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A note on modified abstraction principles

  • John Lake (a1)

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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(zxL) and those of the form ∀zL by ∀z(zxL), 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).

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References

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[1]Hintikka, J., Identity, variables and impredicative definitions, this Journal, vol. 21 (1956), pp. 225245.
[2]Hintikka, J., Vicious circle principle and the paradoxes, this Journal, vol. 22 (1957), pp. 245249.
[3]Shiman, P., Semipredicative set theory, this Journal, vol. 36 (1971), pp. 370371. Abstract.

A note on modified abstraction principles

  • John Lake (a1)

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