Impossible Omnipotence
November 12, 2009 — 9:06

Author: Michael Almeida  Category: Uncategorized  Comments: 26

Many students think that anything that is omnipotent could make 2+2 = 5 or create a round-square, or square-circle or the like. Now these sorts of claims are often dismissed as naive or not well thought out since they amount to the claim that an omnipotent being could do the impossible.
I’m now less sanguine about this sort of response, though I’ve given it before. I don’t think that students or others who claim that an omnipotent being could create a round-square are in fact claiming that an omnipotent being could do the impossible. What they are claiming, I think, is that round-squares would not be impossible were there omnipotent beings or the state of affairs that p & ~p would not be impossible were there an omnipotent being. That strikes me as much closer to a reasonable claim. So, we can formulate the naive claim as the de dicto falsehood in (C0),
C0. It is possible that an omnipotent being brings about the impossible.
That cannot happen, since whatever anyone brings about is possible. But there are better ways to express the worry. It might be true, for P = (p & ~p), that
C1. P is impossible & an omnipotent being possibly brings about P.
In support of (C1), (C2) does seem to be an (at least) non-trivially true counterpossible,
C2. Were there an omnipotent being then he might bring about P.
But of course it matters how we interpret this. Does this mean that contradictions would be true, were there omnipotent beings? We don’t want to say that, since we don’t want an explosion of true propositions on the assumption that there is an omnipotent being. Or does it mean that what we regard as contradictions, or what we can only describe as contradictions, would not be so for God, were there a God? I’m not sure that’s coherent. Better, (C2) might be true because, were there an omnipotent being, he could have made P a non-contradiction.
There is something for theists to say, I think, against this objection. God cannot make a contradiction true, but God has the power to determine what the contradictions are. Does that make better sense? Something like C3,
C3. Were there an omnipotent being, he would have the power to bring about P.
But I suspect (C3) involves cutting big corners. If an omnipotent being has the power to bring about P, and that power is necessarily unmanifested, then there is no world in which he brings about P. But I find the idea of a necessarily finked disposition to bring about P very suspicious. It has nothing to do with the idea that a disposition might be finked, since I have no difficulty with contingently finked dispositions.The main concern is why that disposition is unmanifested at all.

Comments:
  • Anonymous

    What does “finked” mean?

    November 12, 2009 — 11:30
  • Mike Almeida

    Think of a finkish disposition/power as one that is prone to disappear in circumstances that would commonly trigger its manifestation. If there are such, then we could say both that, say, the glass is fragile (disposed to break) and that it does not manifest its fragility in just those circumstances that would commonly birng about that manifestation (say, in the presence of a stone that is thrown at it). Some of God’s powers might be like that. They might be dispositions to act in certain ways (say, in violation of the moral law or in ways that would widen the range of modal possiblity) that are never manifested or necessarily never manifested.

    November 12, 2009 — 11:45
  • Hi Mike,
    A quick comment and a quick question:
    (1) An unmanifestable disposition is not necessarily a necessarily finked disposition. For example, if there are any dispositons with impossible stiumuli, they would be unmanifestable. (Bizarre suggestion: why not say that God’s benevolence prevents Him/Her/It/They from manifesting their disposition to make contradictions true?)
    (2) I don’t see the advantage of saying that God has the power to determine which propositions are contradictions rather than saying that God has the power to make some contradictions true. Could you explain why you take holding the former better than holding the latter?

