The Definition of Omnipotence
Kenny (Anthony)
Source: Morris, T V (ed), The Concept of God, Oxford University Press, Oxford, 1987, pp. 125-133
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  1. (p. 125) It is by no means easy to state concisely and coherently what is meant by ‘omnipotence'. Omniscience appears to be analogous to omnipotence: just as omniscience is knowing everything, so omnipotence is being able to do everything. But whereas it is easy to define what it is to be omniscient, it is not so easy to define omnipotence. A being X is omniscient if, for all p, if p, then X knows that p. We cannot offer a simply parallel definition of omnipotence: X is omnipotent if, for all p, if p, then X can bring it about that p. For this, though it would attribute considerable power to X, would not attribute to him power to do anything which has not already been done, or will not sometime be done. On the other hand, if we drop the if-clause, and say that X is omnipotent iff for all p, X can bring it about that p, then we attribute to X a power far beyond what has traditionally been ascribed to God. For, with the possible exception of Descartes, no theologian or philosopher has seriously maintained that God can bring it about that contradictories are true together. But if, for all p, God can bring it about that p, then, by substitution we can conclude that he can bring it about that both p and not p; that mice are both larger and smaller than elephants, or what you will. Nor can one say that, for all Phi, God can Phi; for it seems clear that there will be some substitutions for ‘Phi' which will not give truths when applied to God, such as ‘cough', ‘sin', or ‘die'.
  2. Aquinas rehearses some of the difficulties about omnipotence in the seventh article of the first question of the De Potentia. He concludes that God cannot be said to be omnipotent in the sense of being simply able to do everything (quia omnia possit absolute). He considers a number of other suggestions.
    (p. 126) One, attributed to St. Augustine, is that God is omnipotent in the sense that he can do whatever he wants to do. But to this there are serious objections. The blessed in heaven, St Thomas says, and perhaps even the happy on earth, can do whatever they want; otherwise there would be something lacking in their happiness. But they are not called omnipotent. So it is not enough for the omnipotence which is a divine attribute that God should be able to do whatever he wants. Indeed, a wise man restricts his wants to what is within his power. If he succeeds in this degree of self-control, it will be true of him that he can do whatever he wants. But it is not true that every wise man is an omnipotent man.
  3. Aquinas turns to the formulation: God can do whatever is possible. He raises the question: what does ‘possible' mean here? Does it mean: whatever is naturally possible, or whatever is supernaturally possible, i.e. possible to God? If the former, then divine omnipotence does not exceed the power of nature and is no great thing. If the latter, then to say that God is omnipotent is a tautology and the analysis a circumlocution: to say that God is omnipotent is merely to say that God can do all that God can do. And once again, in this sense one can claim that everyone is as omnipotent as God: for everyone can do what he can do.
  4. Aquinas's own account is tantamount to the proposal that the omnipotence of God is the ability to do whatever is logically possible. ‘We are left with the alternative', he wrote in the Summa Theologiae, ‘that he is omnipotent because he can do everything that is absolutely possible.' This possibility is absolute possibility in contrast to the relative possibility just discussed, which was possibility relative to a particular agent's powers. ‘Something is judged to be possible or impossible from the relationship between its terms: possible when the predicate is compatible with the subject, as, for Socrates to sit; impossible when it is not compatible, as for a man to be a donkey.'
  5. St Thomas offers a rather dubious reason for this, saying that as God is pure being, not being of any particular kind, anything which qualifies as being (habet rationem entis) is a fit object of God's action. He goes on:
      (p. 127)
      Whatever implies being and not being simultaneously is incompatible with the absolute possibility which falls under the divine omnipotence. Such a contradiction is not subject to it, not from any impotence in God, but because it simply does not have the nature of being feasible or possible. Whatever, then, does not involve a contradiction is in that realm of the possible with respect to which God is called - omnipotent. Whatever involves a contradiction is not within the scope of omnipotence because it cannot qualify for possibility. Better, however, to say that it cannot be done, rather than that God cannot do it1.
  6. Aquinas's solution, however, does not solve the difficulties. We cannot define omnipotence by saying ‘For all p, if it is logically possible that p, then God can bring it about that p.' For there are many counter-examples to this which St Thomas would himself have admitted as counter-examples. For instance, it is no doubt logically possible that Troy did not fall, but according to the common view God cannot (now at any rate) bring it about that Troy did not fall. Moreover, by itself Aquinas's formula does not show us how to deal with a number of familiar puzzles about the idea of omnipotence. It does not show us, for instance, how to answer such questions as ‘Can God make an object too heavy for him to lift? ' ‘Has God the power to make an immovable lamp-post and the power to make an irresistible cannon-ball?'
  7. St Thomas does indeed mention some difficulties of this kind; but before considering them it is worth noting that he seems to prefer the formulation ‘God's power is infinite' to the formulation ‘God is omnipotent'. I shall later argue that this is a sound instinct. However, St Thomas's argument to this effect is unconvincing. God's active power, he says, is in proportion to his actual being; his actual being is infinite; therefore his active power is infinite. Or, in slightly different terms: the more perfect an agent's form, the more powerful it is (e.g. the hotter something is, the better it can heat); therefore, since God's form or essence is infinite, so is his power.
  8. The sense in which God's being is infinite is, however, obscure. From time to time St Thomas explains it along the following lines: while I am a man and this is a table, there are all kinds of things which I am not and which this table is not;
    (p. 128) for example, I am not a horse and this table is not a chair. In the case of God, however, he just is, and his being is not limited by having any cramping predicates stuck on after the copula. Or, as he puts it in the present article, ‘God's being is infinite in so far as it is not limited by any container (recipiens).' Esse appears to be pictured as a sort of fluid which is boundless in itself, and is given form and boundaries by being poured into a particular object as into a bucket. In reading Aquinas on Being, one is constantly torn between considering esse in terms of vivid but inapplicable metaphors, and abstract but ill-formed formulas2.
  9. Among the difficulties which Aquinas raises for his account of omnipotence, however, there is one which deserves to be pondered: ‘Every power is manifested by its effects; otherwise it would be a vain power. So if God's power were infinite he could produce an infinite effect.' In the Summa the answer is given that God is not a univocal agent (i.e., not an agent whose effect is something of the same kind as itself). A human begetter, being an univocal agent, cannot do anything more than breed men, so that the whole of its power is manifested in its effect. The case is different with analogous agents like God and (in Aristotelian cosmology) the sun. The De Potentia gives an alternative answer; the very notion of being made or being an effect is incompatible with infinity, because whatever is made from nothing has some defect. Hence the notion of an infinite effect is incoherent. But might one not go on to conclude that the notion of an infinite power is no less incoherent than the notion of an infinite effect?
  10. Aquinas's objection is an ancestor of a number of modern difficulties. We may consider an instructive question posed by John Mackie in his article ‘Evil and Omnipotence':

