The Leibnizian Cosmological Argument

The deductive cosmological argument from contingency has a long and illustrious history. It’s been exposited and defended by the likes of, e.g., G.W. Leibniz, Samuel Clarke, and recently (e.g.) Stephen T. Davis, Ronald Nash, Robert Koons, and Alexander Pruss. However, a number of contemporary theists seem to shy away from defending it, such as J.P. Moreland, Peter Van Inwagen, and William Lane Craig (although Craig seems to have warmed up to it slightly in recent years, given his more-positive-than-usual assessment of it in his essay in The Rationality of Theism). In this post, I will exposit the Leibnizian cosmological argument from contingency. Then, I will discuss some common objections to the argument that don't seem to work. Finally, I will discuss several decisive criticisms of the argument. In the appendix, I exposit and critique a recent defense of PSR.

I: Exposition
This version of the cosmological argument has been given a number of construals, depending on how its proponents spell out the notions of a contingent being and the Principle of Sufficient Reason (PSR). One common way to spell out these notions is as follows:

A contingent being or state of affairs is a being or state of affairs that exists, but doesn’t have to – its nonexistence is logically (or metaphysically) possible. So, for example, rocks, trees, and you and I are contingent beings, and George W. Bush being the current U.S. President is a contingent state of affairs. By contrast, a necessary being or state of affairs is a being or state of affairs that exists or obtains of logical (or metaphysical) necessity – to use possible worlds talk, one that exists or obtains in all possible worlds. So, for example, if Anselm’s God exists, then it is a necessary being.

Finally, PSR states that (a) for every being that exists, there is a sufficient reason for why it exists, and (b) for every state of affairs, there is a sufficient reason for why it obtains. PSR has prima facie plausibility, and is often defended by offering one or more of the following three considerations. First, it seems to make sense of our intuitions when we reflect on sample cases. So, for example, suppose there is a ball on the lawn in your front yard. No one would say that there is no sufficient reason for why the ball exists, or why it’s there on the lawn. Obviously, the ball has an explanation for its origin (in a toy factory), its continued existence (in terms of, e.g., the properties of the particles that constitute the ball), and its being on the lawn now (your daughter left it there). The same sorts of explanations seem to generalize to any case we can think of. Therefore, we have some support for PSR based on reflection on cases. Second, some have argued that PSR is self-evident. Self-evident propositions are those that can be seen to be true merely by coming to understand what they assert. That is, once you understand what they mean, you can see that they’re true. So, for example, consider the proposition, “all triangles have three angles”. Once I understand the constituent concepts of this proposition, I can see that it’s true. Similarly for “nothing can be red all over and green all over at the same time.” And similarly, say some proponents of the contingency argument, for PSR. Third, even if one remains unpersuaded by the previous two considerations, one may think that it’s a presupposition of rational thought. Compare: Although it's notoriously difficult to justiify the existence of material objects, and the existence of a past, it nonetheless seems pathological to deny that material objects exist, or to deny that the universe has existed for more than ten minutes (as opposed to thinking that it was created ten minutes ago, with an appearance of age, and with false memories of a longer past). All sane people accept these propositions, and -- say some proponents of the argument from contingency -- the same is true of PSR. Thus, even if you think we can’t prove it, you must accept it to be a rational agent. Given these notions, we may now state the argument.

It’s undeniable that contingent beings exist. After all, we came into existence, and could go out of existence without much trouble. The same is true of rocks, trees, our planet, and in fact every object in the universe. In fact, the universe itself seems to be just one big contingent being. If so, then by PSR, it has a sufficient reason for its existence. Now since it’s a contingent being, it can’t account for it’s own existence in terms of its own nature, even if it has existed forever. For even if the contingent universe existed forever, the following contingent state of affairs would obtain:

(CF1) There being an eternally existent contingent universe.

But if so, then by PSR, there is a sufficient reason for why CF1 obtains, in which case we must look for a reason beyond our contingent universe.

Now whatever that “something” is, it can’t just be more contingent beings. For even our universe is explained in terms of an infinite series of contingent beings, the following contingent state of affairs would obtain:

(CF2) There being an infinite series of contingent beings.

But if so, then by PSR, there is a sufficient reason for why the infinite series of contingent beings exists or why CF2 obtains. In short, no matter how many contingent beings we throw into the explanatory “pot”, the existence of our contingent universe – or any contingent being whatever, for that matter – cannot be sufficiently accounted for purely in terms of contingent beings. But if not, then the sufficient reason for the existence of our contingent universe must be in terms of at least one necessary being. And, as Aquinas would say, “this we all call ‘God’.

