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                        The Impossibility of an Omnipotent Omniscient God

Among the most telling atheistic arguments are those to the effect that the existence of any being that meets standard divine specifications is impossible - that there not only is not but could not be any such being.

All such arguments depend crucially on sets of divine specifications. A core traditional notion of God is one that specifies him as necessarily existent, omniscient, omnipotent, and morally perfect. God is also traditionally conceived of as being a free creator, and is often spoken of as immutable or transcendent. Some impossibility arguments attack a single attribute - attempting to show that the notion of omniscience is logically incoherent on its own, for example. Others attack combinations of attributes - arguing that it is not logically possible for a being to be omniscient and a free creator, for example. If either form of argument succeeds, we will be able to show that there can be no God as traditionally conceived.

Because the arguments at issue operate in terms of a set of more or less clear specifications, of course, it is always possible for a defender of the­ism to deflect the argument by claiming that the God shown impossible is not his God. If he ends up defending a God that is perhaps knowledgeable but not omniscient he may escape some arguments, but at the cost of a peculiarly ignorant God. The same would hold for a God that is perhaps powerful but is conceded to be less than omnipotent or historically important but not literally a creator. If the term "God" is treated as infinitely re-definable, of course, no set of impossibility arguments will force the theist to give up a claim that "God" in some sense exists. The impossibility arguments may nonetheless succeed in their main thrust in that the "God" so saved may look increasingly less worthy of the honorific title.

A more frequent reaction, perhaps, is not redefinition but refuge in vagueness: continued use of a term "God" that is allowed to wan­der without clear specification. Here as elsewhere - in cases of pseudoscience, for example - resort to vagueness succeeds in deflecting criticism only at the cost of diluting content. If a believer's notion of God entails anything like traditional attributes of omniscience, omnipotence, and moral perfection, the force of impossibility arguments is that there can be no such being. If a believer's notion of God remains so vague as to escape all impossibility arguments, it can be argued, it can­not be clear to even him what he believes - or whether what he takes for pious belief has any content at all.

In what follows I concentrate on central impossibility arguments turning on (1) omnipotence and (2) omniscience. Problems for the notion of a morally perfect being and against the co-possibility of some standard attributes are given a briefer treatment in a final section.

                                           The Impossibility of Omnipotence

Is it logically possible for any being to be omnipotent?

The traditional problem for omnipotence is the paradox of the stone: Could God create a stone too heavy for him to lift? If so, there is some­thing God could not do - he could not lift such a stone. If not, there is again something God could not do - he could not create such a stone. In either case, there is something God could not do. It follows that there are things no God could do - neither he nor any other being (for we could substitute any other name for "God" that could be omnipotent.)

The history of the problem is a competition between (1) refinements of a notion of omnipotence meant to capture the core of a traditional conception while avoiding such arguments, and (2) more sophisticated versions of the paradox of the stone intended to show that logical prob­lems for omnipotence remain.

If omnipotence means - as it certainly appears to mean - an ability to do anything, then there is an even simpler argument that there can be no omnipotent being. No being could create a square circle or an even prime number greater than two. Because there logically could not be such things, there could be no being that could create them. Here Aquinas' response has been influential: that what omnipotence requires is the ability to perform any task, and "create a square circle" does not specify a genuine task.1 One can hold that contradictory specifications fail to specify anything - precisely because they are contradictory - rather than specifying something of a peculiarly contradictory type. If so, contradictory task specifications fail to designate genuine tasks, and thus fail to designate tasks required of any omnipotent being. With regard to contradictory specifications, at least, God and omnipotence are off the hook.

The paradox of the stone, however, is not escaped so easily. Here we can use a task specification that is clearly not contradictory. I could certainly create a mass of concrete too heavy for me to lift. Could God? If so, there would be something he could not do: lift that mass of concrete.


                                           The Impossibility of Omniscience

Is it logically possible for any being to be omniscient?

