This post is out of date. The latest reply to arguments from contingency is here.
Leibnizian cosmological arguments provide no support for theism
1) By a "Leibnizian cosmological argument" (LCA), I mean any argument that attempts to use some variant of the Principle of Sufficient Reason (PSR), or a causal principle (CP), in order to derive the existence of a necessary being as a cause or explanation of contingent facts, truths, or beings, etc., and then go further and conclude that said necessary being is God, or at least a rational agent with some of the properties usually ascribed to God. 
However, several of the arguments I will make apply to other versions as well.
My goal is to cover all LCA made so far if possible – if not, at least nearly all of them -, as well as a good number of potential alternatives.
3) I will grant for the sake of the argument that the kind of modality used in these arguments (i.e., metaphysical necessity, metaphysical possibility) is a coherent concept.
In addition, unless otherwise specified, I will also grant that there is no modal collapse – i.e., that there is at least one contingent truth; I will further grant that there is at least one contingent being, and even that humans, planets, etc, are contingent.
Generally speaking, I might sometimes grant points for the sake of the argument (e.g., the coherence of libertarian free will (LFW)); that does not mean I actually believe them.
Essentially, the point of this article is to show that LCA provide no support for theism, not to challenge every unwarranted assumption made by those defending such arguments.
4) On a terminological note, I'm using the word “argument” loosely, to refer to both formal arguments, and the informal arguments (in the sense of "arguing a case") used to support the premises of formal arguments. I think this is a common way of speaking, and context should prevent any ambiguity despite some notational abuse.
5) Also, I only refer to different parts of this article as "sections" or "subsections" - i.e., no sub-subsections, etc., but I think links between the relevant parts of the document will prevent any ambiguity.
6) Finally, I don't claim that there is any novelty in the ideas behind my arguments.
LCA have been around for a long time, and so have several of the objections I will raise; I don't know whether all of those objections have been raised before, but I have no sufficient reason to believe otherwise.
1) Pruss' Leibnizian cosmological arguments
In this section, I will address the LCA defended by Pruss , showing that they provide no support for theism.
I will consider some variants theists defenders of a LCA might
attempt, showing that those alternatives fail as well.
Moreover, I'll make general points about the Principle of Sufficient Reason (PSR) and causal principles (CP), which apply not only to Pruss' LCA, but to any argument based on similar principles – which covers most LCA, if not all of them -, and about some other issues relevant in the context of some LCA, like infinite regresses of explanations.
According to Pruss, the basic structure of a LCA is:
(1) Every contingent fact has an explanation.
(2) There is a contingent fact that includes all other contingent facts.
(3) Therefore, there is an explanation of this fact.
(4) This explanation must involve a necessary being.
(5) This necessary being is God.
Premise (1) states the Principle of Sufficient Reason (PSR), in Pruss' formulation.
However, he also defends alternative principles – causal principles instead of the PSR -, so I will consider those principles as well.
In his argument, Pruss uses "fact" to mean "a true proposition".
Other versions of the argument use "facts" differently.
Some of the points I make in section 1 apply to Pruss' usage of fact only – e.g., the points about the Big Contingent Conjunctive Fact (BCCF) -, but others, such as those about the lack of a need to assume such a general principle, about conceivability and the PSR, or about Quantum Mechanics (QM), etc., are more general and apply to other versions of the principle as well.
In this subsection, I will analyze Pruss' version of the PSR, as well as alternative principles, and the arguments in support of them.
One point on which defenders of LCA – including Pruss – seem to agree upon is that the PSR does not entail determinism.
In fact, they claim it's compatible with statistical and/or probabilistic explanations – in particular, non-deterministic interpretations of Quantum Mechanics (QM) -, libertarian free will (LFW), and so on.
Some of the consequences seem rather odd, and also indicate that the name "Principle of Sufficient Reason" is a misnomer (to be fair, Pruss addresses the issue of the name, suggesting an alternative name "Principle of Good-Enough Explanation" ).
Terminology aside, it seems what matters is whether there is an explanation that is good enough.
So, let's take a look at some of the examples of explanations.
For instance, Pruss presents some examples when he challenges Peter van Inwagen's arguments against the PSR:
It seems a perfectly good explanation of why the dog did not bark that neither a stranger came by the dog nor did any other potential cause of the dog’s barking occur.
Pruss maintains that the explanation here does not entail that the dog would bark.
However, if, given the same state of the world, it's possible that the dog would have barked, there is a possible world W at which the dog did bark.
What would explain the dog's barking at W?
It seems that, in absence of any stranger or any potential cause of the dog's barking, then that the dog barked would be a contingent fact without a cause or an explanation.
Granted, that's another possible world; the dog didn't bark in the actual world.
However, if such events – like the dog's barking without any stranger coming by or any other potential cause of the dog's barking – are possible, that entails that the PSR is not necessary – and theists usually claim necessity.
Still, perhaps that particular example is a wrong example, so let's consider another case:
Pruss claims that the fact that the cream in a coffee spreads in some way is explained by some statistical facts about the motion of molecules, which makes the observed phenomenon "very likely". 
It's not clear
whether Pruss is distinguishing between likelihood and probability,
but leaving that aside, Pruss' point is that the explanation does not
entail the explanandum, yet it's still good enough.
Let's grant that it is: what would happen, then, if the cream did not spread?
If there is a possible world W at which the cream did not disperse at all, but remained on a side of the coffee, what would an explanation for that contingent fact be?
If the fact that it's very likely that the cream would spread explains the cream's spreading, would the fact that it's very unlikely that the cream would remain on a side explain the cream's remaining on a side?
It seems not.
Someone might say that there is no such possible world. However, in that case, even if we're accepting the explanation that only results in a "very likely" conclusion, we're still assuming that there is a better one, which entails the explanandum – we just don't need it.
Let's consider cases involving Quantum Mechanics (QM).
Now, there are deterministic and non-deterministic interpretations of QM, but defenders of LCA – including Pruss – generally claim that even non-deterministic ones are consistent with the PSR.
Later, I will argue that that is not true, but for now, let's take a look at the kind of explanation we're talking about.
According to Pruss, even when the probability of an event is low, QM still explains it , so those indeterministic interpretations would be no threat to the PSR.
So, let's suppose a man runs towards a wall, hits the wall and falls to the ground. That's only to be expected.
However, a non-deterministic QM explanation does not entail that he would hit the wall. In fact, it allows that the opposite would happen:.
Let's say that at a possible world W the man actually passes through the wall, without getting a scratch or damaging the wall in any way.
Surely, that's really odd.
But it seems that quantum tunneling would still explain the event, in the sense of "explanation" used here...
Of course, the question is: what's the explanation for the fact that quantum tunneling happened, despite its staggeringly low chance?
It seems that, according to Pruss' position, QM would still counts as good enough an explanation in the context of the PSR.
Alternatively, a theist could claim that the PSR is true, though perhaps not necessary, but even then, there are improbable events that do happen in the actual world, if a non-deterministic interpretation of QM is true.
So, as we can see from this examples, it seems the kind of accounts Pruss regards as good enough explanations do not have to entail the explanandum, or make it likely, or apparently not even not extremely unlikely – like the quantum tunneling example.
I maintain that this very broad understanding of "explanation" is erroneous, but I'll leave that for later.
For the sake of the argument, let's accept such conception for now – i.e., let's accept for now that such explanations would be good enough. We still have to assess whether belief in the PSR is warranted.
The choice of the category of facts that, according to this principle, would have explanations, is "contingent facts" - in this context, contingently true propositions.
Many arguments in support of the PSR present allegedly absurd scenarios that would allegedly result from denying it.
However, there are alternative principles that could deal with those scenarios if they're problematic at all, so the question arises: why choose contingency as the relevant category for a general principle? Moreover, why make a commitment to a general principle at all?
It's not as though necessary truths never have explanations. Often, if not always, they do.
On the other hand, it's not clear – or intuitive, at least as far as I can tell – that contingency is somehow a relevant category regarding whether a fact has an explanation.
I will propose an alternative principle – also, not intuitive -, and compare their advantages and disadvantages.
For that, I'll introduce some terminology:
By "event" I mean "change", following Craig .
By "newcomer" or "newcomer fact" I mean any fact that obtains as a result of an event.
In other words, P is a newcomer if there is a state of the world S at which P is not true, temporally or causally followed by a state of the world S' at which it is.
Let's consider the following principle, which I will call "Principle of Explicable Newcomers" (PEN):
This principle seems to be in line with our intuitions that – for instance – for everything that happens, there is a reason as to why it happens.
Under the very broad conception of explanation accepted by defenders of LCA as good enough, also, there appears to be no obvious exceptions.
So, the PEN is intuitively plausible as true. It's not clear to me that it is plausible as necessary.
In any case, it seems we don't need to take a stance on whether the PEN is necessary, but it's not problematic to grant that, either.
Now, accepting the PEN blocks a number of arguments based on allegedly absurd scenarios, and it seems not to cause any problems – as always, as long as we accept the broad understanding of "explanation".
Someone might object that our basic intuitions about facts calling for an explanation are not about events, but about a broader category, and/or claim that the choice of events in the PEN is ad-hoc.
Furthermore, they might claim that we would still have to accept that some facts have an explanation, even if they're not newcomers.
the same can be said about the "contingent" category:
there are facts that have an explanation even if they are not
Pruss himself mentions some of those cases.
Moreover, if the claim that a proposition P is contingently true but the fact that it's true has no explanation seems intuitively odd (not to me, but let's say that), then it seems to me that the claim that a proposition P in necessarily true but the fact that it's true has no explanation even though P is not logically necessary would be even more counterintuitive; for instance, using possible worlds, instead of saying that P is true at the actual world without an explanation, we would be saying that P is true at all possible worlds without an explanation.
That aside, of course, accepting the PSR does not commit one to a claim that non-contingent facts do not have explanations. However, accepting the PEN does not commit one to a claim that facts that are not newcomers do not have explanations, either.
So, why pick the "contingent" category, rather than the "newcomer" category, or some other category?
Both categories are too narrow in some cases – which would not be a problem -, but perhaps the "contingent" category is too broad in others – i.e., perhaps the PSR turns out to be false.
A I will argue in the next subsection, the PSR is at least suspect.
On the other hand, the PEN is less vulnerable, at least as long as we stick to the broad interpretation of "explanation" used by theist defenders of the PSR, even if it has a narrower scope.
That aside, there is no need to have a general theory about categories of facts that have explanations; in particular, there is no need to hold any particular belief on whether the PSR (or the PEN, for that matter) is true.
On that note, it's interesting to take a look at many of the arguments given in support of the PSR: attempts to show that falseness of the PSR would lead to absurdities try to appeal to our intuitions about certain facts' having explanations.
But then, we can simply use our intuitions in particular cases, without holding any general theory. A person may well remain undecided on that.
That is a more cautious approach – to wait until there are good reasons to accept any such principles.
Moreover, that is a perfectly reasonable approach. We do not need to be committed to any hypothesis about, say, which phenomena are such that human pretheoretical intuitions about time and/or space will work in order to use those intuitions in most cases in daily life, but refrain from trying to apply them to, say, the universe as a whole.
Why should we be committed to any beliefs with regard to the PSR?
Someone might still object: but if the PSR is not true, why are there not violations of it all around, with things just popping into existence inexplicably?
For that matter, someone could define (for instance):
NPSR: For every necessary fact, there is an explanation.
NPSR2: For every necessary concrete object, there is an explanation.
Then, they could ask similar questions: If the NPSR – or the NPSR 2 – is not true, why are there not violations of those principles all around us?
Why is it not the case that we run into indestructible objects that exist in every possible world all around us, inexplicably? Why is it the case that there is no inexplicable necessary brick-generator necessarily making bricks pop into existence all around us? Or why not an inexplicable spaghetti-loving necessary being who just sends anyone who doesn't eat spaghetti to hell?
But then again, why should we have a theory about that?
For instance, one does not need to take a stance on whether all the predictions of General Relativity (GR) will always be correct, to any degree of accuracy, in order to apply GR in many cases, and one needn't have a theory as to why GR usually works, just because one does not take a stance on whether or not it applies perfectly to all cases.
Why should someone who takes no stance on the PSR need to explain why it seems to work in daily life?
At any rate, one can point out that our intuitions about how the world is tend to work pretty well in daily life, but tend not to work so well when it comes to things like the universe as a whole, or the subatomic realm, and that may well justify the use of caution before applying pretheoretical intuitions to the entire universe, or the entire actual world.
Still, leaving that aside, to play along, a potential reply as to why there are no violations of the PSR all around us would be that, maybe, the PEN is true.
Of course, the PEN appears just as arbitrary as the PSR, but if we ought to pick a principle for some unknown reason, why not that one?
Granted, replying that the reason bricks, etc., don't pop into existence all around us is that the PEN is true, amounts to replying that there are no events of the form "X pops into existence" without explanations around us because there are no newcomers without explanations, and those events would entail newcomers without explanations.
But similarly, replying that things don't just pop into existence without explanation around us because the PSR is true [or necessary], amounts to saying that things don't pop into existence without explanation around us because contingent truths have [or necessarily have] explanations, and those events would entail contingent truths without explanations.
There does not appear to be any particular advantage in claiming that the PSR is true or necessary, other than, perhaps, the general advantage of having a theory with greater predictive power – assuming no necessary events -, if the theory is true and the believer is justified in believing so. The other side of the coin is the disadvantage of the greater risk of holding a false principle.
Of course, as a mentioned, a more cautious approach would be to neither accept nor deny either principle.
Still, someone might claim that the PSR is solid enough for some reason, and so it's better to just the PEN, or no general principle at all.
Given that I reject the broad account of explanation, I think neither the PSR nor the PEN is safe enough to warrant belief, but assuming the broad conception for the sake of the argument, it seems to me that the PEN is a better choice, since it doesn't have the problems I'll address in the next subsection:
One way of assessing metaphysical possibility seems to be to use conceivability as a (defeasible) guide.
A problem is that conceivability is also rather fuzzy. But at least we can tell it's not the same as imaginability, in the narrow sense of being able to have a mental picture of the conceived scenario.
For instance, that more than 170 billion galaxies exist is conceivable, but we can't really imagine so many, even if we don't require any greater degree of detail than in, say, imagining common objects like a car or a tree: at most, we could imagine some picture and conceive that those are over 170 billion galaxies, but the same image might as well represent, say, 124.9 billions (for instance).
More subtly, it seems that, say, an eleven dimensional universe is also conceivable, even though not imaginable.
Whether God is conceivable is beyond the scope of this article, but he's surely not imaginable – how could one get a mental image of a bodiless omnipotent, omniscient being?
With that in mind, it appears that if it's true that the PSR entails that there is a necessary being, then that gives us at least a prima facie reason to suspect it's not true.
For instance, if God appears at least prima facie conceivable, then so does an omnipotent being.
But it seems morality has nothing to do with the conceivability of power.
So, it seems that an omnipotent being who isn't morally perfect, and actually could not care less about moral good or evil, appears conceivable as well. Let's call such a being "Gok"
Gok could have different motivations, but morality just doesn't enter the picture.
Now, if Gok is possible, then God is not necessary – since two omnipotent beings can't coexist.
And if an omnipotent, morally perfect being is possible, then Gok is not necessary, either.
But what other being could be necessary?
If it's possible that God – or Gok – exists and there are no other beings – which seems conceivable too -, then it seems no being is necessary.
God and Gok aside, let's consider the following scenario S1:
There is a three-dimensional space, and some indivisible particles that follow certain simple laws. The number of particles and the laws can be described mathematically, so such scenario appears conceivable.
Moreover, one can stipulate that there are no more beings than that. 
Given that, even after that stipulation, there appears to be no contradiction – not in the sense of strict logical possibility, and not after we consider facts such as "Water is H2O", and other such cases -, that too gives prima facie support for the claim that no necessary being exists, since one can just change the scenario to some extent and make one with, say, four dimensions, or two dimensions, etc. - those would be scenarios S2 and S3 respectively -, and conceivability gives a prima facie reason to think that those are possible scenarios that do not contain any of the beings in S1, which does not contain any of the beings in S2 or S3.
Also, the fact that one can't actually imagine – in a narrow sense of "imagine" - such scenarios is no good objection, as explained above, as it's not a good objection to theism the fact that one cannot imagine God. 
Someone might still claim that there may be some hidden contradiction in the proposed scenarios, perhaps after taking into account some unknown facts in the actual world that fix the referent of some words.
It seems, however, that something like "Water is H2O", or any properties of existing persons, beings, etc., are not going to present a problem to S1, S2, or S3, since "Water is H2O", etc., are not existential claims.
Granted, someone could claim that there might be other hidden problems that might be revealed after we learn more about the actual world, or something else that makes S1, S2, S3 or Gok impossible in the sense of metaphysical possibility.
However, my point here is only that we have prima facie reasons to think that S1, S2 and S3 are possible, and that so is Gok if God is.
Thus, we have prima facie reasons to believe that if it is true that the PSR entails a necessary being[12 ], then the PSR is false, and more generally, we have prima facie reasons to think that there is no necessary being.
Another objection that could be raised is the use of negative stipulations, like the stipulation that there are no other beings, as part of the conceivability criterion.
I don't see the problem with that, though: even if somehow positive conceivability or apparent conceivability may give us a stronger guide to possibility than their negative counterparts, negative conceivability seems to suffice at least for having prima facie grounds for belief.
Moreover, in the case of Gok, it seems that his conceivability or apparent conceivability is positive if God's is, so either there is at best negative conceivability in the case of God, or positive conceivability of a being that would rule out God's necessity.
Someone could argue that the conceivability of Gok is only apparent; that would have to be argued for, though; I'm just pointing out some things we have prima facie reasons for believing, on conceivability grounds.
That said, while the above scenarios give us prima facie reasons for believing that there is no necessary being, they only give us prima facie reasons for rejecting the PSR if the latter entails a necessary being. 