II: Giving the Argument its Due: A Defense Against Common Objections
In this section, I continue the task of giving the contingency argument its due. To that end, I briefly discuss three criticisms of the deductive argument from contingency that don’t seem to work. Here I’m just summarizing William Rowe’s points from his Philosophy of Religion (Belmont, Ca: Wadsworth, 1978), pp. 16-30.

1. Dependence and the fallacy of composition:

1.1 The argument fallaciously assumes that because each member of the collection of beings within the universe is dependent, that therefore the whole collection of such beings is itself dependent. But this doesn’t follow.

1.2 Reply: It would be fallacious to assume this, but the defender of the cosmological argument need not assume it for the argument to work. Rather, since the existence of the collection of dependent beings is a positive fact, then it follows from PSR alone – i.e., without the need to rely on an inference from dependence of the parts to dependence of the whole -- that there must be a sufficient reason for why the collection exists.

2. Causation and the fallacy of composition:

2.1 The argument fallaciously assumes that because each member of the collection of dependent beings has a cause, that therefore the whole collection of dependent beings has a cause. But this doesn’t follow.

2.2 Reply: It would be fallacious to assume this, but the defender of the cosmological argument need not assume it for the argument to work. Rather, since the existence of the collection of dependent beings is a positive fact, then it follows from PSR alone – i.e., without the need to rely on an inference from the need for a cause of the parts to a need from a cause of the whole -- that there must be a sufficient reason for why the collection exists.

3. Nothing’s left to explain

3.1 The defender of the cosmological argument fails to see that once the existence of each member of a collection of dependent beings is explained, the existence of the whole collection is thereby explained.

3.2 Reply: It’s not true that explaining why each member of *any* collection of dependent beings exists entails an explanation for why the whole collection exists – why there are dependent beings at all. True, there are cases *of certain sorts* in which explaining the former entails explaining the latter. For example, if a necessary being were the direct cause of each dependent being in the universe, then it would be true that explaining why each dependent being exists would thereby entail an explanation for why the whole collection exists, and why there are dependent beings at all. However, there are cases in which it wouldn’t; just take the necessary being out the previous case, and imagine each dependent being as caused by one of the others. In such a case, explaining why each dependent being exists wouldn’t explain why there are dependent beings at all.

III: Why the Argument Ultimately Fails
This section completes my discussion of the deductive cosmological argument from contingency. In the previous section, I considered a set of objections to the argument that didn't seem to be persuasive. The moral of that discussion seemed to be that the argument stands or falls with the viability of PSR.

Here, I offer objections to PSR that seem to have some force. These criticisms aren’t original with me, but rather are standard objections (except perhaps the last one, although it's based on ideas of other authors). Furthermore, I don’t mean to imply that there aren’t other versions of the argument from contingency that may avoid these criticisms. However, they do seem to apply to the variants of the argument that one finds in standard “intermediate-level” apologetics books. The criticisms can be divided into two broad categories: (i) those that undercut the reasons offered for accepting PSR, and (ii) those that indicate that PSR is positively false or unreasonable.

1. Type-(i) Criticisms:

1.1 Contrary to what its proponents often assert, PSR does not seem to be supported by reflection on cases. Rather what such reflections support is the weaker principle that objects and events are explained in terms of antecedent causes and conditions. In actual practice, ordinary individuals and scientists explain the existence of objects and events in terms of antecedent causes and conditions, provisionally taking the latter things to be brute facts unless or until they, too, can be further explained. But the prinicple implicit in this sort of search for explanations isn't sufficient to generate the need for an explanation of the universe as a whole in terms of a necessary being.[i]

1.2 Contrary to what some of its proponents assert, PSR does not seem to be self-evident. For what makes a proposition self-evident is that grasping its meaning is sufficient for seeing that it’s true. Consider the two standard categories of self-evident propositions: analytic a priori propositions and synthetic a priori propositions. Both sorts of propositions are knowable independently of empirical investigation of the world. But they differ in that the former (analytic a priori propositions) are tautologous and uninformative, while the latter are not. So, for example, "All bachelors are unmarried" is an analytic a priori proposition, while "Nothing can be red all over and green all over at the same time" is arguably a synthetic a priori proposition.

Now consider PSR: (a) For every object, there is a sufficient reason for why it exists; (b) for every positive state of affairs, there is a sufficient reason for why it obtains. This isn't a tautology; so it's not analytic a priori. Furthermore, although it's a substantive claim, its truth or falsity is not evident merely by reflecting on its constituent conceps. Thus, it doesn't seem to be synthetic a priori, either. Perhaps there is another category of self-evident propositions, but if so, PSR seems not to belong to it. For what makes a proposition self-evident is that one can see that it's true merely be reflecting on its contituent concepts, and we have seen that PSR doesn't safisfy this condition.

