The Analogy Argument for a Limited Account of

Omniscience

 

Jonathan L. Kvanvig

 

 

IN COMPARISON with other doctrinesCthe doctrine of omnipotence, for exampleCthe proper formulation of the doctrine of omniscience has not seemed especially problematic. Once we accept the contemporary wisdom that knowledge is knowledge of truths, the formulation of the traditional doctrine seems straightforward: to be omniscient is just to know all truths. What has seemed problematic, rather, is whether the doctrine is itself true. In particular, many have wondered whether anyone can know the parts of the future not necessitated in any way by the present or past.

 

Recently, however, it has been suggested that, although the doctrine of omniscience is false on its traditional construal (because some truths are unknowable), the doctrine ought not to be abandoned. For the fault lies only with the traditional formulation of the doctrine rather than with the doctrine itself. What is needed instead, it is suggested, is a limited doctrine of omniscience.

 

Such a limited doctrine might be motivated in a number of ways, but recent discussion has seen the emergence of one particular kind of argument for a limited doctrine of omniscience according to which the doctrine of omniscience ought to be developed in a way analogous to a proper development of the doctrine of omnipotence. In clarifying the doctrine of omnipotence, theologians have generally been careful to claim that an omnipotent being is not one who can do everything, but rather one who need only be able to do anything possible. Apart from such a restriction, God=s inability to make false what is necessarily true would imply that He is not omnipotent. Defenders of a limited doctrine of omniscience have thought that an analogous restriction on the doctrine of omniscience would b~ able to save the doctrine of omniscience even in the face of the spectre of unknowable truths: we should require, they claim, only that an omniscient being know everything that can be known.

 

I wish to argue two claims. First, I shall contend that the argument for affirming a limited doctrine of omniscience is defectiveCthe best analogies with developments regarding omnipotence simply do not support any limited doctrine of omniscience. Further, the analogy argument is really a wolf in sheep=s clothing to any limited doctrine of omniscience, for the only instructive analogy on how to develop the doctrine of omniscience from the doctrine of omnipotence actually supports the traditional doctrine of omniscience. Thus, if there is a class of truths which are unknowable, it would seem that no being could be omniscient.

 

The issues involved here are important ones, not limited only to those issues local to the understanding of omniscience. One such issue concerns a major premise of the ontological argument. One fairly standard view on the status of that argument is that its soundness hinges primarily on the truth of the premise which claims that it is possible that a maximally perfect being exists. Since it is generally acknowledged that maximal perfection includes omniscience, the move to a limited doctrine of omniscience makes it possible for this premise still to be maintained even in the face of the spectre of unknowable truths. On the other hand, should the move to a limited doctrine of omniscience prove unwarranted, the existence of unknowable truths would undermine not only the doctrine of omniscience but also the possibility of the existence of a maximally perfect being and hence the ontological argument.

 

A word of clarification is in order here to distinguish limited doctrines of omniscience from non-reductive doctrines. Recent work regarding de re and de se belief has suggested to some that one cannot know all there is to know just by knowing all truths. The ground for this suggestion is that de re and de se belief has seemed to involve a sort of awareness which is nonpropositional.2 If this is true, then the traditional account of omniscience will have to be adandoned. Yet, this abandonment of the traditional view is quite different from the sort of abandonment suggested by defenders of limited doctrines of omniscience. Defenders of limited doctrines hold that there are truths which, because they are unknowable, need not be known by an omniscient being. Such a view involves a quite apparent limitation within the arena of propositional awareness, whereas abandonments of the traditional doctrine in the face of objections to a reductive view of intentional attitudes need not involve such an apparent limitation at all. My concern is with alterations of the traditional view that involve limitations on what propositions an omniscient being must know.

 

Swinburne, for example, presents the analogy argument as follows:

 

As we saw in the last chapter, theologians, such as Aquinas, have been careful to explain omnipotence, not as the ability to do anything, but (roughly) as the ability to do anything logically possible. . . . It would be natural to develop an account of omniscience along similar lines, not as knowledge of everything true, but (very roughly) as knowledge of everything true which it is logically possible to know.

