Overcoming the Regress and Taxicab Problems

I have defended three principles, each of which is sufficient to overcome the Glendower Problem: a PSR for contingent propositions, a CP for wholly contingent positive states of affairs, and a CP not just for individual events/substances but for chains of events/ substances. Now the question is whether they are sufficient to overcome the Regress and Taxicab problems and yield the existence of a First Cause. I shall argue in the positive, thereby giving versions of three cosmological arguments by Leibniz, Koons (1997), and Meyer (1987), respectively. I shall follow these three by giving a fourth argument, due to White (1979), and another argument based on the ideas in Pruss (2004a), both of which arguments are based on restrictions of the PSR. The basic argument

Consider once again the BCCF p, which was the conjunction of all contingently true propositions, perhaps with truth-functional redundancy removed. By the PSR, p has an explanation, call it q. What is q like? There are two general options. Either q is necessary or q is contingent. If q is contingent, then it is contained in p, and since q explains p, it follows that q is self-explanatory. Thus, q must be necessary or else contingent and self-explanatory. (Here we are, of course, retracing a part of the van Inwagen argument from Section

Next, observe that it is plausible that contingent existential propositions ultimately can only be explained causally. Since p includes many contingent existential propositions, q must state the existence of one or more causes. If these causes are all contingent substances or events, then the existence of these causes will be among the contingent existential propositions in p that are to be explained. But given a set of contingent entities, these entities can neither collectively nor individually causally explain their own existence. Nothing can be a cause of itself, pace Descartes. The existence of a cause is explanatorily prior to the existence of the effect, but nothing can be explanatorily prior to itself.

So the cause must be something necessary, presumably either a necessarily existing substance or a necessarily occurring event. Plausibly, there can be no events without substances - events are what happens to substances. A necessarily existing event happens to a necessarily existing substance. So we do get to a necessarily existing substance.

Moreover, as far as we can tell, there are three ways that something can be explained. First, one can have a conceptual explanation that explains one fact in terms of a conceptually connected fact entailing it in an explanatorily relevant way, as when we say Pat's action was wrong because it was the breaking of a promise, or that a knife is hot because its molecules have high kinetic energy. A conceptual explanation of a contingent proposition will itself involve a contingent proposition, and a nonconceptual explanation will be needed. We can say that the Queen of England exists because Elizabeth of Windsor is the Queen of England, a conceptual explanation, but the explanation of the existence of Elizabeth of Windsor will involve the gametes of the Duke and Duchess of York, and this will not be a conceptual explanation. Since q is the ultimate explanation of all contingent propositions, it will not be a conceptual explanation, except perhaps in part.

Second, one can explain things scientifically by citing laws of nature and initial conditions. Now, on some accounts of laws of nature, the laws of nature are contingent and non-self-explanatory. They will thus have to enter into the explanandum p, but not the explanans q. Moreover, the most plausible account of laws of nature that makes them necessary grounds them in the essences of natural objects. But natural objects are contingent. Hence, even though the laws of nature will be necessary, which laws are applicable to a given situation will depend on the contingent question of which contingently existing natural objects are involved in the situation. The ultimate explanation q cannot involve laws grounded in the essences of contingently existing natural objects, since q explains the existence of contingently existing natural objects. Moreover, the initial conditions cited in scientific explanations are contingent and non-self-explanatory. But q is either necessary or contingent and self-explanatory. So q cannot be a scientific explanation.

The last kind of explanation we know of involves the causal activity of an agent or, more generally, a substance. The substance will have to be a necessary being, or else it will absurdly be a causa sui, something that causally explains its own existence (since it explains all of the BCCF). Hence, the ultimate explanation involves one or more causally efficacious necessary beings, whom we may call First Causes. Were it not for the Gap Problem, we could now say et hoc dicimus deum. Objection 1: explanations in terms of a principle

The main objection here is that perhaps there is some further mode of explanation, one that is not conceptual, scientific, or agentive. The main actually proposed alternative is explanation in terms of a metaphysical principle. This principle would have to be different in kind from run-of-the-mill metaphysical principles such as the Principle of Identity of Indiscernibles or the Principle of Impossibility of Circular Causation: it must be a principle capable of explaining the existence of the apparently contingent denizens of our world.

