The Divine Liar May 2, 2009
Posted by Colin in Logic, Methodology.trackback
Consider the Divine Liar: it is possible for God to assert “I do not exist”. Whatever God asserts is true, so if God were to assert “I do not exist”, then God would not exist. In order to assert anything God has to exist, so if God were to assert “I do not exist”, then God would exist. Thus, if God were to assert “I do not exist” then God would both exist and not exist. So it is possible for God to both exist and not exist. But whether or not God exists, he does (or does not) necessarily. Thus, God both exists and does not exist.
My dear Colin, it is possible for me to say something false (such as “I do not exist”), but I choose not to.
You could get a similar result just by having such a God assert that God both exists and does not exist.
I think the consistent response is that it is not possible for God to will or assert a contradiction, or something that entails a contradiction. It remains true that anything that God wills to exist exists and any proposition God asserts is true. Yet, in no possible world does God deny God or otherwise assert or will a contradiction.
. . . so if God were to assert “I do not exist”, then God would not exist and not exist.
Not so, I think. The closest world in which God asserts ‘I do not exist’ is unlikely to be one in which a contradiction is true. Rather, the closest world in which God asserts that ‘I do not exist’ is one in which either (i) he is not God and he speaks a falsehood (i.e. his closest counterpart is not God) or (ii) he is God but does not have the typical set of divine attributes or (iii) he does not assert ‘I do not exist’ sincerely, or (iv) he is a God and truly asserts that ‘I do not (restrictedly) exist’ since he’s a transworld object, or . . .something like this. Any one of those would be closer than the contradiction world, I think.
God, thanks for corroborating, all I need is the possibility.
David, good point re: having God assert a contradiction. I guess I like my presentation because it retains the feel of the original Liar (i.e. not the sentence, but the Cretan Liar). I figured someone would suggest that God cannot will anything contradictory, but I would like to hear more about this. For one thing, God suggests above that this might be mistaken. More importantly… I’ve never been clear why this sort of move is not just conceding that God lacks omnipotence. If it not somehow, then I’d also like to hear more about why this particular move (no contradictions) is independently compelling rather than just an ad hoc solution to a problem.
Mike, this speaks to my distaste for Lewis-Stalnaker analyses of counterfactuals. The “closeness” of another possible world is hard to judge, I suppose, but made the worse by conflicting intuitions. However, your suggestions for closest worlds are nice, but I’d be surprised if the argument couldn’t be set up in such a way as to rule out these four options. The bigger question: on what grounds do you judge that these options are closer than worlds where God both exists and does not exist? To play devil’s advocate, I think the actual world is contradictory, so by my lights the mere fact that some other world is contradictory is not enough to make it distant from the actual world. What do you think about that?
Okay.
I’ll talk about willing rather than assertion because its easier to express.
What if I define omnipotence by the conditional (1).
(1) For all states of affairs S, if God wills S then S obtains.
Wouldn’t that make God’s omnipotence and the impossibility of willing some S consistent?
As for the possibility that my move is ad hoc, on the contrary, I think it is just what the divine liar and other like problems prove by modus tollens on (1).
David, not entirely sure why (1) entails that God’s willing is consistent. Is this, as you seem to say, by modus tollens on the assumption that contradictory S is impossible?
(1) does not entail that God’s willing is consistent.
It is simply possible that God could be omnipotent according to this definition and never will a contradiction.
The next step is to say that, therefore, it is impossible that God does will a contradiction if S is impossible.
It may mitigate ad hoc-ness to note that it is not just contradiction that it is impossible for God to will but any impossible state of affairs. So, unless you belief that all characterisable states of affairs are possible, you would have to say that the modus tollens step is motivated for any impossible state of affairs that God might otherwise will and bring about.
So, while I am assuming that contradiction is impossible, I am just applying a rule for any impossible state of affairs: if an omnipotent God is possible then it is impossible for God to will impossible states of affairs (qua impossible states of affairs).
I think I am still not getting it. Are you saying that the quantifier phrase “any state of affairs” implicitly means “any possible state of affairs”? If so, then I see the point re: God can’t will anything impossible on this definition. But then we are just back to the original question about why we should think this apparent limitation is compatible with omnipotence. In other words, why accept a formulation on which God’s will is limited by some antecedently specifiable set of possibilities?
Yes, any possible state of affairs.
It is compatible with God’s omnipotence because the impossibility of God willing S is consistent with the conditional if God wills S then S obtains.
The impossibility of God willing a contradictory state of affairs should be accepted because it is entailed by the further assumption that contradictory states of affairs are impossible.
I think the actual world is contradictory, so by my lights the mere fact that some other world is contradictory is not enough to make it distant from the actual world. What do you think about that?
Colin, this is a strange view (at least to me). I’m guessing you have some reason (likely from Priest, if I can guess) for concluding that this is more likely than not. I can’t make good sense of what it would be for there to exist inconsistent states of affairs (I’m assuming that you have this sort of inconsistency in mind). So, I can’t honestly get to the possibility of this obtaining. Give me a plausible instance.