    November 12, 2009 — 13:50
  • Mike Almeida

    Hey Gabriele,
    (1) An unmanifestable disposition is not necessarily a necessarily finked disposition. For example, if there are any dispositons with impossible stiumuli, they would be unmanifestable.
    That’s a nice idea. But it’s going to generate too many dispositions, no? Take any counterpossible with a consequent specifying that God (or anything, for that matter) does something. A disposition of God to bark, say, were 2+2= 5. But surely that’s no disposition. It is an interesting idea that God’s goodness fink’s his performing a morally wrong action, or God’s rationality finks his disposition to make contradictions true. But that’s an odd fink (as I allude to in the post) since it entails that there are no circumstances under which God manifests the power to do wrong. Can one have a disposition to do X if there are no possible circumstances under which you would display X? That’s not a disposition at all is it, except in some far too generous, Pickwickian sense.
    (2) I don’t see the advantage of saying that God has the power to determine which propositions are contradictions rather than saying that God has the power to make some contradictions true. Could you explain why you take holding the former better than holding the latter?
    I took the distinction to be this: if you make a contradiction true, then (assuming classical logic) you are left with all of the consequences of true contradictions, viz. everything is true. But if you make a p & ~p a contingent truth (supposing some sense could be given to that), you are not left with those consequences. I take it that’s better.

    November 12, 2009 — 14:11
  • Jeremy Pierce

    I don’t think this would change one feature. Even on this way of doing it, you still have the feature that the problem of evil is automatically defeated.
    Suppose the existence of God and the existence of evil did lead to a contradiction. It wouldn’t matter on the view that God can cause contradictions to be true, because that is one of the contradictions God could cause to be true. God could still be omnipotent, omniscient, and perfectly good while there’s evil.
    On this way of doing it, I think you get the same result, because God could have chosen to generate the actually-contradictory result by declaring it not a contradiction.
    So, either way, those who push this kind of super-omnipotence in order to rule out defenses that certain ways of eliminating evil would be contradictory aren’t really making it harder to respond to the problem of evil. They’re making it easier.

    November 12, 2009 — 16:49
  • Mike Almeida

    I don’t think this would change one feature.
    Jeremy, you don’t mean (right?) that (i) you do not think it would change one feature, but that (ii) there is one feature you think this would not change. I take (i) to imply that there is not a single feature that this would change. But it is hard to read the rest of what you say in a way consistent with that reading.

    November 12, 2009 — 17:28
  • Mike Almeida

    So, either way, those who push this kind of super-omnipotence in order to rule out defenses that certain ways of eliminating evil would be contradictory aren’t really making it harder to respond to the problem of evil. They’re making it easier.
    I htink something like this is right. But why think that they’d be making it harder? On the other hand, it might be true that no matter what God does there is some inconsistency (or other) between God and evil. Perhaps in each world w there is some inference pattern P such that God in w is inconsistent with evil E in w.

    November 12, 2009 — 19:11
  • Hi Mike,
    That’s a nice idea. But it’s going to generate too many dispositions, no?
    It depends on one views of dispositions. On my view, it would but I believe there are no such dispositions. Dan Nolan and Carrie Jenkins, however, are working on a paper in which they argue there may be unmanifestable dispositions.
    if you make a contradiction true, then (assuming classical logic) you are left with all of the consequences of true contradictions, viz. everything is true. But if you make a p & ~p a contingent truth (supposing some sense could be given to that), you are not left with those consequences. I take it that’s better.
    My point was that even on your proposal it is not possible to retain classical logic while avoiding “explosion”. This is why. If ‘p & ~p’ is true then both ‘p’ and ‘~p’ are true. and since ‘p’ is true then, for any proposition q, ‘~q->p’ is also true. And since we already know that ‘~p’ is true and ‘~~p->p’ is a tautology, ‘q’ is also true. And you have explosion once again.

    November 13, 2009 — 2:25
  • Mathis

    Why not simply define Omnipotence in terms of maximal power, as Flint and Freddoso did in their paper with the same name?
    http://www.nd.edu/~afreddos/papers/mp.htm

    November 13, 2009 — 6:18
  • Mike Almeida

    My point was that even on your proposal it is not possible to retain classical logic while avoiding “explosion”. This is why
    Gabriele, right, I know how the proof goes. But that’s not what’s in question. The question is what happens when God makes a contradiction a contingent truth. If what happens is what you describe, then there is no difference between making a contradiction true and making a contradiction contingent. I claim there is a difference. If God makes a contradiction contingent, then he cannot simply be making p & ~p true, since p & ~p is not a contingent proposition. Though, I admit, I’m not sure any of the foregoing is intelligible.

