Tuesday, February 15, 2011

Leibniz's other ontological argument

Leibniz was perhaps the first to explicitly realize that from

  1. Possibly, God exists
one can derive:
  1. God exists,
and that (1) is a non-trivial assumption that needs an argument. I am not clear on whether Leibniz's reasoning went through S5, as in the Plantinga ontological argument, but that's not the part of Leibniz's argument that interests me right now. What interests me is Leibniz's argument for (1). Leibniz gave two. One was based on his logical calculus of properties. I think that one failed, though Leibniz liked it. But the other was one that he thought was less powerful, but good enough for practical purposes:
  1. If a concept C is in common use, probably it is the concept of something possible.
  2. The concept of God is in common use.
  3. Therefore, probably, it is possible that God exists.
I think there is a lot to this argument.

There are all sorts of ways of building on Leibniz's argument:

  1. Suppose no clear impossibility has been found in C, while C has been in common-use over a great period of time, by a great number of users a number of whom were of high intelligence and to whom C was of great intellectual importance, then probability C is a concept of a possible being.
  2. But no clear impossibility has been found in the concept of God, etc., etc.
  3. Therefore, probably, it is possible that God exists.
  4. Therefore, probably, God exists.

One might try to parody the argument by finding a concept C such that the existence of something falling under C entails the non-existence of God. Here are some candidates:

  • a universe not created by God
  • a human being not created by God
  • an evil that God would not be justified in permitting.
I do not think any of these concepts have had nearly the same degree of common use, over the same length of time and by the same number of users as the concept of God. (For one, God is probably more central to the lives of typical theists than a universe not created by God is to the lives of typical atheists.) And the probability that (6) confers on the possibility of something falling under C surely depends on these quantities. Thus, the God case still wins out.


Sarraclab said...

Would it be fair to say that many atheists are committed to the belief that God's existence is possible in their accepting claims such as: "The following state of affairs is morally wrong: God exists and sends everyone (or some innocents) to hell."

Can an impossible state of affairs really be morally wrong? Does it make sense to say that it would be wrong for a man with circularly-square head to murder a married bachelor?

Kenny Pearce said...

Incidentally, it seems that Leibniz underwent some development on this point, connected with his decreasing optimism about the universal characteristic. Early on, it seems that Leibniz thought he could establish the possibility of God in a manner similar to what appears in the Godel argument. Later, however, he came to the conclusion that we human beings were not capable of analyzing concepts all the way into their ultimate constituents, and so there could always be conceptual connections we were missing. In post-1700 works, especially New Essays and Theodicy, Leibniz appeals to his doctrine of presumption, taken over from his early work on jurisprudence. It seems to be the view in these late works that there is an across-the-board presumption in favor of possibility. (Do you know of a text in which Leibniz talks about the concept having to be in common use in order for there to be a presumption in favor of its possibility?)

At any rate, post-1700 it seems that Leibniz thinks the strongest argument is the cosmological argument from contingency, partially because he recognizes that he hasn't succeeded in proving (1); he's only got a presumption in its favor.

Alexander R Pruss said...

You know, I confused my improvement on Leibniz with Leibniz. In the text I was thinking of, he only talks of presumption, not of common use.

Do you know any text where Leibniz actually gives the details of his argument for the possibility premise?

Here's an interesting argument I hadn't noticed before, in Gerhardt IV p.405: "On pourroit encore faire à ce sujet une proposition modale qui seroit un des meilleurs fruits de toute la Logique, sçavoir que si l'Estre necessaire est possible, il existe. Car l'Estre necessaire et l'Estre par son Essence ne sont qu'une même chose. Ainsi le raisonnement pris de ce biais paroit avoir de la solidité, et ceux qui veulent que des seules notions, idées, definitions, ou essences possibles on ne peut jamais inferer l'existence actuelle, retombent en effet dans ce que je viens de dire, c'est à dire qu'ils nient la possibilité de l'Estre de soy. Mais ce qui est bien à remarquer, ce biais même sert à faire connoître qu'ils ont tort, et remplit enfin le vuide de la demonstration. Car si l'Estre de soy est impossible, tous les estres par autruy le sont aussi, puisqu'ils ne sont enfin que par l'Estre de soy: ainsi rien ne sçauroit exister. Ce raisonnement nous conduit à une autre importante proposition modale égale à la precedente, et qui jointe avec elle acheve la demonstration. On la pourroit enoncer ainsi: si l'Estre necessaire n'est point, il n'y a point d'Estre possible. Il semble que cette demonstration n'avoit pas eté portée si loin jusqu'icy: cependant j'ay travaillé aussi ailleurs à prouver que l'Estre parfait est possible."

This is, I think, a way of using the cosmological argument to buttress the ontological.

Kenny Pearce said...

My French is somewhat limited. The gist of that text, if I have understood it correctly is that if God is possible he exists necessarily, and we can know that he's possible because we know, by the cosmological argument, that he is actual. Is that right? There's a passage very similar to this in the "Specimen of Discoveries" (c. 1686), Morris and Parkinson, pp. 76-77.