      Can an omnipotent being make things which he cannot control? It is clear that this is a paradox; the question cannot be answered satisfactorily either in the affirmative or in the negative. If we answer ‘Yes' it follows that if God actually makes things which he cannot control, he is not omnipotent once he has made them: there are then things which he cannot do. But if we answer ‘No' we are immediately asserting that there are things which he cannot do, that is to say that he is already not omnipotent3.

    (p. 129) It is, I think, clear that the answer to Mackie's question is ‘No, he cannot': the problem is to show how this answer is not incompatible with omnipotence.
  11. This cannot be done simply by appeal to the notion of logical impossibility: for whether ‘There exists a being whom an omnipotent (god cannot control' is a logically possible state of affairs or not depends on what definition we give of omnipotence, and whether the concept is a coherent one.
  12. On the other hand, it seems that we can reverse Mackie's dilemma and ask: Does it make sense to say ‘X is a being which even an omnipotent being cannot control'? If it does, then God can make such a being without any loss to his omnipotence, since the ascribing of sense to the formula, however it is done, will have shown that failure to control X is not incompatible with omnipotence. If it does not, then it is no limitation on God's omnipotence to say that God cannot bring it about that such a being exists.
  13. Of course ‘X makes a being which X cannot control' is not an impossible sentence frame; but that does not mean that it will give it possibility with every substitution for ‘X', especially if we allow as substitutions phrases like ‘a being which can control everything'. Similarly, the fact that both ‘X shaves Y' and ‘X shaves X' are possible sentence frames does not mean that there can be a barber who shaves all and only those who do not shave themselves.
  14. In discussing Mackie's paradox, Plantinga4 considers a suggested definition of omnipotence different from those we have been criticizing:

      X is omnipotent if X is capable of performing any logically possible action.
  15. This will not do, Plantinga says, because making a table that God did not make is a logically possible action, but God cannot make a table which God did not make. Nor can we say:
      (p. 130)
      X is omnipotent if X is capable of performing any action A such that the proposition ‘X performs A' is logically possible.
  16. For the unfortunate man who is capable only of scratching his ear is capable of performing any action A such that the proposition ‘the man who is capable only of scratching his ear performs A' is logically possible, for the only such action A is the action of scratching his ear:

      We might consider the suggestion that God is omnipotent if God can do any A such that ‘God does A' is logically possible.

    This, of course, would not be a definition of omnipotence but only an explication of divine omnipotence. But even so, Plantinga remarks, it would be an unsuccessful explication. For let A be the action of ‘doing what I am thinking of'. Then ‘God does A' will be logically possible: it is logically possible for God to do what I am thinking of; but if what I am thinking of is creating a square circle, then God cannot do what I am thinking of.
  17. Plantinga in the end abandons the search for a totally satisfactory account of omnipotence, believing rightly that such an account is not necessary in order to counter Mackie's argument. More recently Geach5 has concluded, from difficulties such as the ones we have considered, that the notion of omnipotence is incapable of coherent formulation, and suggests that it be abandoned in favour of the notion of being almighty, i.e., as having power over all things. And Swinburne6 thinks that in answer to puzzles like Mackie's we must say that an omnipotent being can indeed create a being which he cannot control, but that he can exercise this power only at the cost of thereby ceasing to be omnipotent.
  18. I agree with Plantinga that it is difficult to formulate a coherent and elegant definition of omnipotence; and I agree with Geach that the notion of God as almighty is a more essential element in Western theism than the comparatively philosophical notion of omnipotence. But I think that an account of divine omnipotence simpler than Swinburne's can be devised to avoid the difficulties we have been discussing.
  19. (p. 131) Let us consider the following definition of omnipotence: A being is omnipotent if it has every power which it is logically possible to possess7.
  20. The definition must first of all be supplemented with an account of when it is logically possible to possess a power. It is logically possible to possess a power, I suggest, if the exercise of the power does not as such involve any logical impossibility. When I say that the exercise of the power does not as such involve any logical possibility, I mean that there is no logical incoherence in the description of what it is to exercise the power. For a power to be a logically possible power, it is not necessary that every exercise of it should be coherently conceivable, but only that some exercise of it should be.
  21. I shall try to explain the definition, and bring out its merits, by applying it to some of the difficult cases current in the literature.
  22. An omnipotent being can make an irresistible cannon-ball, and he can make an immovable lamp-post; there is nothing incoherent in the supposition that these powers are exercised. Of course there would be an incoherence in the idea of them both being exercised simultaneously; but our definition of the logical possibility of possessing a power did not imply that every formulatable exercise of that power should be logically possible, but only that some should.
  23. The man who is capable only of scratching his ear is not omnipotent by our definition; for there are many logically possible powers which he does not possess (the ability to create a world, for example).
  24. An omnipotent being has the power to do what I am thinking of. It is true that if I am thinking of something which it is impossible to do, then an omnipotent God cannot, on that occasion, exercise the power he has of doing what I am thinking about. But powers are not tied to particular occasions, and it is not necessary, for a power to be genuinely possessed, that it can be coherently exercised on all occasions and in all circumstances.
    (p. 132) Though God has the power to do what I am thinking of, he cannot exercise this power if I am thinking a nonsensical thought; just as, though he possesses the power to make an immovable lamp-post, he cannot exercise that power if he has just then exercised his power to make an irresistible cannon-ball.
