Omnipotence is maximal power. Maximal greatness (or perfection)includes omnipotence. According to traditional Western theism, God ismaximally great (or perfect), and therefore is omnipotent. Omnipotenceseems puzzling, even paradoxical, to many philosophers. They wonder,for example, whether God can create a spherical cube, or make a stoneso massive that he cannot move it. Is there a consistent analysis ofomnipotence? What are the implications of such an analysis for thenature of God?

• 1. Introductory Preliminaries
• 2. The Scope of Omnipotence
• 3. Omnipotence and Unrestricted Repeatability
• 4. Omnipotence and the Shared Histories Approach
• 5. Omnipotence and Divine Moral Perfection
• Bibliography
• Academic Tools
• Other Internet Resources
• Related Entries

1. Introductory Preliminaries

Philosophical reflection upon the notion of omnipotence raises manypuzzling questions about whether or not a consistent notion ofomnipotence places limitations on the power of an omnipotent agent.Could an omnipotent agent create a stone so massive that that agentcould not move it? Paradoxically, it appears that however thisquestion is answered, an omnipotent agent turns out not to beall-powerful. Could such an agent have the power to create or overturnnecessary truths of logic and mathematics? Could an agent of this kindbring about or alter the past? Is the notion of an omnipotent agentother than God an intelligible one? Couldtwo omnipotentagents coexist? If there are states of affairs that an omnipotentagent is powerless to bring about, then how is the notion ofomnipotence intelligibly to be defined? Moreover, an obstacle totraditional Western theism arises if it is impossible for God to bemorally perfect and omnipotent. If an omnipotent God is powerless todo evil, then how can he be omnipotent? Rational theology seeks ananalysis of the concept of omnipotence that provides sufficientgranularity about the powers of an omnipotent agent to resolve thepuzzles and apparent paradoxes that surround this concept. If thenotion of omnipotence were found to be unintelligible, or incompatiblewith moral perfection, then traditional Western theism would befalse.

According to some philosophers, omnipotence should be understood interms of the power toperform certain tasks, for instance, tokill oneself, to make \(2+2=4\), or to make oneself non-omniscient.However, in recent philosophical discussion, omnipotence has beenanalyzed in terms of the power tobring about certain possiblestates of affairs, understood as propositional entities whicheither obtain or fail to obtain (Rosenkrantz & Hoffman 1980; Flint& Freddoso 1983; and Wierenga 1989). Because we believe that itcan yield an adequate analysis of omnipotence, we take this latterapproach in what follows.

Some philosophers have sought to understand omnipotence in terms ofinfinite power. One example of such a philosopher is JohnLocke. In 1689, he writes that:

It is Infinity, which joined to our ideas of Existence, PowerKnowledge, & c. makes that complex Idea, whereby we represent toourselves the best we can, the Supreme Being. (An Essay ConcerningHuman Understanding, Book II, Ch. 23, ¶ 35.)

This quotation suggests that omnipotence can be defined as infinitepower. Leaving aside for the moment the historical question of howLocke understood infinite power, let us explore the suggesteddefinition of omnipotence in the light of the prevailing mathematicalunderstanding of infinity.

This mathematical understanding of infinity views it through the lensof transfinite arithmetic. Transfinite arithmetic presupposes thatthere are infinitely many natural numbers. According to transfinitearithmetic, the cardinal number of the set of natural numbers is\(\aleph_0\) (aleph-null). (Acardinal number is a numberthat can be used to answer the question “ How many?”) Inother words, if it is asked “ How many natural numbers arethere?”, the correct answer is \(\aleph_0\).

The founder of transfinite arithmetic, Georg Cantor (1845–1918),is also a founding father of set theory. He famously proved thatthe set of real numbers has alarger cardinal numberthanthe set of natural numbers; the set of reals has thesame cardinality as thepower set (the set of allsubsets) of the set of naturals. Cantor further argued that\(\aleph_0\) is thefirst (and smallest) transfinite cardinalnumber in an infinite series of increasingly larger transfinitecardinals, \(\aleph_0,\) \(\aleph_1,\) \(\aleph_2\), and so on. Butnote that the numerical subscripts of these alephs do not refer tocardinal numbers, but rather refer toordinal (or ordering)numbers, e.g., first, second, third, and so forth. Accordingto Cantor, there is no largest transfinite cardinal number, andalthough there are infinitely many transfinite cardinal numbers, thereis no cardinal number of them. Rather, the totality of transfinitecardinals isabsolutely infinite in asui generisnon-arithmetical sense. Similarly, in Zermelo-Fraenkl set theory (ZF),and its extension ZFC (ZF + the axiom of choice), the totality oftransfinite cardinal numbers does not qualify as aset havinga definite cardinal number of members. Such a set would be too large;were such a set to exist, paradoxical consequences would ensue akin toRussell’s paradox. ZF avoids these paradoxical consequences bycharacterizing the totality of transfinite cardinals as an infinitelylargeproper class. Within the forms of axiomatic set theorythat have attracted significant support it cannot be proved that oneproper class is larger than another.

Transfinite cardinals may be used to quantify an amount of energy orforce, e.g., \(\aleph_0\) joules, or \(\aleph_0\) newtons. Or they maybe be used to state the cardinal number of a totality of objects,e.g., \(\aleph_2\) states of affairs. Thus, one [first] way in which‘power’ might be interpreted is as a power (or range ofpowers) to produce an energy or force quantified by a transfinitecardinal. One such option is that ‘infinite power’ meansthe power to produce aspecific transfinite quantity ofjoules or newtons, e.g., \(\aleph_0\). The other option is that‘infinite power’ means the power to produceanytransfinite quantity of joules or newtons, i.e., \(\aleph_0,\)\(\aleph_1,\) \(\aleph_2,\) and so onad infinitum. A third,more radical option, is that ‘infinite power’ means thepower to producemore joules or newtons than can bequantified byany transfinite cardinal number. Such energy orforce would appear to qualify as energy or force than which nonegreater is possible.

The alternative way of interpreting ‘infinite power’ is asthe power to bring about infinitely many states of affairs. The threeoptions relevant to this interpretation of ‘infinitepower’ parallel the three options just described. First, that‘infinite power’ is the power to bring about aspecific transfinite cardinal number of states of affairs.Second, that ‘infinite power’ is the power to bring aboutany transfinite cardinal number of states of affairs. Third,that ‘infinite power’ is the power to bring aboutmore states of affairs thanany transfinite cardinalnumber can quantify.