As it turns out, that is not the case, since infinite regresses would satisfy it, but that's of no help for LCA.
Later, though, when I consider the threat of indeterministic Quantum Mechanics, I will give independent reasons to conclude that the PSR is – at least – not necessary, and in any case it appears to be unwarranted.
In different versions of the LCA, theists give a number of different arguments in support of the PSR.
Some of those arguments are based on the alleged absurdities of things popping into existence without an explanation.
However, those are precisely scenarios in which the counterintuitiveness comes from some uncaused event, or inexplicable event, and are thus covered by the PEN.
So, someone could accept the PEN only, and that blocks the arguments for the PSR, since they don't distinguish between the PEN and the PSR (both principles cover such cases), and they don't resolve any of the problems that make the PSR suspect.
Alternatively, they may just go with their intuitions and say that things like bricks, houses, etc., don't pop into existence uncaused – though there is no need to take a stance on whether that's metaphysically impossible.
Still, Pruss gives some arguments in support of the PSR that are not based on scenarios involving newcomers, so let's consider them.
One argument in support of the PSR is based on a causal account of modality. 
a) A state of affairs S is possible iff it's actual or merely possible.
b) S is merely possible iff S is not actual and there is something – an event, being, substance, etc. - with the causal power of bringing about S, either directly or by means of a causal chain leading to S.
c) S is necessary if ¬S is not possible – in other words, if ¬S is neither actual nor merely possible.
Now, let's consider the state of affairs S: = "George W. Bush was elected POTUS in the twenty-first century".
Since that already happened, there is nothing that can bring about ¬S, and that would seem to render S necessary.
Perhaps, then, someone could try to correct this account of metaphysical possibility including actual states of affairs and states that could have been caused by an actually existent being.
However, that "could have been caused" appears to be a modal claim, so that that would appear to render the proposed account of modality viciously circular.
Maybe someone could come up with a way of fixing the problem, or maybe someone could propose a), b) and c) as true, even if not as an account of modality.
Yet, that would have to be argued for, and the burden is on the claimant. 
Still, let's say there is a way around that problem and the account is true; moreover, let's grant the PSR, under this account. Would that provide any support for theism?
Pruss provides an example of how to gain knowledge about causal (and thus, on this hypothesis, metaphysical) possibility on this account. He explains that unicorns are possible because "it would be within the powers of natural selection and variation processes to have produced unicorns"[i.e., to have produced a horse-like mammals with a horn"
Leaving aside circularity issues, it seems to me that we only know that on a compatibilist conception of causal power: natural selection and "variation processes" could have produced unicorns if the conditions under which they happened had been different.
On the other hand, it's not clear that, under the same conditions as there were in the past on Earth, unicorns could have evolved.
Regardless, let's leave that aside and assume that they could have evolved – as before, these seem to be modal claims, but let's put that aside as well.
What we do not know – for instance – is that there is anything with the causal power to have made spacetime not to exist. And if there is, say, an eleven-dimensional universe, the same applies: we don't know that there is anything that could have caused that eleven-dimensional universe not to exist.
In other words, the fact is that under this account, we have no good reason to think that the universe is contingent – of course, in the context of an argument for theism, the theist can't just assume that there is something with that kind of power.
Arguments from conceivability won't help LCA even without this causal account of modality, either, but in the particular case of the causal account, it seems they fail even without taking other factors into consideration, simply because the fact that we can conceive of a certain scenario does not appear provide any good reason to believe that there is a being, event, etc., with the causal power to bring it about.
If a theist claims otherwise, he would have to give some argument for it.
Another argument Pruss makes is based on morality.
As the argument goes, if the PSR is not true, then there might be no explanation  as to why it's not immoral to divert a trolley from a track where there are five people to one where there is only one person, but it is immoral to shoot an innocent person to save five.
But once again, even if these were examples of contingent facts, if one does not take a stance on whether all contingent facts have explanations, it does not follow that one is committed to rejecting one's intuitions that some specific facts do have explanations.
Even ignoring that, and further granting those moral facts for the sake of the argument, they can provide no support for the PSR because they're not contingent – assuming that they're true, of course.
Perhaps, someone could say that they're contingent, since we can conceive of cases in which, say, diverting the trolley would also remotely activate a nuclear bomb that would kill a million people elsewhere – or something like that -, and then it would not be acceptable to divert it.
However, that would be an instance of changing the scenario.
The point is that the scenarios in question have implicit conditions – or else, those aren't moral truths.
In other words, if it's true that it's morally acceptable to divert a trolley from a track where there are five people to one where there is only one person, then what's true is not a general claim "for all x, if x is an instance of diverting a trolley from a track where there are five people to one where there is only one person, then x is morally acceptable", but rather, it's a claim that contains other, even if implicit, conditions.
So, the true claim is something like "For all x, if x is an instance of diverting a trolley under such-and-such conditions, then x is morally acceptable"; if the claim is true – i.e., if it's for all x, under those specific conditions -. then it's (trivially) necessary, precisely because – by assumption – it's true for all actions in the class or category described by the given conditions, whether those actions are actual or not.
A curious claim Pruss makes  is that a "sense of deity" provides justification for the PSR, even in the context of a LCA, and in a non-viciously circular manner.
In the context of his argument, he also makes a moral accusation suggesting that non-theists may be morally guilty just because of their lack of belief that God exists, since they would be immorally ignoring their sense of deity.
While Pruss is not as assertive in his accusation as the theists he cites (namely, Plantinga and Calvin ), the suggestion is still quite offensive, and damaging because it reinforces a common belief against theists.
So, as a reply, a non-theist can reject it as a groundless charge, and further reply that some theists are immorally contributing to a moral condemnation against non-theists for something for which non-theists do not deserve to be morally condemned, by spreading the false belief that non-theists are being immoral just on account of their being non-theists and/or due to some alleged "sense of deity".
But leaving the moral charge aside, obviously, this "argument" assumes that there is such thing as a "sense of deity", which induces in people the knowledge that God exists.
However, there appears to be no good reason whatsoever to believe in a "sense of deity".
In fact, there have been entire civilizations in which there was neither belief nor even the concept of God.
Granted, those people had beliefs in different entities that are nowadays translated into English as "gods" sometimes, though not always – sometimes they're called "spirits", "monsters", etc.
However, and regardless of what we call those entities, they were very different from God.
In fact, in some religions, such entities were very much like humans with superpowers, like comic characters, or ordinary fictional monsters, without omniscience, moral perfection, lack of a body or shape, omnipotence, etc.
Those "gods" would fight each other for pretty much any reason humans fight each other, and sometimes would even kill each other, etc.
A theist might claim that the "sense of God" is only a guide, but needs other factors to actually give the person the concept of God – let alone belief.
However, one can often make ad-hoc hypotheses based on a foregone conclusion and which trivially match the evidence, and adjust them as needed if unwanted evidence is found; for that matter, someone could claim that it's an evil contingent demon who gave humans an oversensitive sense of agency.
The point is that there appears to be no good reason to think that there is a "sense of deity" and, given the available evidence, there appear to be very good reasons to conclude that there isn't one.
That aside, what about Christian philosophers who find LCA unpersuasive?
Are they, too, ignoring their "sense of deity"?
Another line of argument – in this case, to defend the PSR against an objection – holds that objectors to the PSR who claim they can imagine worlds at which the PSR does not hold – which would provide defeasible support for the claim that the PSR is not necessary at least – have failed to actually imagine scenarios in which there are inexplicable contingent truths, or causeless contingent states of affairs, and so on.
On that note, Pruss' presents some arguments against objections to the PSR based on imagination as well. 
Now, even if it's true that the objector fails to properly imagine (in a narrow sense of "imagine") certain worlds, that does not affect scenarios in which one takes into consideration not imaginability, but conceivability, as a – defeasible – prima facie guidance to metaphysical possibility, and the conceivability criterion supports the contingency of all existent beings.
Maybe Pruss is talking about conceivability, and maybe he or other theists would claim that the scenarios and/or beings I presented are also inconceivable, but that would have to be argued for.
not one of Pruss' arguments, but perhaps, someone could insist that
maybe we need the PSR after all: without it, there might
contingent brute fact – more precisely, a state of affairs S
that exists contingently, and inexplicably.
But wouldn't any such state still call for an explanation, even if S is not a newcomer?
Someone could still ask "Why does S obtain at the actual world, rather than ¬S?"
Wouldn't a necessary state of affairs N, without an explanation, resolve the problem, as an explanation for all contingent states of affairs?
I doubt that such an S would call for an explanation – at least, conceivable possible brute facts seem not to call for one, e.g., S1, S2, S3 or Gok.
Still, regardless of whether it's true that S calls for an explanation, the answer appears to be negative, since N would seem to call for an explanation.
Just as someone could ask "Why does S obtain at the actual world, rather than ¬S?", someone could just as well ask "Why does N obtain at every world, rather than ¬N at every world, or N at some worlds and ¬N at others?"
Saying "Because N is necessary" would not give a proper explanation, it seems to me, since the question is, essentially, "Why is N necessary?"
The question seems to make perfect sense.
Someone could say that there are intuitively obvious necessary truths that don't call for an explanation; perhaps, some obvious logical or moral truths. I don't know about that, but in any case, N would not be at all like that.
N would be some kind of concrete state of affairs that obtains necessarily – or a necessary truth with a corresponding necessary concrete state of affairs; the point is that there would be a concrete state of affairs that exists at every possible world.
So, N is not at all intuitively obvious.
In fact, it's very counterintuitive: we can easily conceive of scenarios at which N does not exist – e.g., S1, S2 or S3 -, so if there is such necessary N, then our intuitions would be very misleading.
That calls for an explanation: Why is it that S1, S2, S3,are all impossible?
If Gok does not exist, why is he impossible?
Also, the case of N is not relevantly similar to a case like, say, the conceivability of the scenario in which water is not H2O, but XYZ =/= H2O, and scientists turned out to be mistaken.
That's because what's inconceivable in that case is that, given that water is H2O at the actual world, it's still XYZ at some other world.
In other words, our intuitions are correct in that whatever water turns out to be at the actual world, water is at every possible world.
However, with N, things would be very different: it seems intuitively clear – at least to me – that however things turn out to be at the actual world, scenarios like S1, S2 and S3 are all possible – and Gok is possible if an omnipotent being is.
A theist might – perhaps – suggest that this confuses epistemology with ontology, and/or that in any case, if one accepts that N exists necessarily, the question of a lack of an explanation is irrelevant: we may find the fact that N inexplicably exists at every possible world puzzling, but we've already accepted it, regardless of any puzzlement.
However, in that case, someone could posit that a contingent brute fact S obtains, and if one accepts that S is a contingent brute fact – i.e., a fact without an explanation -, then that's it too: It follows from what we've accepted that S exists inexplicably at the actual world, regardless of any puzzlement.
At least, the contingent brute fact S exists inexplicably at the actual world, whereas the necessary brute fact N exists inexplicably at every word.
Perhaps, a theist could claim that N would not exist inexplicably, but it would be explained by its necessary nature, or something like that.
But what does that mean, other than saying that, by the way N is, it necessarily exists?
That would not provide any explanation to the puzzling matters at hand:
If it's because of its nature, what is it about its nature that makes scenarios like S1, S2 and S3, or Gok impossible?
How is it that the nature of N makes S1, S2 and S3, or Gok impossible?
It all remains deeply puzzling, and it makes the arbitrariness the PSR more apparent.
On the first issue, the answer is negative. For instance, that there are no unicorns is a contingent fact that is not a newcomer. There were never any unicorns.
If unicorns are impossible, we can pick any example of possible beings that have never existed, and the result is the same.
With regard to the second question, perhaps someone could suggest that a LCA can be grounded on the PEN.
Perhaps, they could try to argue that all positive contingent states – not all contingent truths – correspond to a newcomer, or that all contingent beings are like that.
In any case, all of that would have to be argued for, and even then, leaving QM aside, they would still have to face the problem of infinite regress – which would affect a PEN-based argument too, essentially for the same reasons it would affect a PSR-based one.
Even if they managed to derive that there is a necessary being from the PEN and some true propositions, that would only run into the same problems of counterintuitiveness that the PSR runs into, thus actually making the PEN suspect as well, since the PEN, like the PSR, is less intuitive than the intuitions about the possibility of worlds with none of the beings that exist in the actual world.
A defender of a LCA might posit an allegedly weaker and – allegedly – more intuitively clear principle, like:
However, it's easy to see that the PSR and the PSR(b) are actually equivalent.
That the PSR entails the PSR(b) is obvious.
To see the other implication, let's assume that the PSR(b) is true at W, but the PSR is not.
So, at W, there is a proposition P that is contingently true, but there is no explanation of why it's true.
So, let's consider the proposition Q: = That P is true and there is no explanation of why P is true.
Since, at W, P is true and there is no explanation of why it's true, then Q is true as well.
Also, there is a possible world W' at which P is not true, and so Q is not true at W'.
Hence, Q is contingently true at W.
Hence, by PSR(b), there is a possible world W'' at which there is an explanation for Q. But that would be an explanation of why P holds and there is no explanation, which appears to be impossible.
Still, someone might suggest that, perhaps, there is a way around that, and there can be an explanation as to why P holds without an explanation.
I don't see how that would be possible, but even if that were so, then there would be no way or using the PSR(b) in a LCA, since there could still be unexplained contingent truths, even if they possibly have an explanation.
Perhaps, someone might object that the PSR(b) is a more intuitively clear formulation, and that actually gives support for the PSR. A reply would be that that does not appear to be the case, and even if it were, since they're equivalent, our reasons not to accept the PSR are also reasons not to accept the PSR(b).
So far, I have granted, for the sake of the argument, that non-deterministic interpretations of Quantum Mechanics do not pose a threat to the PSR – and, for that matter, to the PEN.
In later subsections, and unless otherwise specified, I will once again assume just for the sake of the argument that there is no such threat, and that the broad interpretation of "explanation" commonly used by defenders of LCA is correct.
However, in this subsection I will argue that a non-deterministic interpretation of QM, if true, would entail that PSR is not necessary, or even true, and then assess some of the consequences for defenders of a PSR-based LCA, and even for theism.
I'll focus on the PSR since that's the principle used by defenders of LCA, but the same holds for the PEN: a non-deterministic interpretation of QM would be a defeater.
According to Pruss, QM explanations are still good enough for the purposes of the PSR, even if the probabilities are low.
In order to show that low probabilities in QM would not be a problem, he brings up an example of a syphilis/paresis case: latent untreated syphilis only leads to paresis in a minority of cases, but even then, that a patient has syphilis allegedly explain why he got paresis. 
However, in the case of the syphilis/paresis, for all we know, there may be a much more accurate explanation Moreover, it's usually assumed that there is one, as I'll show in a moment.
On the other hand, in the indeterministic QM case, there is no further explanation.
That difference turns out to be crucial. When we accept statistical explanations, those explanations are good enough for the purposes for which we need them. We're accepting the limitations to our knowledge. But that's not always the case.
For instance, let's suppose that someone is asking why her 25-years old daughter died, and a police officer replied: "She was human, and x percent of humans die at 25; we just live in a world in which that kind of event occurs; that statistically explains your daughter's death".
Surely, that would be a woefully inadequate attempt at an explanation.
In fact, we can say not just that it was a bad explanation, but that it was no explanation at all, since that such thing happen – i.e., some humans die at 25 – was already discounted; what it was asked was why – given all that -, a particular human being died, even given all that.
So, let's now consider the syphilis/paresis case once again, and let's consider the following dialogue:
Alice: Why does my husband Bob has paresis?
Doctor: Because he had syphilis, and he developed paresis.
Alice: But most people with syphilis do not develop paresis. My question is why did Bob? There has to be an explanation.
Doctor: There has to be one, but I don't know it.
That would be a coherent dialogue, which illustrates the fact that the statistical account fails when we need to explain the particular case, and we're not willing to accept a more limited amount of information.
Perhaps, someone could say those aren't good explanations, but still not completely wrong.
So, let's consider the following case:
A research team is trying to figure out why some of the patients with syphilis develop paresis, and some of them do not.
After years of research, they come up with the following statistical "explanation": "Some of the people with syphilis actually develop paresis, and so that explains why those in the concrete group of people we're studying did develop paresis. We just live in a world in which that kind of event happens".
Once again, the conclusion would be that the research team failed to explain why some people with syphilis developed paresis.
That would be like saying, if bricks and horses popped into existence around us, that we live in a world in which that kind of thing sometimes happens.
So, there was a preexisting condition – namely, a world in which sometimes horses and bricks pop into existence, and that that explains the events.
But surely, that would be no
explanation – and if it were, LCA already lost, since there is
no point in trying to argue that the explanation is God; it might be
just the fact that some things happen!
Now, let's consider the non-deterministic QM case in particular.
Suppose that someone asks: why did particle p – one specific such particle – decay before t?
The statistical answer – which essentially amounts to saying that we just live in a world in which they do – would not seem to provide an explanation any more than the team's answer in the syphilis/paresis case would.
However, in the case of the team who failed to explain why some patients why syphilis develop paresis, other teams could keep looking for an explanation. There may well be one.
In the particle case, though – as always, assuming an indeterministic interpretation of QM -, there is no explanation: it's just a brute fact that the particle p decayed before t, showing that neither the PEN nor the PSR is true.
Maybe this would become even clearer if we take a look at the syphilis/paresis case again: let's suppose that the team of researches came to the conclusion that there is no explanation – known or otherwise – for the fact that some patients with syphilis develop paresis, other than the statistical fact that that sometimes happens – or, if they prefer to put it that way, that we just live in a world in which that sometimes happens.
Would that count as an explanation as to why some people with syphilis develop paresis?
Clearly, the answer is no.
