An account of omnipotence
February 15, 2008 — 9:54

Author: Alexander Pruss  Category: Concept of God Existence of God Free Will  Tags: ,   Comments: 43

Here is a simple proposal:
A being x is omnipotent provided that in every possible world, x’s free choices are collectively the ultimate explainers of the rest of contingent reality.
In particular, only a necessary being can be omnipotent. Whether omnipotence is compatible with created free will depends on how exactly we spell out “ultimate explainers”. We might think that if y in situation S freely chooses to A, and God creates y in S, and y freely chooses to A, then God’s creation is an ultimate explainer (it may or may not be the case that an ultimate explainer of a proposition is an explainer of the proposition).
This definition is incompatible with Molinisms on which God is not an ultimate explainer of conditionals of free will.
If the above account is right, we have a sound ontological argument along the lines of the standard S5 ontological argument:

  1. Possibly, there is an omnipotent being.
  2. Therefore, there is an omnipotent being.
Comments:
  • A being x is omnipotent provided that in every possible world, x’s free choices are collectively the ultimate explainers of the rest of contingent reality.
    I think that’s pretty neat, especially in light of Sobel’s paper, but it might be question-begging. I am assuming that by an omnipotent being you have in mind God. Suppose there is no world in which God makes a false promise. On your analysis, this is simply no limitation on omnipotence, since his free choices might still explain the rest of contingent reality. But we need some explanation. I say that if the utterance U is the making of a false promise, then God can utter U. But were he to utter U, it would not be a false promise. You say flatly that if uttering U is not something God does in any world, that is no obstacle to his being omnipotent. Doesn’t that beg an important question?

    February 15, 2008 — 10:46
  • Christian

    Alex,
    Couldn’t an omnipotent being exist in a world of brute facts? I can’t, off the top of my head, see why not.

    February 15, 2008 — 14:38
  • Couldn’t an omnipotent being exist in a world of brute facts?
    Take a world in which God creates nothing. There are no contingent objects. There are just contingent facts, necessary truths and necessary objects. Even that would not be a world of brute fact. There would be an explanation for every contingent fact. The fact that there are no trees, for instance, would be explained by the fact that God did not create any, even if God’s not creating any was itself a brute fact.

    February 15, 2008 — 15:02
  • Christian

    The idea is to consider a world w where there is, for example, some simple object s. Suppose that s pops into and out of existence, but that there is no explanation of the fact that s pops into existence at t, for some time time t. I want to call that fact a brute fact about a contingent thing. It’s brute since there is no explanation for it. There’s just no true answer to the question: Why did s pop into existence at t?
    The simple proposal says that contingent reality is ultimately explained by the omnipotent being’s free acts. But the contingent reality in w is not explained by free acts since it includes a part that is simply unexplained. I think that a definition of omnipotence should allow for a world like w, but where there could also be an omnipotent being in w.

    February 15, 2008 — 15:29
  • Why oh why would any theist want to say this? It sets up:
    1. Possibly, there is no God
    2. Therefore, there is no God

    February 15, 2008 — 15:49
  • Enigman

    Hi Christian; you say: Why did s pop into existence at t? Because God would have allowed it to? Would God allow stuff to happen without His say-so, if He could help it? That would be irresponsible; and if He could not help it then He would not be very Omnipotent. Still, I think that a being worthy of the title “omnipotent” might be what you have in mind (e.g. if she created this universe, and all contingencies within it).

    February 15, 2008 — 16:05
  • But the contingent reality in w is not explained by free acts since it includes a part that is simply unexplained.
    No, there is an explanation for that, even if it is not governed by some probablistic laws. It is coming into and out of existence at least partly because God is not preventing it from doing so, and since it is contingent, God created it.
    I think that a definition of omnipotence should allow for a world like w, but where there could also be an omnipotent being in w.
    I have no idea how that follows from the concept of omnipotence. The only thing I can think of is the suggestion (in Sobel and others) that an omnipotent should be able to make himself nonomnipotent, and so unable to determine every contingent fact (that is strongly actualizable).

