Friday, February 18, 2011

Can God do the Logically Impossible?

Some, such as Descartes, believed in a sort of “universal possibilism.” This taught that God could do anything, even that which is logically impossible. The question is this: Can God do even what is logically impossible?

In order to answer the question, we must understand the differences between logical possibility and other types of possibility (such as physical possibility). Physical possibility is governed by the laws of physics and nature. For instance, it’s not physically possible for me to start flying. It’s not physically possible to drop a rock from a building and have it go sideways, and up, and down, all on its own. Logical possibility, on the other hand, is strictly tied to that which is conceptually coherent. So, if there are no inherent self-contradictions, or necessary truths in opposition to it, the concept is logically possible (even if it is not physically possible). So that which is logically impossible is a self-contradictory concept, like a married bachelor. It is a concept which is impossible to be true (even if my natural situation would allow me to fly, there is no allowable situation which makes a square a circle, for instance).

Next, we must understand the implications of the claim that God can do the logically impossible. First, if God can do the logically impossible, then he can sin. He can also bring it about that the same act is and is not sin at the same time and in the same sense and by the same person. He may consign us both to heaven and hell at the same time and in the same sense. He may bring about a squared circle, a married bachelor, or even that we do not exist right now!

If God can do the logically impossible, then God could bring it about that the universe does and does not exist. But it gets stranger than this. He would also be able to bring it about that he did all these things while not existing! But how can a God who does not exist do anything?

Finally, if God can do the logically impossible, he can bring it about that it is logically impossible for him to do the logically impossible. This, of course, means that he both can and cannot do any and all of these things at the same time, in the same sense, in the same manner, while existing and not existing—and he can cause even that to be true and false!

We must realize such a view reduces God to nonsense! One may try to protest that God is beyond our understanding, and thus such a view can be true. But this ignores three crucial elements: if it is true, it is also false (and this surely bothers even the proponent that God can do the logically impossible); God is truth (John 14:6, 8:32 [which means there is a standard of true and false which is independently binding upon the universe which can also be applied to God as his nature]); there are things in the Bible God cannot do (such as lie [Titus 1:2]). God himself is the objective standard for truth, logic, and reason!


  1. I am completely law-bound. My desires, my actions, my thoughts, my relationships with people and things. Once I speculate on a world subject to other-laws, I remain bound to the extant laws in my speculation. This means while I might speculate on the laws of physics being different, I cannot move my body according to these different laws. If I try to speculate on the law of non-contradiction being different, I find I cannot. The extant logical law constrains my thinking, as the extant physical law constrains my limbs.

    Long long ago, at a time when I found myself unable to get beyond Descartes' second meditation, and in a confused and untutored state which I might now describe as 'proto-phenomonoligical', I decided (attempted? decided to attempt?) to assert nothing beyond a report of what was present to me.

    Regarding the law of non-contradiction, my assertion was this: that for any proposition P that I was aware of, I was unable to affirm both the truthfulness of P and the falsity of P. I doubted that i would -ever- be able to conceive of any P for which I would be able to do this.

    My -understanding- of the law of non-contradiction was precisely this -confession of impotence-.

    I don't go about instigating discussion on such topics as I once did. My impotence remains. If a person claims that God cannot bring about a particular state of affairs because it is incoherent, I do not maintain that this claim is reducible to a statement about the limits of that person's potency. There are people in the world who are much smarter than me!

    But I do want to say that I believe that God can do anything that he likes, full stop. I don't want to assert this proposition:

    (1) "God can bring about a world in which P is both true and false."

    Why not? It seems that: (a) it gets me nowhere in conversation with others and leads me nowhere in my own thinking, and (b) I don't think I even know what the proposition -means-. [For me, (b) is a way of expressing (a). I want to say that utterance (1) has no role in any real language game.]

    So I do not want to affirm (1) because it is nonsensical to me. I cannot conceive of a world in which P is both true and false. But this means that the negation of (1) is also nonsensical to me.

    I do not want to say "God can do what he wants, without qualification!"

    But I do want to say "God can do what he wants!", without qualification.

    And I want to say that God is not in any way limited my by own impotence in conceiving or imagining.

    My question to you is this. Do you think (or feel) that I have fallen short of meeting my epistemological obligations? If not, would you nonetheless like me to go further? And if so, would you like to be my guide?

    (Some are musically tone dear. I am conversationally tone deaf. I ask all three questions with expectant cheer, notwithstanding how the first question might sound!)

    1. Thanks for commenting! Well, the issue for me is that (1) takes it as a datum that there is such a world, where P is true and P is false, and that seems clearly nonsensical. Logic is transcendental, as even any critique of logic must assume that what it says is right and logic is wrong (which is itself a particular application of the law of noncontradiction). In short, it's inescapable. So, if one argues that it's only inescapable for me, but perhaps the law isn't a law after all, is literally to assume that it's possibly true that the law of noncontradiction applies to me but not to X, where X can perform contradictory actions--but we don't say that claim is also true and false for X, is it? And, if we do, is that further claim also true and false? We could go on ad infinitum, but at some point it seems we must assert that, even for X, it cannot be brought about that it is both true and false.