Until relatively recently, impossibility arguments regarding omniscience have not been clearly developed as those regarding omnipotence. There is no single argument against omniscience within the ancient history and logical impact of the paradox of the stone, for example. There are, however, (1) a handful of major difficulties turning on different types of knowledge and (2) a set of severe difficulties turning on some of the more sophisticated findings of contemporary logic and set theory.

What would it be for a being to be omniscient? The core notion is undoubtedly that of a being that knows all that is knowable, or all that can be known. But it is clear that we speak of a variety of things as knowledge: knowing that something is the case (propositional knowledge), knowing how to do something, and knowing both things and feel­ings by acquaintance. I know that Ottowa is the capital city of Canada, for example, but I also know how to repair a computer, I know the beauty of Rachmaninoff’s music and the sting of disappointment or loss of a family member.

Knowing how raises clear impossibilities for any traditional and omniscient God. If God is a being without a body, he cannot know how to play tennis, how to balance on the parallel bars, or how to compensate for a strained muscle in the right calf. If omniscience demands knowing everything that can be known, therefore, no disembodied being can be omniscient.2  That form of difficulty can also be developed without appeal to other attributes. One of the things that I know is how to find out things that I do not know; I know how to find out what I do not know about solving differential equations, for example. Were an omniscient being to have all propositional knowledge, there would be nothing it did not know in the propositional sense. There must then be a form of knowledge how that I have but that any such being would lack: knowing how to find the propositional knowledge it lacks. Any being that possessed all propositional knowledge would for that very reason lack a form of knowledge how.

Knowledge by acquaintance also raises clear impossibilities for any traditional and omniscient God. Among those feelings that non-omniscient beings know all too well are lust, envy, fear, frustration, and despair. If a God is without moral fault, he cannot know lust or envy, and thus cannot qualify as omniscient. If a God is without limitation he cannot know fear, frustration, or despair.3 Here too the argument can be pressed without appeal to other attributes. One of the feelings I know all too well is the recognition of my own ignorance. An omniscient being would have no ignorance, and thus this is a feeling no omniscient being could know. There can then be no omniscient being.

                                 The Impossibility of Combined Attributes

 Of the three major properties attributed to God in Western theism - omnipotence, omniscience, and moral perfection - impossibility argu­ments against the third are the least developed. One reason for this may be that conflicts between major ethical theories remain unresolved - should one approach the idea of moral perfection in terms of utilitarianism, deontology, or virtue theory? Far from seeming invulnerable to impossibility arguments, however, the notion of divine moral perfection seems ripe for them. This is an area worthy of further work.

There are also a range of impossibility arguments that turn on other attributes in combination with omnipotence, omniscience, or moral per­fection. God is certainly conceived as a free agent, for example - indeed as a free creator. But is that conception consistent with other standard attributes?

It is far from clear that free choice is compatible with omniscience. One cannot make a free choice between options A and B, it can be argued, if one knows with complete certainty in advance that one will take course A. If so, since an omniscient God would know in advance (and from all eternity) all actions it would take, there can be no point at which such a God could make a genuine choice. Omniscience and freedom appear to be incompatible.4

Impossibility arguments regarding divine freedom and moral perfection are the subject of the classical Leibniz-Clarke correspondence.5 Leibniz's problem was that God's moral perfection would entail that he must of necessity create the best of all possible worlds, and thus it could not be maintained that he was free to create any inferior world. Clarke insists on God's freedom, and therefore insists that he could create an inferior world, therefore contradicting a notion that God is of necessity morally perfect. Despite attempts on both sides to finesse a distinction in which God's choice is necessitated in one sense and not in another, the central difficulty remains.

Peter Geach and Nelson Pike have a similar exchange regarding omnipotence and moral perfection.6 Both admit an inconsistency in the idea that any being is both omnipotent and impeccable, or unable to do wrong. Because of that inconsistency, Pike denies impeccability. Geach, on the other hand, denies omnipotence. Either course results in the denial of a traditional God.