    February 15, 2008 — 16:20
  • Christian

    It is coming into and out of existence at least partly because God is not preventing it from doing so, and since it is contingent, God created it.
    and,
    Because God would have allowed it to?
    Okay, I see where you two are going. If I’m right, you’re denying that the simple’s popping into existence is a brute fact as God’s allowing it explains it. And if it has an explanation, then it is not brute.
    I can’t see how this is a strong objection. I’m suggesting this is possible, for there to be brute facts. You are denying it by appealing to facts about God. My modus ponens seems to be your modus tollens’s.
    Here is an independent argument for my view. Explanation is causal. “Allowings” cannot be causes. So God’s allowings are not explanations. Thus, God’s allowing the simple to pop into existence does not explain the fact that it does.
    I have no idea how that follows from the concept of omnipotence.
    It’s not supposed to. I didn’t mean for it to. It’s an intuition aimed to place a constraint on any satisfactory account of omnipotence. The idea would be then to push for a modification of the simple proposal, something in the neighborhood of:
    SP* A being x is omnipotent provided that in every possible world, x’s free choices are collectively the ultimate explainers of the rest of the features of contingent reality that have explanations.

    February 15, 2008 — 16:53
  • Mike Almeida

    I can’t see how this is a strong objection. I’m suggesting this is possible, for there to be brute facts. You are denying it by appealing to facts about God. My modus ponens seems to be your modus tollens’s.
    By hypothesis, Alex is denying that explanation is in general causal. But that aside, you’d certainly explain the fact the child drowned by appeal to the fact that the lifeguard ignored him. In any case, I would.
    But then I say,
    I have no idea how that follows from the concept of omnipotence
    And you reply,
    It’s not supposed to. I didn’t mean for it to
    How is that? Didn’t you say that it should follow by the definition of an omnipotent being that there is such a world? If it follows definitionally, then it follows conceptually. That’s why I mentioned the concept of omnipotence.
    I think that a definition of omnipotence should allow for a world like w, but where there could also be an omnipotent being in w.

    February 15, 2008 — 17:39
  • Christian

    I didn’t realize that Alex was denying explanation is grounded in, or reducible to causal explanations. My argument won’t work on that hypothesis. And the lifeguard case, I think, can be explained away. The water in the lungs causes the death, the lifeguard is responsible in the sense that he allowed the causal relation to obtain…something like that.
    About the definitional bit. What I mean is that the instantiation of “being possibly coinstantiated in a world with brute facts” should be consistent with the existence of an omnipotent being. I don’t think “being possibly coinstantiated in a world with brute facts” is part of the definition of omnipotence, though. It is a necessary condition, but not an analytically necessary condition (if one believes in such things anyway).

    February 15, 2008 — 21:16
  • Alexander Pruss

    It is false that all explanation is reducible to causal explanation. There are also constitutive explanations (the knife is hot because its molecules have high kinetic energy). I do think ultimate explanations of contingent facts are causal.
    I don’t know that I need to revise my claim–I’ve argued elsewhere (my PSR book) that there are no contingent brute facts. But if I had to revise it, I’d say that what I’ve given is a sufficient condition for omnipotence.

    February 15, 2008 — 21:20
  • Chris:
    The fact that (1) is true and that (2) follows from (1) seems a sufficiently good reason for a theist to say it. 🙂
    I also think that while modal intuitions are fallible, we can be surer about positive possibilities than negative ones.
    Consider the claim that possibly there are no horses. To imagine a situation where there are no horses requires one to imagine a whole universe, qua whole, with no horse here, no horse back there, no horse over there, etc. On the other hand, it’s a lot easier to imagine a universe with a unicorn (defined stipulatively as a horse-like mammal with one horn). So we can be somewhat more confident about the possibility of a unicorn than about the possibility of there not being horses.

    February 15, 2008 — 21:27
  • Christian

    Alex,
    I agree there are these other kinds of explanation. And I can see how denying the existence of contingent brute facts avoids the worry.
    I’m going to pick some more (since I like your view and picking is a sign of affection).
    Suppose determinism. God performs one free act of creation. All at once, he creates the laws and matters of particular fact, and these jointly entail whatever comes afterwards. I take it this free act would count as an ultimate explainer, right? Now suppose God is unable to interfere with the laws, unable to really do anything else (he’s too exhausted). In such a world I would think he is not omnipotent though his free act is the ultimate explainer of all contingent reality. So the simple proposal cannot state a sufficient condition for omnipotence.

