S W I N B U R N E ON OMNIPOTENCE J o s h u a Hoffmann & Gary Rosenkrantz*
University of North Carolina at Greensboro. U.S.A.
Some time ago, Richard Swinburne offered an analysis of omnipotence {"Omnipotence", American Philosophical Quarterly, 10, 1973}. Although Swinburne's analysis contains several important insights, our purpose here is to show that it fails to provide logically n e c e s s a r y and sufficient conditions for omnipotence.
The analysis in question {call it A) is as follows:
{S}{t} [ {S is omnipotent at t ~--u(x) ~{x is a logically contingent state of affairs after t} & {the occurrence of x after t does not entail S did not bring about x at t}} ~ {S is able at t to bring about x}}]. Swinburne stipulates t h a t in A, 'S' ranges over existent beings and 'x' over logically possible states of affairs, and he uses the notation --~ to express logical equivalence. Swinburne speaks of states of affairs being logically possible or impossible, and of their entailing or failing to entail one another, and we shall do so as well. According to Swinburne, x is a logically contingent state of affairs after t j u s t when: a. x is a logically contingent state of affairs, and b. x is after t, and c. x's occurring after t is logically compatible with what has happened at or before t. Swinburne provides no explanation whatsoever of what he means when he says in condition b. t h a t "x is after t". The pro-
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blem here is t h a t this can be understood in at least two ways. First, Swinburne may mean t h a t x occurs or obtains at a time which is after t. If this is what he means, then his analysis has the following unacceptable implication: an agent who, at t, is only able to bring about every state of affairs which actually obtains after t, since he is not able at t, for example,to prevent the occurrence of any state of affairs which obtains after t. But there is another, more charitable way to construe Swinburne's meaning. He m a y mean by condition b. t h a t x is a dated state of affairs whose date is later than t. Since this interpretation does not restrict the range of 'x' to states of affairs which actuaUy obtain after t, it avoids the above criticism. The critical points we make below apply on either interpretation of Swinburne's condition b. Because of condition a., an omnipotent agent is not required by A to have either the ability to bring about a necessary state of affairs, or the ability to bring about an impossible state of affairs. The intent of conditions b, and c. is t h a t A not require an omnipotent agent to be able to bring about a state of affairs "where the state of affairs is a state of the universe before or simultaneous with the time at which abilities to bring it about are being assessed" (p. 232}. We agree with Swinburne that an omnipotent agent does not have and hence, should not be required to have, the aforementioned qualities. Finally, note t h a t the antecedent of the analysans of A contains as a conjunct the following condition: the occurrence of x after t does not entail S did not bring about x at t. The intent of this condition is t h a t A not require S to have the ability to bring about any state of affairs which it is logically impossible for S to bring about but which satisfies conditions a., b., c. (see p. 233). Note t h a t this conjunct contains the clause,'S did not bring about x at t'. The natural interpretation of this clause is "S exists & -- (S brought about x at t)". On this interpretation, A requires t h a t a being, S, who is omnipotent at a time, t, have the ability at t, to bring about any state of affairs, x, which satisfies the following four conditions:
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A.,b.,c. above, and d. the occurrence of x after t does not entail [S exists & - {S brought about x at t)]. In order to see t h a t A under the present interpretation is incorrect, let t ~ M a y 31, 1978 A.D., and let x ~ t h a t at t' it is the case t h a t a ball bounced yesterday {where t - - J u n e 1, 1978, A. D.) Call this state of affairs x0. Suppose t h a t a ball bounces on May 31, 1978 A. D., it follows t h a t the state of affairs, at t' it is the case t h a t a ball bounced yesterday, obtains on J u n e 1, 1978 A. D.,~e.at a time after t. In this case, xl is logically contingent, it occurs after t, its date is later than t, and its occurring after t is logically compatible with what happened at or before t. Hence, x~ satisfies conditions a.,b.,c. Does it satisfy condition d.? Provided t h a t S is a contingently existing being, x~'s occurring after t does not entail t h a t S exists, and consequently, does not entail [S exists & -- (S brought about x~ at t)]. Thus, x ~satisfies condition d. Since Swinburne purports to be providing a completely general analysis of omnipotence, his analysis should apply to contingently existing beings and he can have no objection to our provision above t h a t S have contingent existence. In the case we have described, A requires t h a t a being who is omnipotent on May 31, 1978 A. D. have the ability to being about x~. However, since bringing about xl involves bringing about what is past, and since on an ordinary conception of agency and time this is impossible, an agent who is omnipotent on May 31, 1978 A. D. is unable to bring about xl. Therefore, on the suggested interpretation of A, an agent who is omnipotent can fail to satisfy A, and A does not provide a logically necessary condition for omnipotence. However, it is not certain t h a t Swinburne intended the interpretation we have given to the clause,fS did not bring about x at t'. Perhaps he meant it to be understood as "-(S brought about x at t)". If this was his meaning, then A should be understood as containing, instead of condition d., the following condition: d* the occurrence of x after t does not entail -(S brought about x at t). As we have pointed out, it is impossible for any agent to bring about x ~. Hence, the state of affairs,- (S brought about