  2. When you saw we could go on ad infinitum, it brings to mind "What the Tortoise said to Achilles". But if, to take your phrase, I were to say that it is "inescapable for me", I would not go so far as to say that it is "[only] inescapable [only] for [only] me [only]." (I'm not quite sure where to best place the "only".) I would not even go so far as to say that "it is escapable for some", which is a weaker statement. I would not even say "it is possibly escapable for some".

    By saying that the law of non-contradiction applies to me, I am at least saying that I am in some respects impotent when it comes to simultaneously affirming and denying P. Or perhaps I should say I am incompetent to affirm both P and not P. Or perhaps better still: that the utterance "P and not P" makes no sense to me. In this sense of "applicability", to say that the law of non-contradiction does not apply to X is to say that the utterance "P and not P" makes sense to X.

    Suppose now X says of some proposition P that "The proposition 'P and not P' makes sense to X". How am I to refute it? I am happy to say this to X: "be that as it may, the proposition 'P and not P' makes no sense to Bryan."

    I am happy to say this to X as well: 'The proposition that "the proposition 'P and not P' makes sense to X" makes no sense to Bryan."

    Now I could go further than that, and appeal to a law that has transcendent ontological import. And perhaps there is good reason for me to do that. But I do not know any good reason to do that. I don't want to go down any road ad infinitum, for I don't see anything objectionable or incoherent in what I said. If you see anything objectionable or incoherent, do say so. If what I have said is sound, it remains possible (and I will keep saying it remains possible) that I have no said -enough-. Perhaps while being coherent there is some sort of need for me to say something -beyond- this. Some kind of duty to ... take some sort of stand on something?

    Maybe there -is- more that I need to say, or that you want be to say. If so, do tell. I am happy to take that next step down the road. But it is not at all obvious that -that- would not me a roadtrip ad infinitum, for if I am right the pertinent discussion here involves a topical step away from logic per se, and toward our epistemic and elocutionary obligations.

    1. I would just say two comments to this. Even if we affirm that P and not-P makes sense to some agent, we are, in fact, affirming that P and not not-P with respect to P and not-P making sense to the agent; even the agent doesn't affirm P and not-P with respect to P and not-P making sense to the agent, and if he's not referring to the law of noncontradiction it's difficult to say what, precisely, restricts one and not the other. He might say something along the lines of his epistemology, but I see no reason to accept that as true (literally). Now it is true that the laws of logic are not analyzable outside of themselves; but that should not tell us to throw up our hands in logical skepticism (itself a logical position that we are apparently not skeptical of), but that logic is transcendent and, hence, unavoidable.

      The second is to say that the possibility you espouse is only epistemic; we would have to show that it is actually logically possible (as distinguished from metaphysical possibility).

  3. Isn't it possible that God dictated logic, and since He dictated it, that is why nothing can disobey it?

    Thus God could have made 2+2=5, but since He decides that 2+2=4, we can't imagine 2+2=5. It's not possible because He decided it wouldn't be.

    One reason I want to believe He created logic is that if He didn't, then it seems to me that He *discovered* music and colour rather than *created* music and colour (since music and colour are really mathematical/logical ideas in the brain) and I want to praise Him for creating them!

    ... I suppose another possibility is that music and colour weren't made by Him, but He nevertheless deserves praise for them because they are part of Him.

    I wonder whether the reason Descartes believed God was in charge of logic was because that was the being he had in mind ("a supremely perfect being") who he said must exist necessarily? Descartes said he was certain of God before he was certain of his reason and his senses (God was the second thing he was sure of, the first was himself) so at that stage his definition of God was probably all-powerful regardless of logic?

    1. Hi Tim, thanks for your comment! I don't think it works to say God dictated logic. If we do say this, I think we can see immediate problems. For this would mean we can't make any logical statements about God. It is true that one cannot get outside of the logical system to prove logic, but such a claim is more or less to say "It certainly looks impossible, but if logic isn't necessary then it is." Of course, then we have it being not even possible that God created logic (since, after all, possibility is a modality, and modality is logic: I suppose we could say it was neither possible nor impossible for God to create prior to his creation, but again, that sounds for all the world like gibberish!).

      I do hear your concern, however, about colors and music. These are issues of abstract objects (redness, Beethoven, etc.), and while I do take issue with God "discovering" them, I think it's even weirder to think Beethoven discovered his 9th symphony!

      I also think we have a way out or two that don't rely on God's being "subjected under" logic, nor creating logic. That is that God's nature is the ontological ground for logic. Thus, his nature is identified with logic (much like it is with goodness in moral arguments). You hint at this when you mention that "I suppose another possibility is that music and colour weren't made by Him, but He nevertheless deserves praise for them because they are part of Him."

      I think that's right!

      As for abstract objects, some (like my major professor Greg Welty) embrace what is called "theistic conceptual realism" where abstract objects like redness and Beethoven's 9th are thoughts in the mind of God; so when we particularize these things or think about them, we are thinking God's thoughts after him! Another solution is nominalism, that these objects do not actually have real existence, but they express propositional truth (which again finds its ground in God). Either way you go here I think you're good!


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