# On Omnipotence

In my last post, I discussed Sobel's proposal that, since the Stone Paradox shows essential omnipotence to be incoherent, the traditional God, since he would have his properties essentially, would have essential ONSLIP, or only necessarily self-limited power, but that this would not amount to omnipotence. Here I want to propose an alternative account of omnipotence, an attribute worthy of that name and which would be had essentially. First, however, we must distinguish power from freedom. To be omnipotent is to be all powerful. God is also supposed to be free in his exercise of power, and this creates a number of problems, some of which were discussed on my personal blog at the beginning of this series. I take it that the relevant type of power, the kind that agents have, is simply the ability to do what one wants, or to bring about one's ends, whereas freedom is something more complicated. This immediately suggests the following definition of omnipotence:

S is omnipotent =df. necessarily, for any proposition p, if S wills that p, then p.

To prevent any ambiguities, here it is in symbols:
S is omnipotent =df. □∀p[(p is a proposition & S wills that p) -> p]

So an omnipotent being's will would always be fulfilled as a matter of logical necessity. Now that's power! Furthermore, omnipotence, being a modal property, entails essential omnipotence.

Here are some interesting features/consequences of this definition:

1. The definition follows Alexander Pruss's suggestion on the earlier post that omnipotence be construed as having to do with the range of states of affairs God can bring about.

2. If the value of S substituted into the sentence (e.g. 'God') is a rigid designator, and the necessity is interpreted as being of the 'broadly logical' type, then omnipotence, being a modal property, entails essential omnipotence.

3. The conditional in the definition is intended to be a material conditional. As a result, if there are any necessarily false propositions (and there are), then the definition entails, by the Distribution Axiom of modal logic, that, necessarily, those propositions are not willed by an omnipotent being. That is, □~(2+2=5) and God's omnipotence (as defined) jointly entail □~(God wills that 2+2=5).

4. The definition entails that an omnipotent being's higher-order volitions (if any) are satisfied, which is thought by some (e.g. Frankfurt) to be important for freedom. That is, if God wills to will what is good, then (necessarily) he wills what is good.

But you might be worried about something (at least if you are not a Humean about causation and/or abilities): what if S wills only things that come about because S's will is conformed to reality, rather than reality being conformed to S's will? It is not clear that this is coherent: some philosophers think that the difference between belief and propositional desire/volition is the 'direction of fit' - that is, we try to conform our beliefs to the world, but we try to conform the world to our desires. If a being's (so-called) 'desires' were actually conformed to the world, rather than vice versa, they might turn out not to be desires at all, but rather beliefs. But in case this response doesn't work, we can easily modify the formula:

S is omnipotent =df. necessarily, for any proposition p, if S wills that p, then p because S wills it

Now, cashing out the 'because' might be tough, but if we are non-Humean enough to care about the problem, then presumably we are non-Humean enough to think that some sense can be given to 'because' here.

I cannot see that omnipotence, defined this way, generates any paradoxes by itself. Certainly it is unaffected by Sobel's objections. It may, however, have complicated interactions with other divine attributes, especially freedom (there are things that God can't will). The current definition looks like it plays nice with compatibilism, but it is not so clear that it plays nice with libertarianism.

[cross-posted at blog.kennypearce.net.]

S is omnipotent =df. necessarily, for any proposition p, if S wills that p, then p

I can't see much chance of this being right. Let p be the proposition 'God does not will this proposition'. There are such propositions and they are true, but necessarily, God wills them only if they are false. So, God wills such a proposition p only if ~p. More generally, since such propositions exist in every world and relative to every agent, it follows that, necessarily, nothing is omnipotent.

K,

Something important is missing. Things that don't will at all turn out to be trivially omnipotent according to your definition:

S is omnipotent =df. necessarily, for any proposition p, if S wills that p, then p because S wills it.

A few other things.

First, depending on your interpretation of 'because', the definition may rule out the existence of multiple omnipotent beings.

Second, consider "I freely ate ice cream" and suppose God willed it. I say this proposition is only partly true because God willed it, but also partly true because I did. Thus, the 'because' must select some sort of *partial* explanatory relation.

Third, are we supposed to be reading the definition above as saying "necessarily, for any proposition p, if S wills that p *is true*, then p *is true* because S wills *that p is true*? If not, it's hard to read. If so, what do we say about falsehoods? Are false propositions false because God wills that it is true that they are false, or because God fails to will that they are true, or something else?

Finally, unless I'm confused about scope, a being that essentially can only will that it is true that they scratch their ear, and also, scratches their ear because they will it to be true that they scratch their ear, counts as omnipotent on this definition. But that can't be right, I don't think.

What do you think?

