Pretend that the following argument is sound. Let ‘God’ abbreviate the indefinite description ‘a being than which none greater can be conceived’.
Argument EP
- If God exists, then he is omniscient, omnipotent, omnibenevolent and necessarily existing.
- For all x, if x is omnipotent then x can make it true that ~(water = H2O).
- It is metaphysically impossible that ~(water = H2O).
- There exist no omnipotent beings. From 2,3
- /:. God does not exist. From 1-4
As everyone knows, it is necessary a posteriori that water = H2O. And as everybody knows the proposition that ~(water = H2O) does not express a contradiction. It is perfecty consistent with everything said so far that there is a world in which God does exist. That is, (6) is consistent with (1)-(5), (I use ‘epistemic possiblity’ in (6) in the atypical way that Chalmer’s does).
(6) It is epistemically possible that God exists.
And if God exists in any world, then God exists in every world. Now the crucial observation: The proposition expressed by ‘God exists’ is the same from the point of view of every world. That is, in any world in which it is uttered, the sentence expresses the same proposition. But the proposition expressed by ‘water = H2O’ is not the same from the point of view of every world. From the point of view of some worlds, that water = H2O is necessarily true, and from the point of view of other worlds it is just false. That’s how it can be true here that water = H2O (the proposition expressed when the sentence is uttered here) and false here that water = H2O (the proposition expressed when the sentence is uttered in world w1000) without contradiction. But the following two propositions are inconsistent: they cannot both be true here.
(7) God does not exist (i.e., the proposition it expresses when uttered here).
(8) God exists (i.e., the proposition it expresses when uttered in w1000).
So, does God exist here or not? Since it is epistemically possible that God exists, it follows that God exists in every world including our own. How do we know? Look, if there is some world in which God exists, then the proposition expressed by ‘God exists’ is true in every world. But the proposition expressed by ‘God exists’ is the same in any world in which that sentence is uttered. But then the sentence ‘God exists’ uttered here, in the actual world, must express a truth. Therefore God exists. But wait, (3) states:
(3) It is metaphysically impossible that ~(water = H2O).
and (2) states this:
(2) For all x, if x is omnipotent then x can make it true that ~(water = H2O).
So how could it be true that God exists here? The right conclusion, I suggest, is that it is epistemic possibility that matters to proofs that God exists (or not), not metaphysical possibility. Or, rather, if God is epistemically possible, then God is metaphysically possible. But then (3) is true, but (2) is false, and argument EP is unsound.
(3) It is metaphysically impossible that ~(water = H2O).
I think (3) is false and am inclined to think its negation is necessary. Ned Block was just here and suggested that water is constituted by H2O, but since constitution is asymmetric, whereas identity is symmetric, it is false that water = H2O. I find this plausible. Other examples include heat is mean kinetic energy. Here 'is' expresses constitution rather than identity, or the mind is constituted by cetain parts of brain standing in certain relations. The mind is not identical to the brain, but is constituted by it. Perhaps there is another example that would serve your argument just as well.
Mike,
How much work is your preliminary that 'God' abbreviates a particular definite description doing? Is this why you can say that the proposition expressed by the words "God exists" is the same no matter what world those words are uttered in? I'm not sure why *any* string of words would express the same proposition no matter what world they are uttered in.
When you say, "the proposition that ~(water=H2O) does not express a contradiction," are you saying that the proposition expressed by those words is not of the form P & ~P, or that it does not entail a proposition of the form P & ~P?
In the paragraph that begins, "And if God exists..." there is a string of sentences about water = H2O. Would the following be an accurate paraphrase of those sentences?
"But which proposition expressed by the words ‘water = H2O’ depends on the world in which the words are uttered. In some worlds, the words 'water = H2" expresses a proposition that is necessarily true. In some worlds, those same words express a proposition that is false. That’s how the words "water = H2O" can express, when uttered in our world, a proposition that is true in our world, and the same words, when uttered in a different world, can express a proposition that is false in our world, without contradiction.
I'm not sure why *any* string of words would express the same proposition no matter what world they are uttered in.
