Leibniz’s Short Proof of Classical Theism
December 21, 2010 — 13:45

Author: Kenny Pearce  Category: Existence of God  Tags: , , , ,   Comments: 16

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 blog.kennypearce.net)

Comments:
  • 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…

    December 21, 2010 — 13:49
  • David Warwick

    “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”
    “(2.7) Choosing requires understanding and will”
    I don’t see why this is true.
    Imagine a series of remote, uninhabited islands. A single pollen grain is blown into the area on the wind. Must either the pollen grain or the wind understand the alternatives before the pollen grain lands on one of the islands? Is the grain making a ‘choice’?
    If the ‘first cause’ exists, and was a very simple quantum particle only capable of instantly collapsing into one of two states, one of which would lead to universe A and the other of which lead to universe B … by definition it lacked consciousness and the ability to choose.
    So what do ‘reference’ and ‘choice’ mean here?

    December 21, 2010 — 16:04
  • Kenny Pearce

    Hi David,
    (2.7) seems pretty plausible to me. In order to count as ‘choosing’, it seems that you must have some sort of conception of the alternatives, and then favor one of them over the others. The former would be an exercise of the understanding, the latter an exercise of the will.
    I think your objections are better seen as counterexamples to my (2.4). The pollen grain and the particle both seem to become the ‘reason for existence’ of one state of affairs rather than another state of affairs with “equal claim” (whatever that means) without ever making a choice. This is the sort of thing I had in mind in saying that (2.4) would be contentious. It is of course possible to deny that the pollen grain or quantum particle are really the ‘reason for existing’ of any being or state of affairs, but it seems like we would then have to put God in this role, so the argument, thus modified, may be question-begging.

    December 21, 2010 — 16:59
  • Zeb

    It is of course possible to deny that the pollen grain or quantum particle are really the ‘reason for existing’ of any being or state of affairs,

    It is also possible to deny that any state of affairs actually has an equal claim to the pollen grain landing the particular island it does, or the particle collapsing to the state it does. The pollen grain and the quantum particle are not “choosing” their end states because not more than one end state was actually possible. I wonder if David is in fact challenging premise 1.1. If everything must have a reason for its existence, what could that reason be other than choice, determination, or necessity? Of those three, choice is the only one that admits of multiple possibilities. The interpretations of quantum mechanics that maintain ontological, not just epistemic, randomness apparently reject the belief that everything must have a reason for its existence. Perhaps the quantum particle in David’s example ends up in state B, but for no reason.

    December 21, 2010 — 22:47
  • Kenny Pearce

    Well, yes, there are a number of options for how to evade the argument. I was assuming that a cause is always a reason (but not vice versa). Most scientific realists think that quantum mechanics involves indeterministic causation, so in that case the unthinking cause would be the reason for the existence of a state of affairs despite the fact that there is another state of affairs that was equally eligible to have that cause as its reason for existence.
    Of course, I’m being a little sloppy with talk about beings, states of affairs, etc. Typically, philosophers think of states of affairs as abstract objects which exist necessarily but are contingently actualized or not. That’s basically just terminology though.

