Could there be two co-existing omnipotent agents?
June 10, 2004 — 6:41

Author: David Efird  Category: Concept of God  Comments: 9

In a previous entry, on Baldwin’s counter-ontological argument, I considered whether there might be divine twins, that is, two co-existing individuals sharing all of their repeatable intrinsic properties, which are the traditional perfections. One reason for thinking that there couldn’t be two such individuals is that there couldn’t be two co-existing omnipotent agents. I’ve gone through what I’ve written before, and, I think, improved my argument that there could be two omnipotent agents, and I’m posting it below the fold.


There is a standard argument that concludes that there could not have been two co-existing omnipotent agents, which goes roughly like this: if there were two co-existing omnipotent agents, then their wills might conflict, and this conflict amounts to the frustration of both of their wills, which is impossible if they are omnipotent agents. In what follows, I consider a recent form of this argument, and I maintain that the lesson to be drawn from it is not that there could not have been two co-existing omnipotent agents, but rather that contextual factors can render a task incoherent, in a sense defined below.
Joshua Hoffman and Gary S. Rosenkrantz have recently presented the following version of the argument at issue. Suppose for reductio that there are two omnipotent agents, Dick and Jane.
If this were possible, then it could happen that at some time, t, Dick, while retaining his omnipotence, attempts to move a feather, and at t, Jane, while retaining her omnipotence, attempts to keep that feather motionless. Intuitively, in this case, neither Dick nor Jane would affect the feather as to its motion or rest. Thus, in this case, at t, Dick would be powerless to move the feather, and at t, Jane would be powerless to keep the feather motionless! But it is absurd to suppose that an omnipotent agent could lack the power to move a feather or the power to keep it motionless. (2002: 168).
Therefore, Hoffman and Rosenkrantz conclude, neither agent is omnipotent, and so, there could not be two co-existent omnipotent agents.
In response, Hoffman and Rosenkrantz’s argument is unpersuasive because in stating one of their premises: It is absurd to suppose that an omnipotent agent could lack the power to move a feather or the power to keep it motionless.
they have not stated the context in which the actions at issue are to be performed. When this context is made explicit, we have: It is absurd to suppose that an omnipotent agent Dick could lack the power to move a feather which another omnipotent agent, Jane, wills to remain motionless, and that an omnipotent agent Jane could lack the power to keep a feather motionless which another omnipotent agent, Dick, wills to move.
And when stated fully, it is clearly false. It is no more absurd to suppose that Dick and Jane could have lacked the particular powers at issue than that they could have lacked the power to bring about logically contradictory states of affairs. Thus, Hoffman and Rosenkrantz’s argument is unsound, but it does yield an important lesson, which is that the coherence of a task is dependent on contextual factors. Let me explain.
I begin with two stipulations:
A task is coherent just in case it is (i) the bringing about of a logically possible state of affairs, and (ii) bringing about this state of affairs is consistent with the agent of the task’s nature.
An agent is omnipotent just in case she has the power to perform any coherent task.
Now to be sure, both the task of moving a feather and the task of keeping a feather motionless are coherent tasks in many, if not most contexts. However, both of these tasks are rendered incoherent in a particular context, namely, when we have two omnipotent agents, one willing that a feather move and the other willing that that feather be motionless: it is not logically possible, even for an omnipotent agent, to move a feather which another omnipotent agent wills to remain motionless and it is not logically possible, even for an omnipotent agent, to keep a feather motionless which another omnipotent agent wills to move. It then follows that Dick’s powerlessness to move the feather in this scenario is no bar to his omnipotence and Jane’s powerlessness to keep the feather motionless in this scenario is no bar to her omnipotence, and so Hoffman and Rosenkrantz’s argument does not tell against the possibility of two omnipotent agents.
It should be immediately apparent that this resolution of Hoffman and Rosenkrantz’s argument has an affinity with some solutions to the liar paradox. One standard response to the liar paradox is to claim that the liar sentence does not express a proposition, that is, it is not coherent. But the liar paradox arises not only in connection with a special sentence, namely, ‘It is not the case that this sentence is true’. The liar paradox also arises in ordinary but unfavourable contexts. As Kripke (1975) has shown, contextual factors can render ordinary assertions of truth and falsity paradoxical. Consider the following case suggested by Kripke (1975: 691-92). Say that Jones makes the following claim:
(1) Most (i.e., a majority) of Nixon’s assertions about Watergate are false.
This assertion, in and of itself, has no paradoxical features that might be thought to prevent it from being true or false. Say that (1) is the only sentence that Jones utters about Watergate, or that all, except perhaps (1), of his assertions about Watergate are true. Now assume that Nixon’s assertions about Watergate are evenly balanced between true assertions and false assertions, and that Nixon then utters the following sentence:
(2) Everything that Jones says about Watergate is true.
Just as there is nothing intrinsically paradoxical about (1), there is nothing intrinsically paradoxical about (2), but together, they create a paradox. One might say that (1) and (2) are extrinsically paradoxical in Kripke’s thought experiment. With this example we see that, in Kripke’s words: “many, probably most, of our ordinary assertions about truth and falsity are liable, if the empirical facts are extremely unfavorable, to exhibit paradoxical features” (1975: 691). Similarly, many — probably most — of the tasks we take to be coherent in ordinary cases are liable, if the case is extremely unfavourable, to exhibit paradoxical features. These paradoxical features render the sentences and the tasks that exhibit them incoherent. While, on the resolution of the liar paradox I have in mind, the liar sentence is incoherent in any context whatsoever, (1) and (2) are not coherent in the context given by Kripke, even though they are coherent in other, ordinary contexts. One might say that the liar sentence is intrinsically incoherent, while (1) and (2) are extrinsically incoherent in the context given by Kripke, and most, if not all, sentences are either intrinsically incoherent, or liable to be extrinsically incoherent depending on the contexts in which they are uttered. Thus, whether or not a sentence is coherent is dependent on contextual factors. Similarly, while the task of making two and two add up to five is not a coherent task in any context whatsoever, that is, it is intrinsically incoherent, the task of moving a feather and the task of keeping a feather motionless are incoherent in the one offered by Hoffman and Rosenkrantz, that is, they are extrinsically incoherent in this context, even though they are coherent tasks in ordinary contexts. Thus, whether or not a task is coherent is dependent on contextual factors, and an omnipotent being need not be able to perform an incoherent task, regardless of whether it is intrinsically incoherent or extrinsically incoherent.
References
Hoffman, J. and Rosenkrantz, G. S. 2002. The Divine Attributes. Oxford: Blackwell.
Kripke, S. 1975. Outline of a theory of truth. The Journal of Philosophy 72: 690-716.