I could have been clearer. I'm considering worlds as epistemic possiblities here. So, I am asking what the sentence 'God exists' expresses should we discover that some other world is actual. Should it turn out that there is no H2O (it was some scientific hoax, say) but only XYZ, the sentence 'water = H2O' expresses something different from what I think it expresses. But no matter what we discover about which contingent facts actually obtain the sentence 'God exists' expresses the same thing. I'm assuming, though it seems pretty clear, that 'God' is not a name rigidly designating the best being we've got here.
(3) It is metaphysically impossible that ~(water = H2O). I think (3) is false and am inclined to think its negation is necessary. Ned Block was just here and suggested that water is constituted by H2O, but since constitution is asymmetric, whereas identity is symmetric, it is false that water = H2O.
If the negation of (3) is necessary, then (3') is true. I don't know what I think about (3').
(3') It is necessary that it is possible that ~(water = H2O).
In any case, I don't want to arbitrate the debate among those who think of constitution as identity and those who don't. All I need is some metaphysically necessary proposition that will serve.
Hi Mike,
I'm not sure I follow. Why can't the non-theist do the same thing to justify the claim that no necessary being exists? Thus, suppose I consider a godless world as actual -- there are just some occupants that play the role of the fundamental particles, and all else logically supervenes on that. So a godless world is epistemically possible, in which case a godless world is metaphysically possible, in which case a necessarily existent god is metaphysically impossible.
It looks like we have a parity problem here. What got us here? Here's my conjecture: The constraints on Chalmersian epistemic possibility are too permissive.
Hi Mike:
Why think it true that an omnipotent being can make metaphysical impossibilities true?
I.e., what if I said it follows from (2) that (3) is false, so that you can't hold both at once?
(Also, Chalmers' sense of epistemic possibility is, as I understand it, pretty darn strong. Just out of curiosity, where do yo think the argument gets us--what does the conclusion imply about how we ought to assess theistic proofs? I'm having trouble seeing it ... )
Why think it true that an omnipotent being can make metaphysical impossibilities true?
Luke,
Certainly (no?) God might have actualized a world in which the watery stuff is not H2O, despite the fact that, from the point of view of our world, it is necessary that water = H2O.
Felipe, you write,
So a godless world is epistemically possible, in which case a godless world is metaphysically possible, in which case a necessarily existent god is metaphysically impossible.
I'm not sure that a godless world is epistemically possible (in Chalmer's sense of the term). It is so only if it is a priori impossible that God exists. Some people claim that they do not know whether God's existence is a priori impossible or not. Sobel says stuff like that. Maybe that's right, but in fairness I doubt it. All this aside, I'm just trying to show that Kripkean a posteriori necessities (these are often brought up in this context) are just not relevant to the question of God's existence. This I think would be important to know. If God's existence is established independently of the metaphysical necessities that obtain, then claims like the one in (2) (and all of the similar one's we can dream up) are just false, even if (3) is true.
Mike:
I think that's exactly right. In fact, the case of a necessarily existing God is a standard problem case for two-dimensional semantics, since they have to either say that God actually exists or that God is not an epistemic possibility. Chalmers is willing to bite the bullet and say that in his sense, God's existence is not epistemically possible.
Anyway, what this means is that ontological arguments do not need to worry about the fact that there are Kripkean counterexamples to various conceivability principles. For instance, I once proposed the principle: "If it quasi-perceptually seems to someone that p, then possibly p." As a grad student of ours has pointed out (in a paper that I think is under submission), there are Kripkean counterexamples to this. (It quasi-perceptually seems to George that this body of liquid is water. But in fact it is vinegar.) But one can get out of the Kripkean counterexamples by instead affirming the principle "If it quasi-perceptually seems to someone that p, then either metaphysically or epistemically possibly p."
I make this two-dimensionalist move in a paper under submission where I argue that propositions at the motivational centers of flourishing lives are probably possible.
I'm not sure. There might be a really tight link between causal/dispositional features and categorical properties. So that anything that is H2O has the dispositional features associated with the watery stuff around here, and vice-versa. Shoemaker and Bird (and others) have views that suggest this.
Maybe I'm just getting off the train before it leaves the station ...