The best candidate principle is due to John Leslie (2001) and Nicholas Rescher (2000). I will discuss Rescher's formulation here. The idea is to explain the BCCF in terms of the Principle of Optimality: of metaphysical necessity, the best narrowly logically possible world is actual. However, Rescher's suggestion is one that the defender of the cosmological argument need not worry about too much, since it is plausible that the best narrowly logically possible world is a world that contains God, considered as a maximally great being. Rescher himself thinks this. And so, in any case, we get the existence of God, albeit in a somewhat more roundabout way. Leslie does not agree - he opts instead for an infinity of divine knowers. I suspect Rescher is right in supposing a single deity - any particular number of deities other than one would seem ad hoc vis-á-vis optimality, while a world with a single deity has an elegant and valuable unity to it. This is true whether the number is finite, say 117, or infinite, say X117. And if the number is Cantorian "absolute infinity," then it does not seem as though one can make any sense of it.

Moreover, it is plausible (although Rescher denies it) that principles need to be made true by something, and this something must have being. A principle cannot by itself pull beings into existence out of a metaphysical magic hat, since a principle itself must be true of something and true in virtue of something.

Forming the BCCF may present set-theoretic concerns. Not every conjunction of propositions makes sense, as was shown by Davey and Clifton (2001). Modifying their construction slightly, let p be conjunction of all true propositions that do not contain themselves as proper subformulas. Then p is true. Let q be the proposition that p is true. Now, either q is a proper subformula of itself or not, and in either case a contradiction ensues. For if q is a proper subformula of itself, then it is not a conjunct of p. But the only way q could be a proper subformula of itself is if it is a subformula of p, since all proper subformulas of q are subformulas of p. Since q is not a conjunction, the only way it can be a subformula of p is if it is a subformula of one of the conjuncts of p. Now, q is not a conjunct of p, as we said. Hence, q must be a proper subformula of one of the conjuncts of p, say of p1. But p is a proper subformula of q, and p1 is a subformula of p, so it follows that p1 is a proper subformula of itself, and hence not a conjunct of p, contrary to the assumption. Suppose on the contrary that q is not a proper subformula of itself. Then it is a conjunct of p, and hence a proper subformula of itself, and absurdity ensues again.

This argument is a challenge: if some conjunctions do not make sense, how do we know that the BCCF makes sense? One way to meet the challenge is to try to shift the burden of proof. A conjunction of propositions should be assumed to make sense unless it is proved not to.

Alternately, one might use the strategy of Gale and Pruss (2002) here. Replace the BCCF by the BCCF*, which is the conjunction of the following:

(a) all true contingent atomic propositions,

(b) a "that's all clause" that says that any true contingent atomic proposition is one of these ones (this clause will involve an infinite disjunction such as in: "for all p, if p is a true contingent atomic proposition, then p is a1 or a2 or . . ."),

(c) all true propositions appearing in the explananda of contingent atomic propositions or of conjunctions thereof,

(d) all true basic propositions reporting causal relations,

(e) a "that's all clause" that says that all the actual explanatory relations supervene on the facts reported in the above conjuncts. (Gale & Pruss 2002, p. 95)

Here, "basic propositions" might be taken to be ones that are not true in virtue of some more basic propositions' being true, in the way in which the proposition that George is human or rhino is true in virtue of the more basic proposition that he is human. Plausibly, the truth of the BCCF supervenes on that of the BCCF*, and we could probably run our cosmological argument with the BCCF* in place of the BCCF.

Also, some PSR-based cosmological arguments are not subject to this objection. For instance, we could ask why there are any contingent beings. It is highly plausible that that there are contingent beings is itself a contingent proposition. For if it were a necessary proposition that there are contingent beings, then we would have odd necessary truths such as that, necessarily, if there are no contingent nonunicorns, then there are contingent unicorns. Moreover, the explanation of why there are contingent beings cannot involve the causal efficacy of contingent beings. But, plausibly, an existential proposition can only be explained by citing the causal efficacy of something, and hence of a necessary being.

Note that if there is no way of forming something relevantly like the BCCF, then the van Inwagen objection, which is the main objection to the PSR, fails. So it could be a service to a defender of the PSR if nothing like the BCCF could be formed, although harder work would be needed then for running the cosmological argument, perhaps along the lines of the Gale and Pruss (2002) strategy. Objection 3: the Hume-Edwards-Campbell principle

Hume states:

Did I show you the particular causes of each individual in a collection of twenty particles of matter, I should think it very unreasonable, should you afterwards ask me, what was the cause of the whole twenty. This is sufficiently explained in explaining the cause of the parts. (Hume 1907, p. 120)

Paul Edwards (1959) illustrates this with the case of five Inuit on a street corner in New York. If for each Inuit we gave an explanation of why he or she is there, we would thereby have explained why they are all there.