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xj at t}, is necessary. Since a necessary state of affairs is entailed by every state of affairs, the state of affairs, - {S brought about x at t), is entailed by the state of affairs, x j's occurring after t. Thus, x~ does not satisfy condition d* and is not a counterexample to A understood as containing d*. However, replacing d. with d* generates a new problem for A. Let x be any state of affairs which satisfies conditions a.,b..c. Now let S ~- an existent being which is essentially a non-agent, for example, a stone or the number 7 {Swinburne: "And it seems quite plausible to say t h a t it is not logically possible for an inorganic object to do any action at all"; p. 231). Since S is essentially a non-agent, the state of affairs, -{S brought about x at t) is necessary, and thus is entailed by every state of affairs. Therefore, x's occurring after t entails -{S brought about x at t), and x fails to satisfy condition d*. Thus, when S is a stone or any existent being which is essentially a non-agent, condition d* is not satisfied,and the whole analysans of A is trivially true because it is a material conditional with a false antecedent. In other words, on this second interpretation A implies that a stone is omnipotent and that something can satisfy A without being omnipotent. For this reason on this second interpretation A fails to provide a logically sufficient condition for omnipotence. Swinburne can avoid our second counterexample by restricting the range of 'S' to agents, or to existent beings which are possibly agents. What we shall now argue is t h a t even if we allow Swinburne to interpret A as including condition d* and to restrict the range of 'S' as specified above, the resulting analys is subject to refutation by counterexample. Consider the following state of affiars (call it x_,:) at t ' i t is the case that no omnipotent agent ever brings about something. Let t* be a time later than t, and suppose t h a t at t there is exactly one omnipotent agent, Oscar. Suppose, too, t h a t Oscar is contingently omnipotent (Swinburne finds no incoherence in the notion of contingent omnipotence; see pp. 235-36), and t h a t he comes into existence at t', a time j u s t prior to t. Finally, suppose t h a t Oscar is mortal at t, and t h a t Oscar is the only omnipotent agent who ever exists.
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At t is Oscar able to bring about x2? Clearly not. If at t Oscar brings about x2, then some omnipotent agent brings about something. But this contradicts x2, and hence, contradicts the assumption that at t Oscar brings about x2. Therefore at t Oscar lacks the ability to bring about x2 Nevertheless, on the following assumptions, x2 satisfies conditions a.,b.,c., and d*.Assume t h a t at t Oscar has yet to perform any conditions (he only just came into existence). Assume, too, t h a t before Oscar can perform any actions, he is killed by Jones. a non-omnipotent agent, x2 satisfies condition a. because x2 is logically contingent. I t satisfies condition b. on our assumptions t h a t t* is later than t, t h a t Jones bills Oscar at t, and t h a t Oscar is the sole omnipotent agent, x2 satisfies condition c. on our assumption that no omnipotent agent other than Oscar ever exists. Finally, as the following considerations show, x2 satisfies condition d*. d* requires t h a t the occurrence of x2 after t does not entail -(Oscar brought about x2 at t). Since Oscar is contingently omnipotent at t, it is logically possible t h a t he is n o t omnipotent at t and t h a t some other agent is. Hence, it is logically impossible t h a t at t Oscar does what we have supposed Jones to have done, namely, kill the sole omnipotent agent before he brings about something, thereby bringing about x2. Thus, the occurrence of x~ after t does not entail - (Oscar brought about x2 at t), and x2 satisfies condition d* as well a s conditions a.,b.,c. The above a r g u m e n t shows t h a t A requires t h a t if Oscar is omnipotent at t, at t Oscar has the ability to bring about x2. But, as we have seen, if Oscar is omnipotent at t, then at t he is n o t able to bring about x2. Thus, an agent can be omnipotent without satisfying A, and our third counterexample shows t h a t the revised version of Swinburne's analysis does not provide a logically necessary condition for omnipotence. It should be noted t h a t this counterexample also refutes all of the previous versions of Swinburne's analysis which we have considered and rejected for other reasons. Perhaps further changes in A can overcome all of the difficulties we have raised here, but as far as we can see at present, there is no straightforward way of accomplishing this.
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