1.3 Even if PSR were a presupposition of reason, it wouldn’t follow that it would then be true. But in any case, PSR does not seem to be a presupposition of reason. Rather, again, reason only seems to demand that the existence of each object or fact is explained in terms of antecedent causes and conditions, which are provisionally taken as brute facts unless or until they, in turn, can be explained. Reason does not seem to require anything beyond this.[ii]

2. Type-(ii) Criticisms:

2.1 PSR absurdly entails that everything obtains of necessity. The argument for this can be stated as follows. Consider the conjunction of all contingent facts (CCF). By PSR, there is a sufficient reason for CCF. Now the sufficient reason for CCF is itself either contingent or necessary. But it can’t be contingent, because then it would represent a contingent fact, in which case it would itself be a part of the CCF. But contingent facts don’t contain within themselves the sufficient reason for why they obtain – let alone the sufficient reason for why the CCF obtains. Thus, the sufficient reason for CCF must be necessary. But whatever is entailed by a necessary truth is itself necessary, in which case all truths would be necessary truths, and the referents they represent would obtain of necessity. But this is absurd. Therefore, PSR is false. [iii]

2.2 The following scenario is prima facie possible: there are just two kinds of beings that exist: contingent-and-dependent beings (e.g., rocks, trees, planets, galaxies, you and me) and contingent-yet-independent, “free-standing” beings, out of which all contingent-and-dependent beings are made (perhaps matter-energy is like this). If so, then even though there are possible worlds at which the contingent-yet-independent beings don’t exist, they are eternal and indestructible at all possible worlds in which they *do* exist (interestingly, some theists -- e.g., Richard Swinburne -- take God to be just such a being). On this account, then, there are contingent beings that come to be and pass away – viz., the contingent-and-dependent beings. But the beings out of which they’re made – i.e., the contingent-yet-independent beings -- do not; nor can they [iv]. This scenario seems possible. But if so, then since PSR entails that such a state of affairs is impossible, then so much the worse for PSR.

The basic point here is that PSR assumes that dependent beings must have their ultimate explanation in terms of *necessarily existent* independent beings (beings who exist in all possible worlds), when in fact *essentially* independent beings (beings that are independent at all possible worlds *in which they exist*) are all that are needed to do the requisite explanatory work. PSR entails that this isn't enough: if there are any essentially independent, indestructible, free-standing beings, then these must be *further* explained in terms of a *necessarily existent* being. But surely this is explanatory overkill, and since PSR entails that such further explanations are required, this implication undercuts any prima facie plausibility PSR may seem to have had.

These criticisms have varying degrees of force. However, it seems to me that criticism 2.2 is an undercutting defeater for PSR, and that criticism 2.1 is a rebutting defeater of PSR. But if these things are so, then the argument from contingency is defeated.
APPENDIX: A Recent Defense of PSR

(Note: some things I say here are of a technical nature, and thus will probably only be of interest to those with some background in philosophy)

A number of philosophers have attempted to revive the Leibnizian cosmological argument in recent years by advancing a weaker version of PSR. According to their version of PSR, every contingent being has a *possible* explanation in terms of something else. That is, every contingent being is such that there is at least one possible world at which it has an explanation for why it exists. Call this version of PSR, 'Modal PSR'.

Now some authors -- in particular, Garrett DeWeese and Joshua Rasmussen[v] -- offer an argument for Modal PSR . Now I think their argument has a couple of problems, but here I just want to mention one that I think is decisive: The argument uses Modal PSR as a premise to derive the standard version of PSR we discussed above. But this premise is implausible at best, and outright false at worst. For unless they just beg the question and assume that there are no possible beings that lack a sufficient reason, then they must be claiming that, even if there *are* possible worlds at which a given contingent beings lacks a sufficient reason, there are *other* possible worlds at which it does. But this is implausible, For It seems to me that the only way to accept Modal PSR is to reject origin essentialism. Allow me to me unpack and explain this criticism below:

Suppose origin essentialism is true, and suppose we've got our hands on a universe, and we give it a Kripkean baptism: (pointing to the universe) "Let *that* be called 'Uni'. 'Uni' is now a Kripkean rigid designator -- it refers to *that* universe in all possible worlds in which it exists.

So now we have a way to hold Uni fixed, so we can start considering modal claims about *it*. Well, there are two relevant possibilities for us to consider here: (i) Uni has its origin in the causal power of a divine being,and (ii) Uni has no origin. If (i), then, by origin essentialism, this is an essential property of Uni, in which case there is no possible world in which Uni lacks such an origin.

