Only Necessarily Self-Limited Power
October 17, 2010 — 18:34

Author: Kenny Pearce  Category: Books of Interest Christian Theology Concept of God  Tags: , , , ,   Comments: 39

After considering arguments for the existence of God, Sobel has a brief interlude on the divine attributes, before going on to arguments against the existence of God. Chapter 9 concerns omnipotence and the famous Stone Paradox. Sobel defines omnipotence (roughly) as the ability to do anything that can be done. (He improves this basic definition in a few ways, but these need not concern us.) The Stone Paradox, Sobel rightly recognizes, is no real problem for omnipotence as such, for if a being can do anything that can be done, then that being can take away some of the powers it has, just as I can take away some of the powers that I have. As a result, there is no problem with an omnipotent being creating a stone it can’t lift; it is simply that it must lay aside its omnipotence in the process. However, as this analysis shows, essential omnipotence is something else altogether, and this points to a more general problem: the God of the religious tradition has essential properties (in fact, it is most common, historically, for theologians to hold that he has all of his properties essentially). But then there are things I can do that God can’t, such as making myself less knowledgeable. (Of course, God could make me less knowledgeable; what he couldn’t do is make himself less knowledgeable.) Sobel comes up with a proposal for a coherent understanding of the feature the theologians want to attribute to God, but denies that this feature is properly described as ‘omnipotence’. In this post I will discuss Sobel’s proposal. In the next post, I will make a proposal of my own, and argue that it is sensible to call the feature I identify ‘omnipotence.’
Sobel says that although nothing could be essentially omnipotent, a being could possess a feature Sobel calls ‘only necessarily self-limited power’ (ONSLIP). This is the property of being such that:

[one is] capable of each task t that it is logically possible that some being should do, which is such that (i) for each attribute, if any, that x has essentially, x’s performing t is consistent with its having this attribute … and (ii) if x has necessary everlasting existence, then performing t is consistent with its continuing to exist. (p. 365)

In other words, God’s power is limited only by God’s own nature. This is, I think, the sort of thing the theologians have in mind. However, as Sobel points out, a being might have this feature and not be anything like omnipotent. To use his example, a being might be “essentially incapable of creating something from nothing” (ibid.), and so be an ONSLIP without having that power. So Sobel is right that the property of being an ONSLIP ought not to be called ‘omnipotence’ (or ‘almightiness’). I wonder, however, if perhaps we might get an omnipotence “worth the name” by specifying the sorts of attributes the being can have essentially. For instance, an ONSLIP who essentially possesses all positive properties (if we can get a decent understanding of ‘positive’ in this context) is not going to seem limited to us in the way an ONSLIP who is essentially incapable of creating something from nothing does.
[cross-posted at blog.kennypearce.net]

Comments:
  • Mike Almeida

    But then there are things I can do that God can’t, such as making myself less knowledgeable. (Of course, God could make me less knowledgeable; what he couldn’t do is make himself less knowledgeable.)
    If God is essentially omnipotent, it does not entail that he could not make himself less knowledgeable, unless he is also essentially omniscient. And even if he is essentially omniscient, he can make himself less knowledgeable, since he can actualize a world in which there is less to know. Now you might say that the set of contingent truths has the same cardinality in every world, and it is cardinality of known truths that determine how much you (or God) knows. If that’s true, then you cannot make youself less knowledgeable. Since for every proposition p that you fail to know (and which thereby lessens your knowledge) there is another truth that you do know. Namely, that you do not know p. The set of known truths for you stays the same for you, as it does for God.