The standard view is that there is no greatest transfinite cardinal,and that there are proper classes containing more objects than can bequantified by any transfinite cardinal. Moreover, there couldnot be an agent who hasgreater power than anomnipotent agent. Thus, with regards to the two interpretationsoffered, there is some reason to conclude that in each case thethird option is best.

However, a philosopher who haspositivistic or naturalisticleanings might argue that one should posit transfinite cardinalsofonly those sizes required by prevailingscientifictheories. Arguably, the prevailing theory of the space-timecontinuum in physics is committed to the existence of infinitesets which have the cardinality of the set of space-time pointscontained within such a continuum (which is at least \(\aleph_1\)). Ifan argument of that sort is correct, this scientific theory is, inaddition, committed to the existence of the power set of the foregoingset of space-time points – which is needed to accommodatecontinuous and discontinuous linear paths. (This power set has thecardinality of the set of mathematical functions from reals to reals.)But scientific theories donot appear to require theexistence of any setlargerthan that power set. So,a philosopher who has positivistic inclinations might tentativelyconclude that the cardinal number of this power set (which is at least\(\aleph_2\)) is in factthe largest cardinal. In a relatedvein, W. V. O. Quine dismisses “excessive” magnitudes, forinstance, “\(\beth_\omega\) and inaccessible numbers,” asmere fancies of “recreational mathematics” bereft of ofontological import (Quine 1986, p. 400; cf. Quine 1960, Ch. 7). If areader is unfamiliar with Quine’s illustrations ofscientifically gratuitous magnitudes, please note that \(\beth_0 =\aleph_0\), \(\omega\) (omega) is \(\aleph_0\)’s [infinite]ordinal counterpart, i.e., \(\aleph_0\) is the \(\omega\)-thcardinal number, and \(\beth_\omega\) is the \(\omega\)-th iterationof the power set of \(\beth\)₀;inaccessiblenumbers (roughly speaking) are (putative) uncountable largecardinals which cannot be derivedvia summations of, or powerset operations on, smaller cardinals. Quine judges that suchmagnitudes exceed the theoretical demands of the empirical sciencesbecause admitting them would not contribute to the simplication of ourscientific computations and generalizations. Even so, there is a viewof the cumulative set-theoretical hierarchy to which Quine seems(reluctantly) willing to accede, at least in part because it providesa “convenient cut-off” limiting the extent of thathierarchy. According to this view, all sets areconstructible(in a sense defined by Kurt Gödel) from more elementary sets, aposition significantly more restrictive than is needed to avoid theknown set-theoretical paradoxes. But, arguably, when examiningomnipotence, given its robust theological and metaphysical dimensions,a less positivistic or naturalistic, more expansive, criterion ofontological commitment is appropriate. After all, it would be naturalto assume that the Supreme Being has the power to create any number ofpossible worlds governed by different laws of nature. Given thatassumption, it appears that an omnipotent agent’s power wouldnot be circumscribed by theoretical scientific laws governing theactual world.

Even so, the notions ofmore energy or force than can bequantified by any transfinite cardinal, and ofmore states ofaffairs than can be quantified by any transfinite cardinal, aremind-boggling. Moreover, arguably,that much energy or force,or the power to bring aboutthat many states of affairs, isimpossible. For this reason, with respect to each of theinterpretations of ‘infinite power’ on offer, there aredoubts about the viability of the corresponding third option. Thus,with respect to each of these alternate interpretations of‘infinite power’, it is an open question which of thethree corresponding options is best. Until greater clarity is attainedabout this matter, a definition of omnipotence as infinite power isproblematic.

Moreover, it can be plausibly argued that having the power to bringabout infinitely many states of affairs does not entail omnipotence.E.g., intuitively, an agent who has the power to move a feather intoany of infinitely many positions, but lacks the power to move a heavyboulder, would not be omnipotent, despite having the power to bringabout infinitely many states of affairs.

It may be thought that, necessarily, any agent who has the power toproduce an infinitely large amount of energy or force is omnipotent.Yet, this seems not to be true. After all, it seems possible for thereto be an agent who is infinitely powerful in this sense, but whononetheless lacks completecommand and control of theenergies or forces it has the power to produce. If so, anagent’s possessing the power to produce an infinite amount ofenergy or force doesnot entail that the agent in question isomnipotent. As illustrated by the example described above of an agentwho has the power to move a feather into infinitely many positions,but who lacks the power to move a heavy boulder, an agent’s(S’s) having the power to bring about infinitely manythings ofone sort, does not guarantee thatShasthe power to bring about things ofanother sort.

But even if there is some sort of infinite power such that,necessarily, an agent,A, is omnipotent if and only ifA has that sort of infinite power, the definitional claimthat omnipotenceis such power is fartoo general toprovide agranular analysis of omnipotence – the kindof analysis of omnipotence which we are seeking. Proposed granularanalyses of omnipotence offer considerably greaterspecificity about the powers of an omnipotent agent.

Let us return to the historical question of Locke’sunderstanding of infinite power. Locke explicitly rejects the notionthat there is an infinite cardinal number. He takes the contentionthat there is such a number to be absurd. Rather, Locke appears tounderstand infinite power as unlimited power, consistent with theAristotelean notion that infinities are “potential” andnever completed, as well as with the empiricist idea that infinity isa wholly negative notion. The infinite sets discussed earlier are“actual” or completed infinities. According to one fairlycommon understanding of unlimited power, such power includes the powerto bring about or undo necessary states of affairs, e.g., necessitiesof logic, mathematics, metaphysics, or ethics. Yet, it does not appearthat Locke means to attribute this power to an omnipotent agent; henever contends that the Supreme Being has the power to bring about orundo necessities. In any event, we will critically examine the thesisthat an omnipotent agent has the power to bring about or undonecessary states of affairs in what follows.

One sense of ‘omnipotence’ is, literally, that of havingthe power to bring aboutany state of affairs whatsoever,including necessary and impossible states of affairs. Descartes seemsto have had such a notion (Meditations, Section 1). Yet,Aquinas and Maimonides held the view that this sense of‘omnipotence’ is incoherent. Their view can be defended asfollows. It isnot possible for an agent to bring about animpossible state of affairs (e.g.,that there is ashapeless cube), since if it were, it would be possible for animpossible state of affairs to obtain, which is a contradiction (seeAquinas,Summa Theologiae, Ia, 25, 3; and Maimonides,Guide for the Perplexed, Part I, Ch. 15). Nor is it possiblefor an agent to bring about anecessary state of affairs(e.g.,that all cubes are shaped). It is possible for anagent, \(a\), to bring about a necessary state ofaffairs, \(s\), only if possibly, (1) \(a\)brings about \(s\), and (2) if \(a\)had not acted, then \(s\) would havefailed to obtain. Because a necessary state of affairs obtains whetheror not anyone acts, (2) is false. As a consequence, it is impossiblefor an agent to bring about either a necessary or an impossible stateof affairs. Many philosophers accept the principle that if an agenthas thepower to bring about a state of affairs, then thisentails that,possibly, the agent brings about that state ofaffairs. If this principle is correct, then the foregoingabsolute sense of ‘omnipotence’ is incoherent.Among contemporary philosophers, Earl Conee (1991) rejects thisprinciple in order to defend the view that an omnipotent being wouldhave the power to bring about any state of affairs whatsoever.