A simpler impossibility may lie in the notion of necessary moral perfection itself. Mark Twain contrasts his moral status with that of George Washington: "I am different from Washington; I have a higher, grander standard of principle. Washington could not lie. I can lie, but I won't." If God cannot act wrongly, it is impossible for him to face any real moral choices.7 If so, he cannot be praised for making the correct choices, and if he is not morally praiseworthy, he can hardly qualify as morally perfect. Necessary moral perfection seems to exclude the possibility of precisely those choices that genuine moral perfection would demand.

Other impossibility arguments using multiple attributes abound. God's timelessness and immutability appear to be inconsistent with omniscience regarding tensed facts, knowable only at a particular time,8 and immutability may similarly be inconsistent with the notion of a creator God.9

We have seen reason to believe that both omnipotence and omni­science are intrinsically impossible, and to suggest that the same may hold for necessary moral perfection as well. Further impossibilities follow from the assumption of such attributes in combination.

There is a related a-theological argument of major importance that we have not considered here because it relies not on divine specifications alone but on an obvious but contingent fact as well. As such it fails to qualify as a pure impossibility argument in our sense. What that argument demands is the obvious but contingent fact that our world abounds with unnecessary gratuitous suffering and injustice. This is the called the problem of evil and has been dealt with in detail by numerous philosophers since Hume. Theologians have not yet been able to come anywhere near to challenging it.


1.       Thomas Aquinas, Summa theologiae, part I, Q. 25, art. 3. See also I. L. Cowan, "The Paradox of Omnipotence," Analysis 25 (1965/supplement): 102-8, reprinted in Michael Martin and Ricki Monnier (eds.), The Impossi­bility of God (Amherst, N.Y.: Prometheus Books, 2003).

2.       See Michael Martin, "A Disproof of the God of the Common Man," Question 7 (1974): 114-24. Martin develops the idea further in a chapter in Atheism: A Philosophical Justification (Philadelphia: Temple University Press, 1990), reprinted as "Conflicts between the Divine Attributes," in Martin and Monnier, The Impossibility of God. Similar issues are raised in Henry Simoni, "Omniscience and the Problem of Radical Particularity: Does God Know How to Ride a Bike?" International Journal for Philosophy of Religion 42 (1997): 1-22.

3.       The latter point is developed particularly nicely in David Blumenfeld, "On the Compossibility of the Divine Attributes," Philosophical Studies 34 (1978): 91-103, reprinted in Martin and Monnier, The Impossibility of God. See also Marcel Sarot, "Omniscience and Experience," International Jour­nal for Philosophy of Religion 30 (1991): 89-102, and Henri Simoni, "Divine Possability and the Problem of Radical Particularity: Does God Feel Your Pain?" Religious Studies 33 (1997): 327-47.

4.       See, e.g., Tomis Kapitan, "Agency and Omniscience," Religious Studies 27 (1991): 105-20, and later discussion. A form of the argument also appears in Theodore M. Drange, "Incompatible-Properties Arguments: A Survey," Philo 1 (1998): 49-60, reprinted in Martin and Monnier, The Impossibility of God.

5.       Samuel Clarke and Gottfried Leibniz [1717], The Leibniz-Clarke Corre­spondence, ed. H. G. Alexander (Manchester: Manchester University Press, 1956). William Rowe offers a thorough discussion in "Divine Freedom," in the Stanford Encyclopedia of Philosophy, http://plato.stanford.edu.

6.       Peter Geach, "Omnipotence," Philosophy 48 (1973): 7-20, and Providence and Evil, Nelson Pike, "Omnipotence and God's Ability to Sin," American Philosophical Quarterly 6 (1969): 208-16.

7.       It is indeed a tenet of Christian theology dating back at least to Augustine that the saints and angels have been perfected to the degree that they not only do not sin but are no longer able to sin, a perfection applied to God as well. See Pike, "Omnipotence."

8.       See, e.g., Wiliam Lane Craig, "Omniscience, Tensed Facts, and Divine Eternity," Faith and Philosophy 17 (2000): 225-41.

9.       For a range of often novel incompatibility arguments, see Drange, "Incompatible-Properties Arguments."


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