Kenny:

Very interesting take on omnipotence. A couple of thoughts (for your dismantling):

First, you seem to grant Sobel's argument that the Stone Paradox demonstrates that essential omnipotence is incoherent, and thus account for Sobel's move from a definition of omnipotence as the ability to do that which is absolutely (or logically) possible to omnipotence as ONSLIP. But, is it true that our first definition of omnipotence doesn't account for the Stone Paradox?

Take the state of affairs of there being a stone that God cannot lift: is this state of affairs absolutely possible? We can represent this state of affairs in logical notation as (∃x)(Sx · ¬Lx); where Sx stands for “x is a stone” and ¬Lx designates “x is such that God cannot lift it.” If our definition of omnipotence is the ability to do everything that is absolutely possible, then any utterance of the form “God cannot z” entails that z is absolutely impossible. As such, ¬Lx entails that x is absolutely impossible. (No doubt I am here, perhaps problematically, ignoring Morris's discussion of the ambiguity inherent in can or cannot-locutions).

Therefore, God’s inability to create a stone that he himself cannot lift is not problematic, precisely because the state of affairs of there being a stone that God cannot lift is logically or absolutely impossible. If we adopt the state of affairs approach of Flint and Freddoso - here mentioned by Pruss and yourself - then the state of affairs of God performing an evil deed or God making a table that God did not make (and so on) could be dismissed for similar reasons (presupposing some additional amendments).

S is omnipotent =df. necessarily, for any proposition p, if S wills that p, then p because S wills it

Would this be inconsistent with counterfactuals of freedom? (Assuming here that such counterfactuals possess a truth-value).

Volitional Excluded Middle (VEM): S has VEM =df. ∀p(S wills p v S wills ~p)

I'm pretty sure God does not satisfy VEM, since there are propositions p describing the free actions of moral agents such that God does not will p and does not will ~p. Let me note two other problems. One is that there are propositions that God wills and that are not true. Presumably God wills that each person honors his father and mother, since he commands that we do so. But clearly the proposition is not true. Maybe you can command things that you don't will?? The larger problem is that your analysis of omnipotence makes the humble amoeba omnipotent. Since amoebas do not will anything in any world in which they exist, it is true for all propositions p, in all worlds in which they exist, that Amoeba wills p only if p. Of course, you might adopt identity conditions for amoebas that make it possible for one to will something false in some distant world. In that case, take a grain of salt or my left ear or my gas cap or whatnot, which will nothing in any world in which they exist. Or take the number 7. They too turn out to be omnipotent. But that certainly can't be right.

Kenny:

Thanks for the response. You write:

I take it that the problem with the first definition of omnipotence, which makes the Stone Paradox genuinely problematic, is that it says that God can do everything that can be done. As Alexander Pruss pointed out right away, this definition dealt in actions (or rather action-types), rather than in propositions or states of affairs. Now, it is true that there is no such action-type as making a stone God cannot lift, but there is an action-type making a stone one cannot lift, and I can perform this action.

Take the action-type you mention: the act of making a stone one cannot lift. You are correct in supposing that our original definition of omnipotence (vis-à-vis absolute possibility) cannot address this (as stated), but I am not sure this is because our original definition can only function in terms of action-types. Instead, I want to suggest that the state of affairs of making a stone one cannot lift is problematic due to its engendering intensional difficulties (indeed, your own account may in fact face these difficulties).

For instance, suppose that p denotes the proposition "God creates a stone that cannot be lifted by the last being Norman Mailer thinks about." Intensionally, p does not express a logical contradiction, but, assuming that the last being Norman Mailer thinks about is God, then it would entail an absolutely impossible state of affairs. It seems to me that the same sort of thing is occurring in the case of making a stone that one cannot lift.

But, we can avoid this problem by simply limiting our definition of omnipotence - (including yours) - to the actualization of states of affairs that are extensionally consistent. As such, I do not think the state of affairs of making a stone one cannot lift provides any particular difficulty for our original definition of omnipotence vis-à-vis absolute possibility (assuming of course that our definition makes the move from action-types to the actualization of states of affairs).

Also, what precisely does it mean to will the truth of a proposition? Is this not just one way of expressing S's free decision to actualize a particular state of affairs? If so, it seems that your definition of omnipotence might reduce to the one I am defending (but that would be an unhappy consequence for you...). :-)

KP,

"If my theory had the result that there could not be more than one omnipotent being I wouldn't think that would be a problem."

Well, suppose the Doctrine of the Trinity is coherent. Suppose also that x is a different person from y only if x and y have different wills. Thus, suppose that the Father, Son, and Holy Spirit have different wills, even though there is one God.

Presumably, we want to say each is omnipotent since each is God. So, it looks like we want a theory of omnipotence that allows for three distinct omnipotent persons that may very well will together in perfect harmony. But, your account prohibits this unless you allow that each person of the triune God could will that p, and so, each could make make p true, whereas it is also the case that p is true in virtue of their *jointly* willing that p is true. Now, I think you can avoid this worry if you allow that the fact that p is true, when each person of the Godhead wills that p is true, is only partly explained by each of their willings, but *fully* explained by their willing together. Another reason to have 'because' in your formulation to express a partial explanatory relation. You should chat with Shieva about this kind of issue, if you're interested.