We can generalize this to the Hume-Edwards Principle (HEP):

(51) (HEP) In explaining every conjunct of a proposition, one has explained the whole proposition.

If the HEP is true, the PSR-based cosmological argument can be blocked. The objector can simply suggest that one contingent proposition is explained by a second, and the second by a third, and so on ad infinitum, and thereby the whole BCCF is explained.

But the HEP is false. The first objection to HEP is that it does not take into account the fact that there can be more to explaining the conjunction than explaining the conjuncts. If there were a hundred Inuit on a street corner in New York, individual explanations of each one's presence would miss the point of explaining why there are a hundred Inuit all there. There is a coincidence to be explained. This kind of objection has been pressed, for example, by Gale (1999, p. 254).

This response is, however, insufficient. First of all, while sometimes explaining the con-juncts is unsatisfactory as an explanation of the whole, sometimes it is quite satisfactory. If there are two Inuit there on the corner, then to say that one is there to give a paper on the cosmological argument at a conference in the hotel at that corner and the other is there because New York City winter is preferable to Iqaluit winter is likely to be a fine explanation of the conjunction. The cosmological arguer might then be required to show that the BCCF is in fact a case where an explanation of the conjuncts is insufficient for an explanation of the whole. There are issues as to onus of proof here, but it is better for cosmological arguer to sidestep them if possible.

The second problem with this response is that while it provides a counterexample to the HEP, there is a weaker version of the HEP due to Campbell (1996) that these sorts of examples do not address. Campbell agrees that sometimes we need to do more than explain the parts to explain the whole. Indeed, there may be a further story, an Inuit conspiracy, say. However, it might be that the individual explanations of the parts are the whole story and are the explanation of the whole. If there are a hundred Inuit on the street corner, then it seems likely that there is a further explanation beyond individual ones. But there might not be. It could be that it is just a coincidence, and the whole is correctly explained solely in terms of the individual parts.

This suggests the following Hume-Edwards-Campbell Principle (HECP):

(HECP) For any proposition p such that one has explained every conjunct of a proposition, one might have thereby explained the whole.

We can take the "might" as epistemic possibility absent evidence of a further explanation. The HECP is sufficient for blocking the PSR-based cosmological argument. For the defender of the HECP can say we might have explained the whole of the BCCF by explaining one proposition in terms of another ad infinitum, and then the onus would be on the cosmo-logical arguer to provide evidence that there is a further explanation of the BCCF. But if one can provide such evidence, one probably does not need the PSR-based cosmological argument.

However, the HECP is also subject to counterexample, and any counterexample to the HECP will automatically be a counterexample to the stronger HEP. Perhaps the simplest counterexample is the following (Pruss 1998). At noon, a cannonball is not in motion, and then it starts to fly. The cannonball flies a long way, landing at 12:01 p.m. Thus, the cannonball is in flight between 12:00 noon and 12:01 p.m., in both cases noninclusive.

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, for example, 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 whole flight itself. By the HECP we might 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.20

Perhaps the defender of the HECP might say that it is relevant here that there was a time before the times described by the pt, namely noon, and the existence of this time is what provides us with evidence that there is a further explanation. But that is mistaken, for if there were no noon - if time started with an open interval, open at noon - that would not make the given explanation of p in terms of its conjuncts, the laws, and the environmental conditions any better an explanation.

The HECP is, thus, false. But there is some truth to it. In the cannonball case, we had an infinite regress where each explanation involved another conjunct of the same proposition. Such a situation is bound to involve a vicious regress. The HEP and HECP fail in the case where the individual explanations combine in a viciously regressive manner. They also fail in cases where the individual explanations combine in a circular manner. If it should ever make sense to say that Bob is at the party because Jenny is and that Jenny is at the party because Bob is, that would not explain why it is that Bob and Jenny are at the party. A further explanation is called for (e.g. in terms of the party being in honor of George's birthday, and George being a friend of Bob), and if, contrary to the PSR, it is lacking, then that Bob and Jenny are at the party is unexplained. Likewise, if we could explain that Martha constructed a time machine because of instructions given by her future self, and that Martha's future self gave her instructions because she had the time machine to base the instructions on and travel back in time with, that would not explain the whole causal loop. How an explanation of the whole loop could be given is not clear - maybe God could will it into existence - but without an explanation going beyond the two circular causes, the loop as a whole is unexplained.

