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A Leibnizian Cosmological Argument

Sobel's sixth chapter is devoted to, as he says, "proofs a contingentia mundi" (from the contingency of the world). The chief exponent here is Leibniz, though Sobel also considers Hume's Demea and his probable source, Samuel Clarke. Sobel argues that Leibniz's argument is valid ... by contradiction explosion. That is, he argues that Leibniz's premises are inconsistent. In this post, I show how to fix the argument using Leibnizian resources. In the next post, I will give another version of the argument which uses premises which I consider to be anti-Leibnizian, but which I think are more widely held than the Leibnizian premises I use here.

Here is Sobel's reconstruction of the argument:

(1)The World - the Cosmos - exists. (2) The World is contingent, it is a contingent entity. (3) For everything that exists - for every fact and every existent entity - there is a sufficient reason for its existence. (4) The sufficient reason for the existence of any contingent entity runs in the end in terms of an existent being. :. (5) There exists an ultimate reason for the World, which reason is itself a necessary being. (p. 208)

Sobel's charge is this: premise (2) states that The World is a contingent entity, but premise (3), on the intended interpretation, entails that there are no contingent entities. This is because, according to Sobel, a sufficient reason has to be a deduction from necessary premises, and whatever is deducible from necessary premises is necessary, hence not contingent.

Sobel seriously engages with Leibniz's system only in Appendix A to this chapter, and there, I have to say, he does not engage Leibniz very well. In an earlier post, I discussed Leibniz's definition of necessity and contingency in connection with one of Sobel's objections to ontological arguments. Let's try assuming that the argument is written in 'Leibniz-speak' and translating it by replacing 'necessary' with 'finitely demonstrable' and 'contingent' with 'not finitely demonstrable'.

(1)The World - the Cosmos - exists. (2) The existence of The World is not finitely demonstrable. (3) For everything that exists - for every fact and every existent entity - there is a sufficient reason for its existence. (4) The sufficient reason for the existence of any entity which is not finitely demonstrable runs in the end in terms of an existent being. :. (5) There exists an ultimate reason for the World, which reason is itself a being whose existence is finitely demonstrable.

Does this argument work? Well, as it stands, I suppose whether it works depends upon some fact about infinitary logic, which I don't know. But if we take into account how Leibniz thinks these infinite demonstrations work - that they start from the goodness of God and evaluations of the relative goodness of different possible worlds - then perhaps we can introduce the premise that every infinite demonstration has a finite initial segment. So perhaps we should reconstruct the argument as follows:

1. It is true that (W) The World exists.(Premise)


2. (W) is not finitely demonstrable. (Premise)


3. Every truth is demonstrable. (Premise)

Therefore,

4. (W) is infinitely (i.e. non-finitely) demonstrable. (From (1)-(3))


5. Every infinite demonstration has a finite initial segment which is itself a demonstration. (Premise)


6. Every finite initial segment of an infinite demonstration depends on the existence of some being. (Premise)

Therefore,

7. Some being's existence is finitely demonstrable. (From (4)-(6))

The inference from (1)-(3) to (4) is a simple disjunctive syllogism (every truth is either finitely demonstrable or infinitely demonstrable, this truth is not finitely demonstrable, so it is infinitely demonstrable.) The inference to (7) from (4)-(6) relies on the definition of 'demonstration' as 'a deduction from necessary premises'. So the idea is that the infinite demonstration starts by deriving some lemma which is derived in a finite number of steps, so that lemma will be finitely demonstrable. But, according to premise (6), the demonstration of that lemma depends on the existence of some being. Now, either that being's existence was one of the necessary premises we started with, or it was deduced as an earlier lemma. So the existence of that being is finitely demonstrable.

I submit that this argument is valid, Leibniz accepts all of its premises, and the premises do not contain any obvious contradictions. However, it has two serious failings. First, almost no one, other than Leibniz, believes premise (3). Furthermore, premises (5) and (6) are doubtful, and not everyone thinks the idea of an infinite demonstration makes any sense. Second, (5) and (6) might well be question-begging. The only reason I can think of that Leibniz could give for accepting them is that every infinite demonstration proceeds in the same fashion: first, use an ontological argument to establish the existence of an omnipotent and perfectly good God, then compare all the possible worlds and find the best one. Next, conclude that this world will be created by God, and show that the proposition in question is true at that world. Since the infinite demonstrations have this form, they all have a finite initial segment that depends on the existence of a being. That initial segment is the ontological argument for the existence of God. As a result, unless Leibniz can independently motivate (5) and (6), this won't work as an independent argument for the existence of God. Nevertheless, I think Sobel has been too hard on Leibniz: the premises are not inconsistent when interpreted the way Leibniz interprets them.

Posted by Kenny at September 15, 2010 10:40 PM