Colin, on a different question you say,
I’d be surprised if the argument couldn’t be set up in such a way as to rule out these four options.
My guess is that this is not true. As you modify the example what will occur is that the relevant counterparts will change. What will not happen is that worlds containing contradictions are among the most similar worlds (of course, on Lewis logics for counterfactuals, contradictions explode, and that is the main source of dissimilarity).
Mike, on inconsistency, yeah just take a line from someone like Priest. The following contradictory sentence is true.
“This sentence is not true.”
Lots of people have lots of different kinds of complaints about the suggestion that the world is contradictory. I’m not sure what yours is exactly, so let me try asking: what (if anything) is hard to understand about the suggestion that the above contradictory sentence is true?
You might be right about modified versions of the Divine Liar, as I said before, I would have to think more about it. Unfortunately that isn’t something I have time to do right now, so it will have to wait until another time. But I see the point about contradiction as it pertains to Lewis counterfactuals.
This is a variation on the “This sentence is false” business,
and resembles a Medieval problem –can God do something that is against the rules of logic?
For instance, could God make it the case that 2 plus 2
is 12?
If God can do anything—then yes–God can do anything.
Including something that is paradoxical—like exist and not exist at the same time. If we assume that God makes the rules —then paradox –from the human point of view–is no obstacle to action. It is God, after all, who makes something a paradox or not a paradox to humans–if we are talking about God here—omnipotent, omnipresent and so on.
If God wanted to make 2 plus 2 equal 12—and have humans see it as perfectly normal —why wouldn’t he be able to do that? If God really does make the rules.
If it is counter to human logic –it is God who makes it so.
I mean look at the world—paradox and horror all around
—–murder and mayhem and corruption and ugliness mixed with beauty and goodness—-what kind of insanity is this? If there is a God and he makes the rules–then I
say–he is nuts. If he wants to change my mind so that I think all is just ducky in this stupid place—I urge him to do so. And make it snappy.
Molly, indeed it is meant as a variation on semantic paradox, with the twist that it relies on some theological views about the existence of God and all that entails. I agree that it should not be the least bit surprising that if we grant the existence of an omnipotent being, then ‘real true paradox’ becomes possible. Many people infer that if God’s existence entails something paradoxical, then God must not exist. You and I are variously arguing the alternative: that the paradoxes are real and unavoidable.
Of course, Molly, the third option is that God is able to do paradoxical things in the sense that if he wills it then it occurs, but then it is impossible for God to will such a thing (by modus ponens).
Colin thinks this is ad hoc, but I think arguments using modus ponens on a conditional with an impossible consequent is a perfectly well-motivated way of arguing.
Oh, crap. I meant modus tollens, not modus ponens.
Yes, sorry David, I didn’t mean to ignore that option it just wasn’t at the forefront of my thought. Although I still feel that this is just not a good solution. This relies on possibility being primitive and specifiable antecedently to the specification of God’s properties. It seems to me that the ’spirit’ of the claim of God’s omnipotence is roughly that anything characterizable is actualizable.
Okay, but doesn’t that prove too much?
That would mean that, literally, anything is possible.
Think of some state of affairs that you believe to be impossible… turns out it’s not impossible because God could will it.
What about the state of affairs of some x being consistent and not identical to itself?
But what do you mean by “proves too much” here? Are you saying that on my conception of omnipotence, the existence of God would entail what is apparently false? If that is your point, then I don’t see why it is a problem. It is apparently false that some state of affairs could be consistent and non-self-identical, but that appearance is lifted once we take seriously the omnipotence of God. Alternately, perhaps you are worried about charity. My exegesis of theological doctrine should not commit the theist to anything unintuitive unless it is absolutely necessary to preserve the doctrine. I don’t know why we should be quite so charitable. I simply think that the ’spirit’ of the thesis of omnipotence does entail that, as you say, literally, anything is possible. I still can’t see a reason to revise this reading.
Umm… I must have forgotten your original reason for raising the divine liar. I thought you were trying to motivate dialetheism with it.
So, in respose to your preceding comment, can you say some more about why the theist just can’t deny your intuitions about the ’spirit’ of the claim that anything characterisable is actualisable if God is omnipotent?
Sure the theist can deny that, probably fairly easily since I am not even close to an authority on any theistic doctrine. The Divine Liar only motivates dialetheism on the grounds that a number of assumptions are true, amongst which the existence of God. Since I am not going to defend the existence of God, it is (for me) just a fun, throw-away argument meant to incite discussion.
Please check out this Illuminated Understanding of Acausal God
http://www.adidam.org/teaching/aletheon/truth-god.aspx
http://www.dabase.org/dht7.htm
How could this possibly be?
It is all explained in his auto-”biography”
http://www.kneeoflistening.com