Luke,
I'm not sure I follow you. Here we are in the actual world in which it is a contignent feature that the watery stuff is H2O. Now there are some contingent features of worlds that God cannot change--God cannot cause you to freely choose A rather than ~A, despite the fact that it is contingently true that you choose ~A. But how could it be that God could not have cuased it to be true that the watery stuff--whatever is playing the watery role--is XYZ instaed of H2O? He would do so simply by causing those lakes and aquifers to be filled with XYZ instaed of H2O. It is hard to see how this would not be possible. But had he done so, it would not be necessarily true that water is H2O.
Mike,
I think Luke's point is this: if properties are individuated by their causal roles, as some philosophers think, then God could not have caused any other property to have played the causal role that being H20 actually plays.
Still, Luke, he could have filled the lakes with XYZ, where XYZ's causal role is *very similar*, but not identical, to the causal role of H20.
Mike,
You write,
I'm not sure that a godless world is epistemically possible (in Chalmer's sense of the term). It is so only if it is a priori impossible that God exists. Some people claim that they do not know whether God's existence is a priori impossible or not.
I think I need help seeing how this moves us beyond my original point. The same thing could be said, with equal force (if all we have to go on are Chalmers' epistemic possibilities) in defense of the epistemic possibility of a godless world: one's possible only if the other's impossible. But both seem equally epistemically possible. So again, what moves us beyond the parity?
I think Luke's point is a strong one. Bird's stuff on this (I haven't yet read his monograph on the topic, but his paper, "Necessarily, Salt Dissolves in Water" (In Analysis. Can't remember the date of the issue) makes this point.
Thanks Jonathan. This is what I mean.
Right, XYZ's causal role could be very similar to the one played by H20. Maybe this comes down to what we mean by 'the watery stuff around here.' God might be able to make a world where XYZ has many of the causal or dispositional features of the watery stuff we find at the actual world. But I think the Shoemaker-esque view I have in mind would deny that God could make a world where the causal or dispositional features of XYZ are strictly the same as the causal or dispositional features of the watery stuff at the actual world.
God might be able to make a world where XYZ has many of the causal or dispositional features of the watery stuff we find at the actual world. But I think the Shoemaker-esque view I have in mind would deny that God could make a world where the causal or dispositional features of XYZ are strictly the same as the causal or dispositional features of the watery stuff at the actual world.
I'm not sure this is so. Look, suppose the lakes were filled with XYZ. You would then be saying that the dispositional properties of XYZ were those water had in some essential way. That not even God could make it the case that water had the dispositional properties of H2O. But of course he could. Since then I'd be saying that if the lakes were filled with H2O you'd be saying that the dispositional properties of H2O were those water had essentially.
In short, God can choose the dispositional properties that water has essentially--supposing there are in fact any such properties that it has essentially.
I think I need help seeing how this moves us beyond my original point. The same thing could be said, with equal force (if all we have to go on are Chalmers' epistemic possibilities) in defense of the epistemic possibility of a godless world
Perhaps it is at a standoff, but this depends on the a priori arguments for/against. But this is not my main worry. As I said above,
All this aside, I'm just trying to show that Kripkean a posteriori necessities (these are often brought up in this context) are just not relevant to the question of God's existence. This I think would be important to know. If God's existence is established independently of the metaphysical necessities that obtain, then claims like the one in (2) (and all of the similar one's we can dream up) are just false, even if (3) is true.
Mike,
On the view of properties Luke's referring to, the following is true: If, in fact, the complete causal role (dispositional profile, you might say) of H2O is in fact C, then necessarily, no other property else has exactly C as its complete causal role (dispositional profile).
It may be that, in fact, H2O does not have the profile we think it does. And it may be, in fact, that something else has that profile. But whatever it's actual profile, it and it alone has it, of necessity.
Am I correct in thinking you're saying that which property "water" picks out depends on what the world is like. (It's not a rigid designator.) And so God could create one world in which "water" picks out a property with dispositional profile C1, and he could create a different world in which "water" picks out a property (a different one!) with dispositional profile C2?
If so, then your claim is consistent with the view Luke's referring to.
On the view of properties Luke's referring to, the following is true: If, in fact, the complete causal role (dispositional profile, you might say) of H2O is in fact C, then necessarily, no other property else has exactly C as its complete causal role (dispositional profile).