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.

Interestingly, the HEP may be true in finite cases where there is no circularity. Indeed, if we can explain each of the 20 particles, and if there is no circularity, we will at some point in our explanation have cited at least one cause beyond the 20 particles, and have given a fine explanation of all 20. Granted, there may be worries about coincidence, about

20. This counterexample to HECP makes use of the density of time. Many of the best reasons for doubting the density of time involve the sorts of considerations about traversing infinity that are at the heart of conceptual versions of the kalam argument (the Grim Reaper Paradox is the main exception to this). Thus, some of the people who object to the density of time assumption here will therefore have to worry about the kalam argument, which is discussed in Chapter 3 of this book.

whether the whole has been explained, but these worries can, I think, be skirted. For if I have explained individually why each of a hundred Inuit is at the street corner, and done so in a noncircular manner, then I have explained why there are a hundred Inuit there. Now my explanation may not be the best possible. It may not tell me everything there is to know about how the hundred Inuit got there, for example, through the agency of some clever manipulator who wanted to get Inuit extras for a film, but it is an explanation. But that is because the explanation goes beyond the contingent hundred Inuit, if circularity is avoided.

At this point it is also worth noting that anybody who accepts the possibility that an infinite regress of contingent propositions be explained by the regressive explanatory relations between these propositions is also committed to allowing, absurdly, that we can have two distinct propositions r and q such that r has the resources to explain q, q has the resources to explain r, and where the explanatory relations here also have the resources to explain the conjunction r&q. For suppose that we have a regress of explanations: p1 explained by p2, p2 by p3, and so on. Let r be the conjunction of all the odd-numbered p-„ and let q be the conjunction of all the even-numbered p. Since the conjunction of all p, has been explained in terms of the individual explanatory relations, by the same token we can say that r is explained by means of the explanatory resources in q since each conjunct of r is explained by a conjunct of q (p7 being explained by p8 and so on), and q is explained by means of the resources in r since each conjunct of q is explained by a conjunct of r (p8 being explained by p9 and so on). And these relations, in virtue of which r has the resources to explain q and q to explain r, also suffice to explain r&q.

Quentin Smith has argued that the universe can cause itself to exist, either via an infinite regress or a circle of causes. However, while he has claimed that such a causal claim would provide an answer to the question "why does the universe exist?" (Smith 1999, p. 136), he appears to have provided no compelling argument for that conclusion. Hence, it is possible to grant Smith that the universe can cause itself to exist via an infinite regress or a circle of causes while denying that this can provide an explanation of why the universe exists. Granted, in normal cases of causation, to cite the cause is to give an explanation. However, when we say that the universe "caused itself to exist" via a regress or a circle of causes, we are surely using the verb "to cause" in a derivative sense. The only real causation going on is the causes between the items making up the regress or the circle. If we have such a story, maybe we can say that the universe caused itself to exist in a derivative sense, perhaps making use of some principle that if each part of A is caused by a part of B, then in virtue of this we can say that A is caused by B, but this derivative kind of causation is not the sort of causation which must give rise to an explanation. For, in fact, regresses and circles do not explain the whole.21

21. It is worth noting that Smith's arguments for circular causation are weak. One argument relies on quantum entanglement. Smith seems to think that simultaneous but spatially distant measurements of entangled states could involve mutual causation between the states. But that is far from clear; circular causation is only one possible interpretation of the data, and how good an interpretation it is depends in large part precisely on the question whether circular causation is possible. Smith's more classical example in terms of Newtonian gravitation simply fails: "There is an instantaneous gravitational attraction between two moving bodies at the instant t. Each body's infinitesimal state of motion at the instant t is an effect of an instantaneous gravitational force exerted by the other body at the instant t. In this case, the infinitesimal motion of the first body is an effect of an instantaneous gravitational force exerted by the second body, and the infinitesimal motion of the second body is an effect of an instantaneous gravitational force of the first body. This is a case of the existence of a state S1 being caused by another state S2, with the existence of S2 being simultaneously caused by S1" (Smith 1999, pp. 579-80). This is Objection 4: can there be a necessarily existent, causally efficacious being?

Perhaps a necessary being is impossible. Abstracta such as propositions and numbers, however, furnish a quick counterexample to this for many philosophers. However, one might argue further that there cannot be a causally efficacious necessary being, whereas the unproblematic abstracta such as propositions and numbers are causally inefficacious.