If (ii), then Uni lacks an origin in the causal activity of a divine being, and so *this* fact about Uni is essential to it, in which case there is no possible world in which it has an origin in the causal activity of a divine being.

The moral, then, is that if we accept origin essentialism like good Kripkeans, then whether a universe has an explanation in terms of a divine being doesn't vary from world to world. But if so, then Modal PSR is of no help unless we know *beforehand* whether our universe has its origin in the causal activity of a divine being. But if we already knew *that*, then the contingency argument would be superfluous.

Of course, one could always reject origin essentialism, or restrict its scope in a way favorable to the argument, but then the audience for the argument shrinks considerably.

i. This is a rough paraphrase of one of J.L. Mackie’s objections in The Miracle of Theism (Oxford: Oxford UP, 1983), pp. 84-87.

ii. See ibid.

iii. This objection is a rough paraphrase of one of Peter Van Inwagen’s objections in his textbook, Metaphysics, 2nd edition (Boulder: Westview Press, 2002), pp. 119-122.

iv .Another way to see how this could be: contingent-yet-independent beings have indestructibility as an essential property: they are indestructible and everlasting at all possible worlds in which they exist. However, there are possible worlds at which they don’t exist.

v. See their chapter of the recent apologetics book, In Defense of Natural Theology (InterVarsity Press, 2005).


Adrian said...


I have two questions about this argument, maybe you can help me.

First, while PSR may appear to hold at a macroscopic level, it's not at all clear that it holds at a quantum level. There is no cause for virtual particles and so during the inflationary phase of the Big Bang when matter first arose, there is no sufficient cause for matter. So it looks like PSR is contradicted by observation. Can you comment?

Next, PSR may hold for all of the macroscopic events that we see, but that is because we know how balls get onto lawns or how cats get born. We are testing PSR daily. While you may ask us to conclude that since PSR holds for all observations on the earth, it should hold for the entire universe but anyone that knows a bit about physics knows how wrong that really is! Our intuition and our observation cover only a minuscule part of the universe with a fixed gravity and energy, it is no guide at all to the intense energies and masses present at the formation of the universe. It isn't even a guide to how the smallest particles of matter behave. How can anyone use observations of PSR at a macro level and then expect them to transfer to the universe itself without any calculation or even an explanation of what PSR might mean when applied to the beginning of time itself?


John said...

Hey Ex

I think William Lane Craig is going to defend it in His upcoming new addition of Reasonable Faith.

It should be interesting.

exapologist said...

Hey Cole,

Thanks for the information! I didn't know he was updating RF.

Hi Tyro,

That's a great point! You're right that certain quantum-level facts pose problems for PSR, in particular, the clause that requires an explanation for every event obtains. For there are some quantum events that lack such an explanation.

As for your point about virtual particles, some defenders of the argument say that, nonetheless, such entities have a *material* cause -- i.e., they arose from other *stuff*, viz., a sea of fluctuating energy (as opposed to just nothing -- i.e., not even a sea of fluctuating energy).

I left discussion of this (nice) objection out because some defenders of the argument accept an interpretation of quantum mechanics according to which there are "hidden variables" that actually determine quantum events, in which case they don't violate the clause of PSR mentioned above. Rather than quibble with them about that, I tried to stick to objections they're more likely to accept.



Adrian said...


While you're right that many people have fought about hidden variables for decades, Alain Aspect's experiments have essentially demolished this idea. He refined Bell's Inequality to make the contrast more stark and then experimentally confirmed the results.

As for VPs, the popular description is of particles "borrowing" energy or talking about a "seething sea" of energy, but this is just a handy tool for dealing with a general audience. The fact is that the only thing seething are the VPs themselves, and there is no energy present but there must be a minimum uncertainty in the amount of energy which allows VPs to appear. What should be noted is that there is no particle, no force, no interaction of any sort which causes any given VP to appear which is exactly the point.

If particles going through a double slit are detected in one interference band or other, there was nothing which acted upon the particle to cause it to go one way or the other. When a particle decays, nothing acted upon it to decay. When an electron drops to a lower energy state and emits a photon, nothing acted upon it to do this. When a VP appears, nothing acted to cause this to happen.

Since the PSR requires an agent as a cause, or at least some event or some interaction, this is clearly violated. At a quantum level, we no longer have these agents. It is now up to the champions of PSR to reformulate it or abandon it.

Although I see your point about talking in a language that the people posing the PSR can understand. Regrettably, they seem to have little problem talking about physics though they have little understanding of it.