I agree that this is what he has in mind. What I said was that the dispositional properties of water depends on what gets put in the lakes. This is consistent with saying that the dispositional properties of H2O is invariant. H2O might not be the stuff in the lakes, even as we speak.
Am I correct in thinking you're saying that which property "water" picks out depends on what the world is like. (It's not a rigid designator.)
Yes, to the first, no to the second. What 'water' picks out depends on what happens to be in the lakes, etc. We agree that that stuff is not the same in every world. But of course 'water' rigidly designates whatever happens to be there.
Alex,
Nice paper. Thanks for the link.
Right, I've been assuming that we're correct in our belief that water is H20.
If we drop the assumption, why think (3) true in the first place?
But if we're correct that water is H20, then, on the view I'm assuming, we can deny (2). No?
Right, I've been assuming that we're correct in our belief that water is H20. But if we're correct that water is H20, then, on the view I'm assuming, we can deny (2). No?
Either I'm not understanding you, or you me. Let's make the assumption that the stuff in the lakes is H2O. In that case it is metaphysically necessary that water is H2O. Could God have made it the case that water is not H2O? Sure, he could have actualized a world in which XYZ fills the lakes. Had he done so, we would have been refering to XYZ all along when using the world 'water'. So it is necessary that water = H2O but God could have seen to it that ~(water = H2O). Effectively, I am saying that God chooses the a posteriori metaphysical necessities that obtain.
"So it is necessary that water = H2O but God could have seen to it that ~(water = H2O). Effectively, I am saying that God chooses the a posteriori metaphysical necessities that obtain."
This isn't right, is it? What you want to say, I guess, is that while it is in fact necessary that water = H20, God could have made it the case that 'water = H20' is false. He could have done so by making it the case that that sentence expressed a different proposition. So, effectively, you're saying that God could choose which sentences express a posterior necessities. That doesn't imply that God can choose which propositions are necessary.
OK, I think I see more clearly what you're doing, and (after re-reading the last few comments) how the view I've been assuming is consistent with what you're saying. I'll have to think about it more. But thanks, I've found this an interesting discussion.
What you want to say, I guess, is that while it is in fact necessary that water = H20, God could have made it the case that 'water = H20' is false. He could have done so by making it the case that that sentence expressed a different proposition.
I don't think I said anything about propositions. But I might be misunderstanding the worry. I said this,
Effectively, I am saying that God chooses the a posteriori metaphysical necessities that obtain.
The metaphysical necessities that obtain would include that water is XYZ and would not include that water = H2O. But you seem to be saying that the proposition actually expressed by 'water = H2O' is not inconsistent with the proposition that might have been expressed by 'water = XYZ', and indeed the proposition actually expressed by 'water = H2O' is metaphysically necessary in the world that might have obtained in which it is metaphysically necessary that water = XYZ. Is that more or less it?
Mike,
That's more or less it. Let p be the proposition in fact expressed by 'water = H20'. p is not the proposition expressed by that sentence when uttered by my Twin-Earth counterpart. Let that proposition be p*. So, if God had made it the case that my environment was suitably different, he could have made it the case that the sentence 'water = H20' meant p* rather than p. He would not, thereby, have made p false. p would still be true, and necessarily so, though I would not be able to express it by uttering the sentence 'water = H20'. So, given that 'water = H20' in fact expresses p, and p is a necessary truth, there is no world where it is false that water = H20. But, there are worlds where the sentence 'water = H20' expresses a falsehood. Similarly, there is no world where it is necessary that water = XYZ, though there are worlds where the sentence 'water = XYZ' expresses a necessary truth.
He would not, thereby, have made p false. p would still be true, and necessarily so, though I would not be able to express it by uttering the sentence 'water = H20'.
All true. Interesting too, since these are not world indexed propositions which are true simpliciter in some worlds, w, and in every world true-at-w. They are true simpliciter in every world. It does make me wonder about the a posterioricity of the proposition that water is H2O. The truth of that proposition, as expressed here, depends on no contingent facts. It is true in worlds that have no H2O. Suppose I'm in an XYZ world. I would know that the proposition expressed by 'water = H2O' in worlds where the lakes are filled with H2O is true here in my XYZ world too. To know that requires modal knowledge, not empirical knowledge.