Show Summary Details

Page of

PRINTED FROM OXFORD HANDBOOKS ONLINE ( © Oxford University Press, 2018. All Rights Reserved. Under the terms of the licence agreement, an individual user may print out a PDF of a single chapter of a title in Oxford Handbooks Online for personal use (for details see Privacy Policy and Legal Notice).

date: 25 July 2021

Abstract and Keywords

This article's main concern is the notion of model-theoretic consequence. What does it have to do with correct reasoning? The article takes on deductive consequence only by way of contrast. Do these two notions answer to different intuitive notions of consequence? Is one of them primary, and the other secondary? Or perhaps they are autonomous and independent. Maybe there are two distinct notions of correct reasoning, valid thought, and/or inference. For what it is worth, treatments of mathematical logic usually presuppose that the model-theoretic notion is the primary one. For example, one says that a deductive system is sound or complete (or not) for the semantics—not the other way around. If a deductive system is not sound for a given semantics, then that alone disqualifies the deductive system. It is because the deductive system allows us to deduce a falsehood from truths in some interpretation of the language.

Keywords: logical consequence, proof theory, model theory, mathematical reasoning, intuitive notions, model-theoretic notion

Access to the complete content on Oxford Handbooks Online requires a subscription or purchase. Public users are able to search the site and view the abstracts and keywords for each book and chapter without a subscription.

Please subscribe or login to access full text content.

If you have purchased a print title that contains an access token, please see the token for information about how to register your code.

For questions on access or troubleshooting, please check our FAQs, and if you can''t find the answer there, please contact us.