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Universally free logic and standard quantification theory

Published online by Cambridge University Press:  12 March 2014

Robert K. Meyer  and
Karel Lambert
Robert K. Meyer
Affiliation:
Bryn Mawr College, The University of California, Irvine
Karel Lambert
Affiliation:
Bryn Mawr College, The University of California, Irvine
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Extract

Interest has steadily increased among logicians and philosophers in versions of quantification theory which meet the following criteria: (1) no existence assumptions are made with respect to individual constants, and (2) theorems are valid in every domain including the empty domain. Logics meeting the former of these criteria are called free logics by Lambert and have been investigated in a series of papers by him and by van Fraassen, and by Leblanc and Thomason.1

Although it is natural to impose (2) in the presence of (1), the criteria are independent.2 Hence we baptize logics which meet both criteria universally free.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 33 , Issue 1 , 26 April 1968 , pp. 8 - 26
Copyright
Copyright © Association for Symbolic Logic 1968

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