A second sense of ‘omnipotence’ is that ofmaximalpower, meaning just that no being could exceed the overall powerof an omnipotent being. It does not follow that a maximally powerfulbeing can bring aboutany state of affairs, since, asobserved above, bringing about some such states of affairs isimpossible. Nor does it follow that a being with maximal power canbring about whatever anyother agent can bring about. If \(a\)can bring about \(s\), and \(b\)cannot, it does not follow that \(b\)isnot overall more powerful than \(a\), sinceit could be that \(b\) can bring about more states ofaffairs than \(a\) can, rather than the other wayaround. For the remainder of this entry the discussion concentrates onthiscomparative sense of ‘omnipotence’ asmaximal power. Within the context of that discussion, it will beassumed that it isnot possible for an agent to have thepower to bring aboutany state of affairs whatsoever.

That a being is omnipotent just provided that its overall power isnot possibly exceeded by any being may be adopted as the mostgeneral definition of omnipotence in this sense (Hoffman &Rosenkrantz 2010). Still, the availability of a more fine-grained andinformative analysis, directly applicable to the full range of problemcases, is highly desirable. A number of prominent proposals for such amore fine-grained and informative analysis of omnipotence will bediscussed later.

Power should be distinguished fromability. Power isability plus opportunity: a being which has maximal ability but whichis prevented by circumstances from exercising those abilities wouldnot be omnipotent. Nothing could prevent an omnipotent agent fromexercising its powers, if it were to endeavor to do so.

In the light of the foregoing, is it possible that there be aplurality of coexistent omnipotent agents? Among contemporaryphilosophers of religion, Richard Swinburne (2008) holds that aplurality of coexistent omnipotent agents is possible.

If a plurality of coexistent omnipotent agents were even possible,thenpossibly, at a time, \(t\), someomnipotent agent, \(x\), while retaining itsomnipotence, endeavors to move a feather, and at \(t\),another omnipotent agent, \(y\), while retaining itsomnipotence, endeavors to keep that feather motionless. Intuitively,in this case, neither \(x\) nor \(y\)would affect the feather as to its motion or rest. Thus, in this case,at \(t\), \(x\) would be powerless tomove the feather, and at \(t\), \(y\)would be powerless to keep the feather motionless! But it is absurd tosuppose that an omnipotent agent could lack the power to move afeather or the power to keep it motionless. Therefore, neither \(x\)nor \(y\) is omnipotent. This line ofreasoning appears to reduce the notion of a plurality of coexistentomnipotent agents to absurdity. If such areductio adabsurdum is sound, then a plurality of coexistent omnipotentagents is impossible.

It might be replied that while neither of the omnipotent agents inquestion brings about what it endeavors to bring about, each of themcan do so, since each of them has theability to doso; they fail to bring about what they endeavor to bring about onlybecause they lack theopportunity to do so. But earlierobservations about the difference between power and ability and howeach of them is related to omnipotence entail that omnipotence shouldbe understood in terms of the abilityplus opportunity senseof ‘can’. If those earlier observations are correct, then,since neither of the omnipotent agents under discussioncando [in the ability plus opportunity sense] what it endeavors to do,the possible reply under discussion does not succeed.

Or it might be replied that the possible pair(s) of coexistentomnipotent agents wouldnecessarily avoid stalemates of theforegoing sort in virtue of the members of each pair resembling oneanother in some respect. This reply seems suspiciouslyadhoc. It appears that the members of any possible pair ofgenetically identical human twins could be stalemated, e.g., in anarm-wrestling match. Why would not the same be true of a pair ofsimilar coexistent omnipotent agents? It might be answered that eachof the members of any possible pair of coexistent omnipotent agentswould be necessarily omniscient and necessarily morally perfect.Moreover, if two omnipotent agents arenecessarilyomniscient, theywon’t disagree aboutanyfact, and if they arenecessarily morally perfect, theywon’t disagree aboutwhat is morally requiredor aboutwhether they want so to act. It might then beinferred that any states of affairs that a pair of coexistentomnipotent agents would endeavor to bring about at a given time arecompatible. In the literature, the controversialsocialtrinitarianism of Richard Swinburne (2008), implies that theFather, the Son, and the Holy Spirit are a trio of coexistentomnipotent agents each of whom is necessarily omniscient andnecessarily morally perfect.

However, one might object to the preceding reply on the grounds thatif there is a pair of coexistent necessarily omniscient andnecessarily morally perfect omnipotent agents, then there is a pair ofincompatible contingent states of affairs each of which ismorally optional for these agents, that is, neither morallyprohibited nor morally required for them. The objection then proceedsas follows. It may be assumed thatthat the feather moves att andthat the feather remains motionless at t are apair of states of affairs of the sort in question. Apparently, also,possibly, under such circumstances, the state of affairsthat theomnipotent agents in question are stalemated in their endeavors toaffect the feather as to its motion or rest at t is morallyoptional for those agents. Analogously, in an arm-wrestling matchbetween \(A_1 \amp A_2\),possibly, the states of affairsthat \(A_1\) wins the match,that \(A_2\) wins thematch, andthat \(A_1 \amp A_2\) are stalemated in thematch are morally optional for \(A_1\) and \(A_2\). In the lightof the foregoing observations, it appears that if it is possible thatthere are omnipotent agents of the sort in question, then possibly,one of them endeavors to make the feather move at \(t\),while the other endeavors to keep it motionless at\(t\),even given their hypothesized necessaryareas of epistemic and moral agreement. The foregoing defense ofthe possibility of a plurality of coexistent omnipotent agents ispersuasive only if there is a cogent reply to this objection.

Would it strengthen such a defense to further require that thecoexistent omnipotent agents arenecessarily aestheticallyperfect, and hence,won’t disagree aboutwhatis aesthetically required or aboutwhether they want so toact? It appears not. After all, there appear to be incompatible,contingent,aesthetically optional states of affairs, i.e.,states of affairs which are neither aesthetically required noraesthetically prohibited for some agent, and considerations parallelto those adduced above apply. Moreover, it is not clear thatfutile striving necessarily hasnegative aestheticvalue, witness, e.g., Camus’sThe Myth of Sisyphus, andin any case, it can be argued plausibly thatthe equipoise ofopposing forces possibly haspositive aesthetic value,implying that opposed volitional activities of coexistent omnipotentbeings would not necessarily be futile.