    February 15, 2008 — 22:16
  • And the lifeguard case, I think, can be explained away. The water in the lungs causes the death, the lifeguard is responsible in the sense that he allowed the causal relation to obtain…
    Right, this sort of thing is always possible. But it doesn’t show much. I could as well say, well, it wasn’t really the water in the lungs that caused the death, it was rather that he was mammalian and lacked he ability to extract oxygen from water that explains his death. And you could say, it wasn’t really the fact that he was mammalian and could not extract oxygen from water that explains his death. It was rather the gravitational force of the moon, without which the tide would not have been high enough for him to have water in his lungs to begin with. And I could say that it wasn’t the gravitational force of the moon on the tides that explains why he drowned, it was his failure to take hormone injections as a child which explains why he drowned. Had he taken them, he would have been tall enough not to swallowed so much water. And so and so on … The fact that there are alternative explanations doesn’t show any particular one is incorrect.

    February 16, 2008 — 8:30
  • Christian,
    I don’t see why God isn’t omnipotent in that world. Sure, he can’t intervene with the laws. But that’s because the laws are (ex hypothesi) such that it is metaphysically impossible for them to be interfered with.
    (Besides, I think God is outside of time, so I am not sure it makes sense to me to think of several exercises of causal power on his part.)

    February 16, 2008 — 14:05
  • Enigman

    Alex, I’m not sure it makes sense to think of one choice on the part of a being outside of time (if a choice is a plumping for one option from amongst several, the several being live options before the choosing, and not afterwards), but if it does then why not several exercises of causal power? Were they all made timelessly it would not do to think of them being made either at the same time (together) or at different times (although I don’t have the foggiest how to think of them positively).
    Also, you say that your argument is sound, and later you reminded Chris of the fact that the following is true:
    1) Possibly there is a being (God) such that in every possible world, its (His) free choices are collectively the ultimate explainers of the rest of contingent reality.
    But for your argument to be valid, God must exist in every possible world (if I understand your argument, a pretty big “if”). And if God is timeless then he does not exist in time.
    But it is (prima facie) possible for a world to be no more than a universe, of space-time and its contents. And that is a positive possibility (although I’m unconvinced of the force of that distinction, since intuitively it is easier to imagine a world of no horses, e.g. this world with a slightly different prehistory, than a world containing a unicorn, which is a fictional kind of being). E.g. were such a world not prima facie possible we would not need to consider arguments such as yours; i.e. the very fact of your argument existing indicates the positive possibility of a world incompatible with (1). And of course, such a world is much easier to conceive of, than the being mentioned in (1).

    February 16, 2008 — 16:40
  • Enigman

    Er… maybe that was confused; basically, my problem with your argument is that I can’t quite see how it differs sufficiently in kind from the following, invalid argument, in which G is any arithmetical statement that has yet to be refuted or proved (e.g. G could be Goldbach’s conjecture). (I assume that mathematical truths are true in all possible worlds.)
    1. Possibly, G is true.
    2. Therefore, G is true.

    February 16, 2008 — 17:20
  • I can’t quite see how it differs sufficiently in kind from the following, invalid argument, in which G is any arithmetical statement that has yet to be refuted or proved (e.g. G could be Goldbach’s conjecture). (I assume that mathematical truths are true in all possible worlds.)
    1. Possibly, G is true.
    2. Therefore, G is true.

    That argument is not invalid. It’s clearly valid. Though it might be invalid for epistemic possibility (depending on how one understands that operator).

    February 16, 2008 — 17:32
  • Enigman

    Thanks Mike, but that was why I stated at the start that my argument was invalid. G is possibly true because G might be true for all we know, but that’s the wrong sort of possibility for my argument to be valid. As an invalid argument, there is equivocation, although both 1 and 2 seem to be individually justifiable.
    Conversely I could have given a valid but unsound argument, and then tried to hide the unsoundness behind waffle that tried to lead the reader towards making her own equivocations privately. But as God-fearing philosophers we don’t have anything to do with such things, surely.

    February 17, 2008 — 9:46
  • … but that was why I stated at the start that my argument was invalid. G is possibly true because G might be true for all we know, but that’s the wrong sort of possibility for my argument to be valid.
    Not so fast. If G might be true, for all we know, then the argument is still valid. G might be true, for all we know, only if G is consistent with everything we know. Here’s one thing I know: the sky is blue. But if G is consistent with the sky being blue, then G is true.