So here's another related problem which doesn't require delving into nonlocality.

The PSR says "for every being that exists, there is a sufficient reason for why it exists". In the context of PSR, what does it mean for something to exist and what causes is it talking about? You can talk about why humans exist, why buildings exist, why cars and trees exist but in reality, all of the material that makes up the humans, buildings, cars and trees were pre-existing. Nothing really came to exist, but instead pre-existing material was merely transformed. You start with a given number of carbon atoms, and you end with exactly the same number, but in different configurations.

To be precise, this statement should read "every arrangement of matter has sufficient reason for this arrangement." This draws attention to a crucial point: PSR does not deal with anything coming into existence!

I think this highlights the equivocation and fallacious leap they try to pull when they go from talking about how matter is rearranged into trying to talk about how matter or the universe comes into existence. To ask how a cup of tea came to exist (answer: hot water and a teabag) is a very different question than asking how the protons and neutrons in the oxygen atoms in the water came to exist.

exapologist said...

Hi Tyro,

Nice points! You're preaching to the choir -- I agree with everything you say here. So, for example, you won't get a complaint from me about the implausibility of hidden variable interpretations of QM.

I also agree with you about the point about sufficient reasons regarding things *composed* of matter-energy (e.g., the ball in my back yard) vs. sufficient reasons regarding matter-energy *itself*. Thus, there may be sufficient reasons for the existence of the former, but that gives us no reason to think so for the existence of the latter. I tried to bring this out with my last criticism in the original post -- the one about the contingent-and-dependent beings vs. the contingent-but-independent being out of which they're composed: the former may well be finite and dependent beings (viz., dependent on the stuff out of which they're composed), while the latter may be an eternal and independent being, in which case it's odd to think it needs an explanation for *its* existence. And if a scenario like this seems possible, then so much the worse for PSR.

Rayndeon said...

Hi exapologist,

Awesome post! I myself have discussed such issues here at Internet Infidels Discussion Board - Argument from Contingency. Allow me to attempt to strengthen Peter van Inwagen's fatal argument. I was originally going post the following on Victor Reppert's blog, but, in any case,

"Allow me to summarize what I construe as being the strongest objection to any version of the principle of sufficient reason (which holds that necessary facts can explain contingent facts), which Peter van Inwagen raises in An Essay on Free Will (Oxford: Oxford University Press, 1983) pp. 202-4 and can also be found in Metaphysics: Second Edition (USA: Westview Press, 2002) pp. 119-22. Consider the cosmos, which is the set of all contingent state of affairs (and is itself a contingent state of affairs). Now, the explanation of the cosmos is going to be either necessary or contingent. If it is necessary, since the explanation entails the explanandum (recall that it is the Principle of Sufficient Reason, moreover that if the explanation does not entail the explanandum, then what makes the explanandum actual?), it follows that the explanandum is necessary. But, the cosmos is contingent, for the very definition of the cosmos is the set of all contingent states of affairs, which is itself contingent. So, if the explanation entails the explanandum, and the explanation is necessary, then the explanandum is necessary. But, if the explanandum (the cosmos) is contingent, in which case it is not-necessary, it follows by modus tollens that the explanantion is not necessary. But, the explanations is necessary, which is a contradiction. Furthermore, necessary states of affairs are self-explanatory: they must be actual, hence, they are actual. It is difficult to see how necessary SOAs can be explained since nothing makes necessary SOAs actual. This is especially true if construe non-self-explanatory explanations as being plausibly interpreted as being causal ( it seems that explanation consists of figuring out what *makes* a state of affairs actual, or what is the truthmaker of a proposition. The same definition seems to be clear of the word "cause."); however, necessary SOAs cannot stand in causal relations, due to causal asymmetry, for given causal priority, if we construe events in some chain of causation, at the "placeholder" wherein cause exists, the effect does not exist. But, necessary SOAs can never fail to be actual, hence, necessary SOAs cannot stand in causal relation, and hence, cannot be caused. So, we have two good reasons to deny a necessary explanation of the cosmos.

