Impaled by the Two Horns of Logic: The Paradox of Omnipotence and Free Will

In 1955, John Mackie, in his insightful article "Evil and Omnipotence," delivered a cogent version of the problem of evil claiming, "it can be shown, not that religious beliefs lack rational support, but that they are positively irrational...". [1] From this article, there arose two penetrating issues which if either is successful entail a contradiction in the theist's beliefs: Mackie's objection to our current state of free will being the highest good and the Paradox of Omnipotence. Since both arguments proposed severe limits on God's omnipotence, most theists formed a strong line of defense against each. In response to the former, Alvin Plantinga developed the well-known Free Will Defense. As a response to the latter, most theists eventually decided that the paradox was a logical impossibility that lay outside the realm of a logically limited omnipotent God. But in maintaining both of these theistic positions, there is an elusive contradiction. To reveal this contradiction, I will first explain two topics concerning God's omnipotence which are crucial to understanding my analysis. Second, I will explain Mackie's objection. Third, I will discuss relevant segments of Plantinga's Free Will Defense and show that he accepts (9) either as a nonlogical or logical limit on God's omnipotence. Fourth, I will analyze the Paradox of Omnipotence and show that there is only one objection which is valid for the theist and which entails claiming (11'). From my analysis, I will asseverate that a theist who holds that God is limited by free will and refutes the Paradox of Omnipotence believes a logical contradiction.

In contemplating matters of a Judeo-Christian God's omnipotence, there is a manner of speaking which causes some confusion and misplaced criticism. For example if one says, "God can't be ignorant by definition of his omniscience," some theists may reply, "God's omnipotence makes him capable of performing any feat. God can be ignorant if he ever chooses to exercise the ability." This is possible in an unrealized and unimaginable sense, but it is also a logically impossible state of affairs for God. If he ever did become ignorant, then he would not be the God we defined and understand him as. To be clear in this paper, I will explain what I mean by God can or can't do x. If I state God can do x, then I refer to God's ability to do x within a logically possible state of affairs for God. By the same token, if I state God can't do x, then I refer to God's inability to do x (a nonlogical limit) within a logically possible state of affairs for God. More importantly, if I state God can (or could) illogically do x, then I refer to a logically impossible state of affairs which some theists feel is an important potential of an omnipotent God. In the above example, the theist's objection becomes, "God could illogically choose to be ignorant." There are some theists who would be puzzled by this semantic digression because they hold that God's omnipotence as a logical concept is undeterred by anything, including logic. To address this claim, I should observe that although the theist claims his concept of God can illogically do anything (ie make 2+2 =6), the action remains illogical in the eyes of his companions. If he wishes to claim illogic as logic without explaning how it is logical, then I think this argument or any logical argument does not concern him. As Plantinga explains in his free will defense: "What the theist typically means when he says that God is omnipotent is not that there are no limits to God's power, but at most that there are no nonlogical limits to what He can do...". [2] Thus, in this argument I will assume as most theists do that a logical concept of God can't illogically do anything.

In turning to Mackie, we note that as an atheologian, he is concerned with determining if the theist's beliefs are consistent with the ubiquitous presence of evil. The theologian, as the person under rational inquiry who values rationality, is expected to give reasons for his beliefs which are logically consistent. In order to commence our analysis, I will assume the Judeo-Christian definition of God applied to evil and the existence of evil:

1. God eradicates evil to his fullest ability. (perfectly good)
2. God can do anything. (omnipotence)
3. God knows all about evil. (omniscience)
4. Evil exists in this world

From examining these propositions, Mackie objects to the consistency of free will with them. Notice that Mackie has not demurred to free will conflicting with God's omnipotence because the theist has not placed any nonlogical limits on God's omnipotence. Mackie remonstrates that in creating the current state of human free will, God has failed to achieve the highest good possible:

"If there is no logical impossibility in a man's freely choosing the good on one, or on several, occasions, there cannot be a logical impossibility in his freely choosing the good on every occasion. God was not, then faced with a choice between making innocent automata and making beings who, in acting freely, would sometimes go wrong: there was open to him the obviously better possibility of making beings who would act freely but always go right. Clearly, his failure to avail himself of this possibility is inconsistent with his being both omnipotent and wholly good." [3]

Mackie's argument can be divided into these propositions:

5. Since men can freely choose good on one or several occasions, then it is logically possible that men can always freely choose good.