 

Similar versions of the argument have been made by Mavrodes and Hasker.4 In each case, a limited doctrine of omniscience is founded upon an analogy with the doctrine of omnipotence. The argument proceeds as follows. There are, first, initial stabs at understanding omnipotence and omniscience: omnipotence requires being able to do anything; omniscience requires knowing everything true. The second step involves attaching qualifications to each of these initial understandings, qualifications which are supposed to be analogous to each other. In the case of omnipotence, the definition receives restriction in terms of what can be done; in the case of omniscience, the restriction is in terms of what can be known.

 

A moment=s reflection discloses the weakness of this argument, which lies with the initial understanding of omniscience. Whereas omnipotence is understood as requiring the ability to do anything, omniscience is not given a similarly broad understanding. That understanding would take omniscience to require knowing everything; Swinburne, however, characterizes the unrestricted understanding of omniscience as only requiring that one know everything true. In order for the analogy argument to be persuasive, we either need similarly unrestricted initial starting points or we need some defense of the starting points which are adopted. Since we have neither, the appearance is that Swinburne stacks the deck against the traditional doctrine of omniscience by beginning with it when making it the unrestricted starting point. Hence, his argument is not persuasive.

Perhaps, though, Swinburne was just a bit careless, and more careful investigation will support the same conclusion he defends. In order to begin this task, we should first insist on a bit more precision in formulating the various construals of the doctrines in question. Since it is propositions in question in considering the doctrine of omniscience, let us formulate the doctrine of omnipotence regarding propositions as well.

 

One further restriction is needed. Swinburne=s discussion suggests that we are considering various definitions of the concepts of omnipotence and omniscience. Thus, for example, he seems to suggest that an initial account of omnipotence is in terms of being able to do anything, and that a better account can be obtained in terms of being able to do anything that can be done. For those familiar with the difficulties in defining omnipotence, it is obvious that neither of these definitions is adequate. Because of this, a cloud of suspicion would hang over our results should we pretend that obviously bad analyses are good ones. To avoid this problem, I shall address the issues here by formulating conditions of adequacy on proper definitions of the concepts in question, rather than by offering alternatives to an initial, inadequate definition.

 

We can begin then by offering initial definitions of omnipotence and omniscience, definitions which are obviously incorrect. As far as I can tell, there is no reason to accept the initial definition of omniscience with which Swinburne begins, i.e., the traditional construal, except the question-begging response that this starting point-gets us to Swinburne=s desired conclusion. In particular, Swinburne=s two formulations are not equally rooted historically: hardly anyone has defended the unrestricted doctrine of omnipotence, whereas many have found the traditional construal of omniscience acceptable. Hence, it would seem fairest to begin with the following precisely analogous construals of omniscience and omnipotence:

 

P:         B is omnipotent = df. B can bring it about, for any proposition p, that p is true;

S:         B is omniscient df. for all p, B knows p.

 

Clearly, neither definition is adequate. Given the procedure to be followed, our question is: what condition of adequacy on replacements for P and S does the analogy argument appeal to? In the earlier quote from Swinburne, there is reference to altering P so that it only refers to the logically possible. One way to interpret this claim is to take it to be about the possibility of the proposition p referred to on the right side of P. If we adopt this interpretation, the claim is that P is inadequate because it requires an omnipotent being to be able to make true what is necessarily false. Since no omnipotent being needs to be able to make true what is necessarily false, the appropriate condition of adequacy is:

 

RPI:     An analysis of omnipotence may require that an omnipotent being be able to bring about the truth of p only if p is not necessarily false.

 

What would be the analogous restriction on S? Well, a strictly analogous restriction would include the very phrase which follows the >only if@ in RPI; in other words, a strictly analogous restriction to RPl on S would be:

 

RSI:     An analysis of omniscience may require that an omniscient being know p only if p is not necessarily false.

