George Bealer

in Quality and Concept

Published in print May 1982 | ISBN: 9780198244288
Published online October 2011 | e-ISBN: 9780191680762 | DOI:

Series: Clarendon Library of Logic and Philosophy


Show Summary Details


First-order quantifier logic is complete; higher-order quantifier logic is not. A few formally minded philosophers of logic — such as Quine and some of his followers — appear to believe that this is sufficient grounds for concluding that the only legitimate quantifier logic is first-order, not higher-order. However, most leading formally minded philosophers of logic over the past hundred years — Frege, Russell, Church, Carnap, Henkin, Montague, Kaplan — believe that the higher-order approach is a natural generalization of the first-order approach and therefore that quantifier logic is properly identified with higher-order quantifier logic. This chapter departs from this majority opinion. It discusses the underlying philosophical differences between the two approaches to quantifier logic, and attempts to illustrate the greater naturalness and generality of the first-order approach.

Keywords: first-order quantifier logic; higher-order quantifier logic; quantifier logic; Quine

Chapter.  6026 words. 

Subjects: Metaphysics

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.