6. If God can do anything, then God can create men to always freely choose good. (from 2 and 5)

7. If God chose to create men who would freely choose evil sometimes instead of men who would always freely choose good, then God did not eradicate evil to his fullest ability. (from 4 and 6)

8. If God did not eradicate evil to his fullest ability, then God is not perfectly good.

In proposition (5), he explains that it is logically possible, by the most unlikely probability, for men to always choose good. From (5) and (2), God can create men to always freely choose good. In (7), Mackie assumes from (4) that some evil in this world is caused by men. If a theologian believes that it is not men but God that causes evil in this world, then he clearly has not accepted (1). From (4) and (6), God did not eradicate all the evil he could have. If he is able to do everything that is logically possible and chose not to eradicate evil, then we arrive at conclusion (8). Since (8) contradicts with the theist's core belief (1), then the theist holds an inconsistent set of beliefs or an irrational belief in God. Naturally, a theist will not accept such a perturbing conclusion so we shall now turn to Plantinga's explanation of the free will defense.

In prefacing the defense, Plantinga explains that there are "states of affairs that don't include evil...nonetheless God Himself can't bring them about without permitting evil." [4] What kind of states of affairs are these? From (2), these states of affairs must evidently be logically impossible ones. For example, a logically impossible state of affairs could be a round square or a triangle with four angles. They are logically impossible because they are contradictory by definition of the words. But from propositions (1)-(3) on God, does God have to allow evil? If Plantinga were alluding to states of affairs which God can't illogically perform, then he is only being redundant about God's omnipotence. However, if he is alluding to states of affairs which God can't perform, then this newly admitted nonlogical limit would evidently contradict God's omnipotence.

Plantinga continues by defining human free will: "If a person is free with respect to a given action, then he is free to perform that action and free to refrain from performing it; no antecedent conditions and/or causal laws determine that he will perform the action, or that he won't." [5] This raises a perplexing issue. Does this definition of free will constrict God's omnipotence? Since God has complete control in the event of a creation and also controls causal laws, it seems that God would be unable to control these if they affected human free will. In the following paragraph, Plantinga states, "Now God can create free creatures, but He can't cause or determine them to do only what is right. For if He does so, then they aren't significantly free after all; they do not do what is right freely." [6] Plantinga is admitting that God can't illogically perform certain actions, namely cause or create a human to always choose good. But is Plantinga justified in assuming that free will is a logical limit on God?

What logical limits exist on the concept of God? Since the definition of a Judeo-Christian God is the only accepted means of understanding God between theologian and atheologian, God's characteristics can be the only logical limits. If a theist objects that the atheologian is assuming the free will to be false, then he accuses the atheologian wrongly. The atheologian is searching for logical consistency between free will and God's characteristics before accepting the free will defense. If the theologian claims rational belief, then he should be able to explain himself without reverting to unjustified assumptions. If we cogitate God's perfect goodness, there are no logical limits from his omnipotence or omniscience which restrict it. If we ponder his omniscience, there are equally no logical limits from his omnipotence or his perfect goodness which limit it. But (2) is where we meet logical limits on God. He is prevented by his perfect goodness from doing anything which will make him less than perfect good. Likewise, he is prevented by his omniscience in doing anything which will make him less than omniscient. Are there any other logical limits on God's omnipotence? Yes, remembering that we desire our concept of God to remain logical, he cannot illogically do anything (he cannot do anything which is a logically impossible state of affairs). Thus, in addition to being bound by his original definition, God cannot illogically do anything.

Having explained where God's logical limits are, is God logically limited by human free will? Evidently not. Yet the theist argues yes. Since God's perfect goodness has created free will and is now contingent upon it, God's omnipotence cannot do anything to violate free will without logically contradicting the definition of his perfect goodness. But what grave mistake has the theist committed here? The theist, in a rush to defend God, includes in his explanation for the consistency between free will and the definition of God (which determines if free will is an acceptable concept), the presupposition that the free will is already acceptable and thus imposes logical restrictions on God! This is but a ludicrous circular reason since the theist is showing that free will is completely consistent with God's definition by assuming that free will is already consistent. If the theist wishes to maintain rational integrity, he must then explain the unjustified presupposition that free will is already logically possible. With this method of reasoning exposed, what other reason can the theist give for explaining the limiting ability of free will on God's omnipotence? One could claim that we can observe a posteriori that we have free will. True, but this does not justify the claim that free will and (2) are consistent. The only logical explanation is that human free will, as a new nonlogical limit, restricts God's omnipotence. Thus, only by recognizing that human free will limits God can the theist assert that God was forced to create evil.