 

Clearly, RSI is true; however, it does not even remotely resemble a limited (as opposed to the traditional) doctrine of omniscience. Hence, if RSl is the proper analogue of RPl, then the analogy does not help defenders of a limited doctrine of omniscience.

 

Interestingly, though, a more careful evaluation of the differences between omnipotence and omniscience does generate an interesting analogy between the two. It is not, however, an analogy which supports a limited construal of omniscience. Careful evaluation of omnipotence and omniscience reveals that, whereas omnipotence is a modal notion, omniscience is not.    

 Omnipotence has to do with what can be done by a person, not just what in fact is done by that person; omniscience regards what in fact is known, not what can be known. In possible worlds jargon, omnipotence concerns what a person does in any world; omniscience does not concern what a person knows in other worlds, but only what that person knows in this, the actual, world.5

 

The fact that omnipotence is a modal notion and omniscience is not should be reflected, it might be claimed, in the restriction on S chosen to be the analogue of RPI. RSI is an analogue of RPl, but it includes a modal notion after the Aonly if,@ and hence does violence to the intuitive point that omniscience differs from omnipotence in not being a modal notion. In order to honor this difference, a restriction on omniscience is needed which is not modal in character.

 

We saw above that the modal difference between omnipotence and omniscience is reflected in the fact that omnipotence concerns what is done-at-a-world whereas omniscience concerns only what is known-at-this-world. In order to form an analogue of RPl, we must rephrase this difference in terms of propositions and their truth-values. In order to find the appropriate restriction on 5, we need then to consider the relation between what is necessarily false (those propositions referred to after the Aonly if@ in RPl) and what is done-at-a-world. Clearly, the relation is one of incompatibility: what is necessarily false is not brought about (made true) by anyone at any world. In order then to find the analogue of RPI, we need to find a kind of proposition which bears the same incompatibility relation to being known. Clearly, unknowable propositions are not a relevant kind here: being necessarily false is internal to a proposition in a way in which being unknowable is not. Just as clearly, the only relevant kind left is the class of false propositions. The falsity of a proposition is internal to it in a way in which the unknowability of a proposition is not (the second requires reference to knowers and hence is relational in a way that the first is not). So, it would seem, the best analogue of RP1 that honors the difference in the modal status of the notions of omnipotence and omniscience is:

 

RS2:     An analysis of omniscience may require that an omniscient being know p only if p is not false.

 

RS2 is a condition on an analysis of omniscience which supports the traditional doctrine of omniscience; for, if it were the only condition of adequacy on an analysis of omniscience, we could replace S with the analysis which the traditional doctrine assumes and satisfy RS2. Hence, when the analogy argument is developed carefully, interpreting the reference to the logically possible as a reference to the modal status of the proposition on the right sides of P and S, the analogy argument actually supports the traditional doctrine and no limited doctrine at all.

It might seem then that the analogy argument cannot be developed to support a limited account of omniscience but instead supports only the traditional account of omniscience. Things are not that simple, however, for there is another way to read the references to the logically possible in the quotation from Swinburne which allows an analogy to be developed which supports a limited account of omniscience. In the domain of power regarding some proposition p, for example, instead of requiring only that p is logically possible, one might have intended to limit the domain of omnipotence to cases in which the proposition Athe truth of p is brought about@ is possible. If that is their intention, then we should not interpret the condition as in RPI, but rather as:

 

RP2:     An analysis of omnipotence may require that an omnipotent being be able to bring it about that p is true only if the proposition Athe truth of p is brought-about by someone@ is not necessarily false.6

 

The analogous restriction to RP3 needed for the analogy argument to support a limited doctrine of omniscience is:

 

RS3:     An analysis of omniscience may require that an omniscient being know p only if the proposition Ap is known by someone@ is not necessarily false.