    October 17, 2010 — 19:53
  • It seems to me that there are two essentially different ways of looking at omnipotence.
    1. Omnipotence is a doctrine about the range of action-types that God can do, including essentially reflexive or intransitive action types like dancing a waltz (which, by the way, God can do by means of become incarnate).
    2. Omnipotence is a doctrine about the range of states of affairs that God can bring about.
    I think Sobel is focusing on approach 1. This requires all sorts of restrictions beyond the restriction that the action-type be doable by somebody. God can’t lie, he can’t dance-without-having-become-incarnate, he can’t commit suicide, he can’t create a stone lifting which is beyond his power, etc. So, if one takes approach 1, one ends up having to go for something like ONSLIP. But ONSLIP is a poor replacement for omnipotence, since any being that is essentially inert and essentially causally impotent (many philosophers think numbers are like that) automatically satisfies ONSLIP.
    I think it’s more fruitful to use approach 2. On approach 2, we don’t have to worry about coherent de se action-types that make no sense in the case of God. We make an initial restriction to possible states of affairs. Then I think our only worries are about two kinds of states of affairs:
    a. Free actions by creatures.
    b. Evil states of affairs.
    Since there are only two kinds of states of affairs that are problematic, we could simply rule them both out explicitly, or we could try to work harder (e.g., argue with St Thomas that God can cause free creaturely actions, or come up with some general formulation like that God can cause any possible state of affairs that God could have a non-excluded reason to cause). But in any case, it seems we start off significantly ahead of approach 1.

    October 18, 2010 — 9:01
  • Mike Almeida

    This requires all sorts of restrictions beyond the restriction that the action-type be doable by somebody. God can’t lie, he can’t dance-without-having-become-incarnate, he can’t commit suicide, he can’t create a stone lifting which is beyond his power, etc.
    I’m sure why any of these is true. Of course he can lie. It is just that, were he to do so, it would no longer be a lie. For instance, he can tell you that your chair is red, when it is in fact blue, with the intention to get you to believe it is red. That’s a lie. But if God were to utter that lie, it would no longer be one. The chair would be red. He can create a stone too heavy for him to lift. But again, were he try to lift it, it would no longer be too heavy. Counterfactuals operate in very strange ways when we are considering perfect beings.

    October 18, 2010 — 9:36
  • Kenny Pearce

    Mike (on your first comment) – Suppose God is essentially omnipotent and essentially omniscient. Then there is something I can do that God can’t, namely, bring it about that there is a truth that I do not know. For instance, I can roll a set of dice under an opaque cup, and then I will have brought it about that there is a fact about how the dice landed, and that I don’t know that fact. This isn’t quite what I said in the post, but it gets us to the same point.

    October 18, 2010 — 11:14
  • Mike Almeida

    Then there is something I can do that God can’t, namely, bring it about that there is a truth that I do not know.
    Not so! He can also bring about a truth that you don’t know. What he cannot do is bring about a truth that he does not know. But neither can you.
    S. Jeffers,
    Make a mistake? Change His mind? Fall off a chair? Change the past?
    I’m assuming that you’re asking me whether these are a priori possible. The answer is yes. It is apriori possible that God makes a mistake, for instance, since the being playing the God role need not be omniscient. That’s so even if the person in fact playing the God role is essentially omniscient, and necessarily so. Similarly for the rest. So you don’t know that these are apiori impossible. You might think you know apriori that God cannot make a mistake because you think you know apriori that God is omniscient. But you don’t know the latter. Neither does anyone else. At best this is known aposteriori.

    October 18, 2010 — 11:47
  • Joshua Rasmussen

    I propose we define omnipotence this way:
    ‘x is omnipotent’ = ‘x has as much power as is possible for a being to have’.
    We may then either attempt to analyze one’s having power in term of one’s possibly actualizing certain possible states of affairs, or we may simply leave this unanalyzed. I don’t see why we may not leave it unanalyzed.
    Indeed, (inspired by Alex’s dissertation) we might analyze modality in terms of power: ‘x is possible’ = ‘there was a y, such that y had the power to initiate a causal chain that results in x’.
    Interestingly, this account entails that a first cause in the causal order would exist of necessity (as nothing would have had the power to initiate a causal chain leading to the non-existence of the first cause). Also interesting: a first cause would also seem to be among the most powerful possible entities given that at least as many causal chains could result from it as from any causal successor. Thus, given my definition of ‘omnipotent’, it would seem to count as omnipotent.
    So, by seeking to gain a deeper insight into the meaning of ‘omnipotence’, we may have found a reason to think that there really is an omnipotent being. 🙂

    October 18, 2010 — 12:49
  • Mike Almeida

    ‘x is omnipotent’ = ‘x has as much power as is possible for a being to have’.
    Josh,
    It’s going to matter how you understand ‘power’. If you understand power dispositionally, and take dispositions not to be analyzable in terms of possible worlds, then you’ll have the advantage of there being powers that God necessarily fails to exercise. That gives him the power to do all sorts of evil things that are impossible for him to do. This sort of approach goes back to Clarke, but it’s very suspicious looking. Don’t you think?