What objection does Plantinga give against God's omnipotence being nonlogically limited by free will? He states: "As it turned out, sadly enough, some of the free creatures God created went wrong in the exercise of their freedom; this is the source of moral evil. The fact that free creatures sometimes go wrong, however, counts neither against God's omnipotence nor against His goodness; for He could have forestalled the occurrence of moral evil only be removing the possibility of moral good." [7] Throughout this excerpt, Plantinga is unjustifiably assuming free will's consistency with God's characteristics as a reason for why free will does not count "neither against God's omnipotence nor against His goodness." In other words, Plantinga is saying, 'In order to settle this dispute of whether God is consistent with free will, or in other words, whether free will imposes any nonlogical limits on an omnipotent God, I answer God is not nonlogically limited by free will because free will is consistent with God and thus, logically limits God in such and such a manner.' Plantinga does not try to reconcile God's omnipotence, as understood in (2), with free will anywhere else in the argument other than by the above reasoning. I think I have given sufficient argument to show that Plantinga and any free will advocate, who defends free will by unjustifiably referring to a hypothetical world where free will and God's characteristics are already consistent, demonstrate circular reasoning and thus can only claim free will as a nonlogical limit on God's omnipotence.

Almost directly from Plantinga's quote, the new limit on God's omnipotence is:

9. God can create (free creatures which He cannot control to a degree x).

I substituted Plantinga's "can't cause or determine them" with "cannot control to a degree x" where x = 1 is absolute no control and x = 0 is complete control. As the theist admits, x >0 where x is human free will and 1-x is the degree of God's omnipotence. It is important to note that even if the theist denies (9) to be a nonlogical limit, he still assumes it to be a logical limit on God's omnipotence. From (9) and regardless of whether it's accepted as a logical or nonlogical limit, it stands that there is a reasonable objection to Mackie's argument. The theist agrees with (5) because it is logically possible, by probability, that men always choose good. However, God is limited by free will to a degree x, specifically when it concerns causing or determining men that always choose good. Thus, Mackie's (6) is rejected and the rest of the argument is invalid. In admitting (9), the theist is able to successfully object to Mackie and it seems that a rational belief in God is kept.

The other troubling issue for theists upon reading Mackie's article is the Paradox of Omnipotence. Mackie states, "can an ominipotent being make things which he cannot subsequently control? [8] This does pose an equally devastating dilemma to the theist. If he answers yes then he admits that an omnipotent being can make things which then renders him less than omnipotent. If he answers no, then God is unable to do something which makes him not omnipotent. Either answer yields God as not omnipotent which contradicts God's omnipotence. The choices can be shown as follows:

10. God can create (anything which He cannot control to any degree).

11. God cannot create (anything which He cannot control to any degree).

I have substituted "create", as a synonym for "make," and "things" with "anything" since "things" is being used in a general sense. I also added "to any degree" to each choice and will explain later that it has no effect. Mackie explains to the reader that the paradox is a proper question and as an example describes a human mechanic who makes an uncontrollable machine.

But is this a valid analogy? Although God is like a mechanic, he is omnipotent, unlike the mechanic. As Bernard Mayo points out, "That the expression 'things (anything) which an omnipotent being cannot control' is self-contradictory, is scarcely veiled by writing 'he' for 'the omnipotent being.'" [9] Mayo's perspective elucidates this seeming paradox by exposing it to be a rhetorical question. For example, suppose I ask, "Can God make 2+2 = 6?" This would obviously be a logically impossible state of affairs which God cannot perpetuate. In a similar manner, asking if God can create things which he cannot control is illogical by definition of his omnipotence. If we examine (10), it becomes apparent that Mackie is asking if God can do something self-contradictory. In other words, the phrase "things which he (an omnipotent being) cannot control" is logically impossible for God. {This objection completely invalidates (10) because no matter how infinitesimal the degree (hence the phrase, "to any degree") of no control, (10) is logically impossible.} But the theist does not claim that God can do the logically impossible. Since the action required of God has been shown to be logically impossible, revising the semantics of each yield:

10'. God can illogically create (anything which He cannot control to any degree).

11'. God cannot illogically create (anything which He cannot control to any degree).

Since the theist already rejects (10') by what he believes, he is justified in answering (11'). Although this is the common theistic version of refuting the paradox, are there any that do not immediately claim (11')?

In God and Other Minds, Plantinga offers an abstruse objection to the paradox. Instead of claiming a specific objection he asks us to consider two possibilities:

12. "(God is omnipotent and it is possible that there is a being God cannot control)" [10] are consistent or logically possible.

13. "(God is omnipotent and it is possible that there is a being God cannot control)" are inconsistent or logically impossible.

