It is generally recognized that omniscience and immutability are necessary characteristics of an absolutely perfect being. The fact that they are also incompatible characteristics seems to have gone unnoticed.

In the main body of this paper I will present first an argument that turns on the incompatibility of omniscience and immutability and, secondly, several objections to that argument with my replies to the objections.

(1) A perfect being is not subject to change.¹
(2) A perfect being knows everything.²
(3) A being that knows everything always knows what time it is.³
(4) A being that always knows what time it is is subject to change.⁴

Therefore,
(5) A perfect being is subject to change.
Therefore,
(6) A perfect being is not a perfect being.

Finally, therefore,
(7) There is no perfect being.⁵

In discussing this argument with others⁶ I have come across various objections against one or another of its premises. Considering such objections here helps to clarify the line taken in the argument and provides an opportunity to anticipate and turn aside several natural criticisms of that line.

Because premises (1) and (2) present the widely accepted principles of immutability and omniscience, objections against them are not so much criticisms of the line taken in the argument as they are attempts to modify the concept of a perfect being in the light of the argument. And since premise (3) gives every impression of being an instance of a logical truth, premise (4) is apparently the one most vulnerable to attacks that are genuinely attacks on the argument. The first four of the following seven objections are all directed against premise (4), although Objection D raises a question relevant to premise (3) as well.

The denial that a change in the object necessitates a change in the knower depends on imprecise characterizations of the object. For example, I know that the Chrysler Building in Manhattan is 1,046 feet tall. If it is said that the Chrysler Building is the object of my knowledge, then of course many changes in it -- in its tenants or in its heating system, for example -- do not necessitate changes in the state of my knowledge. If, however, it is more precisely said that the object of my knowledge is the height of the Chrysler Building, then of course a change in the object of my knowledge does necessitate a change in me. If a 40-foot television antenna is extended from the present tip of the tower, either I will cease to know the height of the Chrysler Building or I will give up believing that its height is 1,046 feet and begin believing that its height is 1,086 feet. In the case of always knowing what time it is, if we are to speak of an object of knowledge at all it must be characterized not as the state of the universe (which might also be said to be the object of, for example, a cosmologist's knowledge), but as the changing of that state. To know the changing of anything is to know first that p and then that not-p (for some particular instance of p), and a knower that knows first one proposition and then another is a knower that changes.

It seems clear, first of all, that the sort of change in beliefs entailed by knowing the changing of anything is the taking-account sort of change rather than a change of mind. But once that much has been allowed, Objection B seems to consist in no more than an expression of disappointment in the magnitude of the change necessitated by always knowing what time it is. The entailed change in beliefs is not, it is true, sufficiently radical to qualify as a change of character or of attitude, but it is no less incompatible with immutability for all that. If Jones had been immutable from December 1965 through January 1966 he could no more have taken account of the calendar change than he could have changed his mind.

It may be worth noting that just such small-scale, taking-account changes in beliefs have sometimes been recognized by adherents of the principle of immutability as incompatible with immutability. Ockham, for example, argues at length against the possibility of a change in the state of God's foreknowledge just because God's changelessness could not be preserved through such a change. In Question Five of his Tractatus de praedestinatione et de praescientia Dei et de futuris contingentibus Ockham maintains that "if 'God knows that A' (where A is a future contingent proposition) and 'God does not know that A' could be true successively, it would follow that God was changeable," and the principle on which Ockham bases that claim is in no way restricted to future contingents. (As an adherent of the principle of immutability Ockham of course proceeds to deny that God could first know that A and then not know that A, but his reasons for doing so involve considerations peculiar to future contingent propositions and need not concern us here.)⁷

The superficial flaw in this objection is the ambiguity of the phrase 'to know the state of the universe at every instant', but the ambiguity is likely to be overlooked because the phrase is evidently an allusion to a familiar, widely accepted account of omniscience, according to which omniscience regarding contingent events is nothing more nor less than knowledge of the entire scheme of contingent events from beginning to end at once. I see no reason for quarreling here with the ascription of such knowledge to an omniscient being; but the underlying flaw in Objection C is the drastic incompleteness of this account of omniscience regarding contingent events.

The kind of knowledge ascribed to an omniscient being in this account is sometimes characterized as "seeing all time at a glance," which suggests that if one sees the entire scheme of contingent events from beginning to end at once one sees all there is to see of time. The totality of contingent events, we are to suppose, may be known either simultaneously or successively, and an omniscient being will of course know it not successively but simultaneously. In his Summa contra gentiles (Book I, Ch. 55, sects. [6]-[9]) Aquinas presents a concise version of what seems to be the standard exposition of this claim.