    October 18, 2010 — 14:18
  • Mike:
    “This sort of approach goes back to Clarke”
    Actually, it goes back at least to Aquinas. 🙂

    October 19, 2010 — 9:02
  • Steve Jeffers

    “You might think you know apriori that God cannot make a mistake because you think you know apriori that God is omniscient. But you don’t know the latter. Neither does anyone else.”
    Following that line of reasoning, wouldn’t that mean God couldn’t know He was omniscient?

    October 19, 2010 — 10:14
  • Joshua Rasmussen

    “If you understand power dispositionally, and take dispositions not to be analyzable in terms of possible worlds, then you’ll have the advantage of there being powers that God necessarily fails to exercise.”
    I’m not sure about this. Are these jointly incompatible?:
    (1) God has as much power as is possible for a being to have.
    (2) Having power isn’t analyzable in terms of possible worlds.
    (3) God has powers that God necessarily fails to exercise.
    I presently fail to see that they are incompatible. But I’m prepared to see something new. 🙂

    October 19, 2010 — 11:57
  • Joshua Rasmussen

    perhaps it’s the “understanding power dispositionally” that makes the difference…

    October 19, 2010 — 12:01
  • Mike Almeida

    Following that line of reasoning, wouldn’t that mean God couldn’t know He was omniscient?
    *sigh*, no.
    “This sort of approach goes back to Clarke”. Actually, it goes back at least to Aquinas. 🙂
    But Aquinas didn’t hold that God has powers that are necessarily unmanifested, or did he?

    October 19, 2010 — 12:25
  • Steve Jeffers

    “But Aquinas didn’t hold that God has powers that are necessarily unmanifested, or did he?”
    cum “Deus omnia posse” dicitur, nihil rectius intelligitur quam quod possit omnia possibilia, et ab hoc omnipotens dicitur.
    Aquinas makes an explicit exception for God: his power extends to what he can do, not to what he does.

    October 19, 2010 — 14:16
  • Mike Almeida

    Josh, you write,
    (1) God has as much power as is possible for a being to have.
    (2) Having power isn’t analyzable in terms of possible worlds.
    (3) God has powers that God necessarily fails to exercise.

    If you do not analyze powers in terms of worlds (you take powers as primitive, say) then you could say (i.e., some have said, Senor here for instance) that (i) God has the power to act immorally and (ii) there is no world in which he does. This makes the distinction between the modality of ‘having a power’ and the modality of ‘possibility’. So, saying it is impossible that (there is no world in which) God acts immorally (on this account) does not entail that God fails to have the power to do so. For my part, I don’t think the view is finally coherent. It is true that powers/dispositions can be ‘finked’, and that is some reason not to analyze them in terms of worlds. But I don’t think it is coherent to speak of a disposition or power that is necessarily finked.

    October 19, 2010 — 16:39
  • Mike Almeida

    Bad link. Try here

    October 19, 2010 — 16:45
  • Joshua Rasmussen

    “If you do not analyze powers in terms of worlds (you take powers as primitive, say) then you could say (i.e., some have said, Senor here for instance) that (i) God has the power to act immorally and (ii) there is no world in which he does.”
    Right. What I’m not sure of, though, is whether one who takes powers as primitive is committed to saying that. I would assume not. It seems one could think that powers are unanalyzable and also that it is an axiom of powers that no one has a power to do something that’s impossible.

    October 20, 2010 — 9:52
  • Joshua Rasmussen

    By analogy, one could agree with Moore that goodness is unanalyzable and still think there are axioms of goodness: e.g., that justice is good.

    October 20, 2010 — 9:55
  • Mike Almeida

    It seems one could think that powers are unanalyzable and also that it is an axiom of powers that no one has a power to do something that’s impossible.
    I don’t know. That’s getting close to an analysis. S has the power to bring about A only if possible A. I assume that, for similar reasons, you’d hold the converse. Possible A only if S has the power to bring about A. But then you would have an analysis. It would be interesting if you denied the converse.

