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A second order logic of existence1

Published online by Cambridge University Press:  12 March 2014

Nino B. Cocchiarella
Nino B. Cocchiarella*
Affiliation:
Indiana University
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Extract

A. N. Prior in [9] has suggested an approach towards a second order logic of existence where, following medieval logicians, we distinguish “between predicates (like ‘is red’, ‘is hard’, etc.) which entail existence, and predicates (like ‘is thought to be red’, ‘is thought of’, etc.) which do not.”2 Let us refer to attributes (including relational attributes) which are designated by the former kind of predicate as existence attributes, or for brevity, e-attributes.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 34 , Issue 1 , 29 May 1969 , pp. 57 - 69
Copyright
Copyright © Association for Symbolic Logic 1969

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Footnotes

1

I am indebted to the referee for helpful suggestions in revisions of an earlier draft of this paper. For a more philosophical discussion of the present system, especially of the substitution free form of its axiom set, cf. [7].

References

[1]Church, A., Introduction to mathematical logic, vol. 1, Princeton, N.J., 1956.Google Scholar
[2]Cocchiarella, N., Tense logic: A study of temporal reference, Doctoral thesis, UCLA, 1966.Google Scholar
[3]Cocchiarella, N., A logic of actual and possible objects, this Journal, vol. 31 (1966), p. 688f.Google Scholar
[4]Cocchiarella, N., A completeness theorem in tense logic, this Journal, vol. 31 (1966), p. 689f.Google Scholar
[5]Cocchiarella, N., Modality within tense logic, this Journal, vol. 31 (1966), p. 890f.Google Scholar
[6]Cocchiarella, N., A substitution free axiom set for second order logic, forthcoming in Notre Dame journal of formal logic.Google Scholar
[7]Cocchiarella, N., Some remarks on second order logic with existence attributes, Nous, vol. 2 (1968), pp. 165–175.CrossRefGoogle Scholar
[8]Henkin, L., Completeness in the theory of types, this Journal, vol. 15 (1950), pp. 81–91.Google Scholar
[9]Prior, A. N., Past, present and future, Oxford Univ. Press, Oxford, 1967.CrossRefGoogle Scholar