Further doubts about the possibility of a plurality of coexistentomnipotent beings are raised by considerations outlined below whichseem to show that ifsome possible world is maximally good,in other words, isa best possible world, thennopossible world is [uniquely]the best possible world, andlikewise with respect to a possible world that is second best, thirdbest, and so on.

Here it is assumed that if there is a best possible world, then thereis at least one such possible world containing contingently existingindividual substantial individuals. A parallel assumption is madeabout any possible world good enough to be actualized by anomnipotent, omniscient, morally perfect, aesthetically perfect being,e.g., by a maximally great divinity such as God. But, with respect toany possible world containing contingently existing substantialindividuals, it appears that there isanother possible worldexactly resembling it but populated bydifferentcontingently existing substantial individuals. It further appears thatthe value of one of these worlds is equal to the value of another ofthese worlds. So, it appears that if one of these possible worlds isbest, second best, third best, etc., then there is another possibleworld of the ordinal rank in question.

Moreover, different possible goods combined in different possible waysmay constitute different, logically independent, possible total goodsof the same value. The following simple example illustrates thispoint. Let it be assumed that the pleasure which would be produced byJohn’s eating a mushroom pizza for dinner tonight and thepleasure that would be produced by John’s eating a garlic pizzafor dinner tonight are logically independent possible goods of thesame value. All other things being equal, a possible world containingJohn’s eating a mushroom pizza for dinner tonight andJohn’s not eating a garlic pizza tonight, and a possible worldcontaining John’s eating a garlic pizza for dinner tonight andJohn’s not eating a mushroom pizza for dinner tonight,constitute different possible goods of the same value. Generalizingfrom examples of this kind, it appears that if some possible world isbest, second best, third best, and so on, then there areother possible worlds,not exactly resembling them,which are best, second best, third best, and so on.

So, for any possible pair of coexistent God-like omnipotent agents, itappears that one member of that pair couldendeavor toactualize a different, equally good, world than the other memberof that pair, even given their hypothesized necessary epistemic,moral, and aesthetic perfection. In the light of thereductio adabsurdum presented earlier, it appears to follow that such pairsare impossible.

Leibniz argued that there is a uniquely optimal possible world byappealing to thePrinciple of Sufficient Reason and theIdentity of Indiscernibles, notoriously concluding that theactual world isthe best of all possible worlds. Amongcontemporary philosophers, both thePrinciple of SufficientReason and theIdentity of Indiscernibles arecontroversial.

Another possible defense of the possibility of a plurality ofcoexistent omnipotent agents appeals to quantum mechanics. Quantumentanglement seems to be a unique physical phenomenon wherebyconcurrent activities of diverse contingently existing substantialindividuals are directly coordinated in virtue of a necessary linkageof some sort between those substantial individuals. By drawing ananalogy with this phenomenon, one might argue that there could becoexistent omnipotent agents who necessarily avoid stalemates. Quantummechanics implies that there exist pairs of entangled micro-particlessuch that it is causally necessary that one member of the pair isspin up if and only if the other member of the pair isspin up, independently of the locations of thosemicro-particles. Albert Einstein skeptically described the theoreticalphenomenon of entanglement as “spukhafte Fernwirkung,”that is, as “spooky action at a distance.” Nowadays,however, entanglement is an experimentally confirmed part of physics.Arguably, by analogy with entanglement, if a plurality of coexistentomnipotent agents is possible, then there could be“entangled” omnipotent agents, \(A_1\) and \(A_2\), suchthat it is metaphysically necessary that \(A_1\) endeavors to bringabout a certain state of affairs if and only if \(A_2\) endeavors tobring about the same state of affairs. But quantum mechanics furtherimplies that there are entangled pairs of micro-particles such that itis causally necessary that one member of the pair isspin upif and only if the other member of the pair isspin down. Theproperties ofbeing spin up andbeing spin down arecontraries. Thus, if the analogy with quantum entanglement is takenseriously, then by parity of reasoning, one should conclude that if aplurality of necessarily cooperating coexistent omnipotent agents ispossible, thenpossibly, there are “entangled”omnipotent agents, \(A_1\) and \(A_2\), such that it is metaphysicallynecessary that \(A_1\) endeavors to act in some way if and only if\(A_2\) endeavors to act in acontrary way. Given thisconclusion, and in the light of thereductio ad absurdum ofthe possibility of a plurality of coexistent omnipotent agentspresented earlier, an argument in favor of such a possibility byanalogy with quantum entanglement undermines itself, therebyreinforcing thatreductio. So, one cannot credibly defend themetaphysical possibility of a plurality of coexistent omnipotentagents by drawing an analogy with the phenomenon of quantumentanglement.

Finally, could one credibly defend such a metaphysical possibility viathe hypothesis that it is metaphysically possible for there to be aplurality of necessarily indiscernible omnipotent God-like beings (inthe Leibnizian sense ofindiscernible)? Because a pluralityofnecessarily indiscernible objects is of dubiousintelligibility, such a defense would not be credible. Doubts aboutthe intelligibility of such a plurality arise because of perplexitiesconcerning the individuation and separation of any pair of necessarilyindiscernible objects, and because positing the existence of aplurality of such objects is metaphysically extravagant andgratuitous. Indeed it seems that there is just as much reason to positindefinitely many objects of the sort in question as there is to posita pair of them, whereas the intelligibility of anecessarilyself-indiscernible object is not in doubt. A representativeexample of a hypothetical plurality of necessarily indiscernibleobjects is a plurality ofnecessarily coincident geometricalpoints. In addition to the perplexities concerning the individuationand separation of any pair of such points, the assumption that it ismetaphysically possible for there to be a plurality of necessarilycoincident points is metaphysically frivolous. Post-Scholasticridicule of the sort that was directed at the alleged ontologicalexcesses of the Schoolmen, e.g., the query “How many angels mayfit upon the point of a needle?”, is quite appropriatelydirected at metaphysical hypotheses of this sort. For these reasons,the intelligibility of a plurality of necessarily coincidentgeometrical points is suspect; the same is true of the intelligibilityof a plurality of necessarily indiscernible omnipotent God-likebeings.

Could an agent be accidentally omnipotent? At first glance, thisappears possible, but there is the following argument for the oppositeview. On the assumption that God exists, he has necessary existence,is essentially not temporally limited, and is essentially omnipotent.But there could not be two coexistent omnipotent agents. Thus, on theassumption that God exists, an accidentally omnipotent being isimpossible.