Someone might not be persuaded and object that, at least, there is some predictability in the case of QM, with some high degree of accuracy in the cases that matter to most to us.
However, that objection would miss the previous points about the lack of an explanation in cases involving individual subatomic particles, which may not matter so much to most people, but still happen all around us.
Still, in case the previous argumentation isn't persuasive for some reason – but why not? -, let's take a look at the matter from another angle, which at least gives us the conclusion that the PSR is not necessary under such non-deterministic interpretation of QM.
Then, even if bricks, etc., don't pop up into existence in the actual world, it would be possible for that to happen. So, let's consider the following world W:
At W, bricks, horses, planes, etc., sometimes just pop into existence, regardless of any predictions based on modern science.
Moreover, the people at that world still do experiments with particles and the like, and they get the same results as we get here.
However, on their planet, when people are not doing any experiments – i.e., never under controlled conditions – sometimes bricks, horses, planes, etc., just pop into existence, against all the predictions that people over there can make – other than the prediction that, sometimes, somewhere on their planet, things like that will just pop into existence.
Now, W is possible under the given assumptions. And it should be clear that at W, there is no explanation whatsoever of those events – just as there is no explanation in ours of the decay of p.
If that does not appear clear, let's look at the actual world – i.e., let's put ourselves in the situation of the people at W: if those events begin to happen tomorrow, and some scientists come up with the "explanation" that we just happen to live in a world in which all of that can happen even if it's extremely unlikely based on our experiments, it's pretty clear that those scientists would have failed to explain those events, and not only the public but other scientists should reject the so-called explanation.
So, saying that it happens sometimes is no explanation, but then, at W, that's all there is.
Someone might object that bricks, horses, and planes are not popping into existence, since they are made out of preexisting energy or other particles. Moreover, they might say that those preexisting conditions are a cause, and that explains them.
But that would miss the point: Actually, those things are coming into existence even if there are preexisting conditions. And calling preexisting conditions a "cause"does not change the fact that there is no explanation for such events:
For example, if the scientists who are trying to understand why horses, houses and bricks sometimes just come into existence, in an unpredictable way, come up with the answer that there was some preexisting conditions – energy, or other particles -, which constituted a cause, and that explains those events, the conclusion people ought to reach would be that those scientists have failed to explain why horses, houses and bricks sometimes pop into existence, in ways that no one can predict – other than the prediction that sometimes that happens.
Yet, at that world, there would be no explanation at all: those scientists would have failed to explain such events, but no one else would be able to explain them, either, since there would be no explanation to be found.
Back to the real world, as I mentioned earlier, the fact that most people don't care about what individual particles do – they would care about bricks and planes, but not particles – does not change the fact that our world too is filled with inexplicable contingent events – and thus contingent propositions – assuming a non-deterministic version of QM.
Still, if someone finds that "pop into existence" or "comes into existence" is not an adequate description of the previous scenarios, we can present alternative ones, in which there are no objects coming into existence, but the PSR still fails, as the following scenario illustrates:
Starting tomorrow, whenever Alice throws a ball towards a wall saying "go through it" - or a similar utterance, telling the ball to do that -, the ball goes through the wall without touching it. And when Alice says nothing, or tells the ball to bounce off the wall, the ball just bounces off the wall.
The explanation that is offered by scientists is that it just happens to be that each of the times – and only those times – Alice uttered those words, the ball just happened to quantum-tunnel through the wall.
And given that the phenomenon keeps happening, the ball just keeps quantum-tunneling when and only when Alice tells it to go through the wall.
Surely, those scientists would have failed to explain the events.
But let's suppose a non-deterministic interpretation of QM is true.
Then, there is a world W'' at which those events happen, and there is nothing more to it: in other words, the candidate to an explanation offered above actually failed to explain why they happen, and there is no explanation to be found. That just happens.
That would clearly entail that the PSR does not hold at W''.
Perhaps, someone could object to this example because – the maintain – QM does not apply to Alice, and for some reason that's relevant. I can't see why that would be the case, but still, we can always offer alternatives:
a) We can replace Alice by a robot with a complex computer for a brain, which came into existence – programs included – without being designed by anyone – just by extremely unlikely random movements of particles -, and which keeps throwing balls at walls, sometimes uttering the words "go through the wall", sometimes "do not go through the wall", according to its programming – and the balls the robot throws always do what the robot says, inexplicably.
b) Alternatively, let's suppose that there is a specific ball that just keeps going through a specific wall, and there is no explanation to be found: the wall just keeps quantum-tunneling through that wall, inexplicably.
Those examples too would show that the PSR fails. Of course, there are many more scenarios we can come up with, if someone finds all of the previous ones unpersuasive.
For all those reasons, the conclusion is that indeterministic Quantum Mechanics poses a very real threat to the PSR and similar principles.
But there is more: Pruss maintains that if God exists, then the PSR is true.
If he's correct about that, then a non-deterministic interpretation of QM entails atheism – or, at the very least, the non-necessity of God. I'll address this matter in more detail in the next subsection.
Given the results of the previous subsection, it seems any defender of the LCA ought to hold that indeterministic interpretations of QM are not true.
But that's a serious problem, for two reasons:
a) There appears to be no knock-out argument in favor of either deterministic or non-deterministic interpretations.
b) Non-deterministic interpretations entail human determinism, since they don't make exceptions for humans.
Point a) is a problem since it undermines any justification for the PSR – independently of other reasons, such as the ones I provided in other subsections.
Moreover, if it's true that theism entails the PSR, the a) undermines any justification for theism, assuming there were one.
As for point b), it's a problem because defenders of LCA usually believe humans have libertarian free will (LFW); other theists often believe so as well.
Leaving aside the issue of whether libertarian free will (LFW) is coherent, the fact is that determinism alone would be enough to rule it out.
Granted, someone could claim that indeterministic versions of QM are not true, and deterministic versions aren't true when humans – or humans and some other rational beings, etc. - are involved.
However, that would definitely be a serious burden for the claimant – in other words, that would actually...call for an explanation. To be clear, it would not be enough for them to argue that we have insufficient reasons to conclude that QM does apply to humans. They would have to give good reasons to conclude that it does not, since that would be their claim.
A theist might argue that the previous subsection only shows that a non-deterministic version of QM is incompatible with the necessity of the PSR, but not with its truth.
Still, even non-necessity of the PSR would block many of the versions of LCA, and even the possibility of a non-deterministic version of QM would entail that the PSR is not necessary.
Moreover, if theism implies the PSR, then if the PSR is not necessary, neither is God.
However, if a non-deterministic interpretation of QM is possible, then the PSR is not necessary, since there would be a world W at which such non-determinism would hold, and the PSR would not hold there.
Moreover, if there is a world W at which a non-deterministic interpretation of QM is true, the same reasoning used before shows that there is yet another possible world W' at which not only such non-determinism would hold, but at which horses, bricks, planes, etc., would pop into existence without any explanation.
Surely, that too would entail that the PSR is not necessary, and arguably that God isn't. But non-deterministic interpretations of QM appear to be at least conceivable, and conceivability is a guide to possibility.
So, a defender of a necessary PSR – and, perhaps, any theist who maintains that God is necessary – has the burden of showing that non-deterministic interpretations of QM are not only false, but that they're impossible, and that our intuitions about conceivability and/or possibility fail.
While I think that the Problem of Evil and the Problem of Suffering are sufficient to rule out the existence of God even at the actual world, the considerations of this subsection are independent of those arguments, and present a different problem for a good number of theistic positions – probably most of them.
According to Pruss, libertarian free will (LFW) is compatible with the PSR. 
I will argue in this section that does not appear to be the case, given that LFW is a form of event that happens for no reason, but I will also argue that, in any event, LFW is not a correct account of freedom.
To see that, let's consider the following scenario:
Alice has been a good police officer for ten years.
She's kind, committed her job, good to her children, and so on.
Now, one morning, Alice goes to work as usual.
The police get a call about a domestic disturbance, and Alice and another officer are sent to the address they're given.
When they arrive there, they encounter Harry, a thirteen-year old kid high on drugs, acting completely irrationally.
He tells Alice: 'You're a police officer, so you're evil. Why don't you shoot me?'
Alice has no reason at all to shoot Harry.
He poses no threat to her, and can be easily arrested if needed.
However, it's clear that she has the power to shoot him, and is free to choose whether to shoot him.
All she'd have to do is pull her gun, point it at Harry, and shoot.
No one would see that coming, so no one could stop her if she did that – no human, anyway; the point is that she wouldn't be stopped.
But Alice – of course – feels no inclination whatsoever to shoot Harry, does not shoot him, and follows procedure.
The point is that saying that Alice can shoot Harry, that she has the power to shoot him, that she is free to choose whether to shoot him, etc., means that she would shoot him if she chose to do so, that she's not being coerced, etc.
It does not at all mean that, even given Alice's mental state at the time she chose to follow procedure, and even given all the conditions of the world at that time and previous times – including Alice's goals, beliefs, character, etc. -, it was still possible that Alice would shoot Harry.
On the contrary, if, given all those previous states, it was possible that Alice shot Harry, then it seems that there is a possible world W with the exact same past as ours prior to Alice's decision to follow procedure, at which Alice shot Harry instead.
But that is not an exercise of freedom, in the usual sense of the words. Rather, it's an unfortunate event that happens to Alice.
To see this, let's consider Alice's mental processes leading to her 'decision' to shoot Alice – say, decision D. Alice never considered shooting her, and had no desire, intention, etc., before decision D happened.
However, at some time, earlier states of the world, including her earlier mental processes did not determine her later mental processes. There is an event "Alice decides to shoot Harry" that happens irrespective of any previous states of Alice's mind, and no matter how much Alice would loath being a murderer.
All of Alice's previous reasoning, desires, behavior, intentions, etc., are incapable to stop 'decision' D from happening. But how's that Alice's decision?
It seems D is not a decision Alice made, but rather, it's something that happened to Alice.
It's not something Alice could have anticipated, or prevented: at some point her mental processes changed from normal to 'shoot Harry', without forewarning, and without any cause in previous mental processes.
Someone might claim that necessarily, there is always some hidden reason to shoot people, or to do anything one can do, but that would have to be argued for, and even then, that would not change the fact that, in that case, Alice could not have prevented his mental processes from changing at some point from normal to 'shoot Harry', no matter what she did before – and that change could not be reasonably said to be her decision, since she had never considered that before, and the change took her by surprise.
Those considerations show that that kind of thing should not be called 'freedom', but more like 'an unfortunate kind of randomness'.
That does not mean that human non-determinism isn't true. But that is surely not required for freedom, and in fact, it might undermine it, as the previous scenario shows.
Perhaps, there are situations after which, after assessing the pros and cons, a human is undecided between A or ¬A; if so, maybe there is a truly random outcome generator for such cases (which might involve also several mutually exclusive options: A1, A2, A3,...)
However, if that is the case, that is not required for free will: a random generator that delivers 'decisions' in cases in which the mind remains undecided clearly does not result in more freedom than a mind that actually makes decisions.
So, if there is such indeterminism, as long as the indeterministic events happen when a person is undecided (based on her previous feelings, desires, reasoning, etc., she is undecided and does not cause any outcome), maybe that randomness is compatible with free will, but that's all.
On the other hand, if there is an indeterministic feature of human behavior that happens to be like Bob's example above – i.e., if it happens against everything that the person stood for, his previous considerations, etc. -, then, and as the previous example shows, that kind of indeterminism – at least, when it happens – would actually preclude free will; rather, the 'decision' would be an unfortunately random will.
There is another way to see this, taking into account that even under the exact same preexisting conditions – including, of course, the previous mental states of the libertarian-free agent.
So, let's consider the following scenario (relativizing time as required):
Alice is a libertarian-free human, and at t(s), the state of worlds W and W' is exactly the same – that includes, of course, Alice's mental processes.
Later, Alice libertarian-freely chooses A at W, and B at W', even though the states of the worlds prior to Alice's decision were the same (A is different from B).
In other words, W and W' are exactly the same until Alice's mental processes diverge.
Now, let p be a Planck time, and n a non-negative integer, starting with 0.
Let's consider times t(s)+n*p, and the states of W and W', W(n) and W'(n) respectively.
Let n(l) be the last n such that W(n) = W'(n).
Since the 'decision' was made even given the exact same prior conditions, it seems that the 'decision' happened between t(s)+n(l)*p, and t(s)+(n(l)+1)*p = t(s)+n(l)*p+p, in other words, the 'decision' was made in not more than a Planck time.
That's way too fast for any human conscious decision, though. So, it becomes clearer that the first indeterministic event E that distinguishes between W and W' is same random alteration of Alice's mental processes.
Someone might suggest that, previous processes in her mind made E in probable, but weren't enough to bring it about, something still altered her mind randomly; let's assume that that would be a coherent interpretation of probability (else, this objection fails already).
Even then, the fact would remain that her mind was altered without a cause, and with nothing she could do earlier to stop it; moreover, in some cases, the improbable 'decision' might happen. And in those cases in which the improbable 'decision' happens – i.e., the decision that her previous mental processes made improbable – we're back with something like the unfortunate case of the libertarian-free police officer.
Someone might still object that, if such a random change in her mind happened, she still could have changed her mind, and refrained from carrying out the decision – in the case of the first example, the shooting.
The problem is, though, that if you can have such a random event between t(s)+n(l)*p, and t(s)+(n(l)+1)*p, it seems you can have another one at every single Planck time that follows, until the "decision" that was completely against everything the person previously stood for, actually happens.
But let's suppose someone introduces some fuzziness in some way – which they would have to explain, of course; else, the previous reasoning stands. Even then, the fact would remain that the agent would have a random component – a change in her mind she can't bring about, because it happens no matter what she tried previously; it's just that we wouldn't be able to see that by means of analyzing the process step-by-step, but all of the other reasons I've given above remain.
A theist might say that that's 'actually the agent acting', or something like that but – whatever that means -, the fact would remain that that would a partially random agent acting, not one in which mental processes are sufficient to bring about behavior; it would be an agent with a randomly altered mind – i.e., a mind that suffers some alterations that have no sufficient causes; it's akin to dice-throwing, and in some cases, it might go against everything the agent had stood for up till then.
So, for all of the previous reasons, the claim that non-determinism is required for freedom ought to be rejected.
That does not mean we can't act of our own accord, of course. We can and sometimes do have freedom; it's just that indeterminism is not required for that.
Now, there is an objection available to the theist, which seems to be Craig's position: namely, that is lack of causal determination that is required for freedom to exist, not lack of determinism.
However, if an event is determined by previous conditions, then it seems it's causally determined too, since some the previous conditions would be causes. How would it be otherwise?
It seems puzzling.
But regardless, we can make a case against the requirement of causal indeterminism independently. If causal indeterminism is true, then no matter what Alice does up to some time t, all of her thought processes, intentions, desires, memories, reasoning, are all insufficient to bring about her decision. So, it seems that the "decision" might just happen to her, and she might still shoot Harry.
Again, the theist might say that that's the agent acting. But how can she act so quickly – indeed, instantaneously?
An objection to LCA that Pruss challenges is that based on the following principle:
Actually, as Pruss points out, even a weaker principle would be enough to block PSR-based LCA, but he argues that both the HEP and a relevant weaker principle are false.
However, the HEP appears to be true – or a slight modification of it, which I will call the HEP2:
HEP2: If one has an explanation for every conjunct of a proposition, one can give an explanation of the whole proposition.
The only potentially relevant difference is that explaining why explaining every conjunct explains the proposition might be required, so instead of saying that one has explained the whole proposition, HEP2 states that one can give one such explanation. I think the HEP is probably is true as well, but just in case I will argue for the truth of the HEP2 instead.
One objection to the HEP Pruss brings up is that, allegedly, one can't explain why there are a hundred Inuit in a street corner just by explaining why each of them is there: something else needs to be explained.
But the objection misses the point. Let I(n) name one of one of the Inuit, where n is a natural number between 1 and 100, and P(n) be the proposition that I(n) is on street corner X, where "X" identifies some street corner, the same for all n.
The conjunction is Q: P(1)&P(2)&P(3)...&P(100).
Now, suppose Alice has an explanation E(n) for each P(n), and Bob accepts all of the P(n), but still asks why Q is true.
Let's consider the following dialogue:
Bob: Why is Q true? In other words, why is it true that P(1)&P(2)&P(3)...&P(100).
Alice: Q is true because Q is a conjunction, and each of its conjuncts is true.
Further, P(1) is true because of E(1), P(2) is true because of E(2),..., P(100) is true because of E(100).
At this point, it should be clear that Alice has explained Q to Bob.
If it's true that Alice hasn't explained why there are 100 Inuits, then that there are 100 Inuits on corner X – which is not Q, but a different proposition, say R – would require another explanation.
Now, in this particular case, it's hard for me to see how Alice has failed to explain R.
However, that is beside the point; the point is that Q is explained.
So, let's consider the general case, rather than the Inuits on the street corner.
Let's suppose that Q is a conjunction, and for every conjunct P of Q, E(P) is a good-enough explanation.
The question that needs an answer is: "Why is Q true?"
a) Q is true because Q is a conjunction, and every conjunct of Q is true.
That explanation is correct, and surely good enough to explain the conjunction.
The contrastive formulation causes no problems, either. "Why Q, rather than ¬Q?"
The previous explanation shows why Q, and the fact that Q is true explains why ¬¬Q. Alternatively, ¬Q is a disjunction of the ¬P, where P is a conjunct of Q.
Since E(P) explains why P, it also explains why ¬(¬P). And explaining that each disjunct of a disjunction is false is sufficient to explain why the disjunction is false, for similar reasons as in the case of the conjunction.
A key point of this subsection is that what is guaranteed to be explained is Q, and Q alone.
It may be that in apprehending Q, or one of the conjuncts of Q, or one of the E(P), more questions intuitively arise.