    November 13, 2009 — 9:08
  • Mike Almeida

    Mathis,
    The question in play is whether it might be a coherent objection to the claim that something is omnipotent that an omnipotent being could make a round-square. I try in the post to make out a way in which this objection gets some traction. I then try to respond. So, I offer not analysis of ‘omnipotence’, but I do suggest that no such analysis can simply dismiss the objection that were there an omnipotent being, he could create a round-square.

    November 13, 2009 — 9:12
  • Hi Mike,
    Is making a contradiction contingent just making it such that it is possibly true?
    If so, though, if you accept a possible-world analysis of modality (I don’t), then that means that at some possible world the contradiction is true and at that world you have explosion (and so you have that all falsities are only contingently false). If you don’t, how were you thinking of analyzing that claim?

    November 13, 2009 — 13:01
  • Fascinating discussion; it reminds me of disputes about Descartes’s position on eternal truths. Descartes would agree enthusiastically with the claim that what is impossible is impossible, and what is necessary is necessary, because God wills it to be — and due to omnipotence he could have willed otherwise:
    “…God cannot have been determined to make it true that contradictories cannot be true together, and tehrefore…he could have done the opposite….And even if God has willed that some truths should be necessary, this does not mean that he willed them necessarily; for it is one thing to will that they be necessary, and quite another to will this necessarily, or to be necessitated to will it.” (AT IV, 118; CSMK 235)
    He takes it so far that he refuses to reject the possibility that God could have made a creature independent of Him, even though this is a contradiction. So Descartes holds (I am abstracting from quite a bit of controversy, since the eternal truths are a contentious point in interpretation of Descartes):
    (1) Relative to the divine will nothing is impossible, even making a contradiction true, because whether something is true or false is entirely dependent on whether God wills it to be.
    (2) Whether something is necessary or impossible is contingent on God’s having willed that it is necessary or impossible.
    I take it that in a sense what you’re trying to do is keep these two theses split apart, and seeing if there’s a coherent half-Cartesian position here — a way to reject claims like (1) while still accepting claims like (2)?
    I’m not sure how to do that (but I’m not sure how to make the combination of (1) and (2) coherent either), but it seems to me that you would have to go second-order (at least): instead of thinking in terms of possible worlds we would need to think in terms of possible manifolds of possible worlds. So, for instance, to take one of Descartes’s examples on this subject, we can analyze the necessity of ‘twice four is eight’ by taking as our domain possible worlds and saying that this is true in all possible worlds. But to make sense of anything like (2) we may have to take as our domain not possible worlds but domains of possible worlds (a domain of domains), such that some of these domains can have possible worlds that do not exist in other domains of possible worlds and can lack possible worlds in the same way, and such that in the domain of possible worlds selected out by the actual world as the ‘actual’ domain of possible worlds, it is true in all possible worlds that twice four is eight, but that in other possible domains of possible worlds, it is true only in some. But this seems to give us both (1) and (2). Perhaps this can be avoided if our second-order level is thought of in terms of possible manifestations of dispositions: to each possible manifestation of divine power corresponds a domain of possible worlds. In that case we should watch out for scope: the disposition to bring about P is not necessarily unmanifested — it is simply unmanifested, such that P is necessarily false.
    But I’m not sure how far this sort of thing can go.

    November 13, 2009 — 23:18
  • Mike Almeida

    Is making a contradiction contingent just making it such that it is possibly true?
    Gabriele, you’re right that if making some instantiation of p & ~p true is to make it contingent, then we have the same problem. I took it that there is a difference between making a contradiction true and making a contradiction contingent. Otherwise we end up with contingent contradictions. Maybe an analogy would be useful. In S5, ~(Mp -> NMp) is inconsistent. But in T it is contingent. In S5, it’s truth explodes, not so in T.

    November 14, 2009 — 8:48
  • Mike Almeida

    I take it that in a sense what you’re trying to do is keep these two theses split apart, and seeing if there’s a coherent half-Cartesian position here — a way to reject claims like (1) while still accepting claims like (2)?
    Brandon, yes this is the idea. Maybe the example above will help. Some propositions are theorems relative to one logic and contingent truths relative to another. Suppose God gets to decide which logic is right via, say, choosing the truth-makers.