. . . the intellect of one considering successively many things cannot have only one operation. For since operations differ according to their objects, the operation by which the first is considered must be different from the operation by which the second is considered. But the divine intellect has only one operation, namely, the divine essence, as we have proved. Therefore God considers all that he knows not successively, but together. Moreover, succession cannot be understood without time nor time without motion . . . But there can be no motion in God, as may be inferred from what we have said. There is, therefore, no succession in the divine consideration. . . . Every intellect, furthermore, that understands one thing after another is at one time potentially understanding and at another time actually understanding. For while it understands the first thing actually it understands the second thing potentially. But the divine intellect is never potentially but always actually understanding. Therefore it does not understand things successively but rather understands them together.

On this view an omniscient being's knowledge of contingent events is the knowledge that event e occurs at time t (for every true instance of that form). Thus an omniscient being knows that my birth occurs at t_n, that my writing these words occurs at t_n+x, that my death occurs at t_n+x+y. This omniscient being also knows what events occur simultaneously with each of those events -- knows, for example, that while I am writing these words my desk calendar lies open at the page bearing the date "Friday, March 4, 1966," and the watch on my wrist shows 10:15. Moreover, since an omniscient being by any account knows all necessary truths, including the truths of arithmetic, this omniscient being knows how much time elapses between my birth and my writing these words and between these words and my death. But I am writing these words just now, and on this view of omniscience an omniscient being is incapable of knowing that that is what I am now doing, and for all this omniscient being knows I might just as well be dead or as yet unborn. That is what knowing everything amounts to if knowing "everything" does not include always knowing what time it is. Alternatively, that is what knowing the state of the universe at every instant comes to if that phrase is interpreted in the way required by the claim that it is possible to have that sort of knowledge all at once.

According to this familiar account of omniscience, the knowledge an omniscient being has of the entire scheme of contingent events is in many relevant respects exactly like the knowledge you might have of a movie you had written, directed, produced, starred in, and seen a thousand times. You would know its every scene in flawless detail, and you would have the length of each scene and the sequence of scenes perfectly in mind. You would know, too, that a clock pictured in the first scene shows the time to be 3:45, and that a clock pictured in the fourth scene shows 4:30, and so on. Suppose, however, that your movie is being shown in a distant theater today. You know the movie immeasurably better than do the people in the theater who are now seeing it for the first time, but they know one big thing about it you don't know, namely, what is now going on on the screen.

Thus the familiar account of omniscience regarding contingent events is drastically incomplete. An omniscient being must know not only the entire scheme of contingent events from beginning to end at once, but also at what stage of realization that scheme now is. It is in this sense of knowing what time it is that it is essential to claim in premise (3) that a being that knows everything always knows what time it is, and it is in this sense that always knowing what time it is entails incessant change in the knower, as is claimed in premise (4).

In orthodox Christianity the prevalence of the incomplete account of omniscience regarding contingent events effectively obscures the incompatibility of omniscience and immutability. Aquinas, for example, is not content with proving merely that "it is impossible for God to change in any way." He goes on in the Summa theologica (Book I, Q. 14, art. 15) to argue that "since God's knowledge is his substance, as is clear from the foregoing, just as his substance is altogether immutable, as was shown above, so his knowledge likewise must be altogether invariable." What Aquinas, Ockham, and others have recognized is that God's knowledge cannot be variable if God is to remain immutable. What has not been seen is that God's knowledge cannot be altogether invariable if it is to be perfect, if it is to be genuine omniscience.

The importance of this objection lies in its introduction of the pervasive, mysterious doctrine of the trancendence of space and time, a doctrine often cited by orthodox Christians as if it were both consistent with their theology and explanatory of the notion that God sees all time at a glance. It seems to me to be neither.

In Proslogium Chapters XIX and XX Anselm apostrophizes the being transcendent of space and time as follows:

Thou wast not, then, yesterday, nor wilt thou be tomorrow; but yesterday and today and tomorrow thou art; or, rather, neither yesterday nor today nor tomorrow thou art, but simply thou art, outside all time. For yesterday and today and tomorrow have no existence except in time, but thou, although nothing exists without thee, nevertheless dost not exist in space or time, but all things exist in thee. For nothing contains thee, but thou containest all.