In other words, it may be that some of the E(P) themselves call for an explanation, and it may also be that Q plus some other facts allow us to reckon K – whatever K is, but not logically entailed by Q -, and it turns out that K is not explained in terms of the E(P).
That may very well happen, and that point is useful when assessing cannonball example:
On this example, a cannonball is not in motion at noon, and then it starts to fly, and p is a conjunction of the pt, where each pt reports the condition of the cannonball at t, for every t in the open interval (12:00,12:01).
According to Pruss, p has not been explained unless what fired the cannonball is explained.
However, and assuming for the sake of the argument that every single one of the pt has been explained as Pruss says, that view is mistaken: The same procedure applied earlier generally, explains p as well, as long as we actually have explanations of every single one of the pt.
What certainly hasn't been explained is the event E "The cannonball began to move" (or, "The cannonball changed from being at rest, to being in motion.").
That event, however, is not entailed by p, and one does not require to explain E in order to explain p.
What may lead to some difficulty is that, once we know that the cannonball moved in the way described in p, we intuitively reckon – though it does not logically follow – that the cannonball began to move at some time (or, at least, that it changed from some different course at an earlier time to that described in p, but let's simplify), and that is what intuitively we want to see explained, rather than just the conjunction p.
So, Pruss is correct that explaining all of the pt does not give one an explanation of the cannonball's flight, if one understands "flight" including not just the position of the cannonball at every moment, but – much more naturally – also that the cannonball changed from a state of rest to a state of movement in the first place.
However, the key point is that the fact that the cannonball changed from a state of rest to one of movement is not p, or entailed by p, and is not required to explain p.
It's just that explaining p and p alone would not be a satisfactory explanation as to why the cannonball flew in the first place, which is an event we intuitively may well be interested in having an explanation of.
Someone might raise the issue: what if there is no noon? - a case Pruss' considers.
What if the ball was never at rest, and there is no temporally prior state of the universe?
Have we provided a good explanation of the flight by explaining each of the conjuncts of p?
A problem is that in the case of a cannonball, we already know that it was fired at some time. So, denying what we know will never strike us as a good explanation.
In fact, in most cases we already know that there is some event (i.e., some change) involved, even if it's not entailed by the conjunction.
Still, assuming no noon, p still has been explained, for the same reasons as before. As for whether the flight has been explained, here one would need to ask what's meant by "the flight"? Is there an assumption – even if implicit – that there is a state of the world that causally precedes the flight?
Someone might object to the previous reasoning and say that if we consider the proposition q that states that the cannonball is at rest at noon, and then we consider the proposition r:= (p&q), then explaining each one of the conjuncts does not explain r, since r entails that the cannonball began to move.
However, there is a problem: in the previous reasoning, I assumed for the sake of the argument that each one of the conjuncts had been explained. In reality, though, if we're going to explain the movement of the cannonball, modern physics cannot deal with any times less than a Planck time.
The application of Newton's equations to the cannonball in this context is simply not justified.
But what if we assume otherwise? What if the world were such that some equations are exceptionless and can be applied to arbitrarily small intervals, and we know such equations?
Let's consider the case in greater detail:
First, we would need an explanation for why the ball is at rest at noon. But that explanation would not involve, say, gunpowder exploding, or anything that gives the ball some kinetic energy (other than that of the planet; the ball is at rest).
But then, the scenario stipulates that the cannonball is fired. But when is it fired?
If we are justified in talking about the position of the cannonball at every time t later than noon, for t between 0 and 1 minute, then what would a correct explanation of the movement of the cannonball would look like?
When did the gunpowder, or whatever propelled the cannonball, act?
It was not acting at noon, it seems, since the cannonball was at rest. But at any time later than noon, the explanation for the movement of the cannonball is that the cannonball was already moving at some earlier time, plus the laws of motion. So, again, when was the cannonball fired?
It seems that no explanation can be given anyway, at least not with that degree of accuracy. But then, the problem is with the scenario, not with the infinity. That would not be surprising, and it may have to do with an epistemic issue, namely the lack of precision of our terms. Maybe asking for the moment at which the ball begins to move is like asking for the moment at which a person becomes an adult, or even the moment at which an ovum is fertilized; there is no fact of the matter if one wants an arbitrary degree of precision.
If, on the other hand, an explanation can be given as to when the cannonball was fired, to any degree of accuracy, then it seems that there would have to be a cause that operates at some time, but it can't be any time later than noon (since the ball was already moving, and the explanation is the previous movement), so it must be a cause that operates at noon, or before noon.
But then, the conditions are noon aren't just 'the ball is at rest', but rather 'There is some condition already in the ball that will cause its movement', and of course, if we have an explanation of those conditions at noon, plus the explanation of the conjuncts of p, we can explain the movement.
In any case, and to go to the heart of the question, let's suppose it's not a cannonball, but we're talking about the universe, and it turns out there is a beginningless infinite past regress of events.
Will an explanation for each event explain explain the conjunction of propositions asserting that each of those events happen?
For the same reasons as before, the answer is yes, and the construction of the explanation is, once again, the same as before.
Someone might object that explaining the conjuncts alone would not explain whether there is a universe in the first place.
For the sake of the argument, let's grant that that is true, and let's say that the universe is contingent, there is an explanation, and that an explanation has not been given even if one gives an explanation of each of the conjuncts of the conjunction asserting every single one of the events in the beginningless temporal regress of events, and one also points out that a conjunction is true if all of its conjuncts are.
The fact would remain that, by the previous procedure, one has explained the conjunction, which is what's relevant in the context of a LCA.
Another objection might be the following: what if the explanations of some of the conjuncts make explanations of other conjuncts implausible?
For instance – and taking a finite case just for the sake of simplification – what if one has an explanation E(P) of P, and an explanation E(Q) of Q, but when one tries to explain P&Q, it turns out that E(P) raises serious doubts about E(Q), and then one hasn't explained the conjunction because one hasn't explained how it can be that E(P)&E(Q)?
That is a potential worry, but I think it can be averted, for two reasons:
a) That kind of relation between E(P) and E(Q) seems to indicate that one does not really have an explanation of P, and one of Q – not good-enough explanations, which is what we're talking about.
For instance, if E(P) raises serious doubts about E(Q), and one knows E(P), then it's very doubtful that one has a good explanation of Q in terms of E(Q), given how dubious E(Q) itself is.
b) If 1) fails – but why?- then it seem we still have a good-enough explanation of each of the conjuncts, and so the previous explanation can still be given; we've explained P&Q, and now what we need is to explain how it can be that E(P)&E(Q).
In my view, 2) is rather odd, but that may be because of the assumption that 1) fails, which also seems odd: Barring 1), then 2) works, since the failure of 1) indicates that one still has a good-enough explanation of each premise, and so the reasoning given above is not blocked.
Another worry might be that, perhaps what explanations are good might depend on what we need the explanation for; perhaps, that's suggested by some of the previous examples of statistical explanations.
That would have to be argued for, but in that case, it seems to me that would only mean that the explanations of the conjuncts are not good enough in the given context, and we're assuming they are.
Still, let's suppose that one of the two worries is justified – or something else -, and that the HEP2 is not true.
Then, we can propose a weaker principle, following Pruss' HECP :
HECP2: If one has an explanation for every conjunct of a proposition, one might be able to give an explanation of the whole proposition, using only the explanations of the conjuncts and pointing out that a conjunction is true if all of its conjuncts are.
An example that one might be able to do so would be – for instance – Pruss' cannonball example, actually.
Now, according to Pruss, the HECP fails when there is when there is vicious regress, or circularity.
example of the first kind – he maintains – is the
cannonball example. But this is actually an example in which the
HECP, or the HECP2, work.
As for circularity, he uses as an example that if Bob is at the party because Jenny is, and Jenny is because Bob is, then that does not explain why Jenny and Bob are at the party. 
The problem is that Bob's being at the party is not explained just by Jenny's being at the party.
For instance, without implicit assumptions, someone could just ask: but what would the fact that Jenny is at the party have to with Bob's being there? What's the link between two people who, for all we know, might not even know each other, or have any remote relation to each other?
The point is that the fact that Jenny is at the party may explain why Bob is at the party only if we add – implicitly or not – other propositions.
For instance, maybe Bob is at the party because Jenny is, but unpacking a little, it's because Bob likes Jenny, so he decided to show up at the party because he thought there was a good chance that Jenny would be there. And he thought that because she hinted that she'd go. When he arrived, it turns out that Jenny wasn't there yet, but Bob decided to wait for a while, since he arrived more or less early.
Then, Jenny showed up, so Bob decided to stay, and that's why Bob is at the party.
On the other hand, Jenny is at the party because she likes Bob. And she guessed Bob would probably be there because she hinted that she'd be there, and she reckons Bob likes her too. And when she got there, Bob was there too, so she decided to stay.
Given that, one has a good enough explanation as to why Bob and Jenny are at the party...though of course, I'm still making a lot of assumptions about Jenny and Bob.
That's not the point, though. The point is that when we say that some propositions explain another proposition, we have to consider that many other propositions are implicitly assumed, as part of the context – and if we remove assumptions, we have to be add them to the explanation.
However, in the case of the huge conjunctions used by theists defenders of LCA, if they're ever not incoherent, that wouldn't be a worry, since it seems all the required assumptions would also be explicitly stated as conjuncts – or entailed by them -, so each conjunct might be explained by other conjuncts, and so on.
Finally, Pruss claims that anyone who accepts that an infinite regress of contingent propositions might be explained by the explanatory relations between these propositions, is committed to what he describes as an absurdity. 
The most obvious problem is that there appears to be nothing absurd about what he describes: in a denumerable infinite conjunction in which each conjunct explains the next, there is no problem putting the odd conjuncts in one proposition, and the even ones in another proposition.
In order to explain the whole conjunction, one will still need all the conjuncts, unless there is redundancy. In any case, the previous reasoning is not blocked.
Still, just for the sake of the argument, one can point out that the proposition used in Pruss' LCA – the BCCF*, assuming it's coherent – probably has more conjuncts than any cardinality, and it's not clear how Pruss could make his construction in that case, or a similar one.
Aside from the PSR, Pruss defends a causal principle, arguing for an unrestricted rather than a restricted one; in other words, he argues for extending such principle to any mereological sum; according to Pruss, the basic intuition is that objects cannot come into existence uncaused. 
If so, we may propose the following principle:
I don't know that there is an intuitions that such things cannot come into existence without a cause in a modal sense of "cannot", though there seems to be an intuition that they don't do so in the actual world, and in similar worlds.
So, a weaker version would be:
CEC: Every object that comes into existence has a cause.
A question would be whether Quantum Mechanics would be a problem, but assuming it wouldn't be, a problem with those principles is the case of arbitrary mereological sums, since some axioms might entail that sums like the aggregate M of all things come into existence – indeed, a different M comes into existence as time goes by, at least as long as things keep changing -, and that causes can't overlap the effects, so if M counts as an object, that would result in an object that comes into existence uncaused..
So, alternative principles in case we're using mereological axioms – principles which may sound odd, but I think the oddity comes from the odd mereological assumptions it's designed to address – would be the following:
NCEC2: Necessarily, for any x that exists, if there is a state S of the world at which no mereological part of x exists, temporally followed by a state S2 of the world at which at least one mereological part of x exists, then x has a cause.
CEC2: For any x that exists, if there is a state S of the world at which no mereological part of x exists, followed by a state S2 of the world at which at least one mereological part of x exists, then x has a cause.
Many of the arguments presented by Pruss and other theists in support of a CP use scenarios like bricks and the like popping into existence uncaused.
However, the CEC2 would handle such cases, and the NCEC would also handle them in every world – though it's not clear to me that the NCEC is warranted.
As in the case of explanations, though, we don't need to actually assume any general principle; we can simply use our intuitions when assessing the specific cases we encounter.
(32) (C causes E) ⇒ ((~∃D (D causes E)) E did not occur),
That's another example about E's occurring – Pruss' example to illustrate the point is a plane crash.
Our intuitions about causation seem to rule out that an event – i.e., a change – would have occurred at some other world and with no cause.
However, if origin essentialism is not true, then our intuitions of causation do not seem to suggest that, for any caused state S, there is no world W at which S exists, and in which there is no event "S comes into existence": S might exist at some world W without any temporally prior state of that world; furthermore, S might exist at W without any causally prior state of W, if the difference is relevant in this context.
Someone might object that negative conditions such as "no prior state" shouldn't be included in a conceivability criterion for possibility.
I see no good reason to exclude negative conditions, but in any event, this is not one such case, since I'm not taking a stance on whether such W is possible, but rather, pointing out that our intuitions about causation fail to rule that scenario out.
On the other hand, if origin essentialism does hold, then as Pruss points out, it follows that a state S has a cause if and only if it can have a cause.
However, if origin essentialism holds, conceivability of other worlds fail to show anything about causation in the real world, since for every state S of our world, any conceivable and even possible similar state S1 at some other world would not be the same state if it has another origin – and if it has the same origin, then the origin in the actual world is the one that counts, regardless of what scenarios we can conceive of.
Finally, if there are states of affairs for which origin essentialism does hold, and others for which it does not, then:
a) For those states of affairs for which origin essentialism does not hold, there appears to be no good reason to conclude that (32) holds – see above -, and hence, to conclude that if they can have causes, they do have causes.
b) For those states of affairs for which origin essentialism does hold, Pruss' arguments for CP for certain categories of states of affairs, like physical things, or all wholly contingent states, fail because – among other reasons – they rely on the hypothesis that all states for which origin essentialism does not hold have causes if they can have causes, and that's unjustified for the reasons explained above.
Pruss maintains that what he calls a local causal principle is ad-hoc, and should be extended to arbitrary mereological sums as well. However, that seems ad-hoc.
According to Pruss, even if a brick has infinitely many particles, that would not affect our intuitions that the brick cannot come into existence  without a cause.
That seems to be true, but a brick does not resemble any arbitrary infinite chains – let alone mereological sums – in what appear to be relevant senses.
To see this, let's consider an infinite set of causes C(1), caused by C(2), caused by C(3), etc.; that already gives us a cause for each C(n).
Someone could ask about the cause of the "whole chain" C, and/or the mereological sum of the C(n), etc.
However, there appears to be no object "whole chain" other than the C(n).
We're just considering them together for the purposes of analyzing the scenario, but that's all there is to them, and the causes have already been given.
If someone objects that the object C for which we've not given a cause is the mereological sum of all of the C(n), then a principle like NCEC2 would not require C to have any causes, as long as at every state of the world, at least one of the C(n) existed.
Someone might claim that NCEC2 is ad-hoc, but it seems to me that it's not more ad-hoc than unrestricted principles, and in fact it seems more intuitive: the causal account in terms of the C(n) is satisfactory, at least as long as there is no state of the world at which none of the C(n) exists, and NCEC2 captures that intuition to some extent by not stating that there is a cause.
According to Pruss, in the case of the brick, infinite regress would still not help: if one part of the brick caused the other, etc., that would still count as a brick coming into existence uncaused.
However, the case would be different since there would be a state of the world at which no part of the brick exists, temporally followed by a state at which at least one such part does exist.
An objector might insist that even if the brick existed at every temporal state of the world, then that would still be counterintuitive.
But actually, the counterintuitiveness in that case appears to come from the fact that bricks don't do that that – and neither do any of the ordinary objects we encounter in our life.
However, there would appear to be no good reason to extend this from bricks to, say, the universe, or any thing in general. If a theist claims otherwise, the burden is on them.
I will address the issue of unrestricted mereological causal principles in greater detail when addressing Koons' causal principle.
Also, Pruss gives an argument in support of a CP for all "physical things"
It's not entirely clear what "physical things" exactly means: for instance, if panpsychism is true, would basic particles be physical?
But even if my previous counterargument failed, there are specific reasons why this particular argument fails:
According to Pruss, we can get a CP for all physical objects in the following way (simplifying): if we have a de dicto positive description of all the physical things in the universe, then we could imagine a larger world W in which D describes a part of it, which is caused by something else.
He maintains that the description is positive is relevant, because that way there are no clauses that there is no stuff other than what D describes. But there appears to be no good reason to exclude conditions such as "that's all there is".
Moreover, he too is implicitly including at least one relevant negative condition as well: the condition that a complete description of "physical" things would not lead us to find something that would make a cause inconceivable.
For all we know, perhaps, due to something about the nature of time, or an eleven-dimensional spacetime, strings, branes, an infinite multiverse, etc., we might reach that conclusion.
Pruss' arguments do not give or hint at any positive description of any of that, or explain why we wouldn't reach the conclusion that there is no cause of it.
Someone might suggest that our intuitions tell us physical things having causes.
However, modern physics has shown that the there are things in the universe which are very weird and counterintuitive: General Relativity and specially Quantum Mechanics showed that the universe is a lot weirder than we had assumed.
Who knows what new weirdness will come from any unified theory that accounts for the four (known) forces?
Who knows that we would in those cases have any intuitions that all the things involved have causes?
Also, it would not help a theist's case to say that in the case of the physical things we understand, they can have causes, so that gives us reason to believe that that holds for all physical things, because in that case, someone could make the same point about minds we understand.
That aside, and in addition, Pruss includes negative conditions like a "that's all" clause in the formation of a very dubious arbitrarily large conjunction when he defines the BCCF*: why would the inclusion of negative conditions be a problem for conceivability, but not for the coherence of arbitrarily large propositions?
Such propositions are the topic of the next subsection:
In his defense of the LCA, Pruss posits what he calls the "Big Contingent Conjunctive Fact" (BCCF), which is "the conjunction of all true contingent propositions, perhaps with logical redundancies removed", and defends the BCCF against Davey and Clifton's objection , based on a presumption of innocence - i.e., Pruss suggests that a conjunction should be presumed to make sense until proven nonsensical.