 

RS3 does support a limited account of omniscience, one which requires that an omniscient being know only all that can be known. Thus, it is a mistake to conclude that no analogy argument can be developed to support such a limited  account of omniscience. In order to defend my thesis, then, I need to do one of two things: I need to offer some reasons for thinking that RS3 is not a correct condition of adequacy on a proper understanding of the doctrine of omniscience, or I need to give reasons for thinking that one should prefer RPI to RP2 as an appropriate restriction on a proper construal of the doctrine of omnipotence. In fact, I shall do both.

 

First, there are, I believe, good reasons to reject RS3. A first reason concerns the implications of skepticism. For example, if universal skepticism were true (the view which claims that knowledge is impossible, even about what is immediately presented to one=s senses), then every person would be omniscient if we accepted RS3 as a condition of adequacy on an analysis of omniscience. RS3 is attractive only if one is only considering the possibility of severely limited skeptical theses; but the less limited the skeptical thesis, the more obvious is the inadequacy of RS3. Clearly, if universal skepticism were true, no one would or could be omniscient; thus, the fact that RS3 would imply in such a case that everyone would be omniscient shows that RS3 is an inappropriate condition of adequacy on an analysis of omniscience.

 

In addition to being inappropriate, RS3 is inferior to RS2 for another reason as well. This reason concerns what a proper construal of omnipotence ought to imply regarding the following two propositions:

 

(1) Joe will freely ride his bike tomorrow,

(2) A molecule will randomly disintegrate tomorrow.

 

The notions of freedom and randomness are both to be construed here as incompatible with there being any set of causally sufficient conditions for the occurrence of the events in question. Now this understanding appears to cause problems for any analysis of omnipotence which does not include any restriction beyond RP2, for it would seem that God=s bringing about either the riding of the bike or the disintegration of the molecule is incompatible with the riding being free or the disintegration being random in the senses in question. But there is a distinction which has been employed to avoid this apparent problem. One may bring it about that a proposition is true, it is claimed, either strongly and weakly. To bring about the truth of a proposition strongly is to do something which is either causally or logically sufficient for the truth of the proposition in question. Weakly bringing about the truth of a proposition does not involve doing anything which by itself is either causally or logically sufficient for the truth of the proposition in question. Rather, one can weakly bring about the truth of a proposition by strongly bringing about a set of conditions which are counterfactually connected to the truth of the proposition in question. Thus, for example, God can bring it about (weakly) that (I) is true since He can strongly bring it about that some set of conditions C obtain which are such that, if they were to obtain, Joe would freely ride his bike tomorrow. So, contrary to initial appearances, a person (other than Joe) can bring about the truth of (1) in part because of the truth of the counterfactual in question (call it a counterfactual of freedom).7

 

What about (2)? Can a person weakly bring about its truth as well? The answer depends on whether there are counterfactuals of the sort claimed for free actions regarding the random behavior of things. If there are conditions which are such that, in them, the molecule would randomly disintegrate, then a person can weakly bring about the truth of (2). If, however, there are no such counterfactuals (call it a counterfactual of randomness), then the truth of (2) cannot be brought about.

 

We have, then, some ground on which to distinguish whether we wish to accept RPI or RP2 as the proper restriction on an adequate analysis of omnipotence. What we need to know is whether there is some reason to think that the question of the existence of the counterfactuals of freedom is independent of the question of the existence of counterfactuals of randomness.8 As far as I can see, there is no reason for thinking these questions independent. I do not find that either view has greater intuitive support than the other; the connections in each conditional are alike in that each is irreducible to a truth-functional, logical, or causal connection; each is independent of the history of the world in that, in each case, it is logically possible that the same history be followed by an occurrence incompatible with the one required by a true counterfactual. Further, if any explanation at all can be given for the truth-value of such counterfactuals, the truth-value will have to be claimed to be grounded in the randomness of the substances in question: it is an irreducible and essential characteristic of the substances in question that they would behave in the required ways. In particular, one cannot distinguish the two by claiming that, since freedom implies power and randomness does not, (I) can be made true by Joe whereas (2) cannot be made true by the molecule in question. The notion of making true here is not a causal one at all, and hence the sense in which freedom implies a sort of power which randomness does not is irrelevant to the truth of(l) or (2). To make a proposition true is not causally to produce its truth; it is rather to bring it about, or to be responsible for its being true. And it does not take an action for it to be brought about that a proposition be trueCordinary states of affairs involving stones, rocks, even reflexes accomplish it regularly.