He claims that both (12) and (13) invalidate the paradox. In this manner, it seems that Plantinga does not have to admit to anything. Evidently (13) refutes the paradox because it assumes that "things which God cannot control" is logically impossible, leading to (11'). Can (12) also refute the paradox? If we examine (12), it claims the exact opposite of (11'). How is it logically possible that God's omnipotence have no nonlogical limits yet still not have control over a being? Clearly, Plantinga has committed the same specious reasoning as he did in presupposing that free will and God's omnipotence are consistent. (12) could only happen if such a being was a logical limit of God. But which of the three characteristics of God define a being which God cannot control? None. Plantinga has again taken the liberty of assuming that human free will is a logical limit on God without admitting to a nonlogical limit on God. Plantinga gives no reason for accepting (12) and having committed the same fallacy as before we can reject (12). This leaves Plantinga with (13) which is just the same argument given by Mayo. At least Plantinga admits that (13) entails (11'): In accepting (13),"if God is omnipotent, the proposition There is a being God cannot control is necessarily false...then the action of creating a being God cannot control is not logically possible." [11]

In examining (10') or (11'), are there any other possible ways by which the theist can avoid the paradox and not admit (11')? Oddly enough, Mackie offers an explanation that could justify (10): "if an omnipotent being makes it that certain things are independent, then to control these things is to control things that are omnipotently-made-uncontrollable, and this is logically impossible. Hence, by our definition, even an omnipotent being is unable to control such things, and failure to control them does not count against omnipotence." [12] Mackie believes that this possible solution makes (10) justified and since then neither (10) or (11) is more justified, the paradox is reinstated. If we examine Mackie's first sentence, we observe that he commits the same error as Plantinga's (12). To possibly arrive at (10), one must first assume a logically impossible (12). Naturally, if one assumes a logically impossible statement as logical then one can show that statement to be logical. But such a fashion of reasoning is inimical to our understanding because then illogic and logic become indistinguishable. Mackie is no more successful than Plantinga in offering another solution to the paradox. Thus, to avoid the contradictions that arise from answering the paradox, the theist's only viable solution is to offer Mayo's objection and accept (11').

By trying to avoid the piercing horn of the Paradox of Omnipotence, the theist responds with (11') and manages to maintain a consistency in beliefs. However, he is also faced with the equally logical horn of Mackie's objection to free will and thus accepts (9) to temporarily regain rational integrity. Yet the very beast from which he has been trying to escape, has now pinned him:

9. God can create (free creatures which He cannot control to a degree x).

11'. God cannot illogically create (anything which He cannot control to any degree).

The logical contradiction between (9) and (11') has strong ramifications for the theist. In (9) the theist is admitting that "free creatures which He cannot control to a degree x" is logically possible. Contradictorily, the theologian in (11') is claiming "anything which He cannot control to any degree" is logically impossible.

By taking two issues which the theist alternates in refuting, I have shown that if one examines their contradictory responses, the theist holds an inconsistent belief set of (1)-(4), (9) and (11'). Evidently, if the theist decides to only believe in (9) or (11'), then he must face immediate consequences from either Mackie's objection or the omnipotence paradox. In facing Mackie's objection, I have shown that Plantinga's description of what constitutes the free will defense is only circular reasoning. Although I have not objected thoroughly to Plantinga's Free Will Defense, I did object to its core components and consequently have provided a telling counter argument. In showing that the theist's reasoning is based on a presupposition, the theist should accept (9) as a nonlogical limit, which entails God being less than omnipotent, in order to give a justified explanation of his beliefs. However, even if the theist insists that (9) is a logical limit which overcomes Mackie's objection, he still faces the contradiction between (9) and (11') and must explain how God's omnipotence successfully prevails over the Paradox of Omnipotence without claiming (11'). From the Paradox of Omnipotence, I have shown that despite Plantinga and Mackie's arguments, the theologian can only escape its effects by denying (10') and accepting (11'). If the theist had conceded (9) as a nonlogical limit before encountering the Paradox of Omnipotence, he still faces a contradiction with (11'). Considerable revision lie ahead for a theist who believes (1) -(4) unless he concurs with Mackie that his beliefs "are positively irrational."


[1] John Mackie, "Evil and Omnipotence," in Philosophy of Religion: An Anthology, ed. Poj (USA: Wadsworth Publishing, 1998), p. 186.

[2] Alvin Plantinga, "The Free Will Defense," in Philosophy of Religion: An Anthology, ed. Poj (USA: Wadsworth Publishing, 1998), p.197.

[3] Ibid, Mackie, p. 191.

[4] Ibid, Plantinga, p. 202.

[5] Ibid, Plantinga, p. 202.

[6] Ibid, Plantinga, p.203.

[7] Ibid, Plantinga, p.203.

[8] Ibid, Mackie, p.192.

[9] Bernard Mayo, "Mr. Keene on Omnipotence, Mind, Vol. LXX (1961), p.250.

[10] Alvin Plantinga. God and Other Minds. Ithaca, New York: Cornell University Press, 1990. p. 172.

[11] Ibid p.172.

[12] John Mackie, "Omnipotence," in The Power of God: Readings on Omnipotence and Evil, ed. Urban and Walton. New York: Oxford University Press, 1978. p.83.

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