    December 21, 2010 — 23:14
  • David Warwick

    “The pollen grain and the quantum particle are not “choosing” their end states because not more than one end state was actually possible.”
    I don’t understand this. Say there were six islands in the chain, and the wind could have blown the pollen grain to any one of the six islands (or past the islands, or dropped it in the sea). Surely there’s more than one potential end state?
    Kenny,
    “In order to count as ‘choosing’, it seems that you must have some sort of conception of the alternatives”
    This is a much ‘harder’ definition than I thought you would give.
    I’m not sure I think that the very first thing in existence was a consciousness, and clearly it didn’t *have* to be.
    I’m trying to picture how Leibniz sees this first moment, and I see a ‘being’ like a man, with many paths in front of it, and somehow this being knows all the routes of all the paths and consciously chooses to walk down the path with us on it because it considers that ‘best’.
    This can’t be the first state of all existence – there’s a being that ‘has’ a consciousness, one with some sort of value judgement system (so values exist) the paths have been laid out, time would seem to have to exist because however fast this being can weigh alternatives, it would take time.
    Even if we allow the basic picture of this first state, why would the being have to be *perfectly* aware of the alternatives? Couldn’t it have been something like a fly’s consciousness and flown towards the brightest light, or a bacteria’s and moved to what looked like food? Or just moved to the longest or nearest? Why need it have made the ‘best’ or ‘right’ choice?
    And you use the phrase “unthinking cause”.
    If we accept there was a ‘first cause’, couldn’t we say something like:
    1. There was a first cause.
    2. Causes can be unthinking.
    3. Thinking beings are complex, unthinking ones can be simple.
    4. In the universe we observe, the spontaneous formation of simple beings has been observed but not that of complex ones.
    5. In the universe we observe, all the complex beings we know of have developed from simpler beings.
    6. In the universe we observe there are far more unthinking beings than thinking ones.
    6. It is more probable that the first cause was simple and unthinking.
    7. The first cause could have been unthinking.
    Whereas the way I’m reading Leibniz is extremely circular: you can prove God exists because there must have been a perfect consciousness as a first cause.
    Leibniz is cleverer than me, I’m sure you are … this can’t be the argument.

    December 22, 2010 — 7:12
  • Kenny Pearce

    David, I think there is a legitimate circularity worry, but the (possible) circularity is not so obvious/egregious. Leibniz’s implicit epistemology is contextualist: he’s perfectly comfortable, for instance, arguing in one context from the existence of God to the claim that this is the best possible world, and in another context arguing from the claim that this is the best possible world to the existence of God. But he is going to want a particular argument in a particular context to have premises which are plausible independent of the conclusion.
    Leibniz holds that God is simple and atemporal, so it doesn’t make much sense to talk about the “first moment” (though Leibniz sometimes uses imagery of this sort, as in the notorious ‘striving possibles’ story). Rather, God atemporally understands each of the possible alternatives, and wills one rather than any of the others. That’s the view he is trying to support.
    Now lets distinguish between stage 2 and stage 3. In stage 2, we argue that a necessary being has some kind of understanding, will, and power, whereas the perfection claim comes in only at stage 3. The reason I think (2.7) is on solid ground is that even the fly, I think, insofar as it genuinely chooses has some sort of conception, however vague, of the alternatives between which it chooses. That seems clearly right to me. If you don’t have any mental representation whatsoever of the options available to you, then you don’t make a choice. What’s harder is defending (2.4) and getting an interpretation of stage 3 where we get the conclusion to mean what we want it to without invalidating the argument.
    I think Zeb is on the right track as far as how Leibniz defends (2.4): we take a strong version of the Principle of Sufficient Reason (PSR), which is, of course, one of Leibniz’s most fundamental philosophical convictions. We then ask, how can it be that a state of affairs which is genuinely contingent has a sufficient reason? Leibniz answers that the only conceivable way that could happen would be for the sufficient reason to lie in a free choice. Thus everything that could have been otherwise could have been otherwise if someone had chosen differently, but the fundamental laws could have been otherwise, so someone must choose the fundamental laws, etc.
    There are two obvious replies to this line of thought. The first is to simply deny PSR. The second is to say that there is some other way for a genuinely contingent state of affairs to have a sufficient reason, and one might say that this occurs in the chancy causation involved in quantum mechanics.

    December 22, 2010 — 11:44
  • Zeb

    I don’t understand this. Say there were six islands in the chain, and the wind could have blown the pollen grain to any one of the six islands (or past the islands, or dropped it in the sea). Surely there’s more than one potential end state?

    As observers we have to consider more than one potential end state because of our limited knowledge, but in actual fact the prior state of the wind/pollen/islands will allow only one end state result. How do you suppose “the wind could have blown the pollen grain to any of the six islands” (italics mine)? Given the exact same wind/pollen/island situation, the pollen grain will land on the same island every time. That is, unless ontological randomness intervenes, in which case there is no reason why the grain lands on one island rather than another, or choice intervenes, in which case an intelligence is necessary.