    February 17, 2008 — 12:04
  • Enigman

    Well, that’s why I think that it would be very helpful if philosophers were always very clear about the sorts of possibilities they were talking about, especially with respect to the epistemic vs. metaphysical distinction. E.g. if G is Goldbach’s conjecture, then given all that we know, as a civilisation (which is admittedly a fuzzy concept), G could be true and G could be false (at the present time, as far as I’m aware). There is an epistemic possibility that G is true, and one that G is false (compare my nonexistence, which is an epistemic impossibility for me, if not for you; although it is presumably metaphysically possible because I’m not a necessary being, as far as I’m aware anyway – metaphysical possibilities always involve more presumptions, so far as I can tell). But whichever one is actually the case (assuming, for example, that mathematical truth is not Intuitionistic) the other is not a metaphysical possibiity (it is necessarily false, false in all possible worlds).
    Now, if G is true, then it may not be possible for my (1) to be true whilst my (2) is false (if we ignore the possibility that the “therefore” would make it false anyway, which I think we should not do), if we take the relevant sense of “not be possible” to be metaphysical; but does the validity of an argument depend on the sorts of assumptions that go into our favourite possible worlds set-up? Only sometimes I think. Furthermore, G might be some conjecture for which “G is false” is true, in all possible worlds. Finally, even if consistency was good enough for arithmetical truth, something is true for all we know when it is not known to be false (and even then, on some readings of “known” it can be known to be false whilst being an epistemic possibility, e.g. some extremely sceptical scenarios), which should correspond to some basic degree of consistency (since we should avoid inconsistent thoughts) but that is all. If someone says to me “Is there milk in the fridge?” and I say “For all I know there is!” I’m saying that I don’t know that there isn’t any milk; I’m implying that I haven’t looked in the fridge recently, that I’m not that bothered, that it’s not my problem.

    February 17, 2008 — 18:07
  • Enigman

    More to the point; if I choose to make a rude gesture, Alex, after some deliberation, then it seems that I am the ultimate cause of that gesture. Although God made me, and gave me free will, it was surely no part of his reasoning that I would waste my free will on such a pointless act; so the ultimate explanation for my rude gesture is surely my naughty choice to make it. But if so then your Omnipotent being is impossible; and furthermore that scenario is a positive possibility, in that it involves my particular gesture, my personal responsibility, so that it could only be countered by a huge negative possibility (the absence of any such events in any possible world)…

    February 17, 2008 — 18:19
  • Mike Almeida

    … even if consistency was good enough for arithmetical truth, something is true for all we know when it is not known to be false . . ..
    It’s tricky when it comes to propostions C that are either necessary or impossible. When you say that “C is not known to be false”, you have ot be saying something weaker than C is consistent with everything I believe or that it might be true, given what I believe. Since if C is consistent with one proposition that you believe, say p, then {p, C} is satisfiable. But then there is some world in which p & C are true, and so C is necessarily true (and so actually so). You must mean instead that you don’t know if C is consistent with everything you believe and you don’t know if C is inconsistent with everything you believe. But that is a very weak sense of epistemic possibility. In any case, it will make the inference invalid.

    February 17, 2008 — 18:29
  • Christian

    Alex,
    If the view entails that laws of nature our metaphysically impossible, then the inability to violate them makes a being no less omnipotent. I’m inclined to think the laws could have been different, though, even on the supposition that an omnipotent being exists, so also I think I’d resist this account of omnipotence.
    And I find myself thinking it’s incoherent to claim God is outside of time!
    Do you have a barebone sketch of the view of ‘free choices’ in the simple proposal? I’m not free to fly partly because I’m unable to: my abilities partly explain my freedoms. If God’s free choices ground his omnipotence, then do you have an account of these abilities that ground ascriptions of ‘free’ to his free choices?

    February 17, 2008 — 20:28
  • Enigman

    Mike, yes I don’t know for sure that Goldbach’s conjecture is consistent with everything else that I believe. (I tend to think of that as it being true though.) But I didn’t know that was a weak sense of epistemic possibility, so I’m curious about what is a strong sense? Anyway, I actually know that Goldbach’s conjecture is inconsistent with the totality of all that I believe, because I know that I believe some inconsistent propositions. (I suspect we all do, e.g. an insignificant belief that something is a continuous solid, and a general belief that all such things are made of atoms.) That’s another reason for me to think in terms of mathematical truth I guess… By the way, read my words as though they were written by someone struggling to be coherent through a cold, with a naturally messy mind (I’ve just noticed that when I get close to coherent my words look pretentiously pedantic to me).