    November 14, 2009 — 8:53
  • Mike,
    I understand, but I still don’t see how that can help you. Isn’t it contingent in T because it is true in some models of T (that are not models of S5)? If so, how can a proposition be contingent without being possibly true? So, how could God make a proposition contingent without making it possibly true? And, finally, how can an all- powerful God have the power to make a proposition contingent without having the power of making it true? As implausible as it is, I think that the best option is still the one I suggested above–God has the power to make contradictions true but would not exercise it under any possible circumstances.

    November 14, 2009 — 23:01
  • Mike Almeida

    how can a proposition be contingent without being possibly true? So, how could God make a proposition contingent without making it possibly true?
    We’re at cross-purposes. I agree that an omnipotent being cannot make proposition contingent without making it possibly true. I was defending the position that he can make a proposition that is in fact a contradiction or at least necessarily false (the S5 inconsistent proposition) contingently true (in system T) and, assuming classical logic, still avoid the explosion of true propositions. It’s the last conjunct that I took you to be denying.

    November 15, 2009 — 10:46
  • Hi Mike,
    Sorry to be a pain, but as far as I can see the only reason why ~(Mp -> NMp) is contingent in T is that (Mp -> NMp) is not a theorem of T and so no contradiction follows. So how can that case be analogous to that of p&~p, which is itself a contradiction?

    November 17, 2009 — 21:11
  • Mike Almeida

    Gabe,
    The idea is that God makes an inconsistent proposition contingent by determining which is the right logic. If we insist on propositions instantiating p&~p, then God would have to select a paraconsistent logic.

    November 23, 2009 — 10:00
  • An excellent short response to this claim. I personally was one who believed that God could do the logically impossible for quite some time. I recommend Stephen E. Parrish’s book “God and Necessity” for a fairly solid rebuttal of this view. Basically, he states that God is the greatest possible being. As such, God is omnipotent. But omnipotence entails that the being is capable of anything. A square circle, however, is literally nothing, so it doesn’t mean anything to say that any being can create it. I’d like to respond in greater depth but I need to run!

    November 23, 2009 — 18:23
  • Mike Almeida

    J.W.,
    The short response is beside the main point. Virtually everyone says what Parrish says, initially, and I’ve said similar things myself. The point of the post is that this response fails to appreciate the objection. The objection is that IF there were an omnipotent being these things (square circles and the like) would not be impossible. The fact that they are impossible entails that there are no omnipotent beings. The remaining discussion has concerned how something impossible might fail to be so. See the exchange with Gabriele above.

    November 23, 2009 — 18:35
  • I was referring to the main post as the “short response,” not any comment. Sorry for the confusion.
    I think the way I argued is actually different than simply dismissing these things as possible. I would challenge anyone who would like to assert “…IF there were an omnipotent being these things (square circles and the like) would not be impossible” to describe what these things actually are. Assign properties to them. But such a thing as a “square circle” or anything like it can have no coherent properties, which means it is literally nothing. It isn’t just impossible, it simply is nothing.
    I’m agreeing with your initial post and trying to offer a further comment, not trying to respond to any of the discussion after it, as I haven’t digested it, or trying to refute it (as I agree).

    November 23, 2009 — 23:19
  • Mike Almeida

    It isn’t just impossible, it simply is nothing.
    Sorry for the confusion. I’m not sure what distinction you’re making, since impossible things presumably don’t exist (except, I guess, for Meinongians). But the point of the objection in the main post was that what counts as impossible (might) depend on what sorts of beings exist. It’s sort of an exercise in trying to make good sense of such a claim. So, for instance, you might think that ~(Mp –> NMp) is impossible, as many do. But an omnipotent being might be such that he could do sometihng that wasn’t necessarily possible for him to do. He could do that, presumably, because he could determine that the logic of (alethic) modality is weaker than S5. This sort of thing begins to make sense of the claim above. Anyway, that’s the idea.