What if the explanation is contingent? The problem is that any contingent explanandum whatsoever must appeal to contingent explanations that are neither parts of the explanandum nor entailed by the explanandum and it cannot be the explanandum itself. The explanation cannot be a part of the explanandum nor entailed by the explanandum (if the explanation is a part of the explanandum, then the explanandum entails the explanation, for the actuality of the explanandum entails its parts, which therefore, if the explanation is a part, entails the explanation). First, that is not what is meant by "explanation" since to say that something is explained is to say that there is some SOA such that given a different SOA, the latter *makes* the former actual. We cannot, for instance, consider the fact that a car blew up last Saturday explains the fact that the car blew up last Saturday and the smoldering remains fell into a lake. Secondly, if the explanandum entails the explanation, then the explanations explains itself since the explanandum entails the explanation for that the explanation is a conjunct of the explanandum, and explaining a conjunction explains the conjuncts, therefore, the explanation explains the explanation, which I address in below regarding where or not the explanation can be the explanandum. Moreover, the explanation is prior to the explanandum; but, if the explanandum entails the explanation, then the explanandum must exist in the same "placeholder" as the explanation; but if the explanandum is actual, then the explanantion cannot explain the explanandum for the explanandum is already actual then. Therefore, the explanandum cannot entail the explanation. If the contingent explanation is the explanandum, then it follows that explanation and explanandum are one the same; but this cannot be true, for no contingent SOA can be self-explanatory, since nothing makes self-explanatory SOAs actual (for they must be actual), but contingent SOAs do not have to be actual. Furthermore, explanations are prior to the explanandum. But, if the explanation is the explanandum, it follows that the explanation is prior to itself; that in the "placeholder" wherein the explanation is actual, it is not actual, which is a logical contradiction, and therefore, the explanation cannot be the explanandum.

So, no contingent explanation of the cosmos can be the cosmos nor a part of it. But, then, it follows that the cosmos necessarily has no explanation at all for there cannot be any necessary explanations at all, and any contingent explanandum is to be explained by a contingent explanation that is neither entailed by the explanandum nor identical to the explanandum; but the cosmos entails any contingent SOA whatsoever since it is the set of all contingent SOAs and there is nothing contingent outside of the cosmos; therefore, the cosmos is necessarily a brute fact. In any case though, it seems pretty clear even without van Inwagen's objections that it is not entirely clear why precisely we should hold that there cannot be brute facts. First of all, empirical generalizations leading to the PSR are generalizations within the cosmos, so it is difficult to see how this entails application on the cosmos itself. And if we seriously take the Copenhagen interpretation of quantum mechanics, then there are brute facts; for instance, that a specific atom decays at such and such time is a brute fact, under the Copenhagen interpretation. Moreover, it is difficult to see how the PSR could apply to eternal SOAs, since explanation is prior to the explanandum; but there is nothing prior to eternal explanandums, so, it is plausible to regard eternal explanandums as necessarily being brute facts, and the cosmos as also necessarily being a brute fact.

Typically speaking, there are two types of objections to van Inwagen's thesis. The first is a denial that explanations entail their explanandum. The second is an appeal to libertarian free will. What is to be made of the first objection? Well, first of all, it does not seem that it is entirely consistent with the PSR, since the PSR is a principle of sufficient reason, and moreover, that the principle consists of finding the complete explanations of things. Futhermore, it is difficult to see how explanation cannot entail the explanandum, for if it does not, then what is the explanation explaining? For the explanation makes the explanandum actual, so, saying that the explanation does not entail the explanandum is to say that the explanandum is in some sense unexplained. For if in some logically possible world we have the explanation C1 and the explanandum E1 such that C1 is actual and E1 is non-actual, then what makes the explanandum actual? It seems that the actuality or non-actuality of E1 turns out to be a brute fact, which is incompatible with the PSR. Furthermore, suppose we insist that there is a partial explanation for every contingent SOA. First of all, what counts as a partial explanation to begin with? This immediate restriction looks too ad hoc, but I suppose that is merely my perspective. Moreover, to say that an explanation is partial seems to be saying that given some contingent SOA that corresponds to some conjunction [(p & q) & r], one partially explains it by explaining p. But, plainly, we have the same problem as above; for then, what makes (q & r) true at all? Also, doesn't seem clear that explaining p entails p to begin with? Perhaps we wish to insist that other explanations explain (q & r); but, wouldn't those explanations in turn entail (q & r)? Moreover, if we take all those explanations together as one conjunction, surely that explains the original conjunction. It also can't be that we appeal to that there must be some explanation for [p & (q & r)], since while it is true no particular explanation would entail that conjunction, each particular explanation would also be contingent, which is not what the PSR is to show in the first place. Furthermore, suppose we have that that C1 is a partial explanation of E1. So, there seems to be some E2 such that "If C1, then E1" (take "if" in the sense of material implication); but E2 is a contingent proposition since C1 does not entail E2 for there is some possible world wherein C1 holds but E2 does not hence "If C1, then E1" in that world is false. So, this too must have an explanation C2. But, then, what of E3: "If C2, then E2." We can continue this infinitely, creating some infinite chain of explanation wherein the entire chain doesn't even begin to explain E1 to begin with. Surely, these sorts of infinite regresses that do pitiful explanatory work cannot be what PSR intends. Moreover, perhaps we can construe complete explanations such that it is true that [(p → q) & p]; plainly, in all possible worlds wherein this holds, q is true. So, this entails q, so, it is necessary that given [(p → q) & p], q is true.