  25. It will be seen that the definition of omnipotence by generalizing over powers is an attempt to preserve the merits, without the disadvantages, of St Thomas's formulation of omnipotence as infinite power. St Thomas was, I think, right in saying that powers are manifested by their effects or, as he elsewhere puts it, specified by their exercises. That is to say, the power to Phi can only be defined and understood by someone who knows what Phi-ing is. But it is not true that powers are specified by their effects in such a way that an infinite power must have an infinite effect. No power, whether finite or infinite, is logically exhausted by its effect: even the human power to beget, with which Aquinas contrasts divine power, is not a limited power in the sense that the power to beget children is a power to beget some specified number of children.
  26. There are advantages, then, in defining omnipotence as the totality of logically possible powers rather than as the power to perform all logically possible actions or to bring about all logically possible states of affairs. But even so defined as the totality of logically possible powers, omnipotence cannot be ascribed to God. For there are many powers which it is logically possible to have which God cannot have, such as the power to make a table which God has not made. The power to change, to sin, and to die are instances of powers which it is logically possible to have—since we human beings have them—and yet which traditional theism denies to God.
  27. Divine omnipotence, therefore, if it is to be a coherent notion, must be something less than the complete omnipotence which is the possession of all logically possible powers. It must be a narrower omnipotence, consisting in the possession of all logically possible powers which it is logically possible for a being with the attributes of God to possess. (If the definition is not to be empty, ‘attributes' must here be taken to mean those properties of Godhead which are not themselves powers: properties such as immutability and goodness.)
    (p. 133) This conception of divine omnipotence is close to traditional accounts of the doctrine while avoiding some of the incoherences we have found in them.
  28. On this account, an omnipotent God will not have the power to make a table that God did not make. The power to make a table that one has not made is not a power that anyone can have; and the power to make a table that God did not make is not a power it is logically possible for someone to have who is identical with God. Any being with all the attributes of God will of course have, inter alia, the attribute of being identical with God.
  29. What are we to say, on this account, in answer to the question whether an omnipotent God can make a being whom he cannot control? The power to create, while remaining omnipotent, a being that one cannot control is not a logically possible power, since the description of the power contains a hidden contradiction. The power to create a being that one cannot control and thereby give up one's omnipotence is not a power that could logically be possessed by a being who had the attributes of God including immutability. Consequently, the answer to the conundrum is in the negative: but this does not clash with the notion of divine omnipotence as we have now described it.
  30. Powers such as the power to weaken, sicken, and die will not be parts of divine omnipotence since they clash with other divine attributes. What of the power to do evil? Clearly, the actual performance of an evil deed would be incompatible with divine goodness: but some theologians have thought that the mere power to do evil, voluntarily unexercised, is not only compatible with, but actually enhances the splendour of divine beneficence. If so, then the power to do evil, since it is clearly in itself a logically possible power, would be part of divine omnipotence.

In-Page Footnotes

Footnote 1: Summa Theologiae Ia, 25, 3.

Footnote 2: See my Aquinas: A Collection of Critical Essays (London, 1969), pp. 70 ff.

Footnote 3: Evil and Omnipotence', Mind 64 (1955)

Footnote 4: Alvin Plantinga, God and Other Minds (Ithaca, 1967), p. 168.

Footnote 5: Peter Geach, ‘Omnipotence’, Philosophy 48 (1973)

Footnote 6: R. G. Swinburne, The Coherence of Theism (Oxford, 1977), p. 156.

Footnote 7: The reader may be disappointed that this definition is not given quasi-logical form like the definitions rejected above. This is no accident. I have argued, in my paper ‘Human Abilities and Logical Modalities' in R. Tuomela (ed.) Essays on Explanation and Understanding (Dordrecht, 1974), that the current resources of logic are inadequate to analyse the relevant notion of power.

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