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On Meyer and Lambert's quantificational calculus FQ

Published online by Cambridge University Press:  12 March 2014

Hugues Leblanc
Hugues Leblanc*
Affiliation:
Temple University
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Extract

The semantical account that Meyer and Lambert give in [7] of their quantificational calculus FQ can be considerably simplified, and—supposing as the authors do at the close of their paper that ‘ = ’ counts as a primitive sign—so can their axiom system for FQ.

(1) As the authors remark, axiom schema 102 can be simplified to read : A ⊃ (∀Χ)A, where Χ does not occur free in A. Following Tarski's [9], it can be further simplified: A ⊃ (∀Χ)A, where Χ does not occur in A.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 33 , Issue 2 , 23 July 1968 , pp. 275 - 280
Copyright
Copyright © Association for Symbolic Logic 1968

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References

[1]Hailperin, T., Quantification theory and empty individual domains, this Journal, vol. 18 (1953), pp. 197–200.Google Scholar
[2]Hintikka, K. J. J., Existential presuppositions and existential commitments, Journal of philosophy, vol. 56 (1959), pp. 125–137.CrossRefGoogle Scholar
[3]Leblanc, H. and Hailperin, T., Nondesignating singular terms, Philosophical review, vol. 68 (1959), pp. 129–136.CrossRefGoogle Scholar
[4]Leblanc, H., A simplified account of validity and implication, this Journal, vol. 33 (1968), pp. 231–235.Google Scholar
[5]Leblanc, H. and Meyer, R. K., Open formulas and the empty domain, Archiv für Mathematische Logik und Grundlagenforschung (to appear).Google Scholar
[6]Łukasiewicz, J., Elementy logiki matematycznej, Wydawnictwe Kola Matematycznofizcznege Sluchaczow Uniwersytetu Warszawskiege, Warsaw, 1929.Google Scholar
[7]Meyer, R. K. and Lambert, K., Universally free logic and standard quantification theory, this Journal, vol. 33 (1968), pp. 8–26.Google Scholar
[8]Mostowski, A., On the rules of proof in the pure functional calculus of the first order, this Journal, vol. 16 (1951), pp. 107–111.Google Scholar
[9]Tarski, A., A simplified formalization of predicate logic with identity, Archiv für Mathematische Logik und Grundlagenforschung, vol. 7 (1965), pp. 61–79.CrossRefGoogle Scholar