Saturday, December 1, 2007

Relative necessity and the ontological argument

The standard modal ontological argument (e.g., in Plantinga, with roots in Leibniz) says basically:

  1. Possibly, necessarily God exists.
  2. Therefore, necessarily God exists.
But here is something neat that hasn't been explored sufficiently and that I've learned from some remarks by my colleague Todd Buras. The modal ontological argument works with relative necessity in the place of necessity, where we say that a proposition p is necessary relatively to q iff q entails p. Relative necessity is weaker than necessity. In the cases I will be interested in, q is true, since anything that is necessary relative to a true proposition is true. The following argument then is valid:
  1. Possibly, the proposition that God exists is necessary relative to q. (Premise)
  2. Therefore, the proposition that God exists is necessary relative to q.
  3. q holds. (Premise)
  4. Therefore, God exists.
The inference from 3 to 4 holds because, by S5, if an entailment possibly holds, it actually holds. It's worth noting that the "Possibly" in 3 is not relativized, which is a good thing because relative possibility is stronger than possibility (just as relative necessity is weaker than necessity).

So, to make a modal ontological argument work, we don't need to establish that possibly necessarily God exists. All we need to establish is that possibly, God exists relatively necessarily, relative to some true proposition q.

One plausible candidate for q is the proposition is that I exist. For it might be that I find it conceivable that I essentially depend on God for my existence, and conceivability is evidence for possibility, so possibly I essentially depend on God for my existence. Thus, possibly, God necessarily exists (relative to the proposition that I exist), and hence God exists.


Derrick said...

As one that loves the ontological argument, I welcome any attempt to validate it. However, I have two issues. First, how do you show that the possibility of God's existence relative to q is metaphysical rather than simply epistemic? You seem to have justified it as the latter, but what about the former? Secondly, does this modified notion of the possibility premise entail only that God is metaphysically necessary in Swinburne's sense of the necessary?

David said...

It isn't rational to believe that it is conceivable that you depend essentially on God for your existence unless you believe that it is conceivable that God exists. Then,if in the relative necessity argument you use the principle that conceivability is evidence for possibility to establish possibility, you seem also committed to holding that it is possible that God exists. But since if God exists, he exists necessarily, then you are committed to the accepting the first premise of the modal ontological argument. it isn't clear, then, that someone who doesn't already accept the modal ontological argument can accept the new argument. (I'm of course assuming that the modal ontological argument is valid and that the controversial part is whether the first premise is true.)

Alexander R Pruss said...

Thanks a lot for the comments!


Conceivability is a guide not to epistemic possibility but to metaphysical possibility.

The conclusion is indeed not that God's existence is metaphysically necessary, but that God's existence is relatively necessary relative to q.


It seems to me that your comment assumes a principle that if p entails q, then it is not rational to believe p without believing q. But that principle is false. It may be true that if p entails q, then believing p commits one to believing q. But if that's a problem, then it afflicts every deductive argument.

I should add that it is possible to believe that one's existence essentially depends on an essentially omniscient, omnipotent and all good being without believing that that being would exist necessarily.

David said...

Thanks very much for your response to my comment. You are certainly right that the principle that if p entails q, then it is not rational to believe p without believing q is false. But I don't think the first part of my objection rests on this principle. Rather, I think I need only to say that there are instances in which if p entails q, it isn't rational to believe p without believing q. Compare: If I believe that it it is conceivable that Alexander Pruss will post at least three original philosophical arguments next week, it would be a failing in rationality on my part if I lacked the belief that it's conceivable that Pruss exists. In like fashion, it seems to me intuitively obvious that it would be not be rational for someone who lacks the belief that the existence of God is conceivable to think that it is conceivable that his existence depends essentially on God.

I think that your point is valid against my claim that only someone who accepts the modal ontological argument will find the relative necessity argument persuasive. What I should have said is that someone who accepts the relative necessity argument should also accept the modal ontological argument---but that isn't an objection to your argument.

Alexander R Pruss said...


I think rational minds might move in different directions. For instance, I might have a religious experience of myself essentially depending on God. If I am of a skeptical bent, I might not conclude that God exists--I might worry that the experience is non-veridical. However, I might accept that what I am experience is at least conceivable--the experience helps me to conceive it (just like visualizing a geometrical situation helps us to conceive it). Thus, I would conclude that myself essentially depending on God is conceivable, and hence that, probably, possibly I essentially depend on God. Of course I can deduce from the claim that I possibly essentially depend on God that possibly God exists. But that deduction is a genuine deduction, and before I draw it, I only believe that possibly essentially I depend on God, and not that possibly God exists. That I have a delay in drawing a deduction does not make me irrational. :-)

Apolonio said...


i think alex's last comment in his first response to you should be kept in mind. alex's argument does not necessitate anyone accepting the modal ontological argument because God relatively necessary to q does not mean that He is necessary in r, s, t, etc. So, He may be necessary in creating Alex, me, or the actual world but He may be contingent. In fact, I would say that Aquinas' third way argues for relative necessity rather than metaphysical necessity.

It would be interesting to see how the relative necessity of God can give way to metaphysical necessity though.


In response to Derrick, you said, "God's existence is relatively necessary relative to q." Isn't that different from "God's existence is necessary relative to q"? I'm not sure what relatively necessary relative to means.

Also, is the argument the same as Hawthorne's argument from the principle of necessary reason?

Alexander R Pruss said...

By "p is relatively necessary relative to q" I just mean "p is necessary relative to q". There should be a comma between "necessary" and "relative" :-)

Derrick said...

At the risk of sounding thick-headed, I'm not sure what you mean when you say that conceivability is not a guide to epistemic possibility. Given the fact that we find it conceivable that water isn't H2O (a metaphysical impossibility, but a legitimate epistemic possibility) show that it is also a guide to epistemic possibilities?
Also, it's still not clear that conceivability in this case has shown us anything that moves us closer to being justified in saying that it is *really* possible that God's existence is necessary relative to q. Couldn't the atheist simply retort that it is possible that it is not necessary relative to q as well? Have a good night.

Alexander R Pruss said...


We can conceive of lots and lots of stuff that is not epistemically possible. I can conceive of myself having only one arm, of there being unicorns in Paris, etc. None of this conceiving takes much effort at all, but the possibilities conceived of are not epistemically possible for me.

The atheist can make the move you suggest, yes. Then she and the defender of the ontological argument would have to fight it out as to which conception is a better guide to possibility. :-)