The second objection is an objection from libertarian free will. It insists that there is some necessary being such that the necessary being created the cosmos, but that necessary being is insufficient for the cosmos' existence, for agent-causes do not entail their effects. I think this is a confused thesis. First of all, the mere existence of the necessary being is not the explanation of the cosmos. Indeed, when we cite that an agent was responsible for some SOA, we do not cite their mere existence, but that the agent did certain things that then in turn brought about the SOA in question. In this case, the explanation in question is in reality the necessary being willing the cosmos into existence. Perhaps we can picture this necessary being saying "Be!" or something like that, and the cosmos comes into being. But plainly, the necessary being's willing the cosmos is sufficient for the existence of cosmos' existence. But, that is the explanation of the cosmos, not the mere existence of the necessary being. And showing that the cosmos has a necessary explanation is to appeal to an explanation like that. So, it seems that one must admit to that the necessary being wills this cosmos is a contingent SOA (this makes it susceptible to the above arguments against any contingent explanation of the cosmos). However, this explanation is going to be a brute fact of the world since per libertarian free will, that any agent does such and such thing is causally undetermined, and hence, that a necessary being willed the cosmos into actuality is a brute fact. But, this seems to be at odds with the PSR, which would eliminate brute facts. Moreover, why find this brute fact preferable to the brute nature of the cosmos? We have derived some speculative explanation such that that explanation has no explanation at all. But, how is this better than the cosmos has no explanation at all? This is of course all prior to whether or not libertarian free will is a true theory of freedom, which I do not think that it is.

So then, given Peter van Inwagen's objections (with a few extra additions), I find the PSR to be wholly false and construe it as necessary that this cosmos is a brute fact."

Moreover, there is the questionable contention that there can be any concrete necessary being at all. I briefly argue for this at IIDB - For Dean, the Modal Ontological Argument:

"Furthermore, God's necessity seems to indicate a contradiction. Given a certain type of compatabilism, [4] given a certain circumstance, in all possible worlds wherein that circumstance obtains, a person does the exact same thing every single time. So, we have conditional propositions such that

(18) Given a circumstance C and abilities A, a person P will actualize a state of affairs S.

Moreover, these conditionals are grounded in who P is, which is to say that the maximal set of these conditionals (as I detail in the fourth footnote) is individuative; it marks a distinct person. Now, in God's case, the problem is that the exact same C obtains in all worlds in which He exists: He is prior to non-eternal entities. If we include the compatibilist account and cite that the type of God in question is a God who would create a particular cosmos in response to the situation, it follows that in all worlds in which God exists, the exact same cosmos obtains; but if God is necessary, then the cosmos is necessary. But, this means that there is exactly one possible world. But, there can't be one possible world because other worlds are possible. Therefore, the necessity of God (and compatibilism) entails modal fatalism. Moreover, it seems that necessary states of affairs cannot be caused to exist, and furthermore since cause entails effect, it seems that there cannot be any necessary causes either. [5]

Finally, I would offer the same objection that Jade raised, that the ontological argument does not establish the existence of an individual but of a class of entities. From a previous post:

I do not think you grasped my point entirely. I apologize for my ambiguity. Allow me to be more explicit. In order to show that God the concrete entity is necessary, you have to establish all individuating aspects of God as necessary, otherwise God, the individual will be contingent.

This situation is pretty similar to the contingency of the actual world. [Clearly, an actual world must be exist, but no particular actual world must be exist] The necessary parts of the actual world exist in all possible worlds, so that shall not concern us. What makes the actual world contingent is the contingent states of affairs present. No particular contingent states of affairs had to be present, but some contingent states of affairs had to be present. Look: for each contingent SOA, there is some proposition p. Qua contingent states of affairs: ◊p & ◊~p. Now, either p v ~p. Exactly one conjunct is going to be true and it is necessary that exactly one such conjunct be true. But, no particular conjunct need be true, hence, the SOA in question remains contingent even though there must be some actual SOA. So then, the actual world in question is contingent, even though, there must be some actual world since (a) the necessary facts obtain in all possible worlds and hence obtain in an actual world and (b) it is necessary that for every contingent SOA, it is either actual or non-actual, per the above.