However, when it comes to unrestricted infinite conjunctions so big that they have more conjuncts than any cardinality, it seems to me that such presumption of innocence is unwarranted: Given that some such unrestricted conjunctions make no sense, and given that there seems to be no known procedure – not as yet, anyway – that could be used to rule that out – or even to somehow make it improbable -, then it seems to me that in absence of any good reasons to think, in a particular case, that one such conjunction makes sense, one ought not to accept that it does.
Someone might object that it's not the fact that there are more conjuncts than any cardinality what causes the problem, but something else, and that the fact that a proposition has so many conjunctions that there is no set of conjuncts is not a problem.
That may or may not be true, but unless someone explains what the problem is, and gives a procedure to avoid it and make meaningful conjunctions, I think withholding judgment is warranted, especially given that issues of cardinality – or lack thereof – are involved in a number of set-theoretical paradoxes.
That said, I will show that the BCCF makes no sense, assuming only that propositions – and not just sentences – can have subformulas – which Pruss accepts in his defense of LCA – and a principle we could call the "Subconjunctions Principle" (SP").
SP: If a conjunction C makes sense, and P is a property, then the conjunction C(P) of all of the conjuncts of C which have property P makes sense as well.
Since the BCCF is the conjunction of all contingently true propositions, we can use a slightly modified version Davey and Clifton's example and construct a conjunction BCCF(P) of all the conjuncts of the BCCF that do not contain themselves as proper subformulas.
But the BCCF(P) is just the conjunction of all contingently true propositions that do not contain themselves as proper subformulas, since a proposition R is a conjunct of the BCCF if and only if R is a contingently true proposition.
Let Q be the proposition, that BCCF(P) is true.
Since the BCCF(P) is contingently true because every single one of its conjuncts is, then Q is a contingently true proposition as well, and hence Q is a conjunct of the BCCF.
Does Q contain itself as a proper subformula?
Mirroring Pruss' explanation of Davey and Clifton's argument, we can see that either way, a contradiction follows:
If the answer is "no", then Q is a contingently true proposition that does not contain itself as a proper subformula. Hence, it's one of the conjuncts of the BCCF(P), and thus a proper subformula of itself, which contradicts the assumption that the answer is 'no'. Hence, the answer is 'yes'.
So, Q contains itself as a proper subformula, and so it's a subformula of the BCCF(P). But since Q is not a conjunction, it must be one of the conjuncts of the BCCF(P), and thus, it's not a proper subformula of itself.
The conclusion is that the BCCF makes no sense.
Perhaps, someone could object that the "logical redundancies removed" stipulation blocks the argument. But then, that would have to be argued for. It's not clear how the removal procedure works, though. How does one remove something from something that makes no sense?
Pruss also offers an alternative to the BCCF, namely the BCCF*. 
However, given that unrestricted conjunctions sometimes can't be formed – they make no sense -, it's questionable that there are grounds for accepting the BCCF*.
For every infinite cardinal number m, let F(m) be "There are at least m minds in the world".
If all the F(m) are possible but not necessary, then it seems that for all m, either F(m) or its negation would be a conjunct of the BCCF* - since they're atomic propositions -, and hence the BCCF* would have more conjuncts than any cardinality.
If so, and if the BCCF* is proposed as coherent, it seems to me that the proponent should give a good explanation as to why that is so, or probably so.
Else, I would say one ought not to accept the claim that it's coherent, just as one ought not to conclude that the BCCF* is incoherent, either, unless ones finds a specific reason for that.
Perhaps, a theist could insist that the BCCF* would not have a number of conjuncts exceeding any cardinality, and that the F(m) are impossible beyond a certain cardinal. But once again, the burden would be on the claimant.
For the sake of thoroughness, I will assume that there is a necessary explanation or cause – explanation or cause of something that theists could use in the context of a LCA -, and assess Pruss' arguments in support of the claim that the cause or explanation in question is God (or provided by/involving God's activity, etc.).
Pruss, like a number of other theist philosophers, makes a distinction between what he calls "agential explanation" and "scientific explanation", which would be two non-overlapping categories – the third category would be "conceptual explanations".
That implies that usual explanations in terms of the intentions of humans and other animals would not count as scientific, as long as intention is involved
For instance, suppose scientists find a number of mammoth fossils together and in certain positions, and explain the finding by positing that a mammoth got stuck in tar, others tried to help her out, and they all got stuck and died.
It seems that this would not count as "scientific" in this peculiar sense, even though it's obviously a scientific explanation in the usual sense of the words in English.
On the other hand, if someone says a person caught a bad cold just before her wedding because of the bad luck resulting from some alleged astrological fact, it seems that that would count as a scientific explanation – even if a bad one – according to the classification, as long as no agent is said to bring about the undesirable result.
Perhaps, someone might not call the astrological explanation an explanation at all, and limit the classification to correct ones. but even then, if someone asks me why I have a bruise, and I explain that I was hit by a branch that fell from a tree, that would not usually be regarded as "scientific".
So, the fact is that there are plenty of explanations that are given by scientists doing science, and would not count as "scientific", while ordinary explanations in which no science is involved would count as "scientific" under this classification.
Terminology aside, another issue is whether there is any good reason to make this classification in the first place. However, there is no need to tackle that matter here. I will just assume the classification for the sake of the argument and assess Pruss' arguments, but keeping in mind the facts I've just pointed out.
If one accepts that all explanations of contingent states of affairs are either scientific, agential, or conceptual – at least these are all the kinds of explanations we know of, and since the concept of explanation is a concept of ours, we have some insight into what can and cannot yield an explanation – then one can argue that the First Cause is an agent. For the First Cause’s activity does not provide a scientific explanation. As far as we can tell, science explains things in terms of contingent causes.
As I explained, scientific explanations in the sense of "explanations given by science", and "scientific explanations" in the sense of the peculiar classification that Pruss proposes, are very different matters.
More importantly in this context, the fact is that science – at least as of yet – does not take a stance on whether the objects it deals with or posits as causes of others are metaphysically contingent or metaphysically necessary.
In particular, science does not take a stance on whether spacetime is metaphysically contingent, or whether, if there are branes, strings, or a multiverse, those things would be contingent or necessary.
A theist might argue that it still follows from some of the features of those objects, or hypotheses, that they would all be contingent. But that is something that the would have to be argued for.
That is enough to block this particular argument for agency.
Another argument Pruss makes is based on the claim that only agential explanations work in the case of a first cause, because it has to have a contingent outcome and there can be no further explanation – though he says that someone who accepts statistical explanations won't find this argument persuasive.
There is a difference between statistical explanations that are accepted because of epistemic or psychological limitations, and actual non-determinism, which I've addressed earlier, but in any case, the so-called "libertarian free will"(LFW) seems to be incompatible with the PSR.
Assuming otherwise, LFW it does no better than non-agential non-determinism, or a non-intelligent agent with a limited range of causal powers – but still non-deterministic.
For instance, if there is a first cause and it's an agent, for all we know it might be no more intelligent than, say, a mosquito. In fact, it might have no memories or no intelligence at all: just some kind of a basic form of consciousness, with a very limited range of causal powers – just the power to create something like our universe, or similar to it.
Or it could be a non-deterministic non-conscious thing with certain probability to cause certain states, certain probability to cause others, and some limited range of possible causes.
Someone could claim that that's ad-hoc: why would the non-conscious or the non-intelligent cause have just such powers, and not others?
But similarly, why would an intelligent creator have the particular mental make up that results in her wanting to create a universe such as ours?
Note that coming up with a story about reasons for the agent to act in such-and-such way would avoid the problem, since the question is why the agent has the mental makeup that would make him find those reasons appealing or persuasive.
That would be a brute fact with no explanation, and if the claim that it's a necessary one somehow makes it any better, the same can be said about the non-intelligent necessary agent, or the necessary unconscious entity, etc.
One claim is the "fine tune" claim.
But how would anyone measure that?
It's been argued that the universal constants fall into a "narrow range" which makes life possible. But how do they measure "narrow"?
In fact, there could be all sort of other arrangements that would make life, or consciousness, possible, which have nothing like the constants of the universe: why not disembodied minds – assuming that's coherent -, instead of bodies?
Why billions of years of evolution, of the struggle for life and death, of horrible ways of getting killed?
Why so many badly "designed" biological features?
Why not a universe that allows rational agents everywhere, rather than one that is, nearly everywhere, extremely hostile to life, and even more so to rational agents?
Even if there are plenty of planets with life, clearly most of the universe isn't constituted of planets, or of any life-sustaining environment.
Of course, theists could come up with lots of stories as to why a rational agent would create the kind of universe that we see.
An obvious problem is that those explanations seem to be ad-hoc.
For that matter, someone could posit some mindless stuff – or a very basic mind – with a propensity to make universes like our own. It's ad-hoc, for sure, but so is an intelligent agent.
There is another problem with this line of argument: it seems to assume an event of creation of what we see, but even assuming a necessary explanation, that alone wouldn't warrant belief in a "first event": other arguments would be required.
Also, Pruss makes a claim that somehow functional attributions can't be reduced to evolutionary claims: somehow "eyes are for seeing and so on", and suggests that that too supports the idea of a designer.
But eyes evolved as an adaptation because they allow animals to see.
If that's what's meant by "for seeing", then they are for seeing, but that does not help design arguments.
If someone says "for seeing" meaning that they were designed for that purpose, then Pruss gives no good reason to assume that in that sense, eyes are for seeing.
Someone could claim – maybe that is Pruss' claim – that the usual meaning of expressions like "for seeing" entail a designer.
However, Pruss presents no argument in support of that claim, so there is no need for a counterargument. Also, a discussion of that would be essentially a discussion of a type of argument to design, which is beyond the scope of this article.
However – and making more unwarranted assumptions for the sake of the argument -, even a designer wouldn't have to be the necessary cause or explanation of a LCA – it could just be another contingent being.
In other words, there seems to be a disconnection between an argument to design and a LCA. A theist could say – for instance – that it's an inference to the best explanation, but that would also have to be argued for.
In short, any connection between a [assumed] designer of life on Earth, or of the observable universe, etc., and the necessary explanation or cause of a LCA would also have to be argued for. There is no evident connection, even assuming both such a designer and such a necessary cause or explanation.
But still, even if one also grants agency and intelligence of a necessary cause, just for the sake of the argument, and a creation event, that still would not give us good reasons to believe the creator in question is God...which leads us to the next problem:
Assuming for the sake of the argument that a LCA established there is a necessary rational being – say, G -, a question is: Is G plausibly God?
Pruss claims that G there are three options: G is morally evil, morally good, or something in between. 
Pruss gives no argument for that claim, so it seems to me he assumes that all rational agents are moral agents. 
Let's assume for the sake of the argument rational being falls in one of those three categories: even aliens with a completely different mental makeup and who haven't ever heard about morality, have no moral sense, etc., would properly be called "morally good", or "morally evil", or "morally something in between".
So, according to Pruss, in the case of a necessary creator, we can rule out morally evil or something in between.
I will propose an alternative hypothesis: assuming G is a rational necessary creator, G does not care about morality at all, one way or another: in other words, G does not care whether good agents or evil agents are better off, win when they fight each other, etc.
Given that G is by assumption a moral agent, that would mean that G is either morally evil, or something in between, but it's clear that, on this alternative hypothesis, G is not morally good.
So, is Pruss' hypothesis more plausible than the alternative?
Let's consider the reasons given by Pruss in support of the claim that the being in question is morally good?
His first claim is that evil might be "ontologically inferior" to moral good.
While a moral agent who is not morally good is – tautologically – morally inferior to one that is morally good, a claim that evil is "ontologically inferior" is puzzling.
What does that mean?
One can measure inferiority or superiority with regard to some standard – like, say, morality -, but that does not seem to have anything to do with ontology.
Pruss presents some example: somehow evil can be seen as a privation of good, or a twisting of the good, and somehow "metaphysically parasitic".
However, a vastly powerful and knowledgeable being who does not care about morality one iota would not appear to be twisting anything, and it's not deprived of anything.
That being would simply have very different interests from humans, and would not be interested in moral issues, but in other things.
Someone could say that he's "deprived" of having moral interests, but that would be a misuse of the words: for that matter, someone might just as well claim that any mind would be "deprived" of having any interests that it happens not to have.
The claim of metaphysical parasitism also seems puzzling. What does that even mean?
Regardless, a being as the one I described – namely, the one who does not care at all about morality – does not appear to be parasitic on anything; if a theist claims otherwise, the burden would be on them.
As for the claim that evil can't win, that appears unwarranted. Why can't evil agents win?
And if it's not about evil agents' winning, what's the claim about?
Also, Given Pruss' description of how evil can mock good, but can't win, etc., it seems to me that he's thinking of a kind of cartoon-like villain, rather than an agent who does not care about mocking good or evil, or about moral victories, or generally about morality, one way or another.
While Pruss' claims would still be puzzling if someone proposed such a villain, in order to make their case theists would have to deal also with the alternative kind of being I'm suggesting, among others, such as less powerful or knowledgeable beings, etc., even under the assumption that there is a necessary rational being.
Obscure claims aside, Pruss also claims that there is more good than evil in the human world.
That may well be true, but the universe is not just the human world. The fact that humans evolved a propensity to act in a certain way does not suggest that G was particularly interested in them.
Even just on Earth, there were hundreds of millions of years of evolution with no moral agents around, and with agents capable of suffering being torn to shreds in a wide variety of ways – like being eaten alive by predators, for instance.
In fact, that kind of thing has happened and sometimes can still happen to humans too, whether children or adults.
Moreover, moral evil agents are not stopped by G at all, and the kind of things that happen to good agents are incompatible with a sufficiently powerful and knowledgeable morally good G.
Perhaps, G doesn't have the power or knowledge to do anything about it, but he's still good. But then again, perhaps not. There appears to be no good reason to think he is good.
On that note, we can quickly present the problems of evil and suffering – they don't work against a necessary being with very limited power, but given that theists argue for God's existence, they do work.
1) A child is suffering from an illness such as cancer, AIDS, tuberculosis, malaria, cholera, dysentery, etc.
Her parents have a cure, and the cure entails no risk to them or others, and is not painful, but they choose not to use it, and instead they let the child suffer for a long time, and then die.
Would their behavior be morally acceptable?
2) The parents actually infect their own child with something like AIDS, tuberculosis, malaria, cholera, dysentery, or worms that burrow through the child's eyes, perhaps to correct them, or to see how they cope with hardship, or to punish or test another one of their children, or for some other reason that does not involve preventing a worse outcome.
Are those parents good people?
It's very clear that they aren't.
Note that this is the case even if the same parents have other children, whom they treat well: that does not excuse their actions.
Someone could object that, perhaps, there is a greater risk to be avoided. But let's say that there is not – as there wouldn't be in the case of an omnipotent creator.
The point is that G created cancer, polio, cholera, malaria, AIDS, dysentery, polio, tuberculosis, even worms that burrow through the eyes of children; G made them and infected children with them, making them suffer, in many cases horribly, for years, and to death.
In fact, G has caused more pain to innocent people than Stalin, Pol Pot, Ted Bundy, and all human criminals put together.
Someone could object that G just made the laws of nature, but he's allegedly not actively torturing children.
However, in that case, G created those mechanisms, knows what's happening, and just lets it happen.
So, let's consider another scenario:
The parents make a self-contained environment, in which there are threats like, polio, cholera, malaria, AIDS, dysentery, polio, tuberculosis, predators, etc., and then put some of their children in there.
Later, when some of those children are suffering terribly, the parents who made the environment – and who could help, without causing an even worse situation – choose not to act.
Using our moral sense, we can tell that those people would be acting immorally, even if they don't cause that kind of harm on everyone, and even if most of the children in their self-contained environment are doing reasonably well.
Someone could object that,
perhaps, G has mysterious good reasons, and he's morally good after
But for that matter, someone could say that, perhaps, Pol Pot was just G pretending to be a human, and did what he did for mysterious good reasons. So, Pol Pot didn't do anything wrong after all. The point is that the "mysterious reasons" objection is not a reasonable one.
Moreover, apart from the torture of human children, G inflicted horrible suffering on other animals, like australopithecines, Homo Habilis, Homo Erectus, etc., for millions of years.
So, what we can ascertain is that G is not morally good, if he's a moral agent at all.
That aside, one can also take a look at immoral behavior carried out by humans, while G watches without helping.
There are people who engaged, or engage, in acts of torture, beatings, rape, murder, and so on. There are serial killers, serial rapists, bank robbers, tyrants, etc.
Now, suppose let's consider the following situation:
A group of people see a man raping a Bob, a child, apparently for fun.
The rapist does not appear to be armed, or particularly strong – though he's strong enough to rape his victim -, but the people watching him are all armed, and good at fighting.
They have no reason to fear the rapist, or the consequences of intervening.
In fact, they do not fear that any harm would come to them, or to third parties, if they do interfere and save Bob.
However, they decide not to interfere and let the rapist continue to rape Bob. They just keep watching, or look the other way.
It's very obvious that those people would be immorally failing to act.
Note that if they said that they wanted to respect the rapist's freedom, or free will, that would not be an acceptable excuse.
One objection a theist might present is that if G were to act always, there would be no free will at all, or no significant free will, and that would be a result that G should avoid.
However, that would be a very confused reply.
It suggests that the more powerful and knowledgeable an entity is, the less it should interfere to help and prevent evil – or that, the more powerful and knowledgeable it is, the more it should intervene...up to a point, when it shouldn't intervene at all.
That reply is incompatible with usual claims of miracles in specific versions of theism, including the versions held by those theists attempting this reply. But let that pass, since we're considering generic theism.
The fact is that there is no good reason to think that if G intervenes once, it would have to intervene always:
In fact, arguably the use of force is not the correct reply to all immoral actions.
Perhaps, if someone cheats on his spouse, it's not the case that others should forcibly prevent him from cheating, for instance. Instead, moral rebuking him might be appropriate. Maybe shunning him for a while if needed.