    October 20, 2010 — 11:37
  • eliram

    The Stone Paradox, Sobel rightly recognizes, is no real problem for omnipotence as such, for if a being can do anything that can be done, then that being can take away some of the powers it has, just as I can take away some of the powers that I have. As a result, there is no problem with an omnipotent being creating a stone it can’t lift; it is simply that it must lay aside its omnipotence in the process.

    Sorry, this does not solve the “Stone Paradox”, (or, more properly the Omnipotence Paradox). In the scenario you describe, god has not created a stone he cannot lift; rather, he has created a stone he has chosen not to lift.

    If you do not agree, consider this question: having chosen to “lay aside [his] omnipotence”, can god subsequently restore it, so that he can then lift the stone? If your answer is yes, he can in fact lift the stone, so he has not created a stone he can’t lift. if your answer is no, how can he be called omnipotent if he lacks that power? This is the Omnipotence Paradox, properly understood. Sobel’s approach is just a facile attempt to evade it.

    October 21, 2010 — 0:55
  • Kenny Pearce

    He does not in fact lack the power, but if he created the stone he would lack the power. That’s why it isn’t a problem for omnipotence as such, but is a problem for essential omnipotence.

    October 21, 2010 — 1:06
  • Steve Jeffers

    “He does not in fact lack the power, but if he created the stone he would lack the power.”
    If that held, you’d have answered the question. The question is not about the lifting – no actual lifting need take place – it’s about the creation. If the stone can’t be created, it can’t be lifted. If the stone is created, it can’t be lifted. Your solution requires the answer to be ‘God can’t lift the stone’.

    October 21, 2010 — 11:46
  • Kenny Pearce

    Look: omnipotence has been defined as the power to do anything that can be done. Now, it is logically impossible that anyone should create a stone she can’t lift and still be able to lift it. But there is no problem with somebody being omnipotent NOW and having the power NOW to create a stone he couldn’t lift; it’s just that if he created a stone he couldn’t lift, there would be something he couldn’t do, namely, lift the stone and, as a result, he wouldn’t be omnipotent THEN. That’s why the real problem is a problem with essential omnipotence: if, as is traditionally held, it is impossible for God to cease to be omnipotent, then there is a problem here, because then there would be a certain task, namely, bringing it about that there is a stone that one cannot lift, that I can perform but God can’t. Note (as Sobel does) that I can perform this task in one of two ways: by increasing the weight of the stone, or by decreasing my lifting power. (For instance, I could bring it about that I couldn’t lift a 5 lb. stone by cutting off my arms.) Since an omnipotent being’s lifting power is unlimited, an (inessentially) omnipotent being would be able to perform this task in only one way, by decreasing its lifting power. But if God is essentially omnipotent, then he cannot decrease his lifting power, and this is where the real problem comes in.

    October 21, 2010 — 12:22
  • Steve Jeffers

    “Look … there is no problem with somebody being omnipotent NOW and having the power NOW to create a stone he couldn’t lift; it’s just that if he created a stone he couldn’t lift, there would be something he couldn’t do, namely, lift the stone and, as a result, he wouldn’t be omnipotent THEN.”
    I do understand the original problem, and I really do understand the solution you’re proposing. You’re saying God can have his cake and eat it, because he can NOW have the cake THEN eat it. But so can we all. The trick there is for both to simultaneously be true.
    With the Stone Paradox, an essentially omnipotent God has to actualize a stone and subsequently lift the stone which retains the same properties.
    I have to ask: do you personally find ‘he’s not essentially omnipotent’, ‘he doesn’t create the stone, he has the ability to’ or ‘sure he can, he just has to reduce the weight of the stone afterward’ satisfying answers?

    October 21, 2010 — 13:18
  • Would the following count as creating a stone God can’t lift?
    God promises: “I am about to a create a stone I will never lift.” He then creates a pebble.
    He can’t lift it, as he can’t break his promise.
    It’s a little tricky, because maybe we could release God from his promise. But that could be taken care of. Maybe God also promises that henceforth he will always prevent people from releasing him from promises.