For present purposes the spatial aspect of this doctrine may be ignored. What is meant by the claim that an entity transcends time? The number 2 might, I suppose, be said to transcend time in the sense that it does not age, that it is no older now than it was a hundred years ago. I see no reason to quarrel with the doctrine that a perfect being transcends time in that sense, since under that interpretation the doctrine is no more than a gloss on the principle of immutability. But under that interpretation the doctrine begs the question of premise (4) rather than providing a basis for objecting to it.

Only one other interpretation of the doctrine of the transcendence of time suggests itself, and that is that from a God's-eye point of view there is no time, that the passage of time is a universal human illusion. (Whatever else may be said of this interpretation, it surely cannot be considered compatible with such essential theses of Christian doctrine as the Incarnation and the Resurrection.) Under this interpretation the doctrine of the transcendence of time does have a devasting effect on the argument, since it implies either that there are no true propositions of the form 'it is now t_n' or that there is exactly one (eternally) true proposition of that form. Thus under this interpretation premise (3) either is vacuous or has a single trivializing instance, and premise (4) is false. But this interpretation preserves the immutability of a perfect being by imposing immutability on everything else, and that is surely an inconceivably high price to pay, in the view of Christians and non-Christians alike.

The remaining three objections are directed against premises (1) or (2) and may, therefore, be considered not so much criticisms of the argument as attempts to revise the principle of immutability or the principle of omniscience in the light of the argument. Objections E and F have to do with premise (2), Objection G with premise (1).

Objections E and F are attempts to hedge on omniscience as philosophers and theologians have long since learned to hedge on omnipotence. In Objection E this attempt depends on directly invoking one of the standard limitations on omnipotence, but the attempt does not succeed. Perhaps the easiest way of pointing up its failure is to produce analogous inferences of the same form, such as this: since I am a human being and a human being is a mortal rational animal, it is logically impossible that I should live forever: therefore it is no limitation on me that I must die -- or this: since I am a creature of limited power, it is logically impossible that I be capable of doing whatever is logically possible; therefore it is no limitation on me that I cannot do whatever is logically possible. What is wrong with all these inferences is that the crucial limitation is introduced in the initial description of the being in question, after which it does of course make sense to deny that mere consequences of the limiting description are to be introduced as if they constituted additional limitations. It is not an additional limitation on a legless man that he cannot walk, or on a mortal being that it must die, or on a creature of limited power that it cannot do whatever it might choose to do. No more is it an additional limitation on a being that is incapable of knowing what time it is that it does not know what time it is. But any claim to perfection that might have been made on behalf of such a being has already been vitiated in the admission that its transcendence of time renders it incapable of omniscience.

Even if Objection F could be sustained, this particular grasping of the nettle would surely impress many as just too painful to bear, for in deciding whether or not to try to evade the conclusion of the argument in this way it is important to remember that in the context of the argument 'knowing what time it is' means knowing what is going on. Objection F at best thus provides an exceptionally costly defense of absolute perfection, emptying it of much of its content in order to preserve it; for under the newly explicated notion of omniscience Objection F commits one to the view that it is impossible for a perfect, omniscient being to know what is going on.

Objection F attempts to draw an analogy between an explication of omnipotence and a proposed explication of omniscience, borrowing strength from the fact that in the case of omnipotence such an explication has long since been recognized as a necessary condition of the coherence of the notion. In evaluating this attempt it is helpful to note that here are at least three types of provisos that may be inserted into formulas of omnipotence for that purpose. The first is relevant to omnipotence generally, the second specifically to eternal omnipotence, and the third specifically to eternal omnipotence as one perfect characteristic of a being possessed of certain other perfect characteristics. (For present purposes it is convenient to say simply that the third is relevant specifically to eternal omnipotence as one aspect of an absolutely perfect being.) These three types of provisos may be exemplified in the following three formulas of omnipotence:

1. A being that is omnipotent (regardless of its other characteristics) can do anything provided that (a) the description of what is to be done does not involve a logical inconsistency.
2. A being that is eternally omnipotent (regardless of its other characteristics) can do anything provided that (a) . . . and (b) the doing of it does not constitute or produce a limitation on its power.
3. A being that is absolutely perfect (and hence eternally omnipotent) can do anything provided that (a) . . . and (b) . . . and (c) the doing of it does not constitute a violation of somes aspect of its perfection other than its power.