A radical response to this is to question the dogma that propositions and numbers are causally inefficacious. Why should they be? Plato's Form of the Good looks much like one of the abstracta, but we see it in the middle dialogues as explanatorily efficacious, with the Republic analogizing its role to that of the sun in producing life. It might seem like a category mistake to talk of a proposition or a number as causing anything, but why should it be? Admittedly, propositions and numbers are often taken not to be spatiotemporal. But whence comes the notion that to be a cause one must be spatiotemporal? If we agree with Newton against Leibniz that action at a distance is at least a metaphysical possibility, although present physics may not support it as an actuality, the pressure to see spatiality or even spatiotemporality as such as essential to causality is apt to dissipate - the restriction requiring spatiotemporal relatedness between causal relata is just as unwarranted as the restriction requiring physical contact.

Admittedly, a Humean account of causation on which causation is nothing but constant conjunction only works for things in time, since the Humean distinguishes the cause from the effect by temporal priority. But unless we are dogmatically beholden to this Humean account, to an extent that makes us dogmatically a priori deny the existence of deities and other nonspatiotemporal causally efficacious beings, this should not worry us.

Moreover, there is actually some reason to suppose that propositions and numbers enter into causal relations. The primary problem in the epistemology of mathematics is of how we can get to know something like a number, given that a number cannot be a cause of any sensation or belief in us. It is plausible that our belief that some item x exists can only constitute knowledge if either x itself has a causal role in our formation of this belief or if some cause of x has such a causal role. The former case occurs when we know from the smoke that there was a fire, and the latter when we know from the sound of a match struck that there will be a fire. But if something does not enter into any causal relations, then it seems that our belief about it is in no way affected by it or by anything connected with it, and hence our belief, if it coincides with the reality, does so only coincidentally, and hence not as knowledge. Of course, there are attempts to solve the conundrum on the books. But simply not really a case of circular causation. The infinitesimal motion of each body at t does not cause the infinitesimal motion of the other body at t. Nor does the infinitesimal motion of either body at t cause the gravitational force of either body. Nor does the gravitational force of either body cause the gravitational force of the other. Rather, the gravitational force of each body partly causes the infinitesimal motion of the other body. Now, if we throw into the state of each body both its infinitesimal motion and its gravitational force, then we have a case where a part of the state of each body causes a part of the state of the other body. But that is not really circular causation, except maybe in a manner of speaking, just as it would not be circular causation to say that if I punch you in the shoulder while you punch me in the face, a part of my total state (the movement of my arm) causes a part of your total state (pain in your shoulder) and a part of your total state (the movement of your arm) causes a part of my total state (pain in my face). For there are four different parts of the total state involved, whereas in circular causation there would be only two.

the puzzle gives us some reason to rethink the dogma that numbers can neither cause or be caused.

But even if abstracta such as numbers and propositions are causally inefficacious, why should we think that there cannot be a nonabstract necessary being that is causally efficacious? One answer was already alluded to: some will insist that only spatiotemporal entities can be causally efficacious and it is implausible that a necessary being be spatiotemporal. But it was difficult to see why exactly spatiotemporality is required for causal connections. (See also Chapter 5 in this volume on the argument from consciousness.)

A different answer might be given in terms of a puzzlement about how there could be a nonabstract necessary being. The traditional way of expressing this puzzlement is that given by Findlay (1948), although Findlay may have since backpedaled on his claims. A necessary being would be such that it would be an analytic truth that this being exists. But it is never analytic that something exists. If 3x(Fx) is coherent, so is ~3x(Fx). Basically, the worry is caused by the Humean principle that anything that can be thought to exist can also be thought not to exist. But it is by no means obvious why this principle should be restricted, without thereby doing something ad hoc, to nonabstract beings.

Indeed, why should abstract beings alone be allowed as necessary? Why should its necessarily being true that 3x(x is a deity) be more absurd than its necessarily being true that 3x(x is a number)? Perhaps the answer is that we can prove the existence of a number. In fact, mathematicians prove the existence of numbers all the time. Already in ancient times, it was shown that there exist infinitely many primes.

However, these proofs presuppose axioms. The proof that there are infinitely many primes presupposes a number system, say, with the Peano axioms or set theory. But a statement of the Peano axioms will state that there is a number labeled "0" and there is a successor function s such that for any number n, sn is also a number. Likewise, an axiomatization of set theory will include an axiom stating the existence of some set, for example, the empty set. If our mathematical conclusions are existential, at least one of the axioms will be so as well. The mathematical theory ~3x(x = x) is perfectly consistent as a mathematical theory if we do not have an existential axiom. Thus, if we are realists about numbers, we are admitting something which exists necessarily and that does not do so simply in virtue of a proof from nonexistential axioms.