    October 21, 2010 — 14:17
  • Steve Jeffers

    The problem is definitional. If God creates a stone with the specific property of ‘too heavy for even God to lift it’, he would not be able to lift it.
    If he simply creates the heaviest stone he possibly can, he would be able to lift it.
    The paradox being that the first stone can only be *as* heavy as the second, and might be lighter.
    There’s no particular reason why we need bring omnipotence, essential or otherwise, into this. He only needs limitless strength and the ability to conjure up stones of limitless size for this particular test.

    October 21, 2010 — 15:14
  • Mike Almeida

    Now, it is logically impossible that anyone should create a stone she can’t lift and still be able to lift it
    Kenny, I think that’s not quite right.The problem of the stone (or whatever description you’d like to give it) is not difficult to resolve. You just have to keep distinct de re and de dicto modalities. Let S be a stone that has a weight of N contingently. That is S might have weighed less than N. Now, all of the following are consistent.
    1. Necessarily, God does not lift a stone that weighs N.
    2. S weighs N.
    3. S is such that God can lift it.
    4. God can create S.
    So, given (1), (2) and (4), it follows that,
    5. God creates stone S that weighs N & it is impossible that God lifts a stone S that weighs N .
    And given (2), (3) and (4), it follows that,
    6. God creates stone S that weighs N & S is such that, possibly God lifts S.
    (5) expresses the de dicto case: it is impossible that God lifts a stone of weight N. Take that to be the claim that God can create a stone too heavy for him to lift.
    (6) expresses the de re case: S is a stone created by God that weighs N & S is such that possibly, God lifts S. Take that to be the denial that there is a stone such that God created it and it is too heavy for God to lift.
    These are consistent. So God can both create a stone too heavy for him to lift and lift any stone that he creates.

    October 21, 2010 — 16:31
  • Kenny Pearce

    Steve – Reread the beginning of the post. The point is precisely the one you are making: the Stone Paradox as applied to an inessentially omnipotent being, is not a very difficult or interesting problem. However, there ARE problems like this for the traditional God. Isn’t that what you are saying also?
    Mike – Everything you’ve said is true, but I don’t think it solves the problem. There are two distinct problems in your approach. The first is that (1) is necessarily false for all values of N. The second is that there is a danger of equivocation on ‘can’. We need the claim that God is able to lift the stone, not the claim that it is possible that God lifts the stone. Now, in the special case of God, these might be equivalent. I think, though, that we’ll still end up with something like, if God had made the stone lighter he would have been able to lift it. This doesn’t get the result that he is able to lift it now (after he made it weigh N).

    October 21, 2010 — 20:26
  • Mike Almeida

    The first is that (1) is necessarily false for all values of N.
    This is confused, or at least confusing. Look, we want to concede to the atheologian that God can create a stone too heavy for him to lift. If you reject that claim, you lose. The atheologian rightly concludes that God is not omnipotent. So I am conceding (1). You seem to think that I’ve given up on omnipotence in conceding (1). I haven’t. If (1) is not true, God is not omnipotent. So concede that, given his omnipoence, God can create a stone too heavy for him to lift. That’s more precisely stated in (5).
    5. God creates stone S that weighs N & it is impossible that God lifts a stone S that weighs N.
    But then you say,
    The second is that there is a danger of equivocation on ‘can’. We need the claim that God is able to lift the stone, not the claim that it is possible that God lifts the stone.
    ‘Can’ (or ablity, or power or capacity or potentiality etc.) what Lewis rightly calls ‘our many words for much the same thing’ are ALL equivocal. The very way to avoid contradiction is to spell out the difference in this case between de re possibility and de dicto impossibility. In conceding (1) we have not given up God’s omnipotence, since we have not conceded that there is any stone in any possible world that God cannot lift. Indeed, God can lift any stone in any possible world. This is stated more precisely in (6).
    6. God creates stone S that weighs N & S is such that possibly, God lifts S.
    You seem worried about the stone S that God created and that weighs N. It is true that God created S and it is true that S weighs N and it is true that (from 5) it is impossible that God lifts a stone S that weighs N. But don’t try to infer from that that God cannot lift stone S. That’s a bad inference. What follows is that God does not lift stone S. God does not lift any stone that weighs N. Nonetheless God can lift S. That’s how to resolve the problem without remainder and without biting any bullets.

