Friday, May 28, 2010

Ontological arguments

Continuing my project of reading my hitherto unread reading assigned for the medieval comp, I've been reading Anselm's replies to Gaunilo. As it happens, I never read all of it. When I assigned the text for class, I assigned only an abridged version which at one point says "Anselm continues as some length, but much of what he says seems repetitive". Well, maybe it seems that way to the translator, but the full text is really good stuff. I haven't digested it all, but I think there may be more to Anselm's ontological argument than has caught my eye before. It's at least as good as the S5 ontological argument.

That said, here's another ontological argument, inspired, if memory serves, by a humorous remark my wife made to me once.

  1. (Premise) To be incapable of existing is a great impotence.
  2. (Premise) Necessarily, anything that is all powerful lacks all impotence.
  3. (Premise) A being that exists and is all powerful in one world must exist in all other worlds.
  4. (Premise) God is essentially all powerful.
  5. God lacks all impotence. (2 and 4)
  6. Possibly God exists. (1 and 5)
  7. There is a world at which God exists and is all powerful. (4 and 6)
  8. God exists in all worlds. (3, 7 and S5)
  9. God exists and is omnipotent. (4 and 8)

Step 3 gets a subsidiary argument. More than one comes to mind. But here is one:

  1. (Premise for reductio) Suppose x exists and is all powerful at w but does not exist at w*.
  2. (Premise) Necessarily, to be unable to be an efficient cause of any sort (remote or immediate, full or contributing, etc.) of a possible but non-necessary state of affairs is an impotence.
  3. (Premise) Necessarily, nothing is able to be an efficient cause of any sort of its own failure to ever exist.
  4. x's failure to ever exist is a possible but non-necessary state of affairs. (10)
  5. It is true at w that x is unable to be an efficient cause of any sort of its failing to ever exist. (12)
  6. It is true at w that x is not all powerful. (2, 11, 14) Which absurdly contradicts (10).
  7. So if x exists and is all powerful at w, it must exist at every other world w*.

I don't know how seriously this argument is to be taken. By the way, it reminds me of something I heard attributed to Scotus.


Sarraclab said...

If by "I don't know how seriously this argument is to be taken" you mean there's probably some solid objections to it, that's fine. But if not, then why not take it seriously? I'm thinking maybe something along the lines of the attitude that ontological arguments are too good to be true, so we should doubt them. In my opinion, yes, they are to good to be true - personally, that's why I love them. If we have the ontological argument well-defended, wouldn't the task of Natural Theology be accomplished? I think of this Kant quote: "If, therefore, we observe the dogmatist coming forward with ten proofs, we can be quite sure that he really has none. For had he one that yielded... apodeictic proof, what need would he have of the others?"

Also, one common charge against theism is that it keeps rehashing the same arguments and hasn't come up with new ones in hundreds of years, lowering the probability that a new and successful argument will emerge. I see this argument and all your many other yet undeveloped arguments as flying in the face of this. Maybe if theistic philosophers took a break from defending the same basic arguments they could dream up a lot of new and better arguments for the next generation, who knows.

Peter Youngblood said...

Dr. Pruss,

I'm not sure, but something seems wrong with (1). Is it right to say that a mere possibility can be really impotent?

Ap said...

hey alex,

have you looked at Zalta's way of showing the validity of Anselm's argument?

Alexander R Pruss said...


"one common charge against theism is that it keeps rehashing the same arguments and hasn't come up with new ones in hundreds of years"

There may be theorems in Euclid for which this is true. So what?

That said, there are plenty of new and interesting arguments. :-)

I don't know how seriously this argument is to be taken because my fishiness meter goes Ping! (or should that be Splash!?) at (1). However, I think something in the vicinity might be right. There is something to the idea that an impossible being would be imperfect (indeed, it would have all imperfections, since an impossibility entails all properties), so a perfect being must be possible. Hmm. Let me blog that separately.

Alexander R Pruss said...

No, I don't know Zalta's work.

