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The Omnipotence Paradox

Published online by Cambridge University Press:  01 January 2020

Douglas Walton
Douglas Walton*
Affiliation:
University of Winnipeg
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Extract

Can an omnipotent being create a stone too heavy for him to lift? If not, he is not omnipotent. But if so, he is not omnipotent either, since there is something he cannot lift. Hence there can be no omnipotent being. J .L. Cowan's recent reformulation of this paradox of omnipotence (this Journal, vol. III, no. 3, March, 1974) has been sharpened through a number of objections and clarifications, and, in its final form, constitutes a significant problem for the analysis of the concept of an omnipotent agent. I will develop fragments of two systems in which the problem can be defined more exactly, and try to indicate some formal guidelines within which constructive steps towards a solution may be possible. I will argue that the paradox shows the need for a special kind of restriction on omnipotence that can be distinguished from some related restrictions.

Type
Research Article
Information
Canadian Journal of Philosophy , Volume 4 , Issue 4 , June 1975 , pp. 705 - 715
Copyright
Copyright © The Authors 1975

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References

1. For references, vide Cowan, J.L. ‘The Paradox of Omnipotence Revisited,’ Canadian journal of Philosophy, vol. III, no. 3, p. 435.Google Scholar

2. For a similar convention in deontic modal systems, vide Fitch, Frederic B. ‘Natural Deduction Rules for Obligation,’ American Philosophical Quarterly, vol. 3, no. 1, January 1966, 27–38Google Scholar. See especially p. 37f. The convention in question carries with it the implication that it is a rule of inference of System δ that if ϕ is a theorem, δ ϕ is a theorem, parallel to Fitch's System DM.

3. These two stipulations on δ are suggested by Frederic B. Fitch in ‘ A Logical Analysis of Some Value Concepts,’ Journal of Symbolic Logic, vol. 28, no. 2, June, 1963, 135–142.

4. Vide Davidson, Donald ‘The Logical Form of Action Sentences,’ The Logic of Decision and Action, ed. Rescher, Nicholas (Pittsburgh, University of Pittsburgh Press, 1967), 81–95.Google Scholar

5. These two stipulations on the notion of opportunity are suggested by Kenny, Anthony in ‘Freedom, Spontaneity and Indifference,’ Essays on Freedom of Action, ed. Honderich, Ted (London and Boston, Routledge and Kegan Paul, 1973), 89–104Google Scholar. Vide p. 99f. A clear explanation of this notion of opportunity is to be found in Brand, Myles ‘On Having the Opportunity,’ Theory and Decision, vol. 2, 1972, 307–313.CrossRefGoogle Scholar

6. See note 1. A useful article not cited by Cowan is that of Cargile, James ‘On Omnipotence,’ Noûs, vol. 1, no. 2, May 1967, 201–205.CrossRefGoogle Scholar

7. Descartes thought it blasphemous to maintain that God cannot do that which cannot be described in a logically coherent way. See letters to Mersenne, April 15, 1630, and May 27, 1644. These references are found in Frankfurt, Harry G. ‘The Logic of Omnipotence,’ The Philosophical Review, Vol. LXXIII, 1964, pp, 262–263CrossRefGoogle Scholar. See also the discussion in Geach, p. 10f.

8. For some discussion of this problem see Pörn, Ingmar The Logic of Power, (Oxford, Blackwell, 1970), p. 7.Google Scholar

9. Rescher, Nicholas ‘The Concept of Control,’ Essays in Philosophical Analysis, (Pittsburgh, University of Pittsburgh Press, 1969), pp. 327–353.Google Scholar

10. The notion of control stalemate makes it clear that there can be at most one omnipotent agent.

11. To put it bluntly, my argument is that it is a consequence of (TM* δ ) that if there is an omnipotent being, in the sense characterized by (TM* δ ), then there are no other y free agents. This anomaly (like the others adumbrated below) suggests that we need an appropriately qualified characterization of omnipotence. I do not try to propose a workable restriction here, but merely argue for the need of one to complement other restrictions alluded to below and elsewhere (e.g., see Geach, op. cit., note 14).

12. Vide note 11. See also Plantinga, Alvin The Nature of Necessity, (Oxford, Oxford University Press, 1974), ch. 9.Google Scholar

13. Similar proof is found in Fitch. See note 3. See also Douglas Walton, ‘Some Theorems of Fitch on Omnipotence,’ Sophia, forthcoming.

14. Geach, Peter ‘Omnipotence,’ Philosophy, January 1973, vol, 48, pp. 7–20CrossRefGoogle Scholar. See also Geach, Peter ‘An Irrelevance of Omnipotence,’ Philosophy, October, 1973, vol. 48, pp. 327–333CrossRefGoogle Scholar. Walton (note 13) argues that some results can be derived from Fitch's theorems that strongly support Geach's thesis that what is past ceases to be alterable even by an omnipotent agent.

15. This is essentially Geach's suggestion.

16. The concept of a totally self-limiting action, and the consequent demonstration of the need for temporal indices in M* δ , are due to J. E. Bickenbach, whose contribution I gratefully acknowledge.