On the other hand, in the scenario presented above, using force to stop the rapist would be morally obligatory to the witnesses in question.
The same would be the case if the witnesses were vastly more powerful, say, like Superman. And even more clearly, the same would be the case if one of the witnesses were omnipotent, like G.
Granted, that would most certainly reduce the freedom of many evildoers, while not affecting that of many other people, but that's in no way a result that should be avoided – if it were, we might as well tell the police to reduce their effectiveness if they've become too effective at fighting violent crime!
Given all of the previous reasons, it seems G is not God.
Before addressing some objections, some points are in order:
1) We can make truthful assessments, even moral assessments, in logically possible scenarios, even if they're not metaphysically possible.
For example, let's suppose that water is not H2O – say, scientists got it wrong.
In that scenario, if a scientist claimed that water is H2O, his claim would be false. If he later realized that water is not H2O, and pointed that out, his claim would be true. If he killed his spouse, just for fun, his action would be immoral.
2) Let's suppose that an omnipotent, omniscient creator G(2) tortured people for eternity, just for fun.
Clearly, in that scenario, it's not the case that G(2) is morally good. As long as the scenario is logically possible, we can make that assessment, which is intuitively obvious.
3) Let's suppose now that G is an omnipotent, omniscient creator that does not go to the same extreme as G(2) in the previous scenario, but creates a world just like ours, causes suffering and allows agents to behave in the manner described above.
Then, and for the reasons described there, G would not be morally good – granted, he would not go to the extreme of torturing people for eternity for fun, but he would still act and refrain from acting in ways that rule out the claim that he's morally good.
Now, if someone objected to my earlier argument concluding that G is not God by saying that God has no obligations, and so he's good regardless of what he did or didn't do, a reply would be that point 2) shows clearly why that objection fails:
Someone could make the same claim and say that monsters who tortures people for eternity just for fun is morally good, which is obviously not true.
Furthermore, 3) and the previous considerations show that G is not God, and so God does not exist.
If someone claimed that 2) and 3) are metaphysically impossible scenarios, a reply would be that whether or not they're metaphysically possible is beside the point, as 1) illustrates.
Finally, someone might raise the objection that non-theism entails that there morality is illusory: i.e., there is no right or wrong, moral good or evil, etc.
However, that would have to be argued for; there appears to be no good reason to think that any metaethical argument of that sort succeeds, though that's beside the scope of this article.
In any event, the Problem of Evil and Suffering can be put in terms of a dilemma:
a) If there is no right or wrong, moral good or evil, etc., in particular it's not the case that there is a morally good creator, and so theism is not true.
b) If there is right and wrong, moral good and evil, etc., then the previous considerations show that theism is not true.
One way or another, theism is not true.
Another point Pruss raises is that, apparently, if the creator weren't simple one could raise the question: Why are the parts united?
Somehow, that would mean that the first cause is not self-explanatory.
There are a number of plausible replies to this – apart from pointing out that Gok can be simple if God is -, but let's consider a couple of them:
First, an omnipotent, omniscient, morally perfect, etc., being is most certainly not self-explanatory, either. Nor is the necessary existence of any beings.
But if someone can just say that since the being is necessary, it requires no further explanation, then someone could claim that a being with parts has its parts necessarily attached.
Second, all the minds we know of require brains.
Even more, roughly, the more information a mind can hold, the more complex a structure it needs.
Why would anyone think that if something is simple, it would have a mind at all – let alone one which has an infinite amount of information?
Third, let's suppose that someone posits that an eleven-dimensional universe, or multiverse is necessary. What would be the parts of that?
The universe would just be that necessary structure, with certain laws, not the planets, etc., which would be contingent.
The contingent stuff would be made of matter/antimatter/energy/whatever the universe necessarily has, and the total amount would be preserved via necessary conservation laws.
Are planets and the like parts of the structure?
If a necessary rational agent with contingent mental states makes sense, why wouldn't a necessary universe with contingent energy/matter states make sense as well?
I'm not suggesting this as a plausible necessary being. But the question is: how is that less plausible than a "simple" mind – which is, nonetheless, omniscient – or knowledgeable at all?
Pruss also uses Thomistic ontological considerations to support the claim of simplicity.
A discussion of why Thomistic ontology is mistaken would be beyond the scope of this article, so I will just point out that Pruss does not make any arguments in support of Thomistic ontology.
Finally, Pruss gives an argument intended to breach a gap from a necessary cause that explains all contingent truths in the actual world to an omnipotent necessary cause of all contingent truths in all worlds , and which is based on an argument by Gellman. 
First, let's take a look at an assumption he makes, which Pruss calls "Iterativeness Postulate": 
(IP) If x has the power to gain the power to do A, then x already has the power to do A, although x might have to take two steps to do A (first acquire a power to directly do A, and then exercise the power).
That looks rather counterintuitive to me.
For instance, let's suppose Bob is a normal human who has a pill that will give any human Superman's powers – without the kryptonite problem -, and Bob has the power to take that pill.
But let's suppose that Bob believes – for whatever reason – that it's his moral obligation not to take the pill, and further to destroy it so that no one takes it.
So, Bob goes ahead and destroys the pill.
Did Bob have. say, the power to fly faster than a speeding bullet?
Or did he have the power to gain the power to fly faster than a speeding bullet, but chose to not gain it?
It seems to me it's the latter.
But let's say that (IP) is true.
Let's suppose that N1 is a necessary being that explains contingent truths at W1 – a being whose existence is somehow established via a LCA, using the PSR or one of the CP , who contingently has power P1, and let's assume for the sake of the argument that libertarian free will (LFW) is some form of freedom , and is compatible with the PSR.
The explanation for why N1 has P1 is the following:
N1 necessarily has the power to create contingent rational beings C(2), C(3),..., C(k) - each of them with libertarian free will -, and those beings plus N1 jointly would have the power to give power P1 to N1.
However, N1 did not have the power to acquire P1 on her own, or without the participation and agreement of all of the C(j).
So, N1 chose to exercise her power and created C(2), C(3),..., C(k) and they libertarian-freely chose to cooperate with one another and with N1 to give P1 to N1.
Generally, N1 might contingently hold powers that she can only have with the cooperation of other libertarian-free agents, some – or all – of whom might be contingent.
In other words, as long as we exclude libertarian-free choices from what N1's causal activity has to explain, then there might be plenty of contingent facts that are not explained by N1's causal activity, but by something else, since they may result from the causal activity of other libertarian-free agents.
Some of those facts might include how the necessary being came to have certain powers.
Under the LFW assumption, this blocks Pruss' argument for oneness and omnipotence.
Also, we don't need the LFW assumption to make that objection, since LFW is no more of an explanation than non-agential non-determinism. So, it might be that the necessary cause can create non-agential entities that could give her some power, but could also fail to give her that power.
Perhaps, someone could say that the argument for oneness and omnipotence works if one assumes that the entity N1 explains all contingent facts, and there are no facts that can only be explained by means of the libertarian-free choices of other agents, or other non-deterministic entities.
However, if there are no contingent non-deterministic things, then why would anyone assume that a necessary thing would be non-deterministic?
And if the necessary thing that allegedly explains everything is deterministic, we get modal collapse, which means that the PSR is vacuously true, and then there is no contingent fact to be explained in the first place.
In this section, I will reply to the cosmological argument defended by Koons, showing that that argument, and variants using similar premises, fail to provide any support for theism.
1) In his version of the cosmological argument, Koons uses "facts", "states of affairs", and "events" - which he uses indistinctively – to denote the "kinds of objects that can serve as relata for causal relations"
In particular, he says that facts are things in the world that make some propositions true and other false, not propositions. Also, he makes it clear that what he calls "negative conditions" are not the same as facts,  and that "facts", "states of affairs" and "events" are concrete parts of the world. 
In this section (i.e., section 2), unless otherwise stated, I will use "states of affairs" and "facts" in Koons' sense – except for expressions like "in fact", in which I will follow common usage.
However, I will use "event" to mean any change – following Craig .
2) Koons uses the term "wholly contingent" to mean a state of affairs all of whose parts are contingent.
I will follow that terminology.
3) He defines C as the aggregate of all wholly contingent facts (i.e., C is the mereological sum of all wholly contingent facts). I will follow that notation as well
4) By "God" I mean not what Koons means (i.e., "the necessary being included in the cause of the cosmos"), but "an omnipotent, omniscient, morally perfect uncaused being".
It seems to me that the definition I just provided resembles the most common usages of the word "God" among philosophers a lot more than Koons' definition, and that following the latter might be somewhat confusing in this context.
5) Unless otherwise stated, I will grant for the sake of the argument all of the mereological axioms that Koons' uses.
6) With regard to Koons' formulation, the details are developed in Koons' paper .
I will outline a somewhat different argument, simplified since I'm already granting that there are contingent facts, and also leaving the axioms and some of the steps implicit.
While that's not the way Koons' makes the argument, it's clear that the essential points are the same – assuming the implicit premises, etc., -, and the different formulation will have no impact on the substantive objections I will raise.
P1: Every wholly contingent fact F has a cause C(F)
C1: All the parts of a necessary fact are necessary.
C2: Every contingent fact has a wholly contingent part.
C3: C is a wholly contingent fact.
C4: C has a cause.
C5: Every contingent fact overlaps C.
C6: C has a cause that is a necessary fact.
One of the mereological axioms that Koons' uses, and which I will address in particular, is the following:
P0 states that a cause and its effect cannot overlap. Let's grant that, for the sake of the argument.
A consequence of that is the elimination of all causal relations between the parts of a mereological sum M from any causal account of M – i.e, none of the parts of M count as causes of M.
For instance, let's consider an arbitrary aggregate.
Let M(BHA, N) be the aggregate of the supermassive black hole at the center of the Andromeda galaxy and Napoleon.
A cause of M(BHA, N) is, for instance, Napoleon's mother.
While she's not a cause of all of the parts of the aggregate, she's a cause of one of them, and a cause of the aggregate too.
Now, let M(BHA, N, NM) be the aggregate of the supermassive black hole at the center of the Andromeda galaxy, Napoleon, and Napoleon's mother.
If someone asked for a list of causes of Napoleon, his mother and the black hole, actually Napoleon's mother would be on the list, since she's a cause of Napoleon, and Napoleon is one of the objects we're looking the causes of.
However, even though there is no object M(BHA, N, NM) over and above the three parts used to make up the aggregate, Napoleon's mother does not count as a cause of the aggregate.
In short, this procedure of taking arbitrary aggregates has the effect I mentioned: it removes actual causes from our causal account.
In the extreme case of taking the mereological sum or aggregate of all facts (let's call it "CAF"), all causes between the parts of CAF are eliminated from a causal account, since all facts overlap CAF.
Hence, the conclusion is that CAF is an uncaused fact.
If anyone finds the fact that we could just conclude that there is this big uncaused state of affairs surprising, all they need to do is keep in mind that we've just artificially eliminated all real causes from our causal account by the procedure of taking an arbitrarily large mereological sum, but that does not seem to tell us anything about reality.
P1 states Koons' causal principle, namely that every wholly contingent fact F has a cause C(F).
Koons' claims that there is plenty of evidence for the CP because we keep finding causes of wholly contingent facts, and that the category of wholly contingent facts is not gerrymandered.
However, the choice of the category actually seems unjustified.
What we keep finding causes of is just facts.
It's not as if we find causes of wholly contingent facts, but not of facts that aren't wholly contingent.
The facts whose causes we find may be wholly contingent – perhaps, so let's say they are.
But they're also facts in the universe. They're also contingent facts. And they're also not arbitrary mereological sums.
Maybe it's no coincidence that we keep finding causes of facts.
For instance, maybe we keep finding causes because all facts in the universe have causes.
Or maybe we keep finding causes because simply because we don't eliminate all actual causes from our causal account by the procedure of taking arbitrary mereological sums.
In any case, the question is: Why should we believe that arbitrary mereological sums of facts in the category "wholly contingent" have causes?
On that note, let's consider another category: contingent facts.
We keep finding causes of contingent facts.
Yet, it's not the case that we're justified in extending a causal principle to any arbitrary aggregate of contingent facts.
In fact, we can tell that such a principle would be false – at least, under the assumption that P0 is true:
CCF is obviously a part of CAF, and since CAF has contingent parts, it's contingent and it's a part of CCF.
So, it follows that CCF is equal to CAF.
Also, CCF is a contingent fact – since it has contingent parts.
That means that there is a category of facts – namely, contingent facts – such that we keep finding causes of them, and yet it's not true that we can extend a causal principle to any arbitrary aggregates of them.
Of course, another such category would be simply facts.
So, it seems that extensions to arbitrary mereological sums are suspect.
Why should we believe, then, that the category "wholly contingent facts" is unlike "contingent facts" or "facts" when it comes to extending causal principles to arbitrary mereological sums?
In other words, why should we believe that such an arbitrary sum of wholly contingent facts will not also yield an uncaused wholly contingent fact, as it does in the cases of the two other categories?
In yet other words, why should we believe that a procedure that has the effect of eliminating actual causes from our causal account will not eliminate all causes when applied to the category "wholly contingent facts", as it does when applied to, say, "contingent facts"?
In slightly different terms, we can put it as follows:
The previous constructions using the aggregate of all facts CAF, and the aggregate of all contingent facts CCF, give us examples of how improper it would be for us to ask for a cause of an aggregate, when we've just artificially eliminated all causes from our causal account by means taking arbitrary mereological sums.
However, there appears to be no good reason to assume that a procedure that will eliminate all wholly contingent causes, and all causes that overlap wholly contingent causes, from our casual account, will not in fact eliminate all causes from our causal account.
So, such causal principle seems to be unwarranted.
Also, the conceivability criterion suggests it's false, given that such a principle would entail a necessary cause, and the criterion in question suggests all causes are contingent.
However, there is no need to claim that the principle is false; a more cautious approach – which I prefer – is to take no stance on such causal principle involving an arbitrary aggregate.
On the other hand, if P0 is not true, then the CP is plausible if we assume no QM objection succeeds – though that assumption is itself debatable.
However, without P0, Koons' causal principle would be of no use to a LCA, since the causes of C might well be all wholly contingent and be parts of C.
Alternatively, someone who does not claim P0 might propose the following causal principle:
CP2: For every wholly contingent fact x, there is at least one cause y that does not overlap x.
However, the same reasons given above show that an extension to arbitrary mereological sums is unwarranted in this case as well.
So, in short, the previous considerations show that Koons' causal principle is unwarranted, and that is sufficient to block his mereological cosmological argument.
However, let's grant the CP for the sake of the argument, and assess the rest of his LCA:
2.4) God, other conscious beings, decisions, parts, and axiom 4
Let's consider any contingently true proposition; for instance, the proposition that there are no unicorns – if unicorns are impossible, any contingently true proposition will do.
Let's assume that God exists.
A question is: What is the actual fact that exists, then?
In other words, what is the concrete state of the world, which can enter into causal relations, etc.?
It seems that the actual, concrete fact that exists is an omnipotent being who – among other features – is aware of the negative condition  that there are no unicorns.
In other words, there is an actual state of the world consisting on an omnipotent being who – among other features – is aware of the who is aware of the negative condition that there are no unicorns.
Let's call that state SU.
Since God can exist in worlds at which there are unicorns, and SU can't, then by axiom 4, SU is not a part of God, and so it has a part SU2 that does not overlap God.
But what can be a part of a concrete state consistent of an omnipotent being who – among other features – apprehends that there are no unicorns, and which does not even overlap such being?
That seems absurd.
Someone might say that apprehending that there are no unicorns is not an essential property of God, but that would miss the point, which is that the actual state of the world is SU, and there appears to be no part of SU that does not overlap God, in any usual sense of parthood.
Alternatively, instead of the state of God's being aware of a negative fact, we could have chosen – for instance – the state of God's making a contingent decision, and the result would be similar.
Dropping now the assumption of God's existence, let's consider the case of any arbitrary conscious being – let's call her "Alice".
Let's say that Alice makes a conscious choice, D. Let's stipulate that there is a possible world W at which Alice exists but does not make decision D.
The actual, positive state of the world that exists consist in Alice's making decision D.
Yet, by Koons' axiom 4, and since Alice can exist without making decision D, then the actual state that consists in Alice's making decision D is not a part of Alice, and so it has a part that does not overlap Alice.
But what could be a part of the state consisting in Alice's making a conscious decision that does not overlap Alice?
That seems absurd as well.
So, it appears that axiom 4 is – at least – not justified, either.
Perhaps, someone might try to make a mereological LCA without axiom 4.
However, without axiom 4, Koons' argument concluding that all parts of a necessary fact are necessary, is blocked. And without that conclusion, even if planets, stars, etc., were contingent mereological parts of spacetime – for instance -, it wouldn't follow that spacetime is contingent.
In his paper, Koons' identifies the aggregate of all wholly contingent facts with the cosmos.
However, he uses "cosmos" in an unusual way, limiting the term only to what actually exists; he uses "universe" in such an unusual way as well. 
For instance, let's say that determinism is not true, and thus the future does not yet exist. Then, the aggregate of all facts – and hence, the cosmos, and the universe – does not include future facts.
However, since the cosmos, the universe and C are aggregates, they cannot exist unless all of their parts do, in light of axiom 4.
That means that, say, yesterday, the universe and the cosmos did not exist!
Only a part of them existed, but the universe or the cosmos did not.
Moreover, had you chosen not to read this essay – had you done something else instead – then the universe and the cosmos we live in would not have existed; different ones would have existed instead.
That's clearly not the result we'd get on any usual understanding of the words "cosmos" and "universe", even under the assumption of non-determinism.
Potentially confusing terminology aside, let's assess whether Koons' arguments provide any good reason to believe that the universe, or the cosmos – in any usual sense of the words – are contingent.