The only argument of any strength I can think of to distinguish the question of the existence of counterfactuals regarding (I) and (2) centers on the notion of probability. Suppose the claim is that in circumstances C, Joe would so act that (I) is true; and suppose the claim is that in C*, a molecule would behave so as to insure the truth of (2). One might claim that the first counterfactual is true whereas the second is not because there is a probabilistic relation greater than one-half between C and Joe=s riding, whereas there is no such relation between C* and the disintegration of the molecule. The intuitive idea is that being more probable than not is compatible with freedom but not with randomness.

 

The difficulty with this argument for distinguishing between the status of counterfactuals of freedom and randomness concerns the notion of probability. Probability claims are ambiguous: sometimes one means to be talking about a subjective estimate of the chances of a certain event occurring (or perhaps our best estimate of these chances); sometimes one means to refer to the relative frequency of a certain event=s occurring in the long run; and sometimes one speaks of some a priori determination of likelihood. No subjective or epistemic sense of probability will be relevant here, for the issue of the truth of the counterfactuals in question is an objective issue and hence logically independent of what we think about the issues. Thus, even if certain probability differences were to be found regarding Joe=s riding in C and the molecule=s disintegration in C*, nothing would follow about the objective truth-value of the corresponding counterfactuals. On the frequency interpretation, the probability claim will sometimes be true and sometimes not, depending on how many times the action in question occurs with the circumstances in question: if C occurs only once in the history of the world, then the probability of Joe=s riding his bicycle given that C occurs is either 0 or I (in the relative frequency sense). Yet it is possible that the following conjunction is true: (I) C occurs and Joe does not freely ride his bike; and (2) if C were to occur, Joe would freely ride his bike. This conjunction could be true if the occurrence of C were conjoined to, say, the death of Joe; in such a case (I) would be true and there would be nothing to prevent the truth of (2), for (2) is a different claim than the claim that if C were to occur and Joe were to die, Joe would freely ride his bike. Given these claims, though, the relative frequency sense of probability can result in the probability of (I) being 0, even being 0 given C, even though if C were to obtain (I) would be true. Hence the frequency sense will not do. That leaves only the a priori sense of probability. The difficulty with mounting an argument based on this notion of probability is that any claims about the probability of (I) given C in this sense will be wholly arbitrary: no one has any idea, beyond simple mathematical cases, what the a priori probability of an event is. In all, then, the probabilistic argument aimed at separating the status of counterfactuals of freedom from counterfactuals of randomness fails.

 

If I am right that there is no ground on which to separate these questions, then, it would seem, we have reason to reject RP2 and accept only RPI. For, supposing there are no counterfactuals of freedom or randomness, RP2 exempts an omnipotent being from having to be able to make (2) true though it does not exempt an omnipotent being from having to be able to make (I) true, since someone (namely, Joe) can bring about the truth of (I) (and hence RP2 does not exempt an omnipotent being from having to be able to bring about the truth of (I)) but no one can bring about the truth of (2) (and hence RP2 does exempt an omnipotent being from having to be able to bring about the truth of (2)). Yet, if no ground is ~ forthcoming for distinguishing the questions regarding the two kinds of counterfactuals, then no restrictive condition should be accepted which treats (I) and (2) differently. Further, RPI does not treat them differently: it does not exempt omnipotence from being able to make either (1) or (2) true. Hence, there may be good reason to choose RPI over RP2, for RPl exhibits a neutrality on the issue of whether there are counterfactuals of freedom or randomness which RP2 lacks.