Comments:
  • Mike

    David says: _…when we have two omnipotent agents, one willing that a feather move and the other willing that that feather be motionless: it is not logically possible, even for an omnipotent agent, to move a feather which another omnipotent agent wills to remain motionless…_
    That’s false, isn’t it? It is logically impossible for O to move F and O* to prevent O from moving F ONLY IF O* is essentially omnipotent. If O* is not essentially omnipotent, then there is a world in which O* is not omnipotent. But then there is a world in which O moves F and O* fails to prevent O from moving F. But then it is not logically impossible for O to move F while O* is preventing O from doing so.

    June 10, 2004 — 9:53
  • I think David meant it to be a de dicto claim, in which case it’s true. If it’s de re, you’re right, I think.

    June 10, 2004 — 12:30
  • Mike

    If it is meant de dicto then it is not relevant to the existence of two omnipotent beings. There could be two such beings, if one of them is contingently omnipotent. And that is consistent with the de dicto impossibility (assuming that is what was intended).

    June 10, 2004 — 15:50
  • Chris

    Ed Weirenga defends an account according to which there are three such beings here:
    http://www.rochester.edu/College/REL/trinity.pdf
    I think he holds that they can’t differ in what they will to be the case. (His account is an interesting attempt to solve the problem that arises from the claim that there is one God who is three persons; the three constitute God, though none is identical with Him. The three persons are divine, however; each is, for instance, omnipotent.)

    June 10, 2004 — 19:47
  • David Efird

    Good points all ’round.
    I think this is what I meant:
    Given that both Dick and Jane are omnipotent, and that Dick wills that the feather move and Jane wills that the feather remain motionless, it is not logically possible that: Dick moves the feather or Jane keeps the feather motionless.
    and I think it fixes up the argument. (When we evaluate the claim:
    Dick moves the feather or Jane keeps the feather motionless.
    we consider only worlds in which both Dick and Jane are omnipotent and their wills conflict, and in none of those worlds is either disjunct true, so the disjunction is not logically possible.)

    June 11, 2004 — 4:48
  • Mike

    David-
    This again won’t show that there is any incoherence in there existing two omnipotent beings. There is no reason to assume that omnipotent beings have necessary existence. And so we can have two omnipotent beings existing in different (i.e., disjoint) sets of worlds. In this case your disjunction is a contingent statement. In worlds containing an omnipotent being, it is true. In worlds containing no omnipotent beings, it is false.

    June 11, 2004 — 10:07
  • David Efird

    Mike–
    I think that my last go really does fix it up. When evaluating:
    Dick moves the feather or Jane keeps the feather motionless.
    we consider only worlds in which both Dick and Jane are omnipotent. In those worlds both Dick and Jane exist, since they have a property, namely, being omnipotent. And in those worlds, they have the wills specified. And in none of those worlds is either disjunct true. Hence the disjunction is false. Hence,
    *Given that both Dick and Jane are omnipotent, and that Dick wills that the feather move and Jane wills that the feather remain motionless*, it is not logically possible that: Dick moves the feather or Jane keeps the feather motionless.
    Thanks for your comments.

    June 11, 2004 — 11:31
  • Mike

    David says: “. . .we consider only worlds in which both Dick and Jane are omnipotent and their wills conflict, and in none of those worlds is either disjunct true, so the disjunction is not logically possible.”
    How could this be right? Here’s the disjunction:
    1. Dick moves F OR Jane keeps F motionless.
    Let w be one of the worlds containing these two beings and their conflicting wills. There is presumably nothing else affecting the feather or its movement. Both disjuncts are supposed to be false in w. Consider the first disjunct:
    2. Dick moves F.
    (2) is false in w. But then it must be true that the feather is motionless in w. That is a necessary condition of (2) being false. And so the second disjunct in (3) is true.
    3. Jane keeps F motionless.
    But (3) is supposed to be false in w! Suppose then that (3) is false in w. It then follows that the feather moves in w. But then (2) is true in w. So there is no world in which both disjuncts are false. Of course, all of this assumes that there is nothing else operating on the feather: no third omnipotent being, no gusts of wind moving the feather, etc. etc. I take it that all of these assumptions are built into the case already.

    June 11, 2004 — 11:50
  • jamasiel

    But then wouldn’t it be more along the lines of a negation of each omnipotent power:
    -the feather will not-move towards Jane because she is countering the omnipotent will of Dick.
    -the feather will not-not-move towards Jane ~because~ Dick is countering Jane’s omnipotence.
    So it ends up with Jane’s desire – for it to not move – but not directly because she’s willing it to not-move towards herself, but because neither ends up having a direct effect on the feather, but because they cancel each other out. So the feather goes on doing whatever feathers do in the midst of two omnipotent beings.

    June 16, 2004 — 8:07