This argument against the possibility of accidental omnipotencepresupposes traditional Western theism. However, traditional Westerntheism is highly controversial, andneutrality about whetherGod exists has some advantages. If one is neutral about whether Godexists, then omnipotence shouldnot be assumed to beattributableonly to the God of traditional Western theism oronly to an essentially omnipotent being.

2. The Scope of Omnipotence

The intelligibility of the notion of omnipotence has been challengedby the so-called paradox or riddle of the stone. Can an omnipotentagent, Jane, bring it about that there is a stone of some mass, \(m\),which Jane cannot move? If the answer is‘yes’, then there is a state of affairs that Jane cannotbring about, namely, (S1)that a stone of mass \(m\)moves. On the other hand, if the answer is‘no’, then there is another state of affairs that Janecannot bring about, namely, (S2)that there is a stone of mass \(m\)which Jane cannot move. Thus, it seems thatwhether or not Jane can make the stone in question, there is somepossible state of affairs that an omnipotent agent cannot bring about.And this appears to be paradoxical.

A first resolution of the paradox comes into play when Jane is anessentially omnipotent agent. In that case, the state ofaffairs of Jane’s being non-omnipotent is impossible. Therefore,Jane cannot bring it about that she is not omnipotent. Since,necessarily, an omnipotent agent can move any stone, no matter howmassive, (S2) is impossible. But, as we have seen, an omnipotent agentis not required to be able to bring about an impossible state ofaffairs.

If, on the other hand, Jane is anaccidentally omnipotentagent, both (S1) and (S2)are possible, and itispossible for some omnipotent agent to bring it about that (S1) obtainsat one time,and that (S2) obtains at a different time. Thus,there is a second solution to the paradox. In this case, Jane’sbeing non-omnipotent is a possible state of affairs; thus, we mayassume that itis possible for Jane to bring it about thatshe is non-omnipotent. So, Jane can create and move a stone, \(s\),of mass, \(m\), while omnipotent, andsubsequently bring it about that she is not omnipotent andpowerless to move \(s\). As a consequence, Jane canbring about both (S1) and (S2), but only if they obtain at differenttimes.

It might now be conjectured that omnipotence can be analyzed simply asthe power to bring it about that anycontingent state ofaffairs obtains. However, the following list of contingent states ofaffairs shows that there can be contingent states of affairs that anomnipotent agent is powerless to bring about, and hence that thissimple analysis is inadequate:

1. that a raindrop fell;
2. that a raindrop falls at \(t\) (where \(t\)is a past time);
3. that Parmenides lectures for the first time;
4. that the Amazon River floods an odd number of times less thanfour;
5. that a snowflake falls and no omnipotent agent ever exists;and
6. that Plato freely decides to write a dialogue.

Note that (a) is a past state of affairs. Presumably, it is notpossible for an efficient cause to occurlater than itseffect. However, an agent’s bringing about a state of affairs isa kind of efficient causation. Therefore, it is not possible for anagent to bring about anything that is in thepast. In otherwords, it is impossible forany agent to have power over whatis past. Hence, no agent, not even an omnipotent one, can bring itabout that (a) obtains. Likewise, despite the fact that (b) can bebrought aboutprior to \(t\), theimpossibility of an agent’s having power over what is pastimplies thatafter t even an omnipotent agent cannot bring itabout that (b) obtains. In the case of (c), prior toParmenides’s first lecture, an omnipotent agent can bring about(c). But once Parmenides has lectured, even an omnipotent agent cannotbring it about that (c) obtains. As for (d), prior to theAmazon’s third flooding, an omnipotent agent can bring it aboutthat (d) obtains, while after the Amazon’s third flooding, evenan omnipotent agent cannot bring it about that (d) obtains. (e)introduces a special difficulty. Although it is obvious that (e) couldnot be brought about by an omnipotent agent, it can be arguedplausibly that itis possible for a non-omnipotent agent tobring about (e) by causing a snowflake to fall,provided thatno omnipotent agent ever exists.^[1] But, as we argued earlier, a maximally powerful being need not havethe power to bring about every state of affairs that any other beingcould. Lastly, while if the libertarian theory of free will iscorrect, an omnipotent agent (who is, of course,other thanPlato) cannot bring about (f), apparently a non-omnipotent agent,namely, Plato, can bring it about that (f) obtains.

Consequently, a satisfactory analysis of omnipotence ought not torequire that an omnipotent agent have the power to bring about (a),(b), (c), (d), (e), or (f), if it is assumed,arguendo, inthe case of (f), that libertarianism is true.

Because of the wide disparity among contingent states of affairs,(a)–(f), one might despair of finding an analysis of omnipotencethat both deals satisfactorily with all of these states of affairs andimplies that an omnipotent being has, intuitively speaking, sufficientpower. Is such pessimism warranted, or is omnipotence analyzable?

There are at least two approaches to analyzing omnipotence that holdout some hope of success. The first utilizes the notion of anunrestrictedly repeatable state of affairs, and the secondutilizes the notion oftwo worlds sharing their histories up to atime. Although these approaches to analyzing omnipotence differin important ways, they are in broad agreement on the leading ideathat maximal power has logical and temporal limitiations, includingthe limitation that an omnipotent agent cannot bring about, i.e.,cause, another agent’s free decision in the libertarian sense.In the following two sections, some recent instances of theseapproaches are set forth and compared.

3. Omnipotence and Unrestricted Repeatability

One attempt to analyze omnipotence in terms of unrestrictedrepeatability is the account of Hoffman and Rosenkrantz. According totheir approach, by identifying certain features of (a)–(f), wecan find a feature that none of them possesses, and in terms of whichan analysis of omnipotence can be stated. To begin, unless it ispossible forsome agent to bring about a given state ofaffairs, an omnipotent agent ought not to be required to be able tobring about that state of affairs. But (a) is not possibly broughtabout by any agent.

Next, while (b) and (c) are possibly brought about by some agent, theyare notrepeatable: it is not possible for either one of themto obtain, subsequently fail to obtain, and then obtain again. Notethat if, because (a) is not possibly brought about by someone, anomnipotent agent is not required to be able to bring about (a), thenfor the same reason, that agent is also not required to be able tobring about impossible or necessary states of affairs. Moreover, if,because (b) and (c) are not repeatable, an omnipotent agent is notrequired to bring about (b) or (c), then for the same reason, thatagent is also not required to be able to bring about impossible ornecessary states of affairs. These reasons for not requiring anomnipotent agent to have the power to bring about impossible ornecessary states of affairs cohere with our earlier independentarguments for these restrictions.