Provisos of type (c) only are at issue in Objection F, no doubt because provisos of types (a) and (b) have no effective role to play in the explication of omniscience. No being knows anything that is not the case; a fortiori no omniscient being knows anything that cannot be the case. So much for type (a). As for type (b), since certain things the description of which involves no logical inconsistency would if done incapacitate the doer -- committing suicide, for example, or creating another omnipotent being -- there is good reason for such a proviso in the explication of eternal omnipotence. It might likewise be claimed that an omniscient being knows everything except things that would if known limit the being's capacity for knowledge, the formal justification for this claim being just the same as that for the corresponding omnipotence-claim. The significant difference between these two claims is that the omniscience-claim is evidently vacuous. There is no reason to suspect that there are things that would if known limit the knower's capacity for knowledge. More directly to the point at issue in the argument, there is no reason whatever to think that knowing what is going on is a kind of knowing that limits the knower's capacity for knowledge. Thus although a type (b) proviso is needed in the explication of eternal omnipotence in order to preserve the coherence of the notion of eternal omnipotence, no such proviso need be inserted into the formula of omniscience in order to preserve the coherence of that notion.

The putative analogy in Objection F presupposses that a proviso of type (c) will preserve omniscience as it preserves omnipotence in such a (Cartesian) argument as the following. It is impossible for an absolutely perfect being to lie, for although such a being, as omnipotent, has the power to lie, the exercise of that power would violate the perfect goodness of the being. To say that it is impossible for an absolutely perfect being to lie is not to say that it lacks the power to lie but rather that its absolute perfection in another aspect -- perfect goodness -- necessitates its refraining from the exercise of that power. Whether or not this line of argument succeeds in doing what it is designed to do, it seems clear that there is no genuine analogue for it in the case of omniscience. Consider the following candidate. It is impossible for an absolutely perfect being to know what is going on, for although such a being, as omniscient, has the power to know what is going on, the exercise of that power would violate the immutability of the being. To say that it is impossible for an absolutely perfect being to know what is going on is not to say that it lacks the power to know what is going on but rather that its absolute perfection in another aspect -- immutability -- necessitates its refraining from the exercise of that power. A being that has the power to do something that it refrains from doing may not thereby even jeopardize its omnipotence. All the same, a being that has the power to know something that it refrains from knowing does thereby forfeit its omniscience. Omniscience is not the power to know everything; it is the condition of knowing everything, and that condition cannot be preserved through even a single instance of omitting to exercise the power to know everything.

Therefore, whatever strength Objection F seems to derive from its appeal to the putative analogy betwen omnipotence and omniscience in this respect is illusory, and this attempted evasion of the argument's conclusion reduces to an arbitrary decision to sacrifice omniscience to immutability.

Objection G proceeds on the asumption that immutability is ascirbed to a perfect being for only one reason -- namely, that all change in such a being must constitute deterioration. There is, however, a second reason, as has been indicated at several points in the discussion so far -- namely, that any change in a "perfect" being must indicate that the being was in some respect not in the requisite state of completion, actualization, fixity. The aspect of absolute completion is no less essential an ingredient in the concept of absolute perfection than is the aspect of absolute excellence. Moreover, those such as Aquinas and Ockham who argue against the mutability of a perfect being's knowledge would surely agree that the change they are intent on ruling out would not constitute deterioration, since they regularly base their arguments on the inadmissibility of process in an absolutely perfect being.

An absolutely perfect being may be described as a being possessing all logically compossible perfections. Thus if the argument had shown that omniscience and immutability were logically incompossible, it would have called for no more than an adjustment in the concept of absolute perfection, an adjustment of the sort proposed in Objection G. The proposition 'things change' is, however, not necessarily but only contingently true. If as a matter of fact nothing else ever did change, an omniscient being could of course remain immutable. In Objection G, however, an absolutely perfect being has been confused with a being possessing all really compossible perfections, the best of all really possible beings. Perhaps, as the objection implies, the most nearly absolutely perfect being in the circumstances that happen to prevail would be mutable in the respect necessitated by always knowing what time it is. But that is of consequence to the argument, which may be taken as showing that the prevailing circumstances do not admit of the existence of an absolutely perfect being.

This concluding section of the paper is in the nature of an appendix. It might be subtitled "Omniscience and Theism"; for it may be shown that the doctrine that God knows everything is incompatible also with theism, the doctrine of a personal God distinct from other persons.⁸

Consider these two statements.

S₁. Jones knows that he is in a hospital.
S₂. Jones knows that Jones is in a hospital.

It may fairly be said of God, as it once was said of William Whewell, that "omniscience [is] his foible."