    February 17, 2008 — 21:14
  • Alexander Pruss

    Christian:
    I am not sure I understand your worry. Couldn’t it be the case that it’s a law of nature that A’s are always followed by B’s, but God still miraculously makes some A not be followed by A?
    Enigman:
    The ultimate explanation of your free choice is going to have to involve an explanation of why you have free will and, even more basically, why you exist.

    February 18, 2008 — 0:20
  • Enig,
    Here are two senses in which one might urge that some proposition p is epistemically possible.
    1. Mp iff p is consistent with everything we know to be true.
    2. Mp iff. we do not know that p inconsistent with everything we know to be true.
    There are some propositions that turn out to be possible on (2) that do not turn out possible on (1), the conjecture, for instance. So the conditions on epistemic possibility in (2) are weaker than those in (1).

    February 18, 2008 — 9:20
  • Alexander Pruss

    Mike:
    I am not sure I would put “know” in an account of epistemic possibility. I’d say “think you know” or maybe just “believe”. It seems that if someone thinks she knows p, then not-p is not epistemically possible for her, even if in fact she doesn’t know p because p is false.
    Interestingly, if one replaces “know” with “believe”, then it might be that nothing is epistemically possible. For we might know, based on pessimistic observations about our epistemic limitations, that our beliefs are logically incoherent (without being able to point out where the inconsistency lies), in which case every proposition will be known to be incompatible with our beliefs.

    February 18, 2008 — 10:22
  • Enigman

    Alexander, the ultimate explanation of my rude gesture may well include an explanation of why I exist, why I have free will, why I have fingers… but why would it not have to inlude my free choice? Either my free choice is random (it has no explanation) or it can be fully explained without my input (in which case I am not really responsible, for anything) or else my input, my free choice to make that gesture (rather than another) originates in me, so it must be amongst the ultimate explainers, which cannot be reduced to x’s free choices alone.
    As you say, at the start, God would be an ultimate explainer, but your definition requires that God’s free choices amount to all of them (to justify the ‘omni’ bit). You say it depends upon how we spell out “ultimate explainers,” and you allude to but skate over (I felt) how it depends upon how we spell out “moral responsibility.” (Your argument therefore risks clashing with “problem of good” arguments.)
    Mike, thanks. I need talk of strength spelled out for me, as I find it counter-intuitive. E.g. a weak interpretation of knowledge (e.g. scientific facts, such as time being ‘known’ to be part of relativistic spacetime) would incline me to reject the strong notion of epistemic possibility for disallowing too many live possibilities…

    February 18, 2008 — 10:32
  • I am not sure I would put “know” in an account of epistemic possibility.
    You have to put ‘know’, even if you use ‘believe'(since everything you know, presumably, you believe). So perhaps these conditions express just a necessary condition. But then epistemic possiblity becomes radically relativized to individual sets of beliefs. And it does not fit well with the common (albeit vague) phrase that is supposed to capture epistemic possiblity, viz., for all we know, it’s true that p. In any case, given my discussion, it would make the same point.

    February 18, 2008 — 10:36
  • Enigman

    But even when faced with a paradox (where I am aware of holding two conflicting beliefs) it is coherent (rational, if not consistent) for me to accept some possibilities but not others; I don’t find it at all plausible that I should not be able to bracket the paradox, and the associated beliefs. In fact, I should actually start to allow more possibilities (in order to resolve the paradox) not less; much as we might precisify our fuzzy predicates to whatever degree the contradictory context required.

    February 18, 2008 — 10:45
  • Enigman

    Alexander, I may be misinterpretting your point (due to my cold), but did you just reply to my question by briefly (and indirectly) correcting my english? I should perhaps have said “an irreducibly” instead of “the,” although please note that your use of “an” and “the” was questionable too, as aforementioned (and that in my context, common usage does allow my “the,” whereas your context was one of precise definitions); but would it be terribly rude of me to ask why? (It’s a good rhetorical ploy of course, often deployed when no better reply is available:-)

    February 18, 2008 — 12:04
  • Christian

    Alex,
    I’m considering a candidate ultimate explanation ‘U’. ‘U’ is God’s freely creating facts f1…fn and the deterministic laws according to which the facts evolve. Suppose U is God’s only act, and, it is in fact the ultimate explanation for all contingent facts since U is causally sufficent for all contingent facts.
    My claim: Possibly, there is world in which U occurs and in which God is not omnipotent. God could ground all contingent truths, but unless he can change them after so grounding them, he is not omnipotent (not the way he is traditionally understood to be). An account of omnipotence deserving of the name must explain why God, in such a world, could violate the laws. Appealing to U will not do this. So, appealing to ultimate explanations will not do this.