Jarrett Cooper said...

With these ontological arguments, how confident do find using the axiom S5 (hopefully I said that properly).

I'll see in blogs (atheism blogs) that S5 is suspect. I've seen one cite Hugh Chandler, “Plantinga and the Contingently Possible,” Analysis 36 (1976): 106-109; and, Nathan Salmon, “The Logic of What Might Have Been,” Philosophical Review 98 (1989): 3-34. These papers also argue against S4, and B.

I notice, however, these papers are not new by any means. Just curious on how confident you feel using S5.

Alexander R Pruss said...

I have arguments for S5. First, S5 seems to follow from my account of modality in terms of powers (together with one or two reasonable assumptions).

It's easy, I think, to argue for S4. Metaphysical possibility is an ultimate possibility. This means that there isn't some weaker kind of non-arbitrary possibility. But if S4 is false, then there is a weaker kind of non-arbitrary possibility: possibility-of-possibility.

B is harder, but I do have the intuition that what is couldn't have been impossible.

Think also of metaphysical possibility as conformity with the most fundamental laws. If these laws can differ from world to world, they are not fundamental. But if they can't differ from world to world, S5 is true.

Unknown said...

Dr. Pruss, I've been working on a kind of cosmological-ontological argument:

1. There is a possible state of affairs in which no contingent being exists. (Premise)

2. It is necessarily the case that possible states of affairs are at least partially explicable. (Premise)

3. It is necessarily the case that something is explicable only if something exists. (Premise)

4. Therefore, a necessary being exists.

(4) follows from S5, but I think the argument can even work without it.

Any thoughts?

Alexander R Pruss said...

Sounds good to me. :-) I'd change 2 to say "contingent" in place of "possible", though.

Unknown said...

I can't remember off the top of my head what your position on this is, but does a necessary being have an explanation? I'm thinking it would be explicable (re: capable of explanation) in terms of its own self-sufficiency.

Alexander R Pruss said...

I leave that open. My official PSR is that every contingently true proposition has an explanation. I suspect that every true proposition has an explanation.

James Bejon said...
This comment has been removed by the author.
James Bejon said...

Here's a sort of ontological argument I've been considering for a while:

(1) It is good for any wrongdoer to be completely forgiven his wrongs (given his meeting certain conditions), that his wrongs not be incureable.

(2) From (1), it is possible that any wrongdoer's wrongs be completely forgiven, completely put right.

Now, call F the forgiver that grounds (1)'s possibility. What sort of thing must F be? Clearly, F must be a person. But F cannot be the wrongdoer himself (or soceity as a whole), for such candidates for F may not have the power to make restitution for the wrongdoer's wrongs in a material sense (suppose the wrongdoer has murdered someone, or destroyed an object he can't replace).

F must therefore be all-powerful. (If he isn't, there are wrongs he can't put right).

It also seems clear that F must be all-good. (Suppose F' is an all-powerful being who is not all-good. Then F' is capable of sin. But it does not seem fitting for F' to forgive himself. Yet there cannot be more than one all-powerful being. So, there is nothing to ground the possibility of the sin of F' being curable, which contradicts (1)).

What else can be said of F?

Well, we seem to have the intuition that forgiveness must in some sense be 'on behalf of' the wronged party. But for this to be possible, the forgiver must be very 'close' to the wronged party. Consider a tribe somewhere where a young boy has been murdered and the tribe plan to punish the murderer in some way. A stranger to this tribe has no right to ask that the penalty be waived. But someone close to the victim (say, his mother) does seem to have this right--perhaps because of her responsibility for her son, or her love for him, or her knowledge of his character, or some other property, suggesting that forgiveness can take place where there is sufficient closeness between the forgiver and the wronged party. F must therefore be something like the ground of all being.

I know this isn't very rigorous. But it seems to me like a lot of the attributes of God can be derived from considering the nature of the forgiver who makes (1) possible. In which case

(3) Possibly, God exists.

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