Third, while (d)is repeatable, it isnotunrestrictedly repeatable, that is, it cannot obtain, thenfail to obtain, then obtain again, and so on, eternally.

Fourth, while (e)is unrestrictedly repeatable, it is acomplex state of affairs, namely, aconjunctivestate of affairs whose second conjunct isnot repeatable.These examples suggest a hypothesis about repeatability and itsrelation to power, namely, that an omnipotent agent shouldnot be required to have the power to bring abouteither a state of affairs that is not unrestrictedlyrepeatable,or a conjunctive state of affairs one of whoseconjuncts is not unrestrictedly repeatable.

Lastly, although (f)is unrestrictedly repeatable, (f) isanother type of complex state of affairs. In particular, it isidentifiable with or analyzable as a conjunctive state of affairs.This state of affairs has three conjuncts, the second of which is notpossibly brought about by anyone. The conjunctive state of affairs inquestion can be informally expressed as follows: Plato decides towrite a dialogue; and there is noantecedent sufficientcausal condition of Plato’s deciding to write a dialogue; andthere is no concurrent sufficient causal condition of Plato’sdeciding to write a dialogue. Because it is impossible for an agent tohave power over what ispast, the second conjunct of thisstate of affairs is not possibly brought about by anyone. Thus, anomnipotent agent ought not to be required to have the power to bringabout a state of affairs that is identifiable with or analyzable as aconjunctive state of affairs one of whose conjuncts is not possiblybrought about by anyone.

According to the account of Hoffman and Rosenkrantz, incoporatingthese ideas, omnipotence can be analyzed in terms of the followingthree definitions.

(D1)

The period oftime \(t\) is a sufficient interval for \(s =_{df} s\)is a state of affairs such that: it is possible that \(s\)obtains at a time-period which has the duration of\(t\).

For example, any period of time with a duration of 7 seconds is asufficient interval for the state of affairsthat a ball rolls for7 seconds.

(D2)

A state ofaffairs, \(s\), is unrestrictedly repeatable \(=_{df}\)\(s\) is possibly such that: \(\forall n\existst_1\exists t_2\exists t_3 \ldots \exists t_n [(t_1 \lt t_2 \lt t_3 \lt\ldots \lt t_n\) are periods of time which are sufficient intervalsfor \(s \amp s\) obtains at \(t_1 \amp s\) doesn’t obtain at\(t_2 \amp s\) obtains at \(t_3 \amp \ldots \amp s\) obtains at\(t_n)\) if and only if \(n\) is odd].^[2]

For instance, the state of affairsthat a ball rolls for 7seconds is unrestrictedly repeatable.

(D3)

\(x\) is omnipotent at \(t =_{df} \forall s\)(if it is possible forsome agent to bring about \(s\) then at \(t\) \(x\) has it within hispower to bring about \(s)\).

In (D3), \(x\) ranges over agents, and \(s\)over states of affairs that satisfy the followingcondition:

(C)

(i) \(s\)is unrestrictedly repeatable, and of the form‘in \(n\) minutes, \(p\)’,& \((p\) is a complex state of affairs \(\rightarrow\) (each ofthe parts of \(p\) is unrestrictedly repeatable &possibly brought about by someone)), or (ii) \(s\) isof the form ‘\(q\) forever after’, where\(q\) is a state of affairs which satisfies (i).^[3]

In applying (D3) to states of affairs like (e) and (f) it should beobserved that aconjunct of a conjunctive state of affairs isapart of such a complex state of affairs.^[4]

As intended, (D3) does not require an omnipotent agent to have thepower to bring about either impossible or necessary states of affairs,or states of affairs such as (a)–(f). Furthermore, (D3) does notunduly limit the power of an omnipotent agent, since an agent’sbringing about a state of affairs can always be “cashedout” in terms of that agent’s bringing about anunrestrictedly repeatable state of affairs that it is possible forsome agent to bring about. That is, necessarily, for any state ofaffairs, \(s\), if an agent, \(a\),brings about \(s\), then either \(s\) isan unrestrictedly repeatable state of affairs which it is possible forsome agent to bring about, or else \(a\) brings abouts by bringing about \(q\), where \(q\)is an unrestrictedly repeatable state of affairswhich it is possible for some agent to bring about. For instance, anomnipotent agent can bring about the state of affairs,that in onehour, Parmenides lectures for the first time, by bringing aboutthe state of affairs,that in one hour, Parmenides lectures,when this lecture is Parmenides’s first. And although the formerstate of affairs is a nonrepeatable one that (D3) doesnotrequire an omnipotent agent to be able to bring about, the latterstate of affairsis an unrestrictedly repeatable state ofaffairs that (D3)does require an omnipotent agent to be ableto bring about.

4. Omnipotence and the Shared Histories Approach

The alternative approach to analyzing omnipotence in terms of twoworlds sharing their histories up to a time is exemplified by theaccounts of Flint and Freddoso, and Wierenga. As we shall see,although these two accounts are similar, they differ in certainsignificant respects.

Flint and Freddoso’s account of what it is for an agent \(S\)at a time \(t\) to be omnipotent in apossible world \(W\) is formulated as follows.

The notion of a world-type-for-\(S\) \(Ls\) is to beunderstood in the following way. Aworld-type is “a setwhich is such that for anycounterfactual of freedom, i.e.,any proposition which can be expressed by a sentence of the form‘If individual essence \(P\) were instantiated incircumstances \(C\) at time \(t\) andits instantiation were left free with respect to action \(A\),the instantiation of \(P\) wouldfreely do \(A\)’—either that counterfactualor its negation is a member of the set” (Flint & Freddoso1983, p. 96). It may also be stipulated “that for any twomembers of the set, the conjunction of those two members is a memberof the set as well” (Flint & Freddoso 1983, pp.96–97). Moreover, “a world-type istrue just incase every proposition which is a member of it is true” (Flint& Freddoso 1983, p. 97). In addition, it is presupposed that“for any free agent \(x\), there will be a set ofall and only those true counterfactuals of freedom (or true negationsof such counterfactuals) over whose truth-value \(x\)has no control” (Flint & Freddoso 1983, p. 97). A set ofthis kind is referred to asthe world-type-for-x. Finally,‘\(Lx\)’ designates the true-world-type-for-\(x\).

The notion of actualization employed in this account of omnipotencecalls for some explanation. If an agent, \(S\), bringsabout a state of affairs, \(p\), then \(S\)actualizes \(p\). However, thisaccount presupposes that an agent may [weakly] actualizeanother agent’s making afree decision withoutbringing about orcausing that decision. Inparticular, it is assumed that an agent may weakly actualize adecision that is free in the libertarian sense by bringing about theantecedent of a true “counterfactual of freedom.”