"In part of this, I think you are having the same problem as Mike, namely, trying to read an if and only if. I don't say that necessarily whatever is true is willed by God, but only that necessarily whatever God wills is true."

"It might be enough if omnipotence grounds counterpossibles - e.g. if it were (non-vacuously) true that if (per impossibile) God DID will that 2+2=5, then 2+2 would =5."

I'm not sure I understand this alternative or how it might help with the ear-scratcher (not my example). The worry is that an omnipotent being must be able to do all sorts of thing. Thus, even if a being can make things true just by virtue of willing them, and even if these things he wills to be true are, in some sense, grounded by the very fact that he has willed them, this is insufficient for omnipotence. You have to add that an omnipotent being's will is (in some hard to pin down sense) unrestricted. I think this is crucial. But, like you, I don't really know how to spell out the relevant sense in which an omnipotent being's will is unrestricted.

Kenny:

This is an elegantly simple account.

I agree with Christian that there is a problem with beings whose will is constrained. And I don't think it's a problem just about freedom. It's also a problem about power.

Intuitively: if x is omnipotent and y is not omnipotent, then x is more powerful than y.

Suppose x essentially can only will to scratch his ear, and suppose that necessarily x always succeeds at scratching his ear.

Let y be Barak Obama. Then y is more powerful than x. Anything x can do, y can do (e.g., y can order secret agents to kidnap x and bring it about by electroshocks that x scratches his ear), but there is a lot that y can do that x can't do. It's not just that y's will is freer than x's. y is just plain more powerful. But x by the definition is omnipotent, while y isn't.

The being that can do nothing but scratch its ear surely is not as powerful as the world's greatest weightlifter.

One difficulty is with beings whose will is highly constrained. An example Richard Gale gives adapts to this case. Suppose Sam has the essential property that the only thing he can will is to whistle Yankee Doodle, and suppose that Sam is essentially efficacious in this regard: necessarily, Sam whistles Yankee Doodle whenever he wills it. Then, necessarily, if Sam wills p, then p is true (and p is true because Sam wills it). But it doesn't seem that Sam is omnipotent.

Aquinas has a similar idea, but he has a subjunctive conditional instead of a material one, and that may work a little better, at the cost of some obscurity.

It seems to me that what you've defined is God's essential efficacy of will, which is, I think, distinct from omnipotence (maybe it's entailed by omnipotence).

Alexander:

Originally, I shared your hesitations about Mr. McEar (assuming of course that I am reading you correctly); but doesn't Kenny's introduction of the universal quantifier avoid this difficulty? Mr. McEar or Sam are omnipotent under the following definition of omnipotence (à la Plantinga):

x is omnipotent if and only if x is capable of performing any action A such that the proposition x performs A is logically possible.

But doesn't Kenny's definition say something rather different? Namely, that for all p, if S wills that p, then p? That is to say, for any possible logically consistent proposition p, S's being omnipotent is such that, should S will p, then p.

Granted, Sam can only perform the action described by the proposition Sam whistles Yankee Doodle, but Sam cannot (given the constraints enumerated) perform the action described by the proposition Sam whistles Dixie. But, then again, Sam doesn't will to sing Dixie, and so perhaps your right to say that Sam is omnipotent under the present definition.

What of the following amendment:

S is omnipotent =df. □∀p[p is a proposition -> (S wills that p -> p)]

In the course of this reply, when from disagreeing with you to agreeing with you. Thoughts about the amendment?

Kenny:

I really like the idea of separating efficacy from freedom. So:

Definition. x is omnipotent iff x has a perfectly efficacious will and x is perfectly free.

Now we have two separate tasks: figure out what it is to have a perfectly efficacious will, and figure out what it is to be perfectly free. These are separate tasks (though they may be related) and so we've made progress. We have a definition of omnipotence!

Moreover, we get a bit more precision with regard to problems like that God can't do evil. God's inability to do evil doesn't seem to be a problem for his perfect efficacy of will. So it seems plausible that it's only going to be a problem for omnipotence if it's a problem for perfect freedom. But now we see that the question about God's inability to do evil isn't a question about omnipotence as such, but about freedom, and I think this will help us make progress. If, for instance, we find plausible the Augustinian line that the ability to do evil is not a part of the best kind of freedom, we have a complete answer to the problem that the inability to do evil poses for omnipotence. Or maybe we like some other solution, like that freedom is about genuine self-origination of action, and in a being that is simple and a se perfect freedom does not require the possibility of doing evil. Whatever we say about this, it is important that we're talking about perfect freedom not about omnipotence.

