Chapter

Terms and Questions

Stewart Shapiro

in Foundations without Foundationalism

Published in print March 2000 | ISBN: 9780198250296
Published online November 2003 | e-ISBN: 9780191598388 | DOI: http://dx.doi.org/10.1093/0198250290.003.0001
 Terms and Questions

More Like This

Show all results sharing this subject:

  • Philosophy of Mathematics and Logic

GO

Show Summary Details

Preview

A logic consists of a formal language, a deductive system and/or a model‐theoretic semantics. A formal language is a mathematical model of a natural language, focusing attention on features relevant to inference. A deductive system is a model of the practice of correctly inferring conclusions from premises; and model‐theoretic semantics is a model of the ways that sentences are about objects, and the ways that sentences can be true or false. These models can be good or bad, depending on the underlying purpose of the enterprise. On the view developed here, there is no question of finding the ‘correct’ or ‘true’ model. Different purposes suggest different models. The role of properties or sets in the semantics of second‐order logic is treated, marking the distinction between the logical conception of set and the iterative conception of set.

Keywords: deduction; formal language; inference; logic; mathematics; model theory; property; semantics; set; truth

Chapter.  11262 words. 

Subjects: Philosophy of Mathematics and Logic

Full text: subscription required

How to subscribe Recommend to my Librarian

Buy this work at Oxford University Press »

Users without a subscription are not able to see the full content. Please, subscribe or login to access all content.