The basic idea of this account of omnipotence is that an agent isomnipotent just when he can actualize any state of affairs that it ispossible for someone to actualize, except for certain“counterfactuals of freedom”, their consequents, andcertain states of affairs that are “accidentallyimpossible” because of the past.

With respect to so-called counterfactuals of freedom, this accountpresupposes that some of them, for example,

If Jessica were offered the grant, then she would freely decide toaccept it,

aretrue. Some philosophers hold the contrary view that asubjunctive conditional of this kind isnecessarilyfalse. Why do these philosophers reject the claim that some“counterfactuals of freedom” are true? Presumably, whatdistinguishes a subjunctive conditional from a corresponding materialconditional is that only the former expresses a strong or necessaryconnection of some sort between the conditions specified by theantecedent and the consequent. Seemingly, the only kinds of strong ornecessary connections available in this case are relations [broadlyspeaking] of eithercausation orentailment.Consequently, it appears that the subjunctive conditional underdiscussion is necessarily false, since if Jessicafreelydecides to accept the grant [in the relevant libertarian sense], thenher making that decision is neithercaused norentailed by her being offered the grant. If the foregoingline of reasoning is correct, then the notion of a true“counterfactual of freedom” is incoherent. Since Flint andFreddoso’s account of omnipotence presupposes that there aresuch “counterfactuals of freedom,” it can be argued thatthis account is incoherent.

Moreover, it can be argued that a state of affairs discussed earlierprovides a counter-example to Flint and Freddoso’s account ofomnipotence, namely:

(e)

A snowflake fallsand no omnipotent agent ever exists.

A non-omnipotent agent can bring about or actualize (e) by bringing itabout that a snowflake falls when in fact no omnipotent agent everexists. But, it is clear that an omnipotent agent cannot bring aboutor actualize (e). For although an omnipotent agent can bring it aboutthat a snowflake falls, surely, an omnipotent agent cannot bring itabout thatno omnipotent ever exists, nor would this conjunctof (e) obtain if there were an omnipotent agent. Moreover, we mayassume that there are possible worlds, \(W\) and\(W^*\), such that \(W\) and \(W^*\) share the samehistory up to a time \(t\), no omnipotent agent everexists in \(W^*\), and a contingently omnipotent agent, Oscar, isomnipotent for the first time at \(t\) in \(W\).We may also assume that \(W^*\) is a world in whichat \(t\) some non-omnipotent agent actualizes (e). Onthe other hand, evidently, if in \(W\), Oscar isomnipotent at \(t\), then at \(t\) Oscarcannot actualize (e). Note that since the second conjunct of (e) isnot unrestrictedly repeatable, this is consistent with Hoffman andRosenkrantz’s account of omnipotence; their account does notrequire an omnipotent agent to be able to bring about a conjunctivestate of affairs one of whose conjuncts is not unrestrictedlyrepeatable. On the other hand, Flint and Freddoso’s account ofomnipotence implies that in \(W\), at \(t\)Oscar has the power to actualize (e). Thisimplication holds for the following reasons. First, (e) is not amember of a world-type-for-Oscar, inasmuch as (e) is neither a“counterfactual of freedom,” the negation of one, nor aconjunction of such “counterfactuals of freedom.” Second,we may assume that a world-type-for-Oscar is true in both \(W^*\) and\(W\), since the assumption that an agent is notomnipotent in one possible world, and is omnipotent for a time inanother possible world, does not necessitate any difference in theworld-type for that agent which is true in those worlds. Third, it ispossible for someone at \(t\) to actualize (e) in aworld, \(W^*\), that has the same history up to \(t\)asW.^[5] Thus, arguably, Flint and Freddoso’s account of omnipotencerequires that in \(W\) an omnipotent agent, Oscar, at\(t\) has the power to actualize (e), when Oscar lacksthis power. If this is right, then their account does not provide alogically necessary condition on omnipotence.^[6]

A counter-example of this kind assumes that an analysis of omnipotenceshould allow for the possibility of an omnipotent agent other thanGod. Given this assumption, (e) seems to provide a counter-example toFlint and Freddoso’s account of omnipotence, but not to theaccount of Hoffman and Rosenkrantz.

Let us now turn to Wierenga’s account of omnipotence. The basicidea of Wierenga’s account of omnipotence is that an agent isomnipotent if and only if he can do anything that it is possible forhim to do, given the past. According to this account, we can analyzewhat it is for an agent, \(A\), to be omnipotent at \(t\)in a world \(W\) in terms of what itispossible for A to strongly actualize at \(t\)in worlds having the same history as \(W\)up to \(t\).

Wierenga’s account of omnipotence, like Flint andFreddoso’s, relies on the intuitive idea that two possibleworlds can share the same past or history up to a certain point intime, and then diverge. According to Wierenga’s account, twoworlds of this kind share aninitial segment, where \(S (W,t)\) is an initial segment of a possible world \(W\) upto a time \(t\) (Wierenga 1989, pp. 18–20).Unlike Flint and Freddoso’s account, Wierenga’s account isnot stated in terms of what an agent can actualize, but rather interms of the narrower notion of what an agent canstronglyactualize. An agent, \(A\), strongly actualizesjust those states of affairs that \(A\) brings aboutdirectly or those actions that \(A\) does notdoby doing something else (Wierenga 1989, pp. 20–23).Of course, an agent may actualize a state of affairsindirectly by strongly actualizinganother state ofaffairs. Wierenga’s account of omnipotence is formulated asfollows.

A being \(x\) is omnipotent in a world \(W\)at a time \(t =_{df}\) In \(W\) it istrue both that (i) for every state of affairs \(A\), ifit is possible that both \(S (W, t)\) obtains and that \(x\)strongly actualizes \(A\) at \(t\),then at \(t, x\) can strongly actualize \(A\),and (ii) there is some state of affairs which \(x\)can strongly actualize at \(t\).(Wierenga 1989, p. 25)

This account of omnipotence may be vulnerable to a counter-example ofthe following kind. Arguably, there could be an agent, \(x\),such that: \(x\) has a wide range ofpowers, \(x\) is essentially limited to these powers,and \(x\) essentially lacks a power, \(P\),which an omnipotent agent ought to possess. Ofcourse, \(x\) would not be omnipotent. Yet,Wierenga’s account of omnipotence paradoxically implies that \(x\)would be omnipotent. Hence, it can be argued thatWierenga’s account does not provide a logically sufficientcondition for omnipotence. The assumption that there could be anon-omnipotent agent that is essentially limited in its powers can bedefended as follows. An omnipotent agent has the power to overrule (orsupersede) any law of nature (a merephysical necessity). Forexample, God has the power to overrule the law of gravity by bringingit about that a mountain floats in midair without any physical cause.Yet, arguably, it is possible for there to be a non-omnipotent agentwho essentially lacks the power to overrule any law of nature. Forexample, it can be argued that there could be a physical or materialagent who isessentially subject to certain laws of nature.Surely, such an agent would lack the power to overrule any law ofnature, and so would not be omnipotent.