1 This principle of immutability is regularly supported by one of two arguments. (I) From Supreme Excellence: A perfect being is a supremely excellent being; thus any change in such a being would constitute corruption, deterioration, loss of perfection. (See Plato, Republic, II, 381B.) (II) From Complete Actualization: A perfect being is a being whose capacities for development are all fully realized. A being subject to change, however, is in that respect and to that extent a being with an unrealized capacity for development, a being merely potential and not fully actualized, a being in a state of process and not complete; hence not perfect. (See Aristotle, Metaphysics, XII, 9 1074b26.) The principle of immutability is a thesis of orthodox Christian theology, drawn from Greek philosophy and having among its credentials such biblical passages as Malachi 3.6 and James 1.17. (See Aquinas, Summa theologica, I, Q. 9, art. 1.)

2 Being incapable of knowing all there is to know or being capable of knowing all there is to know and knowing less than that are conditions evidently incompatible with absolute perfection. Hence (2), which seems even more familiar and less problematic than (1).

3 Part of what is meant by premise (3) is, of course, that a being that knows everything always knows what time it is in every time zone on every planet in every galaxy; but it is not quite in that horological sense that its knowledge of what time it is is most plainly relevant to considerations of omniscience and immutability. The relevant sense can be brought out more easily in the consideration of objections against the argument.

4 Adopting 'it is now t_n' as a convenient standard form for propositions as to what time it is, we may say of a being that always knows what time it is that the state of its knowledge changes incessantly with respect to propositions of the form 'it is now t_n'. First such a being knows that it is now t₁ (and that it is not now t₂), and then it knows that it is now t₂ (and that it is not now t₁). To say of any being that it knows something different from what it used to know is to say that it has changed; hence (4).

5
[1f] (x)(Px ⊃ ∼Cx);
[2f] (x)(Px ⊃ (p)(p ≡ Kxp)) [K: . . . knows that . . .];
[3f] (x)((p)(p ≡ Kxp) ⊃ (p)(Tp ⊃ (p ≡ Kxp))) [T: . . . is of the form 'it is now t_n']
[4f] (x)((p)(Tp ⊃ (p ≡ Kxp)) ⊃ Cx);
[5f] (x) (Px ⊃ Cx) [entailed by 2f, 3f, 4f ];
[6f] (x)(Px ⊃ ∼Px) [entailed by 1f, 5f];
[7f] (x) ∼Px [equivalent to 6f].

The formalization [3f] is an instance of a logical truth; nevertheless, premise (3) is not one of the established principles in philosophical or theological discussions of the nature of a perfect being. Not only is it not explicitly affirmed, but it seems often to be implicitly denied. This circumstance may arouse a suspicion that the formalization [3f] is inaccurate or question-begging. Any such suspicion will, I think, be dissipated in the course of considering the objections to the argument, but it may be helpful in the meantime to point out that the validity of the argument does not depend on this formalization. It is of course possible to adopt less detailed formalizations that would not disclose the special logical status of premise (3) and would nevertheless exhibit the validity of the argument. For example, [2f '] (x) (Px ⊃ Ox); [3f '] (x) (Ox ⊃ Nx) together with a similarly imprecise formalization of premise (4) would serve that purpose.

6 I am indebted especially to Miss Marilyn McCord and to Professors H. N. Castaneda, H. G. Frankfurt, C. Ginet, G. B. Matthews, G. Nakhnikian, W. L. Rowe, S. Shoemaker, and W. Wainwright.

7 The most interesting historical example of this sort that I have seen was called to my attention by Professor Hugh Chandler after I had submitted this paper for publication. It is Problem XIII in the Tahdfut al-Faldsifah of al-Ghazali (d. ea. 1111): "REFUTATION OF THEIR [i.e., the philosophers', but principally Avicenna's] DOCTRINE THAT GOD (MAY HE BE EXALTED ABOVE WHAT THEY SAY) DOES NOT KNOW THE PARTICULARS WHICH ARE DIVISIBLE IN ACCORDANCE WITH THE DIVISION OF TIME INTO 'WILL BE', 'WAS', AND 'IS'" (tr. S. A. Kamali; Lahore, Pakistan Philosophical Congress, 1963; pp. 153-162). This work was not known to medieval Christian philosophers. [See Etienne Gilson, History of Christian Philosophy in the Middle Ages (New York: Random House, 1955), p. 216.]

8 The following argument was suggested to me by certain observations made by Professor Hector Castaneda in a paper entitled "He," presented at the Wayne State University philosophy colloquium in the fall of 1964.