It seems to me that Aquinas/Pearce line about the nature of perfect efficacy is pretty good. I don't want to say it's a definition--I am allergic to definitions using counterfactuals--but it's a plausible necessary and sufficient condition.

That still leaves the question of what perfect freedom is. But it's almost universally acknowledged that the nature of human freedom is an extremely hard problem. It is asking for too much from the person proposing an account of omnipotence to give an account of freedom or perfect freedom.

This would make a nice, snappy paper.

Alex wrote:

"This would make a nice, snappy paper."

I second this. It's a more informative account of omnipotence than I've run across. Perhaps it would be good to look up papers on 'can' and conditional accounts of it from the free will literature.

Also, it has already been noted that we shouldn't count anything as omnipotent which satisfies the definition vacuously.

That's a sort of cheap way to avoid counterexample, wouldn't you say? What you've got to do is modify the analysis to avoid this problem in a way that is principled and motivated. Simply saying "that doesn't count" is not exactly how it's played.

1. S is omnipotent =df. necessarily, for any proposition p , if S can will p & S wills that p, then p.

(1) can't be true either, since it is vacuously satisfied. Maybe (2)?

2. S is omnipotent =df. necessarily, for any proposition p, such that S can will p, if S wills that p, then p.

(2) also can be vacuously satisfied. Gotta run, let me think about other possibilities.

in order to be omnipotent, a being must both satisfy the definition I originally gave AND have a perfectly free will.

But we're not any clearer on perfect freedom than we are on omnipotence, are we? Anyway, you're suggesting something like this, I think.

O. (Vx){x is omnipotent iff. [necessarily, x wills p only if p] & [necessarily, x is perfectly free]}.

Aside from vacuous satisfaction worries (which your second conjunct on the right mitigates), don't you have worries about possible beings that do not will much? What about the possibility that S does not will much in any world in which S exists, everything he does will in each world is true, and S satisfies perfect freedom. That is, imagine it is true that the greatest possible being is not that great. He wills a few things in every world in which he exists and he is perfectly free (maybe that means that he always will's what is best or good or whatnot). We would not count such a being as omnipotent, would we? But he turns out to be so on this analysis.

What's causing problems is the conditional in the first conjunct, right side. It is satisfied not only by things that cannot will anything, but also by beings that do not will much in any world.

I don't know, why would we think that someone who necessarily can't speak a falsehood is perfectly free? Why would we think that somenone who necessarily can't break a promise is perfectly free?

To avoid these obvious counterexamples, Alex effectively 'moralized' perfect freedom. Perfect freedom is the best kind of freedom, it is not the most extensive sort of freedom. If the dialectical move is to make perfect freedom a qualitative notion in order to avoid counterexamples arising from obvious limitations in the extent of God's freedom, then you cannot now complain that my counterexamples display a being whose freedom is not sufficiently extensive to count as perfect freedom. If it's the extent of freedom that matters, then we have obvious counterexamples from God's inability to do the vast swath of actions that morally perfect beings cannot perform. If the quality of the freedom is what matters rather than the quantity, then we have the problem of beings who perform all and only actions of the right quality, but not a great quantity of them. Either way, we have a counterexample.

I would say that an ability to act badly is not a restriction on one's freedom when one is an uncaused simple being. If we were unable to act badly, that would be a restriction on our freedom as we are caused beings.

Another option is this. Being fully impressed by all the relevant reasons makes it impossible to act badly. But perfect freedom requires being not only aware of but fully impressed by all the relevant reasons. Hence only beings that are not fully impressed by all the relevant reasons can act badly.

And here is a third option. A necessary, but not sufficient, condition for perfect freedom is that one's decision-making be perfectly conformed to one's higher order desires and that one's higher order desires be properly informed by what is actually valuable. But any being whose higher order desires are thus informed will desire never to make the wrong decisions, and hence any perfectly free being will make decisions in a way that is perfectly conformed to the restriction that one not make wrong decisions.

And one last remark (for now). The division of omnipotence into perfect efficacy and perfect freedom is helpful in the following way, even if analyzing perfect freedom is hard. Theism is, I think, committed to the claims that perfect efficacy and perfect freedom are divine attributes. Moreover, it is very plausible that omnipotence is entailed by and entails the conjunction of perfect efficacy and perfect freedom.

And progress is made when one sees that what previously one saw as problem cases for omnipotence are problem cases for omnipotence precisely because they are problem cases for perfect freedom. Even if some competing account could show how these cases can be overcome by some clever alternative account of omnipotence, nonetheless they would still be problem cases for perfect freedom, and perfect freedom is surely an attribute of God. Directly addressing the cases as probelms for perfect freedom is intellectually more economical.

I dont even know what omnipotence is. You have to define what you are saying and the meaning of the words you are using.

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