 

If we accept RPI and not RP2, though, then as we have seen the analogy argument supports a traditional construal of omniscience and no limited one. Hence, for the analogy argument to work for them, defenders of a limited doctrine should give us some reason for distinguishing existence claims regarding counterfactuals of freedom from those regarding counterfactuals of randomness.

 

Hence, careful consideration of the analogy argument shows that, at least, no limited doctrine is supported by it. Another point may also hold, if I am right that there is no good ground for distinguishing between counterfactuals of freedom and counterfactuals of randomness. If there is no such ground, then we should prefer RP2 to RPI; and, as we saw, careful attention to the analogous restriction to RP2 regarding omniscience yields just the restriction implied by the traditional doctrine of omniscience: that a candidate for omniscience should not be required to know falsehoods. Thus, the analogy argument may in fact support only the traditional construal of omniscience.

 

I have not defended that no limited doctrine of omniscience is correct (if by a limited doctrine one only means a doctrine which allows there to be an omniscient being that does not know all truths), nor have I claimed that the traditional doctrine is required (though I believe both of these to be true). My conclusion is conditional only: if it should turn out that there is a sound skeptical argument for the claim that there are unknowable truths and the only support for a limited doctrine is the analogy we have considered, the proper conclusion to draw would be that there is no omniscient beingCnot that there is an omniscient being on some pared-down construal of Aomniscience.@9

 

 

Notes

 

1.                   For a contemporary consideration of this issue, cf. Richard Swinburne, The Coherence of Theism (Oxford: Oxford Univ. Press, 1977), pp. 172C78.

 

2.                  See Roderick Chisholm, Person and Object (LaSalle: Open Court, 1976); The First Person (Minneapolis: Univ. of Minnesota Press, 1981), for discussion of the issues surrounding the reductive thesis that all awareness is propositional awareness.

 

3.                  Swinburne, p. 175.

 

4.                  George Mavrodes, Self-Referential Incoherence,@ American Philosophical Quarterly 22 (1985), 69; William Hasker, Foreknowledge and Necessity,@ Faith and Philosophy 2 (l985), 128.

 

5.                  Though, of course, what a person knows in other worlds is relevant to the doctrine of essential omniscience, the doctrine which claims not only that there is a person who is omniscient, but who could not fail to be omniscient.

 

 

6.                  For an analysis of maximal power that accepts RP2, ef. Thomas P Flint and Alfred J. Freddoso. AMaximal Power,@ in The Esis fence and Non4re of God (Notre Dame: Univ. of Notre Dame Press. 1983). pp. 81CI 14.

 

 

7.                  The notion of a counterfactual of freedom can be traced to Luis de Molina, a 16th century Jesuit theologian.  A more recent account of the impact of this notion of issues regarding omnipotence the problem of evil can be found in Alvin Plantinga, The Nature of Necessity (Oxford: Clarendon Press, 974). Plantinga holds that, for some actions which a person might do, it is possible that there is no true counterfactual such that God=s weakly actualizing its antecedent would result in that action being performed. If this is true, additional complications not relevant to our discussion would have to be introduced in the doctrine of omnipotence.

 

 

8.                  Many have found the notion of such counterfactuals of freedom quite problematic. Cf., e.g., Anthony Kenny, The (;od of the Philosophers (Oxford: Clarendon Press, 979); Robert Adams, AMiddle Knowledge and the Problem of Evil,@ American Philosophical Quarterly 14 1 l977), l09Cl7. I attempt to answer the problems such a view faces in The Possibility of an All-Knowing God (London: Macmillan, 1986).

 

9.                  I wish to thank Jerome Gellman, who commented on an earlier version of this paper delivered at the Eastern Division meeting of the American Philosophical Association in December, 1986, and Hugh J. McCann for their valuable contributions to this paper.