The Gale-Pruss cosmological argument for the existence of God

Richard Gale and Alexander Pruss have advanced an interesting update on the traditional Cosmological Argument for the existence of God.[i] This argument begins with some definitions.

A possible world is a “maximal, compossible conjunction of abstract propositions. It is maximal in that, for every proposition p, either p is a conjunct in this conjunction or its negation, not-p, is, and it is compossible in that it is conceptually or logically possible that all of the conjuncts be true.”[ii]

The Big Conjunctive Fact for a possible world consists of the conjunction of all of the propositions that would be true if that world were the actual world.  Some of these are necessarily true. But the Big Conjunctive Fact of each possible world also contains propositions that are contingently true- true in some possible worlds and not in others. Each possible world contains a unique conjunction of contingent propositions. Gale-Pruss refer to this as the Big Conjunctive Contingent Fact, or BCCF. It is the BCCF of a world that individuates that world, distinguishing it from all other possible worlds. Let p be the BCCF of the actual world.

Is there an explanation for p- an explanation for why this particular set of contingent facts is the case, rather than not?

At this point the defender of a traditional Cosmological Argument would introduce the Principle of Sufficient Reason:

For every proposition, p, if p is true, then there is a proposition, q, that explains p.

But it may not be reasonable to expect the skeptic to accept this principle. In its stead, Gale-Pruss offer a weaker form of the Principle of Sufficient Reason:

For any proposition, p, if p is true, then it is possible that there exists a proposition, q, such that q explains p.

Unlike traditional cosmological arguments, Gale-Pruss’ argument does not require us to assume that there actually is an explanation for p. It only needs to be possible that there is such an explanation. Gale-Pruss assert that it is: There is some possible world, W1, in which p is true, and in W1, some proposition q is true, and q explains p.

Now, are W1 and the actual world the same world? Gale-Pruss insist that they are. For p is the Big Conjunctive Contingent Fact of the actual world; p is true in W1, and the BCCF of a given world is what individuates it. Therefore, there is some proposition q that is true in the actual world and explains p, the BCCF of the actual world. Now, what sort of explanation is it?

According to Gale-Pruss there are only two kinds of explanation: Scientific, and personal. Personal explanations are explanations in terms of the intentions of some person. But q cannot be a scientific explanation. A scientific explanation “must contain some law-like proposition, as well as a proposition reporting a state of affairs at some time.”[iii] But these are contingent propositions, and therefore members of p. Yet they purport to explain p, as well as each proposition contained within p, which means they would explain themselves, and this is impossible.

Therefore q must be a personal explanation. Now what sort of person does q invoke? It cannot be a contingently existing being, since a proposition asserting the existence of a contingently existing being would be part of p and once again, q would explain itself. So q explains p, the Big Conjunctive Contingent Fact of the actual world, by reference to the intentional action of a necessary being. The proposition q, then, asserts something like this:

               “There exists a necessary being who intentionally creates the world.” [iv]

Analysis

Gale-Pruss treat q as though it is not one of the member-conjuncts of p. This is well motivated. For one thing, if q were contained within p, the Big Conjunctive Contingent Fact of the actual world, then q would be part of the very state of affairs that it hopes to explain. But worse than this, to define p as the BCCF of the actual world, and then to presume that q is contained within p, is to presume at the outset that the actual world is explained by the intentions of a necessary being, and this is what the argument seeks to prove.

And yet, as Gale-Pruss acknowledge, q is a contingent proposition,[v] and so prima facie, one would think that for any possible world, either it, or its negation, is a member-conjunct of that world’s Big Conjunctive Contingent Fact.[vi] But let us set this observation aside and follow Gale-Pruss in treating q as though it is not contained within p.

Since q is a contingent proposition, there are possible worlds in which it is not true. That means that in addition to W1, which contains p and in which p is explained by q, there is another possible world, W2, which contains p, and in which p is not explained by q, because it is not true in W2 that there is a necessary being who intentionally creates that world. As it turns out, if a Big Conjunctive Contingent Fact does not contain either q, or its negation, then pace Gale and Pruss, it does not individuate a possible world.

This means that a world’s containing p does not imply that it is identical with the actual world. Gale and Pruss are not entitled to infer, from the fact that p is true in W1, that W1 is identical with the actual world, since p is true in W2 as well.

The actual world is identical with one of these worlds, W1 or W2, but the Gale-Pruss argument leaves us with no reason to prefer one over the other. Since they hoped to prove that the existence of the actual world is explained by the intentions of a necessary being, and they can do this only if they can show that the actual world is identical with W1 rather than W2, Gale and Pruss’ argument fails.

