Pruss's Cannonball and the Leibnizian Cosmological Argument


A standard criticism of the Leibnizian cosmological argument exploits the point that there are cases in which a whole is explained in virtue of its parts. Examples:

Hume such a chain or series of items, each part is caused by the part that preceded it, and causes the one that follows. So where is the difficulty? But the whole needs a cause! you say. I answer that the uniting of these parts into a whole, like the uniting of several distinct counties into one kingdom, or several distinct members into one organic body, is performed merely by an arbitrary act of the mind and has no influence on the nature of things. If I showed you the particular causes of each individual in a collection of twenty particles of matter, I would think it very unreasonable if you then asked me what was the cause of the whole twenty. The cause of the whole is sufficiently explained by explaining the cause of the parts.
-Dialogues Concerning Natural Religion, Part IX
Paul Edwards:
The demand to find the cause of the series as a whole rests on the erroneous assumption that the series is something over and above the members of which it is composed. It is tempting to suppose this, at least by implication, because the word "series" is a noun like "dog" or "man." Like the expression "this dog" or "this man" the phrase "this series" is easily taken to designate an individual object. But reflection shows this to be an error. If we have explained the individual members there is nothing additional left to be explained. Supposing I see a group of five Eskimos standing on the corner of Sixth Avenue and 50th Street and I wish to explain why the group came to New York. Investigation reveals the following stories: 
- Eskimo No. 1 did not enjoy the extreme cold in the polar region and decided to    move to a warmer climate. 
- No. 2 is the husband of Eskimo No. 1. He loves her dearly and did not wish to live without her. 
- No. 3 is the son of Eskimos 1 and 2. He is too small and too weak to oppose his parents. 
- No. 4 saw an advertisement in the New York Times for an Eskimo to appear on television. 
- No. 5 is a private detective engaged by the Pinkerton Agency to keep an eye on Eskimo No. 4. 
Let us assume that we have now explained in the case of each of the five Eskimos why he or she is in New York. Somebody then asks: "All right, but what about the group as a whole; why is it in New York?" This would plainly be an absurd question. There is no group over and above the five members, and if we have explained why each of the five members is in New York we have ipso facto explained why the group is there. It is just as absurd to ask for the cause of the series as a whole as distinct from asking for the causes of individual members.
          -"The Cosmological Argument" (1959)

Alexander Pruss offers a reply (section to this sort of objection. His strategy is to use the examples from Hume and Edwards to generate a variations on a general explanatory principle (the so-called 'Hume-Edwards Principle'), and then to offer counterexamples to them. Thus, after some chisholming, Pruss considers the following explanatory principle to be the most plausible:

(HECP) For any proposition p such that one has explained every conjunct of a proposition, one might have thereby explained the whole.
(where "might" is construed as epistemic possibility)

In reply, Pruss offers the following as a counterexample to HECP:

At noon, a cannonball is not in motion, and then it starts to fly.  The cannonball flies a long way, landing at 12:01 pm.  Thus, the cannonball is in flight between 12:00 noon and 12:01 pm, in both cases non-inclusive. 
Let pt be a proposition reporting the state of the cannonball (linear and angular moment, orientation, position, etc.) at time t.  Let p be a conjunction of pt over the range 12:00 < t < 12:01.  I now claim that p has not been explained unless we say what caused the whole flight of the cannonball, e.g., by citing a cannon being fired.  This seems clear.  If Hume is right and it is possible for causeless things to happen, then it could be that there is no cause of the whole flight.  But that is just a case where p has not been explained.  To claim that there was no cause of the flight of the cannonball but we have explained the flight anyway would be sophistry. 
But if the HECP is true, then there might be an explanation of p without reference to any cause of the flight of the cannonball.  For take any conjunct pt of p.  Since 12:00 < t, we can choose a time t* such that 12:00 < t* < t.  Then, pt is explained by pt* together with the laws of nature and the relevant environmental conditions, not including any cause of the flight itself.  By the HECP wemight have explained all of p by giving these explanations.  Hence, by the HECP we might have explained the flight of a cannonball without giving a cause to it.  But that is absurd.
What to make of this reply? One might worry that it's uncharitable to assume that Hume and Edwards are assuming a general explanatory principle in their examples and relying on it for the epistemic force of their point. Relatedly, one might worry that making such an attribution and then offering counterexamples to it is a red herring, as such general principles aren't required for the success of their criticisms. For their success only requires that (i) they represent singular epistemically possible cases where an explanation of each part of a thing or state of affairs thereby provides an explanation of the whole, and that (ii) such cases are relevantly similar to those the cosmological argument must exclude; showing that there are counterexamples to the general principles that Pruss attributes to Hume and Edwards is consistent with the claim that the particular examples of Hume and Edwards (or analogues thereof) are genuine, relevant cases of wholes explained in terms of facts about their parts. 

But let's waive these worries, as Pruss seems to recognize as much:
Thus not only is the HECP false in general, but it is false precisely in the kind of cases to which Hume, Edwards and Campbell want to apply it: it is false in the case of an infinite regress of explanations, each in terms of the next.
Is Pruss's reply, thus sharpened, successful? 