    October 22, 2010 — 9:24
  • Mike Almeida

    Everything you’ve said is true, but I don’t think it solves the problem. There are two distinct problems in your approach. The first is that (1) is necessarily false for all values of N.
    Kenny,
    I actually don’t follow this part of your comment. The first problem you note is not consistent with your first sentence, as far as I can see. In any case I’ve shown you that God can lift every possible stone in every possible world. There are literally no stones in any world that God cannot lift, unless some stone has weight N essentially. But no stone has it’s weight essentially, since every stone is possibly weightless. So that’s no worry.

    October 22, 2010 — 12:21
  • eliram

    It seems to me that the Omnipotence Paradox is not being fully understood on this blog. Forget lifting stones, that is beside the point. God’s supposed omnipotence, “essential” or not, requires contradictory powers (or perhaps I should say, “the power to do contradictory things”). The question is, what would happen if these powers were to collide? For example, what happens when god’s unlimited power to protect and preserve an object collides with his unlimited power to annihilate that same object? Since no possible answer can be consistent with omnipotence, we must conclude that omnipotence is self-contradictory and impossible. Talking about god deliberately restricting his own power will not save you here.

    October 22, 2010 — 13:53
  • Kenny Pearce

    eliram – Almost every theologian in the tradition of western monotheism has agreed that God does not have the power to bring it about that there are true contradictions. This is simply not what is meant by omnipotence. Now, surely omnipotence does require that God has two powers, x and y, such that if God exercises x he cannot exercise y, but this is really not a problem for omnipotence either, since it is really reducible to bringing it about that there are true contradictions, which is not an ability that has typically been ascribed to God under the attribute of omnipotence.
    We might say, naively, that being omnipotent means having the power to do anything. But there is no such thing as making 2+2=5.

    October 22, 2010 — 14:12
  • Mike Almeida

    Since no possible answer can be consistent with omnipotence, we must conclude that omnipotence is self-contradictory and impossible.
    eliram,
    This is just question begging. The very problem is to show that apparently inconsistent abilities are genuinely compossible. If it cannot be shown, then they are inconsistent. But I’ve offered you one way (there are others, of course) in which they’re only apparently inconsistent. The appearence of inconsistency is a result of being inattentive to the consistency of p’s being de re possible and and p’s being de dicto impossible.

    October 22, 2010 — 17:58
  • eliram

    Kenny and Mike,

    Perhaps you could tell me then, what would happen were god to pit his powers against each other? Or, what would happen were god to create a second omnipotent being, then pit his powers against the second being’s powers?

    October 22, 2010 — 19:23
  • Kenny Pearce

    In precisely the same way as there is no such action as making 2+2=5, there is also no such action as bringing it about that there is a conflict of omnipotent wills. So even on a relatively naive view of omnipotence, on which it means ‘being able to do anything’, this is not a problem. (‘Anything’ includes all the actions there are.) However, on a naive view like this, the Stone Paradox is, at least prima facie, a problem, because there is such an action as making a stone too heavy for one to lift, and it is an action some creatures can perform.

    October 22, 2010 — 21:29
  • Kenny Pearce

    My intuition is yes, but this is open to dispute. See Sydney Shoemaker, “Causality and Properties” in Peter van Inwagen, ed., Time and Cause. Shoemaker argues that the properties and laws of our world are so intertwined that a world with different laws would be a world in which none of the same properties were instantiated, so it is a necessary truth about the property mass that E=mc^2.

    October 23, 2010 — 15:04
  • Steve Jeffers

    “it is a necessary truth about the property mass that E=mc^2”
    Could God break the law of conservation of energy? A universe where conservation of energy didn’t hold would certainly qualify as one with ‘different laws’.
    A universe where the law held would place pretty profound constraints on any God.

    October 23, 2010 — 16:21
  • Kenny Pearce

    Yes, but God freely chose to create this kind of universe.
    Also, even if the laws are necessary, some people would deny that that prevents God from breaking them. Many theories of laws allow that there is a difference between a world where a law is broken and a world with different laws.

    October 23, 2010 — 16:27
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    October 26, 2010 — 13:09
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    October 26, 2010 — 13:21