David Corner
Department of Philosophy
Sacramento State

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[i] “A New Cosmological Argument,” Richard M. Gale and Alexander R. Pruss; Religious Studies, vol 35, Number 4 (Dec 1999), pp. 461-476

[ii] “A New Cosmological Argument,” p. 461. For a more detailed explanation of the notion of a possible world, see https://plato.stanford.edu/entries/possible-worlds/.

[iii] Ibid. p 465

[iv] Gale-Pruss realize that they have not proven the existence of the God of Western theism, since they have not proven that this being is omniscient, omnipotent, and benevolent. They require only that God be powerful enough to create the actual world. But they think- and I agree- that their more limited conclusion is still an interesting one.

[v] In fact they argue for this claim on p. 466ff

[vi] It seems likely that Gale-Pruss are thinking of q as having some kind of special status that sets it apart from ordinary contingent facts. Perhaps they wish to say that it is a supernatural fact, because it reports the intentions of a necessary being. (On p. 468 they claim that a necessary being is a supernatural one.) In this case p is really the Big Conjunctive Contingent Natural Fact. I do not have space to pursue this suggestion here, which does not, in any case, seem to affect my analysis.

A dilemma for elementalism

Teaching history of philosophy always produces in me a lively sense of contingency in intellectual history. One example stands out: Leucippus and Democritus proposed an atomic theory around 440 B.C. This striking proposal ran into the sand, however, and never produced a viable research program.

Why not? All you need, technically speaking, are devices for measuring and weighing small amounts of material fairly precisely. The ability to do that was not significantly greater in the early 1800’s when Dalton and Avogadro succeeded in reviving atomism.

I used to think that the Greek atomists just had the rotten luck to live at the same time as two of history’s greatest philosophers, Plato and Aristotle. Atomism, though right, lost the dialectical battle.

I now think that western philosophy tacks between two strategies for explaining What Goes On.

One strategy explains the properties and behavior of entities by appeal to composition: the properties and behavior of the fundamental objects that make the entity up. Call this strategy ‘Elementalism’.

The other strategy explains the properties and behavior of entities by appeal to their kind: and a full understanding of the essential properties of the kind will explain what the entity does. Call this strategy ‘Formalism’.

Formalism dominated from 400 BC until 1400 AD. Our course in early modern philosophy is the story of its overthrow by elementalism in the Scientific Revolution.

Either strategy yields philosophical problems, problems which the other strategy tends to solve – at least for a time.

The main problem besetting any elementalism is composition.

Matthew hits a baseball toward the house and breaks a window. [1]

Elementalism explains this by the bonds which hold atoms together into molecules: the molecules forming the baseball (B) and the window (G). The velocity of B on G is sufficient to disturb the molecular bonds of G.

This explanation makes no reference to the baseball, the window, or to Matthew. What matters for causal explanation is what goes on at the level of B and G. Baseballs, windows, and teenagers with poor judgment may as well not be there. Since we need not countenance them in order to make our best (elementalist) theories true, we can be anti-realists about macro-objects.

If we wish to believe in baseballs and grandchildren – and we do – we could suppose they supervene on the fundamental particles. But then they're epiphenomenal: their presence makes no difference in the world.

If they’re to make a difference, we seem to be committed to saying not only that “Events involving B cause events involving G,” but also “Events involving the baseball cause events involving the window.”

But that gives us two causal relations: double determination. What goes on is over-oomphed.

Indeed, since we have many levels operating:

• atomic
• molecular
• macro- (baseballs and windows)
• physiological (Matthew’s hitting the baseball)
• neural (events in Matthew’s brain causing his motor movements)
• mental (Matthew’s ill-considered decision to hit the ball toward the house)

what goes on is umptly over-oomphed.

Here’s the dilemma.

Either:

The higher-level events purportedly involving higher-level entities are not, strictly and literally, real events at all, or derivatively real.

But then they would be entirely epiphenomenal – not really part of the causal story of the world.

Or:

They are real, with their own causal relations.

But then ‘what goes on in the world‘ is over-determined.

In short, the constant dilemma with elementalism is that it threatens to give us either too little reality (no grandchildren) or way too much. Indeed, since there may be no limit to the number of levels at which causal explanation can take place unintelligibly too much.

But we thought elementalism was superior as an explanatory strategy.

Does formalism do any better? Arguably, yes.

One promising formalist strategy currently emerging is a revival of Aristotelian-style Hylomorphism. Robert Koons gives a nifty summary of the current state of this research project. [2]

On Koons’ version, the causal powers of a substance’s parts become powers of the whole substance, and so the over-determination problem doesn’t arise:

“(I)f I stand on a scale, is it I (as a whole) or my parts (collectively) that cause the pointer to move? If the powers associated with weight have migrated from my proper parts to me, my weight can be the unique and non-redundant cause of the scale’s response.” (Koons 2014, 8).