A similar, though weaker, sort of objection concerns McEar, ahypothetical agent who essentially has the power to do onlyone thing, namely, scratch his ear. It may be objected thatWierenga’s analysis of omnipotence falsely implies that McEarwould be omnipotent. But it might be replied that an agent such asMcEar is impossible. It can be cogently argued that, necessarily, ifMcEar has the power to scratch his ear, then healso has thepower to move a part of his body to scratch his ear, for instance, hisarm (Wierenga 1989, pp. 28–29). So, it appears that there couldnot be an agent that has the power to do only one thing. In reply tothe stronger sort of objection discussed earlier, it may be suggestedthat, necessarily, forany power, if an agent lacks thatpower, then an omnipotent being could give that agent that power(Wierenga 1989, p. 29). The difficulty with such a reply is that therecould be a non-omnipotent agent whoessentially lacks thepower to overrule any law of nature, and hence that not even anomnipotent agent could give this non-omnipotent agent that power.

5. Omnipotence and Divine Moral Perfection

It has been argued that the traditional God has incompatibleattributes, namely, necessary existence, essential omnipotence,essential omniscience, and essential moral perfection (Pike 1969).^[7] The contention has been that it is impossible for God to have thepower to bring about evil, while non-omnipotent (and morallyimperfect) beings may have this power. The precise form of such anargument varies depending on what precisely the relation between Godand evil is assumed to be. However, generally speaking, it is arguedthat divine moral perfection and omnipotence are incompatible becausedivine omnipotence entails that God has the power to bring about evil,whereas divine moral perfection entails that God is powerless to bringabout evil.

One can respond to arguments of this kind as follows. Assume that ifGod exists, then this is a best possible world.^[8] In that case, if God exists, there could not be an evil unless itwere necessary for some greater good, in which case any state ofaffairs containing evil incompatible with there being a maximally goodworld isimpossible. But it be may be assumed that it is notpossible forany agent to bring about an impossible state ofaffairs. Thus, if God exists, any moral evil, that is, any evilbrought about by anyone, and any natural evil, or any evil which hasan impersonal, natural cause, must be necessary for some greatergood.

Suppose that God exists and that some other person, for example, Cain,brings it about that an evil, \(E\), exists. There aretwo possibilities that need to be considered here. The first is thatCain’s decisions and actions are causally determined, as are alloccurrences in the created universe. Then, given our assumptions,since Cain’s bringing it about that \(E\) existsis necessary for some good which more than compensates for \(E\)’sexistence, it is consistent with God’smoral perfection that God [remotely] brings it about that Cain bringsit about that \(E\) exists.

The second possibility is that Cain’s decision to do evil isuncaused by anything other than Cain and free in the libertariansense. In that case, God didnot [remotely cause Cain freelyto] bring it about that \(E\) exists, while [let usassume] Caindid freely bring it about that \(E\)exists. If so, then it must be the case thatGod’s creating Cain and permitting Cain freely to do what hechooses to do [in the context of the entire creation] brings aboutmore good than hisnot creating Cain and thusnotpermitting him freely to do what he chooses to do. It might beobjected that if Cain can bring about a state of affairs that Godcannot, namely,that E exists, then God is not omnipotent.But, as we have seen, an agent’s being omnipotent does notrequire of that agent that it be able to bring abouteverystate of affairs whichany other agent can bring about. Itdoes, of course, require that an omnipotent agent have morepower than any other agent. And God, of course,would havemore power than Cain, even though Cain could bring about somethingthat God could not. For there are many more states of affairs that Godcould bring about and that Cain could not, thanvice versa.At this point, it might further be objected that an omnipotent agent,one that was morally imperfect, whocould bring it about that\(E\) exists, as well as all the other states ofaffairs that God could bring about, would be more powerful than God.But recall that if God exists, then he exists eternally in everypossible world. Recall, too, that apparently there cannot be more thanone omnipotent agent. Thus, it appears that if God exists, then anomnipotent agent who is morally imperfect isimpossible.Thus, this second objection is based on an assumption that seems to beimpossible, namely, that if God exists there could exist anotheromnipotent agent who is morally imperfect and who is therefore morepowerful than God.

Of course, if God exists, then any evil state of affairs, \(s\),whichis incompatible with a maximally goodworld isimpossible. And if \(s\) isimpossible, then neither God nor any other agent has the power tobring it about that \(s\) obtains. God would lack thepower to bring it about that \(s\) obtains because ofhis moral perfection, and any created agent would lack the power tobring it about that \(s\) obtains either because (i)God would not create an agent who had the power to bring it about that\(s\) obtains, or (ii) God would not permit any createdagent to bring it about that \(s\) obtains. Thus, tothe extent indicated, if God’s attributes impose moralrestrictions on the nature of the universe and on what he can bringabout, then they impose parallel restrictions on what any other agentscan bring about.

The foregoing line of reasoning implies that God’s moralperfection and omnipotence are not incompatible.^[9]

This argument about God and the possibility of evil has been disputedby theists such as Alvin Plantinga, who do not hold that God’sexistence implies the existence of a maximally good world, but do holdthat God seeks to create as good a world as he can.^[10] Theists such as Plantinga allow for there to be evil that isunnecessary for any greater good that outweighs it. An evilof this kind involves free decisions of non-divine agents, which Goddoes not prevent, but which these other agents can prevent. Plantingacontends that God is not wrong to permit an evil of this kind, sinceGod cannot bring about a vital good, the existence of free humanagents, without there being such an evil. Alternatively, it might beargued that God does no wrong in this sort of case, because he doesnot know how to do better (knowledge of the future free actions ofcreated agents being impossible). However, as an omnipotent God isnot required to have power over the free decisions ofnon-divine agents, it follows that on these views, his omnipotence andmoral perfection are compatible, roughly to the extent indicatedearlier in our discussion of the view that God’s existenceimplies a maximally good world. Of course, nothing that has been saidhere answers the question of how much, if any, evil is compatible withthe existence of the traditional God. This question is central to theproblem of evil for theism.

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