To make this a little bit more precise and avoid lack of clarity due to Koons' unusual usage of the words, let's use the word "universe" not in Koons' sense, but to denote all of space – whatever the number of dimensions turns out to be, or which theory of time is correct -, plus some laws like equivalences of energy and mass, conservation laws, or whatever laws actually hold.
Hypothesis H1 holds is that the universe is necessary, though stars, planets, Napoleon, etc., are contingent states of the universe. Perhaps, some fundamental particles are necessary, or one or more temporal dimensions; H1 takes no stance on that – as it takes no stance on which specific conservation laws are necessary.
Why should we believe H1 is false?
To be clear, I make no claim that H1 is true; my question is for the justification of a belief that it's false.
Granted, by axiom 4 and some other axioms, H1 entails that planets, stars, etc., are not mereological parts of the universe and thus have parts that do not mereologically overlap the universe.
Someone might say that all the particles we know of are contingent – they can cease to exist – and if so, then they could all cease to exist, and then the universe would cease to exist, so it's contingent.
However, the conclusion would be unwarranted.
Even if there are no necessary particles, there might be necessary laws by which those particles would turn into energy and/or other particles, and so on.
More generally, the universe might still exist, even if all of the particles had ceased to exist, transformed into something else according to some laws – which do not need to be deterministic: the laws might simply impose constraints on what can happen to a particle, without determining it.
Alternatively, someone might try to use the conceivability criterion as a means of supporting a claim that H1 is not true.
So, one way or another, there appears to be no good reason to believe that H1 is false – no good reason a theist defender of a LCA can use, anyway.
Still, someone might wonder whether some of Koons' arguments regarding what properties a necessary being would have, could provide a good reason to believe that the universe is contingent.
So let's assess those arguments:
Koons' maintains that it's reasonable to assume that what he calls "measurable" attributes can possibly be had in greater or lesser degrees, so that a necessary being would not have any measurable attributes by necessity.
On the other hand, he claims that a necessary being can have attributes that involve whole integers by necessity, like "existing at three persons".
In any usual sense of the word "measurable", attributes that involve whole integers are measurable, but leaving that aside, this seems like an ad-hoc construction to support Christianity – not to mention that there appears to be no good reason to think that "existing as three persons" is coherent at all.
But that aside, even if it made sense to exist as three persons, how does it matter that it does not make sense to exist as 3.01?
If it made sense to exist as 3 persons, it would made sense to exist as 4, or 5, or 2 persons.
But why would it be more reasonable to assume that no attribute that is part of a continuous spectrum can be had by necessity, but on the other hand, attributes that are whole integers can?
Someone who proposes that the universe might be necessary, might also suggest that maybe the total amount of mass/energy is not finite or is zero – considering negative amounts, and adjusting conservation hypotheses as required -, the number of dimensions is either infinite or a natural number, maybe space is infinite, or maybe it's finite but its volume is not necessary – only that there is space is necessary -, and so on.
Alternatively, or additionally, they might suggest that, perhaps, all attributes are discrete, so whether we use integers or other numbers to talk about them is merely a notational matter.
In short, there are still a number of alternatives, even granting Koons' claim.
However, alternatives aside, the main problem with this part of Koons' argument is the apparent arbitrariness of it all.
Why should we believe that necessity has anything to do with whether some attribute is part of a continuous spectrum?
That is enough to reject this particular argument, but there is another problem:
Koons provides no good reason to think that attributes like personhood and generally what he regards as not "measurable" are somehow ontologically different from other attributes.
For instance, someone can be an adult, or not be an adult.
Our language does not seem to consider that there is a continuum here.
However, it seems clear that one can have properties in different degrees, even in many cases in which our language is not adequate to express that.
For instance, there appears to be no "first nanosecond" at which the claim that a specific person is an adult is true. In other words, it seems there is no fact of the matter  as to exactly when a person becomes an adult. Our language is too imprecise for that.
What about, say, horseness?
It seems our language assumes no continuum. Horses evolved gradually from other animals.
Is there a fact of the matter as to what the first nanosecond at which a horse existed is?
In other words, is there a "first nanosecond" at which "horses exists" is true?
It seems very doubtful. The word "horse" seems not to be precise enough for that.
Of course, in that regard, the example generalizes to other species, like cats, humans or dogs – and there appears to be no good reason to suspect that person is any different.
Is there a first picosecond at which there was a person on Earth?
Even what's called "fast" evolutionary changes would probably be too gradual for words like "horse", and similar ones: any animal in the chain leading to horses was very much like its parents.
Moreover, even if there were a "first horse", that would not entail that there is a "first nanosecond" at which horses exist.
On that note, let's consider the process that goes from an unfertilized ovum to an adult horse – including the process of fertilization. Is there a first nanosecond, through that process, at which there is a horse?
Once again, that seems very doubtful – and we can take even periods shorter than a nanosecond.
If a theist claims there is a first nanosecond, yoctosecond, etc., at which there is a horse, it seems to me that they'd have to argue for it.
In short, we have the following:
a) If there are no continua in reality, then no attribute meet Koons' criterion for measurableness.
b) If – as it seems intuitively plausible – there are continua in reality, then they appear to be all around us.
Limitations of our language – such as the ones described above – do not imply ontological differences, and claiming that somehow horseness or personhood are not parts of a continuum while, say, volume is, is something that would have to be argued for.
c) In any case, there appears to be no good reason to believe that properties that are part of a continuum cannot be had by necessity, but properties that aren't can.
According to Koons', a necessary being is not essentially located in space or time.
A question is: What does he even mean by that?
However, it seems to me Koons would count that as located in the whole of space and time, or something along those lines.
So, what is he saying, then, when he claims that the necessary being that causes the cosmos would not be essentially located in space or time?
What would it mean for a being not to be located in space or time? 
Still, let's say that his claim is clear, and I'm just not getting it.
The fact remains that the argument he gives for the claim that a necessary being would not be essentially located in space or time assumes his previous claim, namely that a necessary being would not have what Koons calls "measurable" attributes necessarily – but that claim appears to be unjustified.
Still, let's stipulate, for the sake of the argument, that all of my previous objections fail, and that there is a necessary being N that caused what Koons' calls the "cosmos", and that N is not what I called the "universe".
Then, other questions arise, such as whether that entity is purposeful and intelligent; that's the matter of the next section:
But he provides no good reason to believe that there is an end, even if the universe is such that conscious life would eventually arise.
In fact, the vast majority of our universe is space, hostile to all forms of life.
And the places that could sustain some basic life, are in most cases hostile to conscious life.
Even on Earth, conscious life is fragile and very short-lived, compared with geological times, or times of existence of, say, black holes.
Why should we believe that our universe was created with the purpose of the development of conscious life?
We don't have evidence of the existence of "junk" universes, but we have plenty of evidence that the vast majority of our universe is extremely hostile to life, let alone to conscious lifeforms.
Surely, a sufficiently powerful being with an interest could create a realm that would be far friendlier to consciousness, if he wanted to.
Of course, someone could come up with all sorts of motivations for a creator. It's often not difficult to make up a story and say that a sufficiently powerful being did it for some mysterious reason – or just posit some reason, and if there is a problem, then change it, and so on.
Leaving aside the ad-hoc nature of those hypotheses, the question remains:
Why should we believe that an entity with such intentions exists, even if there is a necessary cause which caused the universe?
Koons makes two claims against an unconscious first cause: he claims that, given some "anthropic data", there are two possible explanations: a conscious designer and a first cause that caused a "junky cosmos", where there are universes with all possible sets of laws (or "natural laws", in his terminology).
He further claims that, in the case of the junky cosmos, induction would be demonstrable unreliable.
On the "junky cosmos" hypothesis, Koons does not explain why there would be more possible universes with the same past as ours in which the previous generalizations do not hold, than universes in which they do. How is he counting universes?
Furthermore, how is he attributing probabilities?
In fact, Koons does not even explain which universes are possible ones.
Is it every mathematical structure a possible universe?
If so, there are more than any cardinality.
How does Koons assign probability in such a space – let alone count the numbers?
Maybe it's not all mathematically structures, but something else.
Still, the problem remains: how can Koons know which structures count, or how to assign probability?
But let's leave that aside, and let's concede that a "junky cosmos" would be really bad for induction.
The problem is that the assumption that an unconscious necessary cause (let's call it "U") would entail a junky cosmos is unjustified, as is the assumption that somehow a conscious, purposeful and intelligent necessary first cause (let's call it "G") would somehow make our previous generalizations reliable.
In fact, G might choose to create universes that break apart at some point, so that all previous generalizations break apart. 
On the other hand, U might not have the causal power to make a junky cosmos. It might have the causal powers only to bring about universes with some laws, and even with laws that are very similar to those of our own universe. In other words, U itself might have necessary ordered laws.
Someone might claim that there is no good reason to believe that U might be like that.
But if so, we can similarly ask: What reason do we have to believe that G would want our inductive reasoning to be reliable?
Why would G not create a cosmos in which previous generalizations break apart at some point in all universes?
Or why would G not deceive us, making it look as though the universe is old, or putting us in a matrix, etc.?
Coming up with reasons for G not to do that and make our previous generalizations reliable would miss the point, for we can also come up with reasons for G to actually make any of the other, non-nice things; whether any reason we can come up with is persuasive to G depends, of course, on G's psychological (i.e., mental) makeup, and we can ask: "Why should we believe that G would have a "nice" psychological makeup?"
In short, assuming that there is an intelligent necessary being, why should we believe that G would be nice at all?
Someone might suggest that, in the case of an intelligent purposeful being we can use the intelligent purposeful beings we know of as a guide to ascertain what kind of properties G would have, including preferences, propensities, etc.
However, if we're justified in using objects we're familiar with as a guide, then as it turns out, the non-conscious objects we're familiar with only seem to have limited causal powers, and they're quite predictable.
Moreover, if we compare, say, physics with psychology – human psychology or the psychology or other animals -, we can tell that we can usually make more accurate predictions in general in the case of physics.
So, if an unconscious first cause N caused our universe – which, so far, is reasonably predictable -, then that gives us reasons to expect N to be the kind of non-conscious thing that predictably causes reasonably predictable effects.
Granted, it would still be a necessary brute fact without an explanation that N happen to be like that, but the same can be said in the case of the preferences of the alleged conscious necessary being G.
So, it seems the have no good reasons to believe that an intelligent G would make things any better than an unconscious N, in terms of the reliability of our previous generalizations. 
Moreover, in the case of G, if he were omnipotent and omniscient, we can conclude that he would not have preferences that are at all like those of (normal) humans – the problems of evil and suffering show that.
summary, even assuming a necessary being for the sake of the
argument, Koons' argument provides no good reason to believe that
said cause would be purposeful and intelligent, let alone God.
On the other hand, there are good reasons to believe that such a necessary being would not be God.
In this section, I will address the Leibnizian cosmological argument defended by William Lane Craig, and make some points that would apply to similar arguments as well.
Craig's formulation of the LCA is as follows: 
1) Anything that exists has an explanation of its existence, either in the necessity
of its own nature or in an external cause.
2) If the universe has an explanation of its existence, that explanation is God.
3) The universe exists.
4) Therefore, the universe has an explanation of its existence. (from 1, 3)
5) Therefore, the explanation of the existence of the universe is God. (from 2, 4)
Premise 1) is Craig's version of the PSR.
Craig explains that the principle only applies to things – i.e., beings -, not to all facts.
That indicates that Craig uses "fact" in the common sense of the word – usage I will follow throughout section 3 -; for instance, the non-existence of unicorns is a fact, but not a being.
A first objection to this PSR would be the threat from indeterministic interpretations of Quantum Mechanics.
But let's assume for the sake of the argument that QM objections fail, and let's take a look at Craig's PSR in more detail:
According to Craig, that's a "modest" version of the PSR, because it's limited to "things", which are classified in contingent and necessary.
But what's "the necessity of its own nature", and how does that constitute an explanation?
That's puzzling. What does it even mean?
Craig claims that mathematical objects would be good candidates for necessary things.
However, Craig provides no good reason to even suspect that sets, numbers, etc., should be called "things" in the same sense in which, say, a table is.
In fact, Craig does not claim they are, and claiming that they are would be incompatible with his views on time and infinity. 
Other theists may have different views on time an infinity, but it makes one wonder why Craig would bring up numbers and sets in the first place.
In any event, there is no good reason to believe that there is such thing as things being explained "by the necessity of their own nature", in the cases of numbers, etc.
For instance, perhaps, someone could ask: but why is it true that the empty set exists?
But as far as I can tell, that would be because the abstract scenario we're talking about – plausibly, the class of all hereditary sets – contains the empty set, simply because that's how that scenario – intuitively or explicitly – is defined.
But we may let all of that pass, and even assume that the previous understanding of mathematical existential claims is mistaken.
Even then, a reply like "the empty set exists because of the necessity of its own nature" would not seem to explain anything: it would be puzzling.
Moreover, let's suppose someone claims that there is a necessary concrete thing – a concrete thing that exists at every possible world -, and that the explanation of its existence is "the necessity of its own nature".
After the initial puzzlement, it seems to me that a reasonable question would be: but why is it necessary?Why does it exists at every possible world?
The question appears perfectly coherent, and it's not a good answer to insist that the explanation is that it exists because of the "necessity of its own nature" because that's only puzzling – i.e., it does not explain things -, and because the question is: why does it exist at every possible world?
I addressed this problem in more detail in section 1.2.5, so I will not repeat the points for the sake of brevity.
In brief, Craig's "modest" PSR appears very odd at best.
More modest alternative principle would be the following principles, which we could call the "Principle of Explicable New Things".
Someone could – purely for example -, hold that the PENT is true, or even necessary, and take no stance on Craig's PSR.
A more cautions approach would be to keep in mind that there is no need to have a general theory about categories of facts that have explanations; in particular, there is no need to hold any particular belief on whether the PSR, or some other principle, is true.
As I explained earlier, we can simply use our intuitions in particular cases.
Still, let's consider Craig's arguments in support of this "modest" PSR:
In order to support the PSR, Craig presents the example of a translucent ball on the forest floor, and claims that it would be bizarre to say that it exists without explanation.
That appears to be true, but what would be even more bizarre would be to say that the ball exists in the forest in all possible worlds, without any explanation other than "the necessity of its own nature".
How bizarre would that be?
How would that explain anything?
Making the thing an omnipotent person instead of a ball in the forest won't help, since it's still strongly counterintuitive, and this is so because the thing in question is claimed to exist at every possible world; that calls for an explanation.
Someone might think that we can intuitively tell that the translucent ball is not necessary, so it's not that "the necessity of its own nature" fails to explain things in general, but that we're intuitively rejecting the claim that the ball is necessary.
However, while it's true that we intuitively reject the claim that the ball is necessary, the point is that using our conceivability intuitions would yield the same result for a person, or any other thing, and so a claim that a thing exists at every possible world calls for an explanation.
Also and additionally, we can also intuitively reject a claim that the ball never came into existence, and then use the PENT to conclude that it has an explanation, or just use we're intuitions to conclude that a ball in the forest would have an explanation, without being committed to any general principle about explanations.
That is enough to reject Craig's LCA, but now let's grant Craig's PSR for the sake of the argument, and assess the rest of the argument, under that assumption:
Now, even granting the PSR, an infinite regress of explanations for all contingent beings is not ruled out.
Let's suppose a contingent being B(1) has an external contingent cause B(2), etc.
Someone could claim that there must be a cause of the whole chain and/or the mereological sum of the B(n), etc.
But then again, the whole chain might not be a being, so that blocks the argument.
Alternatively, if the whole chain is a being, there can be, of course, another contingent cause B(2,1), caused by B(2,2), and we can keep going.
But let's suppose someone claims that there is a cause of the whole chain, net, etc., of chains, nets, etc.
Once again, the problem is that there is no good reason to think that such an arbitrary aggregate would be a thing – i.e., a being -, and thus that the PSR would apply.
In fact, that Craig's PSR entails that not all arbitrary mereological sums of beings are beings, as long as the existence of a thing entails the existence of all of its parts.
For, let T be the mereological sum of all beings.
Now, T is not necessary, and it does not have an external cause.
Alternatively, one can take the mereological sum T1 of all concrete beings, and the same result follows.
I have no problem with a claim that arbitrary mereological sums of beings aren't beings, but the fact is that in that case, the sum is not covered by Craig's PSR.
Perhaps, someone could reject the assumption that a mereological sum cannot exist without all of its parts, further claim that the sums in question are beings, and then claim that T and T1 are necessary beings.
However, all of that that would have to be argued for, and in order to argue for that, the claimant would have to show that there is a necessary being. There appears to be no good reason to think so.
So, even granting Craig's PSR, Craig's LCA argument is blocked, and so are arguments based on relevantly similar PSR.
Someone could claim that an infinite explanatory regress is impossible, but that would have to be argued for as well.
That aside, let's also assume for the sake of the argument that there is indeed a necessary thing, and assess premise two.
According to Craig, the cause of the universe must be non-physical, non-material, and transcend space and time. 
This creates new problems:
What do all of that even mean?
These are not words that are used in common speech, and Craig provides neither a definition, nor a way to figure out that the claims mean.
For instance, it's not clear what it would even mean for an object to "transcend space and time", and trying to conceive of a mind without time appears to be an impossible task.
In short, it's not clear that this claim is even coherent. If Craig claims it is, he should explain what he means by it.
Craig also claims that only a mind or an abstract object can fit the description. 
it's not even clear how abstract objects can even be beings.
Leaving all that aside, another problem is that Craig appears to be trying to use the kinds of things we've encountered in order to make an assessment about what the cause of the universe could be – assuming there is one such cause.
However, if we're going to use the kind of things we're familiar with in order to make an assessment about what a necessary cause could be, someone might as well reason as follows:
1) Since all of the concrete beings we've encountered are at least partially physical, that gives us grounds to believe that all concrete beings are at least partially physical.