Tom Pyne

Department of Philosophy

Sacramento State

Diagnosing the abortion debate

Reporting back in January showed that abortion rates have fallen to levels lower than any year since 1973, the year of the Roe v. Wade decision, and reflect about a 50% decrease in the rate from its peak in 1981. The study, conducted by the Guttmacher Institute, which favors legal protections for a right to have abortions, cites as causal factors greater access to contraception as well as laws in many states that restrict clinics or require ultrasounds. Of course, pro-life groups still ultimately want to see Roe overturned. This would mean that individual states would determine what legal restrictions, if any, would apply to people seeking and providing abortions.

Abortion rights and restrictions pose a special challenge to the justificatory test for legitimate coercion in the law that I’ve defended in my work in political philosophy. That principle says, roughly, that for coercion to be legitimate, it must be publicly justified, or based on reasoning that is public in the requisite sense. For example, on Rawls’ view, public justification is grounded in reasons that all can reasonably accept. The test excludes reasons that are not reasonably acceptable to all from being able to do justificatory work and so prevents these reasons from being a legitimate basis for law.

For a variety of reasons I won’t rehearse, I favor a more recent specification of the principle by Jerry Gaus at the University of Arizona. His view is more permissive in that any of a citizen’s reasons may play a part in justifying laws. Laws can be justified to each citizen on the basis of their complete set of beliefs, values and commitments, so long as these are intelligible. Any intelligible reason can feature within the overall public justification of a law. However, people whose beliefs, values and commitments provide them with an intelligible rationale for rejecting it have a defeater for it and, when that’s true, it’s illegitimate to subject them to it. The law would lack authority from their point of view.

What does this view make of the abortion controversy? First, notice how easy things would be if this disagreement weren’t based on reasonable considerations. If it were flatly unreasonable to deny fetal personhood, then it would be much easier to justify a law against abortion. And if it were flatly unreasonable to ascribe personhood to fetuses, then there would no accounting for such a law. But reasonable people disagree about fetal personhood.

More: both parties to this disagreement reasonably believe that the other side is involved in imposing serious harms to the interests of others. This means that abortion law will lack authority for pro-choicers if pro-lifers have their way politically. It’s relatively obvious how this is so: pro-choicers have an intelligible rationale grounded in their beliefs, values and commitments for rejecting various restrictions on abortion. These restrictions violate privacy or bodily autonomy. But abortion law will also lack authority for pro-lifers when pro-choicers have their way politically. The reason is that, since pro-lifers reasonably believe that fetuses are persons with a right not to be killed, they have adequate justification for protecting them by imposing coercive measures that increase the costs of people killing them. Pro-lifers have an intelligible rationale for rejecting laws that carve out space for women to kill their child.

This situation, then, describes something like a moral state of nature between the two sides. We’ve failed to achieve coordination. Pro-choicers know that, even after engaging in careful and respectable reflection on the relevant moral and empirical evidence, pro-lifers won’t acknowledge the right of women to have an abortion. Public reason has run out. But this doesn’t mean that they just let pro-lifers violate women’s bodily autonomy. Pro-choicers are left as their only option taking up what P.F. Strawson called the objective attitude towards pro-lifers. They will see pro-lifers as a force to be reckoned with, managed and kept at bay as best they can as they go about their affairs, but that’s different than exercising genuinely normative authority over them.

In the same way, pro-lifers know that abortion-seekers won’t acknowledge the personhood of fetuses, even after careful and respectable reflection on the relevant moral and empirical evidence. Public reason has run out for them, too. But this doesn’t mean that pro-lifers just let women seeking abortions kill their children. From the pro-life perspective, women seeking abortions are doing something similar to driving a car towards a person in the street they can’t see. They have reason to stop her or make her swerve. In other words, pro-lifers similarly must treat abortion-seekers as mere objects of social policy rather than people with whom they are interacting on genuinely moral terms.

Disagreement doesn’t always lead to this kind of social breakdown of public reasoning and moral community. I can think of some other examples, but it’s relatively rare, which is a good thing. It also seems pretty isolated most of the time -- thankfully, a disagreement and breakdown in this area hasn’t led to a more general breakdown of moral relations among people who are on opposite sides of the abortion issue. Most people even have friends who disagree with them about abortion.

In fact, I suspect that this lends some credibility to the explanation of the abortion debate that I’ve offered here. It’s a case where we are forced to take the objective attitude towards our opponents because it turns out that they aren’t true moral subjects of the proposed requirements. Strawson’s participant reactive attitudes wouldn’t be warranted since they suggest serious culpability for violating something everyone is in on and knows better than to do. Sure, one side calls the other “murderers” and the other calls the one “women-haters” but we don’t generally act like we regard each other as such.

Kyle Swan

Department of Philosophy

Sacramento State