    November 24, 2009 — 7:24
  • Mike,
    The idea is that God makes an inconsistent proposition contingent by determining which is the right logic. If we insist on propositions instantiating p&~p, then God would have to select a paraconsistent logic.
    I thought the whole point was to retain classical logic! Was I wrong? For example, earlier you wrote:
    I was defending the position that he can make a proposition that is in fact a contradiction or at least necessarily false […] contingently true […] and, assuming classical logic, still avoid the explosion of true propositions.

    November 25, 2009 — 1:36
  • Mike Almeida

    Gabe,
    True, the idea was to retain CL. There are other ways, though I’m less familiar with the details. There are restrictions on impossible worlds that Brit Brogaard talks about to constrain explosions that I think are consistent with CL.

    November 25, 2009 — 8:38
  • Very interesting discussion so far!
    The argument of the contingency of propositional contradicitons might prove helpful at some point (as well as the term “necessarily finked”, which was new to me).
    However, I would like to make the point that in my view the advantage of avoiding an explosion of true propositions is only kept for our world but not for the perspective of an omnipotent God (i.e. for an standpoint outside of our framework). God’s possibility to decide about contingent contradictions from outside our world (or ‘before’ creation) might look like the following (1) (p ∧ ~p) ⊥ (p ⊥ ~p), since God has to create some kind of framework that allows contradictions (at least for worlds like ours). But then, this is a contradiction in itself (either in word W there are round cubes or not) and a omnipotent being (in this sense) should be able to make this contradiction contingent, so that (2) (p ∧ ~p) ∧ (p ⊥ ~p) could be possible (and would analogical mean something like an explosion of true metapropositions).
    So God’s decision would not be between certain propositional contradictions but between world-sets that have (contingently different before creation but ‘necessary’ within each world) contradictions (1) and other world-sets that don’t have the distinction between diction and contradiction (2) (whatever that is supposed to mean).
    Unless I am very mistaken, the initial problem is just postponed to a meta level, leading to regression eventually.
    I would prefer treating the question not so much as a metaphysical speculation but as a problem of language. What do the terms ‘omnipotent’ and ‘impossible’ mean as they are used here? J.W. Wartick actually has a point here in my opinion.
    If one really interprets – what I wouldn’t want to – the ‘omni’ as a very abstract ∀ (which doesn’t even relate to distinct variable objects anymore), ‘omnipotence’ is already a concept beyond our language and framework. The problem arises where we don’t recognize this and treat the term as still inside the framework. (This interpretation is not even paradoxical, because a true paradox is aporetic and therefore a limitation of language in itself.) To understand omnipotence in this sense means confusing language: It is not the same for us – though it might seem – to talk philosophically of “unmarried bachelors” or of “married bachelors”. The first is linked to a concept (in language expressed in the term ‘bachelor’ alone), the second is linked to no philosophical concept (although it might be used as a device in art, poetry etc) at all. So, when we talk of God creating a married bachelor, our language indeed refers to nothing. Maybe there is a world where God creates married bachelors, but it doesn’t matter to us, because we don’t know what we are talking about. Epistemologically, we are tied to the logical propositions our language is capable of representing. Any propositions outside of it cannot interest us in a philosophical sense: our knowledge about God is certainly not increased (although aesthetic and religious language – even true paradoxa – might point to God’s reality beyond the boundaries of our language), therefore it doesn’t matter if God is or is not capable of ‘impossibilities’.
    The statement “The objection is that IF there were an omnipotent being these things (square circles and the like) would not be impossible. The fact that they are impossible entails that there are no omnipotent beings.” is a good example for confusing views from inside and outside of languages and worldframes: If there were ‘impossible things’, they would not carry the notion of ‘impossibility’ for us resp. ‘impossibility’ would refer to something completely different and maybe similarly puzzling. The true surprise is that our language is capable of transgressing the limitations of our creaturely existence (or seems to anyway) even more than our own imagination, thereby confusing our talk of God.
    Further thoughts:
    http://www.arsdisputandi.org/publish/articles/000102/index.html

    December 15, 2009 — 4:49