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A note on modified abstraction principles

Published online by Cambridge University Press:  12 March 2014

John Lake
John Lake*
Affiliation:
Bedford College, London, N.W. 1, England
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Extract

The abstraction principle is

for K any formula not involving x. This is well known to be inconsistent and in [1] Hintikka proposed two modified versions of (0) which we briefly describe. First, he suggested

where K is any formula not involving x, and K+ is obtained from K by replacing subformulae of the form ∃zL by ∃z(z ≠ x ∧ L) and those of the form ∀zL by ∀z(z ≠ x → L), etc. The second version is

where K+ is a formula of the type described for (1) and z1 …, zk are all the free variables in (2).

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 38 , Issue 1 , March 1973 , pp. 77 - 78
Copyright
Copyright © Association for Symbolic Logic 1973

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References

REFERENCES

[1]Hintikka, J., Identity, variables and impredicative definitions, this Journal, vol. 21 (1956), pp. 225–245.Google Scholar
[2]Hintikka, J., Vicious circle principle and the paradoxes, this Journal, vol. 22 (1957), pp. 245–249.Google Scholar
[3]Shiman, P., Semipredicative set theory, this Journal, vol. 36 (1971), pp. 370–371. Abstract.Google Scholar