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Leibniz's Short Proof of Classical Theism

In a single paragraph near the beginning of the Theodicy, Leibniz gives a very compressed version of an argument a contingentia mundi (from the contingency of the world) from which he purports to derive not just the existence of God, but several of the most important traditional divine attributes (from which, Leibniz seems to think, the other divine attributes follow). In this post, I'll try to unpack Leibniz's reasoning. I'm not going to do too much evaluation of the arguments, since this post will be long enough without that; I'll just lay out the arguments as I see them and we can discuss their soundness in the comments.

First, here's the paragraph:

God is the first reason of things: for such things as are bounded, as all that which we see and experience, are contingent and have nothing in them to render their existence necessary, it being plain that time, space and matter, united and uniform in themselves and indifferent to everything, might have received entirely other motions and shapes, and in another order. Therefore one must seek the reason for the existence of the world, which is the whole assemblage of contingent things, and seek it in the substance which carries with it the reason for its existence, and which in consequence is necessary and eternal. Moreover, this cause must be intelligent: for this existence being contingent and an infinity of other worlds being equally possible, and holding, so to say, equal claim to existence with it, the cause of the world must needs have had regard or reference to all these possible worlds in order to fix upon one of them. This regard or relation of an existent substance to simple possibilities can be nothing other than the understanding which has ideas of them, while to fix upon one of them can be nothing other than the act of the will which chooses. It is the power of this substance that renders its will efficacious. Power relates to being, wisdom or understanding to truth, and will to good. And this intelligent cause ought to be infinite in all ways, and absolutely perfect in power, in wisdom and in goodness, since it relates to all that which is possible. Furthermore, since all is connected together, there is no ground for admitting more than one. Its understanding is the source of essences, its will is the origin of existences. There in a few words is the proof of one only God with his perfections, and through him of the origin of things (Theodicy, tr. Huggard, sect. 7)

Alright, let's see what we can make out of this. It will help to divide the argument into several stages. In the first stage, we show that a necessary being exists. In the second stage, we show that some necessary being has understanding, will, and power. In the third stage we prove that some necessary being is "absolutely perfect in power, in wisdom and in goodness." In the fourth stage, we show that the necessary being is unique. In the fifth and final stage we show that the unique necessary being (God) is the ground of both possibility (essences) and actuality (existences). The last two stages are so elliptical and opaque that I am not going to try to reconstruct them, for now. Besides, the first three stages are enough to count as a proof of the traditional God: if sound, they would show that, necessarily, there exists a being who is perfectly powerful, perfectly wise, and perfectly good.

Stage 1: Some Necessary Being Exists

(1.1) Everything has a reason for its existence. (Premise)
(1.2) A being which is or contains its own reason for existence is necessary. (Definition)
(1.3) A being which has a reason for existence distinct from and not contained in itself is contingent. (Definition)
:. (1.4) Every being is either necessary or contingent. (From 1.1-1.3)
(1.5) Every collection of contingent beings is itself a contingent being. (Premise)
(1.6) The World, the most inclusive collection of contingent beings, exists and is non-empty. (Premise)
:. (1.7) The World is a contingent being. (From 1.5 and 1.6)
:. (1.8) The World has a reason for existence distinct from and not contained in itself. (From 1.4 and 1.7)
:. (1.9) A necessary being is the reason for the existence of The World. (From 1.4 and 1.8)

The only slightly tricky inference is the last one. Depending on how we set up the logic of collections of contingent beings (that is, depending on our strategy for avoiding Russell's Paradox), we will say either that the World is the collection of all contingent entities, or that it is the collection of all contingent entities other than itself. (I tried to state the premise in a way that would side-step this issue.) Either way, if the reason for the World's existence is not the World itself or anything contained in the World, then the reason for the World's existence is not contingent, i.e., is necessary. (In this stage I assume, for simplicity, that nothing can be truly predicated of what does not exist, so "a necessary being is the reason..." implies "a necessary being exists." This assumption could be dropped at the cost of a little additional complexity and, indeed, will have to be dropped in the next stage.)

Stage 2: Some Necessary Being Has Understanding, Will, and Power

(2.1) Whatever has a reason for existence is actual. (Premise)
(2.2) Only one world is actual. (Premise)
:. (2.3) The reason for existence of The World (henceforth 'The Reason') is not a reason for existence for any other possible worlds. (From 2.1 and 2.2)
(2.4) If a being B1 is the reason for existence of a being B2, and there is a merely possible being B3 which has an "equal claim" to have B1 as the reason for its existence, then B1 must choose B2 over B3. (Premise)
(2.5) There are many possible worlds which have "equal claim" to have The Reason as the reason for their existence. (Premise)
:. (2.6) The Reason chooses The World over any other possible world. (From 2.3-2.5)
(2.7) Choosing requires understanding and will. (Premise)
:. (2.8) The Reason has understanding and will (From 2.6 and 2.7)
(2.9) A being B1 which chooses a being B2 is thereby the reason for B2's existence only if B1 has power. (Premise)
:. (2.10) The Reason has understanding, will, and power. (From 2.8 and 2.9)

Premise 2.2 follows fairly easily from 1.6, above. 2.4 will no doubt be contentious. Also, I don't know what "equal claim" means in this argument.

Stage 3: Some Necessary Being is "absolutely perfect in power, in wisdom and in goodness"

This part is really interpretively difficult, so let's remind ourselves of what Leibniz actually says:

Power relates to being, wisdom or understanding to truth, and will to good. And this intelligent cause ought to be infinite in all ways, and absolutely perfect in power, in wisdom and in goodness, since it relates to all that which is possible.

I'm not entirely sure how this is supposed to work, but I think the last clause, "since it relates to all that which is possible," must be the key component of the argument. Here's one possible reconstruction:

(3.1) The Reason chooses The World from among all the possible worlds. (Premise)
(3.2) There are infinitely many possible worlds. (Premise)
(3.3) A being which can choose between several alternatives must understand each of them. (Premise)
(3.4) A being which understood infinitely many distinct alternatives would be infinitely wise. (Premise)
:. (3.5) The Reason is infinitely wise. (From 3.1-3.4)
(3.6) A being which can choose between several alternatives must have the power to bring any of them about. (Premise)
(3.7) A being which could bring about any of infinitely many alternatives would be infinitely powerful. (Premise)
:. (3.8) The Reason is infinitely powerful. (From 3.1, 3.2, and 3.6)
(3.9) To choose something is to judge it the best among alternatives. (Premise)
(3.10) A being which could make a judgment as to which of infinitely many alternatives was best would be infinitely good. (Premise)
:. (3.11) The Reason is infinitely wise, infinitely powerful, and infinitely good. (From 3.1, 3.2, 3.5, and 3.8-3.10)

(3.9) is, of course, the Platonic/Augustinian theory of the will, which Leibniz consistently endorses (though sometimes in rather more subtle forms). Unfortunately for the argument, 3.9 and 3.10 are rather implausible, and 3.4 and 3.7 are open to question. 3.4, 3.7, and 3.10 could be taken as definitions (and this may be how Leibniz intends them), but then it wouldn't be clear whether the meaning of the conclusion was as interesting as it initially appears to be.

(Cross-posted at The Prosblogion)

Posted by Kenny at December 21, 2010 10:13 AM