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A note on existential instantiation

Published online by Cambridge University Press:  12 March 2014

Dag Prawitz
Dag Prawitz*
Affiliation:
University of Stockholm
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Extract

The presence of a rule for existential instantiation (EI) in a system of natural deduction often causes some difficulties, in particular, when it comes to formulate necessary restrictions on the rule for universal generalization (UG). A system containing rules for EI and UG that avoided Quine's rather cumbersome restrictions on these rules was formulated by Copi [2], but the system was found to be inconveniently restrictive. A less restrictive system was therefore suggested by Copi [3]. Also that system forces some deductions to be unnecessarily long as is shown in Prawitz [5, Appendix C, p. 104], where a way to liberalize Copi's restriction on UG is suggested (p. 105). However, the system suggested by Copi [3] is also incorrect (i.e. unsound) as has recently been shown by Parry [4] in this Journal.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 32 , Issue 1 , June 1967 , pp. 81 - 82
Copyright
Copyright © Association for Symbolic Logic 1967

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References

[1]Borkowski, L. and Słupecki, J., A logical system based on rules and its applications in teaching mathematics, Studia logica, vol. 7 (1958), pp. 71–106.CrossRefGoogle Scholar
[2]Copi, Irving, Symbolic logic, Macmillan, New York, 1954.Google Scholar
[3]Copi, Irving, Another variant of natural deduction, this Journal, vol. 21 (1956), pp. 52–55.Google Scholar
[4]Parry, William, Comments on a variant form of natural deduction, this Journal, vol. 30 (1965), pp. 119–122.Google Scholar
[5]Prawitz, Dag, Natural deduction. A proof-theoretical study, Almqvist & Wiksell, Stockholm, 1965.Google Scholar
[6]Rosser, Barkley, Logic for mathematicians, McGraw-Hill, New York, 1953.Google Scholar