Of course, one might not be a realist about abstracta. One might think that we do not need to believe that there necessarily exist propositions, properties, or numbers to be able to talk about necessarily true propositions or necessarily true relations between numbers or properties. But if the critic of the PSR had to go so far as to make this questionable move, the argument against the PSR would not be very plausible.

In any case, not all necessity is provability. We have already seen that the work of Godel questions the thesis that all necessity is provability or analyticity (cf. Section, above). Kripke (1980), too, has questioned the same thesis on different grounds. That horses are mammals is a proposition we discover empirically and not one we can prove a priori. But it is nonetheless a necessary thesis. So is the proposition that every dog at some point in its life contained a carbon atom.

Now, it is admittedly true that the Kripkean necessities are not necessities of the existence of a thing. But they provide us with an example of necessarily true but not analytic propositions. Another such example might be truths of a correct metaphysics, such as that it is impossible that a trope exists, or that it is necessary that a trope exists in any world containing at least two material objects that are alike in some way, or that there are properties, or that there are no properties. But, likewise, it could be that the true system of ontology entails the existence of God.

Another option for the defender of the epistemic possibility of a necessarily existing deity is provided by the ontological argument. The ontological argument attempts to show that from the concept of God one can derive the necessary existence of God. A necessary being could then be one for which there was a successful ontological argument, although perhaps one beyond our logical abilities. While the extant ontological arguments might fail (although see Chapter 10 in this volume), the best ones are valid and the main criticism against them is that they are question-begging. Thinking about such arguments gives us a picture of what it would be like for something to have a successful ontological argument for the existence of something. It could, thus, be that in fact God exists necessarily in virtue of an ontological argument that is beyond our ken, or perhaps the non-question-begging justification of whose premises is beyond our ken, while we know that he necessarily exists by means of a cosmological argument within our ken. We do not, after all, at present have any good in principle objection to the possibility that a sound ontological argument might one day be found (cf. Oppy 2006, chap. 2). Objection 5: the Taxicab Problem

Since the First Cause that this cosmological argument arrives at is a necessary being, while the PSR as defended applies only to contingent states of affairs, the problem of applying the PSR to the existence of the necessary being does not arise. And even if one defended a PSR that also applies to necessary beings, one could simply suppose that the being's existence is explained by the necessity of its existence, or that there is a sound ontological argument that we simply have not been smart enough to find yet.

However, a different way to construe the Taxicab Problem is to ask about what happens when we apply the PSR to the proposition allegedly explaining the BCCF. But this issue has already been discussed when we discussed the van Inwagen objection to the PSR. There are two live options at this point. The proposition explaining the BCCF might be a contingent but self-explanatory proposition. For instance, it might be that the proposition that a necessarily existing agent freely chose to do A for reason R is self-explanatory in the sense that once you understand the proposition, you understand that everything about it has been explained: the choice is explained by the reason and the fact that the choice is free, and the necessity of the agent's existence is, perhaps, self-explanatory, or perhaps explanation is understood modulo necessary propositions. The other, I think preferable, option is that the BCCF is explained by a necessary proposition of the form: a necessarily existing God freely chose what to create while impressed by reason R.

One might continue to press a variant of the Taxicab Objection on this second option, using an argument of Ross (1969). Granted, it is necessary that God freely chose what to create while he was impressed by R. Let q be this necessary proposition. Let p be the BCCF. Then, even though q is necessary, it is contingent that q explains p (or even that q explains anything - for if God created something else, that likely would not be explained by his being impressed by R, but by his being impressed by some other reason). And so we can ask why q explains p.

But at least one possible answer here is not particularly difficult. The question comes down to the question of why God acted on R to make p hold. But God acted on R to make p hold because he was impressed by R. And God's acting on R to make p hold is explained by his making a decision while impressed by R, with its being a necessary truth that God's action is explained by R and by every other good reason. So, ultimately, q not only explains p, but also explains why q explains p. Had God acted on some other reason S that he is also impressed by to make not-p hold, then we could say that this was because he was impressed by S. (See Section, above.)

And so the PSR-based argument circumvents the Regress and Taxicab problems.

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