    February 18, 2008 — 14:16
  • James Gibson

    Alex,
    I want to go back to Chris Hallquist’s objection on Feb. 15th and your reply. His critique was that there is an analogous argument to the ontological argument from which it follows that there is no God. You responded by claiming that modal intuitions are fallible, but that we could be more sure of positive possibilities than negative ones.
    I think this is an interesting move. But I wonder if it works if we change Chris’s example a bit. Let’s change his argument:
    (1) Possibly, there is no god.
    (2) Therefore, there is no god.
    To
    (1′) Possibly, there is a person who knows there is know God.
    (2′) Therefore, there is no God.
    Does (1′) count as a positive or a negative possibility?

    February 18, 2008 — 14:34
  • overseas

    Imagine a being able to cause effects only by means of other beings’ activities: perhaps it can terminate only dense causal series. If such a being existed necessarily, it could meet your df’s condition, if it stood in enough such series and they allowed its choices to be the ultimate explainers etc. Yet it would not be able to directly, immediately cause any effects. Should such a being count as omnipotent?

    February 19, 2008 — 4:14
  • overseas

    Your df. is *very* close to James F Ross’.
    Your df. doesn’t let an omnipotent being have contingent mental states it did not choose to have. But couldn’t an omnipotent being just ab initio, from all eternity, contingently like chocolate better than vanilla?

    February 19, 2008 — 6:08
  • overseas:
    On the mental states issue, wouldn’t that be a kind of impotence on the part of the omnipotent being, to be subject to contingent mental states he did not bring about? (A similar issue is with conditionals of free will. I deny those. And I think God doesn’t have any contingent mental states that do not modally supervene on the state of creation.)
    On the causal chain issue, maybe I could say that the being would still be more potent than any other possible being, since any other being would have its powers on sufferance from it, or something like that.

    February 19, 2008 — 13:42
  • Alexander Pruss

    James:
    (1′) is relevantly like the conjunction of a negative and a positive possibility, since in saying that x knows p, we’re also saying that p is true. In fact, it might literally be such a conjunction if “x knows p” is to be analyzed as “p and x believes p and R(x,p)” (whatever R is).
    At the same time, I feel the force of your claim to some extent.
    Talking of positiveness, here’s an interesting variant of my original argument.
    Premises:
    i. Omnipotence is what I say it is.
    ii. Omnipotence is a positive property.
    iii. If A is positive, not-A is not positive.
    iv. If A is positive and A entails B, then B is positive.
    Conclusion:
    v. There is an omnipotent being.
    That (v) follows from (i)-(iv) is a consequence of Theorem T1 of my paper on Goedelian ontological arguments as soon as we observe that omnipotence entails necessary existence.

    February 19, 2008 — 13:51
  • overseas

    Alex,
    If it is a being’s nature to have such mental states (though not to have the particular ones it does), there is no impotence involved in having them: inability to do the impossible (in this case, not be as one’s nature dictates) doesn’t count against a being’s claim to power.
    If God has no contingent mental states that don’t supervene on the state of creation, HE has none prior to there being a Creation. What then can explain His choosing to create one sort of universe in possible world W, and another in W*?
    On the causal chain issue: other beings would be able to cause effects directly and immediately. The being I describe couldn’t. It’s as if they can strongly actualize states of affairs and the being as I described it can only do something like weakly actualizing them (only like, b/c molinist conditionals aren’t involved). Surely something that can’t directly and by itself actualize states of affairs, but must get them actualized by intermediary others, is pretty weak!

