16 January 2010

George Tourlakis
Affiliation:
York University, Toronto
Get access

Summary

Logic is the science of reasoning. Mathematical logic applies to mathematical reasoning – the art and science of writing down deductions. This volume is about the form, meaning, use, and limitations of logical deductions, also called proofs. While the user of mathematical logic will practise the various proof techniques with a view of applying them in everyday mathematical practice, the student of the subject will also want to know about the power and limitations of the deductive apparatus.We will find that there are some inherent limitations in the quest to discover truth by purely formal – that is, syntactic – techniques. In the process we will also discover a close affinity between formal proofs and computations that persists all the way up to and including issues of limitations: Not only is there a remarkable similarity between the types of respective limitations (computations vs. uncomputable functions, and proofs vs. unprovable, but “true”, sentences), but, in a way, you cannot have one type of limitation without having the other.

The modern use of the term mathematical logic encompasses (at least) the areas of proof theory (it studies the structure, properties, and limitations of proofs), model theory (it studies the interplay between syntax and meaning – or semantics – by looking at the algebraic structures where formal languages are interpreted), recursion theory (or computability, which studies the properties and limitations of algorithmic processes), and set theory.

Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2003

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.

  • Basic Logic
  • George Tourlakis, York University, Toronto
  • Book: Lectures in Logic and Set Theory
  • Online publication: 16 January 2010
  • Chapter DOI: https://doi.org/10.1017/CBO9780511615559.002
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.

  • Basic Logic
  • George Tourlakis, York University, Toronto
  • Book: Lectures in Logic and Set Theory
  • Online publication: 16 January 2010
  • Chapter DOI: https://doi.org/10.1017/CBO9780511615559.002
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.

  • Basic Logic
  • George Tourlakis, York University, Toronto
  • Book: Lectures in Logic and Set Theory
  • Online publication: 16 January 2010
  • Chapter DOI: https://doi.org/10.1017/CBO9780511615559.002
Available formats
×