No, it isn't. For there are at least two different sorts of infinite regresses to consider here: (i) those involving a clear case of a prior originating cause of the series, and (ii) those that don't. Now Pruss's cannonball example seems telling against the sufficiency of HECP for adequate explanations of facts in a type-(i) series.  But the problem is that the relevant sort of infinite regress here is that of type-(ii). For what cries out for explanation in Pruss's cannonball case is the cannonball's transition from a state of rest to a state of motion. The relevant sort of parallel case here would thus be one involving an explanation for a transition from a state of there being no universe (or at least no matter-energy) to a state of there being a universe. But most naturalists take the universe's history (or at least matter-energy's history) to be beginningless, and therefore lacking any such transition. Unlike Pruss's cannonball scenario, therefore, the former scenario lacks a comparable transition that cries out for explanation. It therefore looks as though Pruss has failed to deflect the Hume-Edwards criticism at issue.


Steve Maitzen said...

Hi, Ex.

One disanalogy between Pruss's cannonball flight and the history of the contingent universe is this: the cannonball flight clearly has only a finite duration, whereas (I think it's plausible to hold that) the history of the contingent universe stretches back infinitely into the past, including prior to the Big Bang (even if our current understanding of physics happens to go silent at that singularity). I don't think our intuitions demand a cause for a series that goes infinitely far back in time, at least not the way they do for a series that started finitely long ago.

In any case, let's not forget the dialectical situation. Cosmological arguers claim that the existence of the contingent universe can't be explained without invoking something that's not part of the contingent universe. As Rowe puts it, you can't explain the existence of the entire series of dependent beings just by invoking dependent beings. But why not? Cosmological arguers bear the burden of answering that question before their opponents need say another word. As best I can tell, the answer they give assumes that "dependent being" (or "contingent thing") names a kind of being, which it doesn't, much less a kind of being whose instantiation requires some uniform cause or explanation.

Angra Mainyu said...

Hi, ex-apologist

Very interesting points.

Intuitively, I find infinite regress much more satisfactory, from an explanatory point of view, than a concrete being that exists necessarily.

With regard to the cannonball example, I posted a reply elsewhere, arguing that it does not provide good grounds to reject a general principle (i.e., as a counterexample, it fails).

The reply is as follows:

One first difficulty is that we're not justified in applying Newton's laws or any other present-day model to arbitrarily small amounts of time, so we would not have a (good) explanation of each conjunct regardless of other considerations. But let's assume that the universe is actually such that there are laws that we can correctly express with some formulas F that apply to any arbitrarily short period, and that we know the formulas.
Even then, there is a problem, namely that the firing of a cannon is a gradual process, even if pretty fast compared with ordinary events in our lives. It doesn't happen instantaneously.
If the process of the cannon's firing took place during some interval (t0, noon], then it seems that the ball is not at rest at noon, contradicting the scenario, since the energy has already been transferred to the cannonball at noon.
So, the conclusion is that the firing of the cannon continues for some time after noon, and thus, for t sufficiently small, the individual conjunct pt is not explained by a previous conjunct, plus the laws F. Instead, a proper explanation of pt would require a reference to the firing of the cannon.
That seems to block the cannonball argument.

exapologist said...

Nice points, guys. Thanks for your insights.

Angra Mainyu said...

You're welcome, and thanks for your insights as well.

On that note, and on the issue of your point that what cries out for an explanation is the change from a state at which the ball is at rest to a state at which it's not, it seems to me that that's not only accurate, but may illustrate a more general problem with the cannonball's example and similar ones.

For instance, let's say we see a ball rolling on the floor, and we ask for an explanation as to why there is a ball rolling over there. Normally, we wouldn't accept as an explanation that, say, 1/(100000000) seconds earlier, there was a ball rolling at a very small distance of its current position (or particles that make up the ball, etc.), and that that ball 1/(100000000) seconds earlier (or particles, etc.), together perhaps with other objects, brought about the effect, namely that there is a ball rolling on the floor now..

That's just not the kind of explanation we're looking for. What we're normally asking (which plausibly be what influences our intuitions about what counts as a good explanation) is how the ball got there in the first place (i.e., why it started rolling, maybe something else).

So, while it's true that we normally wouldn't accept an explanation as to why the ball is rolling in some temporal interval (t1,t2) in terms of an infinite series of explanations in which the explanation as to why the ball is in each position is given in terms of earlier positions in (t1,t2), it seems we wouldn't accept the single cases, either.

On the other hand, if we were to accept the explanation of each conjunct, it's hard for me to see why the conjunction wouldn't be explain in terms of the explanations of each of the conjuncts, even if it can also be explained in terms of something that happened earlier.

So, while I'm not sure it's always the case that if one has an explanation of each conjuncts, one has an explanation of a conjunction in terms of those explanations, I have to say that I've not been able to find any exceptions so far, so I'd say that at least, usually that is the case.

Anonymous said...

A guy named Hassan have raised this objection on Pruss's blogg - Lets see what the answer will be :)

Anonymous said...

It seems to me that Pruss thinks that the set of all things is itself a 'thing' which is in need of an explanation. But that is just absurd.

wissam h said...

This pdf article nicely defends the different cosmological arguments for God's existence (the ones by Gale and Pruss, Koons, etc.)

I would like to see what you make of it.

wissam h said...

Oh, and on the Prosblogion, Rutten answers objections to his argument.

exapologist said...

Thanks for the pointer to Rutten, Wissam. I'll give them a look.