    December 22, 2010 — 11:51
  • David Warwick

    “Given the exact same wind/pollen/island situation, the pollen grain will land on the same island every time.”
    OK … I think I see the difference, thanks.
    But surely, applying the same logic, 3.9 says God would pick the ‘best World’ from infinite options. So given the same situation, God will necessarily choose the same World every time, so only one end state is allowed.
    This choice is allowable, of course, but not as first cause.

    December 23, 2010 — 7:06
  • Kenny Pearce

    Yes, that’s right. This is fine for Leibniz, because he’s got a funky theory of contingency: a proposition is contingently true iff the predicate can be shown to be contained in the subject only by an infinite analysis. Since there are infinitely many possible worlds, and to show that one world is best requires making a pairwise comparison between all of the worlds, it is contingent that this world is best, and so it is contingent that God chooses this world (although it is necessary that God chooses the best world). This is pretty weird, and has some problems, so maybe we shouldn’t go all the way with Leibniz here. Personally, I think 3.9 is false anyway.

    December 23, 2010 — 13:38
  • Dan Johnson

    Kenny,
    This is very helpful. If you write this up, even in draft form, I hope you’ll let us know about it.

    December 23, 2010 — 15:14
  • David P

    Tangential question: I’ve yet to get a good grasp on is the difference between material and logical implication.
    P->Q versus P=>Q
    I’m told that ‘all propositions’ entail all necessary propositions, and that ‘all propositions’ are entailed by all impossible propositions.
    Doesn’t this fall prey to Russell’s paradox? Are entailment statements immune to the problem of having a proposition about all propositions?
    Relevant question: has anyone every objected to the premise about the World being contingent on the grounds of it being a fallacy of composition?

    December 23, 2010 — 17:47
  • Kenny Pearce

    The material conditional P->Q means “it is not the case (in the actual world) that P and not-Q.”
    The entailment operator P|=Q (I have never seen it written =>) means “from the premise P it is possible to deductively prove that Q.”
    I’m not aware of anyone objecting that this was a fallacy of composition. (Indeed, this wouldn’t be a fallacy, properly speaking, in the present argument; it would amount to saying that 1.5 is false, not that the argument is invalid.) Some people have thought that necessarily there is a world (sometimes on grounds that every possible world is a world), and a few people (e.g. Spinoza) have thought that this world is necessary. The former view would not affect this argument. The latter would reject premise 1.6 by saying that the collection of all contingent beings is empty. (Note that premise 1.6 defines a technical term, The World, which refers to the collection of all contingent beings; Leibniz is pretty explicit in Theodicy about using the term in this way.)

    December 24, 2010 — 11:44
  • David P

    Thanks Kenny, I should have given my comment more thought.
    The definition “A necessary proposition is one that is entailed by all propositions” (here) just has me confused. I take the essence of Russell’s paradox to be that there can be no propositions about all proposition. I’m sure this is just an example of a beginner’s blunder. 🙂
    I was confusing entailment with logical implication (P=>Q as “P implies Q”).
    You are correct, I was assuming that Leibniz’s support for 1.5 was fallacious and not the premise itself or the argument you’ve given. I thought he was using the form, “all parts have property x, therefore the whole has property x.”
    Cheers.

    December 24, 2010 — 12:11
  • Jeff Cokenour

    I should like to ask a question. Leibniz wrote, “Power relates to being, wisdom or understanding to truth, and will to good”. Is this necessarily so? Must will relate to good? What if the power he discussed possessed an evil will?
    For clarification, I am not a philosopher, I am a Christian biologist, but I love your site.
    Blessings!
    Jeff Cokenour

    January 7, 2011 — 11:57
  • Kenny Pearce

    Hi Jeff,
    According to the Platonic/Augustinian theory of the will which Leibniz endorses, it is a necessary truth that the will always inclines to a perceived good. That is, we will what seems good to us. As I recently discussed discussed on my personal blog, Leibniz has a somewhat more sophisticated version of the theory than Plato or Augustine: he allows that what seems good to us might not be the same as what we judge or believe to be good. The same line applies to wisdom or understanding: necessarily, we believe what seems true to us. But there is no guarantee that what we will is actually good, or that what we believe is actually true. As far as power and being, that one is more complicated, and I don’t have an off-the-cuff answer for it.

    January 7, 2011 — 12:07