    February 20, 2008 — 4:43
  • Enigman

    Ah, maybe that was terribly rude of me… still, the fact remains that your argument is either clearly invalid or else clearly unsound (as above), for all that there is an admirably sophisticated obscurity as to which it is. But seriously, if you met God and He told you that He made this universe as His free creation, that He can do anything He wants with it, but that it so happens that He also has some property to an arbitrary transfinite degree that He did not choose (any being with that property to a greater degree would be a lesser being since unreal, He adds, and He could not have chosen the degree because having that property to some set-theoretic degree was necessary for His being able to choose anything at all; it may be analogous to the cardinality of our temporal continuum, for example, since we must exist in something like time in order to choose anything), then you would think that there was also, in addition to this your God, a being omnipotent by your definition (as your argument, if sound and valid, shows)?

    February 20, 2008 — 20:39
  • Enigman:
    If the modality is metaphysical, and theism is true, then premise (1) is true. If the modality is metaphysical, then (2) follows from (1) and my definition of omnipotence, assuming S5. So the argument is valid. And it is sound if and only if there is an omnipotent being (in my sense). So to show that it is unsound, you’d need to show that there is no omnipotent being.
    Now, maybe the criticism you want to levy is a bit different, namely that the argument is question-begging. There you would have more of a leg to stand on.

    February 21, 2008 — 10:23
  • Enigman

    Thanks Alexander,
    (sorry for the delay replying; my cold is only slowing going)… I cannot show you that your argument is unsound, but I can say that it is (as you can say that it is sound, without showing that it is). I can show you that it is probably unsound (as you cannot show that it is probably sound). That modality (“probably”), by the way, is epistemic.
    You imply (with your initial “If”) that the modality of your argument is metaphysical, but what is a metaphysical modality? It is (I would say) when we are considering what is possible given some assumptions about what might otherwise have been. Your argument is therefore very clearly question-begging (furthermore if those assumptions cannot be given then you cannot even have an argument, whence it would be invalid). (And crucially, to the meaning of your argument, what is the modality of your “If” anyway?)
    I say that your argument is, if sound, invalid; but is it sound? Of course, you don’t have to show that your argument is (probably) sound; it is your argument. But the leg I would (and indeed did) choose to hop about on, for a bit, is my thought-experiment (previous comment)… Maybe the response that you would choose to make is to say that such a God could not appear to you (as your argument shows), but if so then there would, actually, be other ways of showing that your argument is unsound (?)

    February 23, 2008 — 9:33
  • Enigman

    Hi again Alex,
    We seem to have got off on the wrong foot! To begin again, my problem (which need not concern you, of course; and if you show me I’m wrong then thanks) with your proposal is that it ends with a Very Bad argument (I’ll explain those Caps shortly), as though that was its justification, if not its purpose. Otherwise, it seems like a nice proposal for an appropriately maximal kind of omnipotence (although I find more useful definitions that are more intimately related to reality)…
    Your argument really annoys me (but I’m hoping that it is supposed to annoy)… You are, I gather, a conservative Christian philosopher, in which case you believe in God (whence my choice of thought-experiment), which concept is fascinating for many reasons, and very Difficult! In particular, since God created this universe (and possibly our logic) hence there is a real enough sense in which God exists metaphysically rather than physically. As philosophers we should be aiming to clarify such difficult concepts (it is one of the few place where we should have something to contribute to theology). That is the opposite, so far as I can see, of the deliberate fabrication of a Bad argument (and quite generally philosophers of all sorts should be in the business of unpicking Bad arguments, of showing them to be bad, not constructing them except for educational purposes, whence my aforementioned hope).
    The argument is Bad because it is bad (it is, as you almost admit, at the very least question-begging; if fully written out it would contain within its assumptions that which it explicity claims to show) but seems to try (I’m being very charitable here, as were such an argument in the mouth of a policitican it would obviously be Bad) to look like a good argument. It seems to get all its force from its superficial similarity to a good sort of argument, from equivocation (that is what is meant by saying that your argument’s “Possibly” looks epistemic), in what is to us philosophers an obvious way (so don’t play innocent about that please). So in many ways the validity of your argument only adds (if it exists) to the problem.
    A very well-respected philosopher of religion puts forward a sound and valid argument for the existence of an omnipotent being. You do see how (good) that sounds? That is what makes it a Very Bad argument. Please have more respect for your own God, is what I would add to end with, were I not hoping that this exercise is supposed to be subtly educational (you see, if not then you’re Very Bad too, however well you can defend the literal truth of your deliberately deceptive words). God bless and take care…

    February 23, 2008 — 10:43