It appears that I was wrong in my last comment: Leibniz continues to think he has a possibility proof pretty much to the end of his life. (I think I read otherwise in a secondary source somewhere.) He refers to (but doesn't give) one in NEHU 4.10.7. Remnant and Bennet say that the reference is to a work called "Extrait d'une lettre touchant la demonstration cartesienne de l'existence de Dieu," which I don't think I have (perhaps it is in Loemker; I haven't been able to acquire a copy of that). Also, there is Monadology 45: "And as nothing can prevent the possibility of something which contains no boundaries, no negation, and therefore no contradiction, that in itself is enough for us to perceive the existence of God a priori" (tr. Woolhouse and Francks).

The Sobel book I've been reviewing quotes the following from Loemker, p. 166: "By a perfection I mean every simple quality which is positive and absolute or which expresses whatever it expresses without any limits. But, because a quality of this kind is simple, it is unanalyzable and indefinable ... From this it is not difficult to show that all perfection are compatible with each other or can be in the same subject." This text is dated November 1676 - very early - and looks a lot like Godel's argument.

Alexander R Pruss said...


I think the argument I quoted is something like this:

1. x is a necessary being iff x exists of its essence iff x exists of itself.
2. [Necessarily] if nothing exists of itself, then nothing exists of another.
3. So, if it is not possible to have a necessary being, it is not possible to have a being that exists of itself.
4. So, if it is not possible to have a necessary being, it is not possible to have a being that exists of another.

I assume that Leibniz then intends us to say:
5. It is possible to have a being that exists of another.
6. So, it is possible to have a necessary being.

But now that I've written it out I don't see the point. After all, if you have 1, 2 and the uncontroversial claim that there is a being that exists of another, you can directly conclude to the actuality of a necessary being, without any recourse to the ontological argument. The cosmological argument here reminds me of Aquinas' Second Way--there we get the idea that there cannot be intermediate causes without a non-intermediate cause.

The one place I know where Leibniz gives something like a possibility argument is in his letter to some high-placed woman whose name I can't swear to right now. The argument there seems to be that, as you say, all basic perfections are compatible. I've assumed that the reasons weren't Goedelian, but rather that he thought that basic perfections are the basic qualities out of the combinations of which all other qualities are built in his logical calculus. Thus, the idea would be that all combinations of basic perfections would be coherent, and in particular it would be coherent to have the conjunction of them all.

If that's his argument, there is a serious problem. Either necessary existence is a basic perfection or not. If it is a basic perfection, and all combinations of basic perfections are coherent, we get an infinite number of necessary beings of all weird sorts, as there are infinitely many combinations of the other basic perfections that can be combined with necessary existence. So we have lots of parodies. If necessary existence is not a basic perfection, then the ontological argument will require that necessary existence be entailed by the conjunction of the basic perfections. But Leibniz hasn't given us an argument or this entailment. Maybe it's intuitive.

Alexander R Pruss said...


Maybe an impossible state of affairs can be morally wrong. Consider this state of affairs: Napoleon sends everyone, including innocents, to hell. If a state of affairs can be wrong (I am not sure--maybe only actions and omissions can be wrong), this one is wrong. But it's also impossible.

Kenny Pearce said...

I would've thought that part of the point of bringing in the ontological argument is to show that God is "an explanation with which to stop." God's existence needs explanation too, just not efficient causal explanation. We can explain why the number 2 exists: its non-existence implies a contradiction. Similarly, the ontological argument is supposed to show that God's non-existence implies a contradiction. That, I think, is why Leibniz thinks it is still important to run the ontological argument, even after we've already established that God exists. It explains God's existence.

Emanuel Rutten said...

Dear Alexander,

An opponent of theism might try to defuse the ontological argument by providing the following argument:

(1) Possibly, God does not exist.
(2) Therefore, God does not exist,

This argument, he or she might say, together with the ontological argument, brings us in a state of equipollence.

How would you respond to such an opponent?

Kind regards,
G.J.E. Rutten

Alexander R Pruss said...

First of all, equipollence is progress from atheism. Atheists don't accept equipollence.

Second, my defeasible principle of possibility does not apply in the case of this argument. Remember, the principle is, in its simplest form, that if a concept C is in common use, probably it is the concept of something possible. The concept of God is in common use, so probably it is the concept of something possible.

But I don't think one can successfully use the principle to support "Possibly God doesn't exist".

Emanuel Rutten said...

Hi Alexander,

Plausibly, the proposition that naturalism is true implies the proposition that God doesn't exist.

Now, our opponent might argue that the concept of naturalism (spacetime and its contents is all that exists) is in common use as well.

Therefore, he or she might say, by following your principle, naturalism is actually the concept of something possible, i.e. the concept of naturalism refers to a possible state of affairs.

But this does in fact support the proposition "Possibly, naturalism is true" and thus, by implication, it supports the proposition "Possibly God doesn't exist" as well.

G.J.E. Rutten

Alexander R Pruss said...

Naturalism is a doctrine or a proposition, rather than a state of affairs.

Now, maybe, you could talk of the concept of the state of affairs of the world being naturalistic. Since naturalism is in part a negative doctrine, whether this makes sense depends on whether negative states of affairs make sense. I don't even know if naturalists employ the concept in question--some naturalists don't believe in states of affairs, some of those who do, don't believe in negative ones, etc. Armstrong, though, will be an example of someone who has such a concept.

Sam Calvin said...

Alex, I think the letter to which you refer was written to Lady Anne Conway. I'll see if I can track it down.