Now, we have the same sort of case with God for at best we have established (if the ontological, cosmological, and conceptualist arguments work) necessary conditions for His individuality, but not sufficient conditions. So, at best, the ontological, cosmological, and conceptualist arguments establish that of the universal "God," it is necessary in all possible worlds that there be some particular that instantiates this universal, but there is no necessity of that there be an individual that is necessary; therefore, this arguments fail to establish the necessity of God the individual or even God the person.

So, I do not regard the ontological argument a good argument at all. And, if anything, it is impossible for there to be any necessary concrete entity whatsoever."

I have personally defended the incoherency of libertarian free will and the necessity of compatibilist freedom at IIDB - Theodicies and Skeptical Theism, towards the bottom of the post.

Rayndeon said...

A brief edition: I accidentally made the statement "it seems that explanation consists of figuring out what *makes* a state of affairs actual, or what is the truthmaker of a proposition." What I actually meant is that explanation (of a non-necessary entity) consists of figuring out what makes the SOA or the truthmaker of the proposition actual i.e. one does not explain a contingent proposition by pointing out the truthmaker of the proposition, but by explaining the truthmaker of that proposition.

exapologist said...

Hi Rayndeon!

Thanks for the clarification in your second comment.

That was a *very* nice explication of Van Inwagen's primary criticism of the Leibnizian cosmological argument. Nice work! :-) I look forward to reading through your threads at IIDB -- thanks for pointing the way to some of them!

All the best,


Rayndeon said...

Hello exapologist,

Thank you for your kind remarks. In particular, I wished to bring out and address two common objections raised by defenders of the argument from contingency, namely, a denial that explanations entail their explanandums and the appeal to libertarian free will. Both routes appear to be taken up by Alexander Pruss in Ex Nihilo Nihil Fit: Arguments New and Old for the Principle of Sufficient Reason, where he discusses the van Inwagen objection.

I would also inquire as to whether or you feel that the failure of PSR is "infectious." Namely, what I mean is that the failure of both the argument from contingency and the ontological argument lend themselves to the failure of theism as an explanatory hypothesis; consider, for instance, the fine-tuning argument. We can cite impressive objections such as the Renormalization Objection; but, in reality, when it really comes down to it, we realize that the teleological argument is predicated on a pseudo-problem. In general, we have order and regularity in the world. Now, the teleological argument asks for the explanation of such order and regularity. But, this is mistaken for an explanation can only be as such in terms of order and regularity in the first place. So, what we are simply asking for is to push back the initial regularity another step, in this case, a personal God.

But, here is where the failure of PSR is significant. We may ask, well, what accounts for the existence of God? We have attempted to explain the natural order of the world by appealing to another regularity. But, what about *that* regularity? And so the theist replies that God is eternal and hence a brute fact. But, what leads one to conclude that the personal order that accounts for natural order is eternal? We have replaced the brute fact of natural order with the brute fact that there just *happens to be* some personal entity who had the desire to create a world with natural order.

And if we stipulate libertarian free will, the problem grows worse for the agent in question simply *happened* to have the intention to create a world with natural order, as free acts qua LFW are brute facts. So, why should we prefer this brute fact over the bruteness of natural order? So, theism is a worthless explanatory hypothesis, since it simply moves the explanation back a step by positing that there just happened to be an entity who had such an such desire i.e. theism "explains" things *tautologously* and is purely ad hoc. So, it seems that the cognizance that PSR is necessarily false. When it comes down to it, that's really how theism "explains" anything at all. We have a being who is omnipotent and hence can do anything at all. Moreover, it seems that ultimately, any decision by this entity will be arbitrary. Why, for instance, would such an entity create a world at all? We humans are motivated by needs and desires, but such an impressive entity would have no such thing. Nothing *specific* follows from the existence of such an entity. And so, we stipulate as a matter of brute fact, that there just happens to be such an entity who just happened to have the desire to create the item in question. This is not an explanation at all. This problem grows worse on the presumption of libertarian free will as mentioned, and on the notion of skeptical theism, as we have no clue as to the desires such an entity would have. So, I think a strong case against theism can be made from the failure of PSR.

What do you think about that?

On a completely unrelated note, how precisely does one gain access to your blog? I am not able to access it.



exapologist said...

Hi Raydeon,

Once again, very nice comments! I could (and can) only comment on one of your points -- the one about the unwelcome implications of PSR -- as I'm pressed for time at the moment, and I'd like to take a few days to think about your other points. However, I plan to discuss them with you as soon as I get a chance.

You can get onto my blog by just emailing me at Once I get your email address, I can register you to the site.

All the best!