2) Since all of the causally effective beings we've encountered are at least partially physical, that gives us grounds for believing that all causally effective beings are partially physical.
3) Since all of the conscious beings we've encountered came into existence, that gives us grounds to believe that every conscious being came into existence.
4) Since all of the conscious beings we've encountered are contingent, that gives us grounds to believe every conscious being is contingent.
5) Since all of the concrete beings we've encountered – except, perhaps, the universe – came into existence, that gives us grounds to believe that either the universe did not come into existence, or that every concrete being came into existence.
There are more options, of course, but this is just a sample of the problems the theist faces.
That aside, there are yet even more problems with Craig's arguments:
Craig claims that the explanation of the universe must be a transcendent – whatever that means – mind without a body, and that that's what most people traditionally meant by "God".
However, the claim that that's what's traditionally been called "God" is puzzling.
In fact, it's not even clear what he means by "traditionally"; whose people is he talking about?
For most of history, the vast majority of people did not even have the concept of an unembodied creator of the universe, for instance.
Perhaps, he's talking about most people in the US?
If so, many people would not call such an entity "God" unless he's also – for instance – morally good, or compassionate, or even omniscient, or at least intelligent, or self-aware.
Craig provides no good reason to suspect that most people traditionally meant by "God" what he claims they meant.
Second, and definitions aside, if
it's true that only abstract objects and a mind can have the required
properties – assuming the universe is contingent -, that mind
would not even have to be self-aware, let alone intelligent.
In fact, it could just be some very basic type of consciousness, with no memory, no self-awareness, and basically no intelligence at all.
Why would it create the universe, someone might ask?
But that would be because its only causal powers are to create a limited range of things, very much like the universe, and it has – as a brute fact – a propensity to do that.
To be clear, I'm not suggesting that, under the assumption that the universe has an external cause, we would be warranted to conclude that it's that kind of cause.
Rather, what I'm saying is that even making the assumption that the universe has an external cause, and granting that Craig's claims are coherent, etc., we would still have no good reason to conclude that there is a creator that is remotely like any religion has ever called "God", or even intelligent.
Someone could often come up with reasons as to why an intelligent being would want to create a universe such as ours; that does not work if the being is also omnipotent, omniscient, and morally perfect, but leaving that aside, the question is: why would the necessary cause have the kind of mind that finds those reasons appealing?
That would be just a brute fact, with no explanation – and if the "explanation" is the "necessity of its own nature", then similarly, a simple non-intelligent, non-self-aware, no-memory, basic consciousness with a propensity to create things like our universe would be "explained" by the "necessity of its own nature" - yet theism would be false.
In short, the assumption that the universe is contingent appears to be unjustified, Craig's description of the necessary cause may not even be coherent, and even leaving both those points aside, we wouldn't be warranted in reaching the conclusion that there exists anything remotely like what any religion has ever called "God", or anything even intelligent.
That said, let's assess Craig's arguments in support of his claim that the universe is contingent:
Craig first argues for the contingency of the universe based on conceivability: he oddly claims that a possible world at which no concrete object exists seems conceivable. 
Of course, that would entail that God is either conceivably not existing, or an abstract object.
Still, maybe that claim was just a typo, so let that pass.
Craig also claims that we usually trust our modal intuitions, and that if a non-theist claims that the universe is an exception and we should not trust our modal intuitions in that particular case, then he would have to provide some reason for his skepticism.
Since our modal intuitions lead us to the conclusion that there is no necessary being, and in particular that God is not necessary, the non-theist can simply trust them at least in absence of defeaters, and leave it to the theist to make his case against our modal intuitions.
And even if there is justification for the belief that a necessary being exists, then that alone shows that our modal intuitions fail – and badly -, so it would be up to the theist to explain why God and not the universe or any of the other possibilities is a better candidate for a necessary concrete thing – i.e., why our modal intuitions failed just in the way that would make theism true, and not instead in any other of many potential ways.
That aside, Craig makes more arguments for the contingency of the universe, so let's see how they fare against hypothesis H2: (for instance; there are many options)
H2: Space is necessary – whatever its actual number of dimensions turns out to be -, as well as the laws of the universe – whatever the actual laws are, if our models are only approximations.
H2 is compatible with the claim that some particles more fundamental than quarks and/or some temporal dimensions are also necessary, but that's not part of the claim.
Why should we believe H2 is false?
Craig claims that at a certain point in the past, none of the objects we observe existed.
Well, space did. Time obviously did. Mass/energy did too. And so on.
Essentially, that the particles we know did not exist makes no dent on H2; even if no particle existed, that does not affect H2.
Craig then claims it's easy to conceive a world in which all of the quarks in an object can be replaced by other quarks, and that a universe consistent of a totally different collection of quarks is not the same as ours.
But actually, if all of the quarks decay or are transformed into energy by some process – whatever that process is -, and later new quarks form, that does not affect the claim that space is necessary, that the laws are, etc., or that we would still be in the same universe.
In other words, Craig's scenarios do not undermine H2, let alone show it to be false. And H2 is just one possibility, among many we could come up with – including necessary spacetime and/or strings, branes, etc.
In any event, all these arguments are still arguments from conceivability, and the conceivability criterion does not help LCA, for the reasons explained in the present subsection, and earlier in this article: namely, the conceivability criterion supports the claim that all existent things are contingent.
Given that no stipulative definition of terms like 'metaphysically possible', 'metaphysically necessary', 'metaphysically impossible' is provided, we need to use examples of propositions that fall under such categories in order to grasp the meaning of such terms, and also to present hypotheses about their meaning.
So, I will briefly try to analyze what the terms mean.
Clearly, we can tell the following, for any proposition P.
a) P is metaphysically necessary if and only if ¬P is metaphysically impossible.
b) P is metaphysically possible if and only if P is not metaphysically impossible.
So, it's enough to try to figure out what it means for P to be metaphysically impossible.
We know that if P is logically impossible (i.e., if P logically entails a contradiction), then it's metaphysically impossible.
However. there are propositions that are metaphysically impossible, but not logically so.
A classical example of this is PW: = "Water is not H2O".
Clearly, one can posit a hypothetical scenario that states that scientists are mistaken and water is not H2O, but XYZ, which is a different compound. That hypothetical scenario is not contradictory.
take into consideration that water is H2O at the actual world, then
we can tell that it's impossible that water is something else at some
Moreover, even if we don't know that water is H2O, we can tell, by the meaning of the word 'water', that if water is ABC at the actual world (whatever ABC is), then it is metaphysically impossible that water is not ABC at some other world.
The same can be said about other examples, for instance that gold has some atomic number, etc.
But that seems to suggest that, despite the name 'metaphysical possibility' (or necessity, or impossibility), to say that P is metaphysically impossible is to say that it's logically impossible given the meaning of the words, including cases in which the meaning is such that the referent in the actual world fixes the properties in all worlds.
For instance, the meaning of 'water' is such that 'water' stands for whatever we call 'water' in the actual world. So, it can't be something else, given that.
But if that is the correct account of modal impossibility (and thus, modal possibility and necessity), then it seems clear that there is no necessary being, since there is no contradiction in stating that there is no being at all.
Perhaps, someone could object that numbers, propositions, etc., exist, and that it's contradictory to say otherwise, or at least contradictory after we consider the properties of the referent in the actual world.
I do not agree. The number 5 (for instance) exists in the set of rational numbers, but not in the set of negative integers. Saying that 5 exists at some world or another would be at best obscure. Worlds would need to be scenarios that include abstract constructs as well as beings that exist 'out there', to use a non-philosophical but hopefully clearer expression than 'mind-independent'.
In any case, we do not need to get into that. We can simply posit that there is a possible world at which no concrete particular exists, since 'no concrete particular exists' is not contradictory (if anyone claims otherwise, the burden would be on them, but that seems very clear), and it seems to me that no matter what the properties of those particulars at the actual world are, the conclusion remains the same.
Note that this is not at all like the 'water is not H2O' example; even without knowing that water is H2O, we can tell that it's impossible for water to be anything but whatever it is at the actual world, and we can tell that by the meaning of the word 'water'.
But on the other hand, if 'God' means something like 'an omnipotent, omniscient, morally perfect being', then saying 'God does not exist' is not contradictory.
might object to that and say that perhaps 'God' means something like
'a being that exists necessarily, and with such-and-such properties'.
But that would not seem to work; by the meaning of some words, the referent at the actual world fixes the properties that the thing in question would have at every world, not whether such being exists in any given world.
Perhaps, another way to see that is the following: let's say that there is an actual concrete particular, and let's name it 'Bob'. Now, Bob exists at the actual world, and has some properties P1, ..., Pn (or infinitely many ones; that's not the point). Regardless of which properties are fixed by 'Bob' (if any), even assuming such fixing, the fact remains that a stipulation 'Bob does not exist' appears not to be contradictory.
Granted, someone might argue for a hidden contradiction, but that would have to be argued for.
Also, someone might argue that the previous account of metaphysical modality is incorrect; I do not see any counterexamples, though. At least, by the way I grasp the terms, the above account seems correct. I would invite readers to look for any such counterexamples (of course, someone might reply that the counterexample is precisely God. But doing that would look like special pleading).
Going by the previous understanding, it seems clear to me that the PSR is also false, unless infinite regresses of explanations satisfy it. For instance, the proposition 'there are concrete particulars' is contingently true, but plausibly there is no explanation for why it's true, except perhaps for an infinite regress.
In any case, I would like to briefly address once again an issue that I considered before:
Let us suppose that someone claims that a being B exists at every possible world, and furthermore, that there is no explanation at to why B exists.
Granted, others may have different intuitions on the matter, but the claim in question would seem bizarre to me, unlike a claim that, say, states there is some world W at which an entity E exists without an explanation, but E does not exist at some other world W' (for instance).
Based on the previous considerations, one can safely conclude all the variants of Leibnizian Cosmological Arguments – and many others, which are relevantly similar – provide no support for theism: While this article focuses on some specific LCA, most if not all other LCA seem to be relevantly similar to at least one of the previous arguments, and so they're likely covered by one or more of the objections I presented, and which consider not only Pruss', Koons', and Craig's arguments, but a number of potential variants.
Whether or not the claim that the necessary being in question is a certain kind of rational agent is part of a LCA is a terminological matter. Given that the arguments for a necessary cause and/or explanation are usually given in support of theism, I think the inclusion is adequate.
Pruss, Alexander, "The Leibnizian Cosmological Argument", in "The BlackWell Companion to Natural Theology", Edited by William Lane Craig and J. P. Moreland, © 2009 Blackwell Publishing Ltd. ISBN: 978-1-405-17657-6. Pages 24-100.
Pruss, Alexander, "The Leibnizian Cosmological Argument", in "The BlackWell Companion to Natural Theology", Edited by William Lane Craig and J. P. Moreland, © 2009 Blackwell Publishing Ltd. ISBN: 978-1-405-17657-6. Page 25.
Pruss, Alexander, "The Leibnizian Cosmological Argument", in "The BlackWell Companion to Natural Theology", Edited by William Lane Craig and J. P. Moreland, © 2009 Blackwell Publishing Ltd. ISBN: 978-1-405-17657-6. Page 54.
Here, Pruss challenges an implication of one of van Inwagen's premises, namely Pruss challenges "(27) If q explains p, then q entails p" 
Pruss, Alexander, "The Leibnizian Cosmological Argument", in "The BlackWell Companion to Natural Theology", Edited by William Lane Craig and J. P. Moreland, © 2009 Blackwell Publishing Ltd. ISBN: 978-1-405-17657-6. Page 51.
Pruss, Alexander, "The Leibnizian Cosmological Argument", in "The BlackWell Companion to Natural Theology", Edited by William Lane Craig and J. P. Moreland, © 2009 Blackwell Publishing Ltd. ISBN: 978-1-405-17657-6. Page 52.
Pruss, Alexander, "The Leibnizian Cosmological Argument", in "The BlackWell Companion to Natural Theology", Edited by William Lane Craig and J. P. Moreland, © 2009 Blackwell Publishing Ltd. ISBN: 978-1-405-17657-6. Page 58.
Craig, William Lane, and Sinclair, J.P, "The Kalam Cosmological Argument", in "The BlackWell Companion to Natural Theology", Edited by William Lane Craig and J. P. Moreland, © 2009 Blackwell Publishing Ltd. ISBN: 978-1-405-17657-6. Page 106.
I don't think that they should be counted as "beings" in the sense that is relevant to a LCA, or that "exists" is used in the same way and to talk about objects in the same domain – i.e., what some might call a mind-independent world, the world "out there" so to speak.
However, there is no need to settle any of that.
If numbers, propositions, etc., are beings, then one can just substitute "concrete being(s)" for "being(s)" in the relevant parts of this article, and the points are the same (e.g., the conceivability criterion supports the contingency of all concrete existent beings).
If the description is insufficient to pick a specific being and, for some reason, we can't just assume that it has some other properties and is one specific being - but why not? theists do that with God...-, then let's call any omnipotent being who isn't morally perfect and doesn't care at all about moral good or evil, a "gok"; the relevant points are unaffected.
Whether a conceivability objection against theism would work is a different matter, but that's beyond the scope of this article.
Pruss, Alexander, "The Leibnizian Cosmological Argument", in "The BlackWell Companion to Natural Theology", Edited by William Lane Craig and J. P. Moreland, © 2009 Blackwell Publishing Ltd. ISBN: 978-1-405-17657-6. Page 43.
There is no need to present an alternative account – it's enough to show that the proposed account of modality shouldn't be accepted -, but I will propose a tentative hypothesis:
a') A state of affairs S is metaphysically possible iff S is logically possible once we've accounted for words in which some of the properties of the referent are fixed by those the referent actually has or had (this depends on the meaning of particular words, of course).
b') A state of affairs S is metaphysically necessary iff ¬S is not metaphysically possible.
For instance, on this account, "Water is XYZ" is necessary if and only if it's true at the actual world, because of the semantics of the term "water", which let the actual properties fix the referent.
Of course, it would still be difficult in some cases to ascertain whether something is metaphysically possible, since sometimes the semantics of a term may not be difficult to study.
So, someone could wonder whether this account could shed any light on the subject, or is just trivially true.
I think this account – if correct – would make claims of metaphysical possibility much less obscure or mysterious – and, perhaps, suggest that the also obscure name "metaphysical possibility" may be misleading.
To be clear, if this account turns out to be false, then the case against Leibnizian cosmological arguments succeeds just as before because the arguments against LCA I make in this article do not assume that this account of metaphysical modality is true, or use it in any way.
Does reason-giving in moral argumentation – say, why it's immoral to cheat on one's partner, under such-and-such conditions – is a way of giving explanations in the same sense of "explanation" in which, say, one can explain a mass extinction pointing to the impact of an asteroid?
There is no need to settle the matter here.
I will assume no equivocation; if there is one, then both the arguments given in support of a LCA incurring that error and my reply can simply be ignored.
Pruss, Alexander, "The Leibnizian Cosmological Argument", in "The BlackWell Companion to Natural Theology", Edited by William Lane Craig and J. P. Moreland, © 2009 Blackwell Publishing Ltd. ISBN: 978-1-405-17657-6. Pages 45, 46.
Pruss, Alexander, "The Leibnizian Cosmological Argument", in "The BlackWell Companion to Natural Theology", Edited by William Lane Craig and J. P. Moreland, © 2009 Blackwell Publishing Ltd. ISBN: 978-1-405-17657-6. Pages 47-50.
Pruss, Alexander, "The Leibnizian Cosmological Argument", in "The BlackWell Companion to Natural Theology", in "The BlackWell Companion to Natural Theology", Edited by William Lane Craig and J. P. Moreland, © 2009 Blackwell Publishing Ltd. ISBN: 978-1-405-17657-6. Page 55.
Pruss, Alexander, "The Leibnizian Cosmological Argument", in "The BlackWell Companion to Natural Theology", in "The BlackWell Companion to Natural Theology", Edited by William Lane Craig and J. P. Moreland, © 2009 Blackwell Publishing Ltd. ISBN: 978-1-405-17657-6. Pages 80-81.
Pruss, Alexander, "The Leibnizian Cosmological Argument", in "The BlackWell Companion to Natural Theology", in "The BlackWell Companion to Natural Theology", Edited by William Lane Craig and J. P. Moreland, © 2009 Blackwell Publishing Ltd. ISBN: 978-1-405-17657-6. Pages 81-82.
Pruss, Alexander, "The Leibnizian Cosmological Argument", in "The BlackWell Companion to Natural Theology", in "The BlackWell Companion to Natural Theology", Edited by William Lane Craig and J. P. Moreland, © 2009 Blackwell Publishing Ltd. ISBN: 978-1-405-17657-6. Page 83.
Pruss, Alexander, "The Leibnizian Cosmological Argument", in "The BlackWell Companion to Natural Theology", Edited by William Lane Craig and J. P. Moreland, © 2009 Blackwell Publishing Ltd. ISBN: 978-1-405-17657-6. Page 61.
Pruss, Alexander, "The Leibnizian Cosmological Argument", in "The BlackWell Companion to Natural Theology", Edited by William Lane Craig and J. P. Moreland, © 2009 Blackwell Publishing Ltd. ISBN: 978-1-405-17657-6. Page 65
Moreover, I'm assuming it's a chain rather than some much more complex structure – perhaps, we could call it a "net" -, also for the sake of simplicity. Proposing other alternatives would not make things easier for the theist – on the contrary, they would have even more cases to argue against -, so the simplification is acceptable.
Pruss, Alexander, "The Leibnizian Cosmological Argument", in "The BlackWell Companion to Natural Theology", Edited by William Lane Craig and J. P. Moreland, © 2009 Blackwell Publishing Ltd. ISBN: 978-1-405-17657-6. Page 67.
Pruss, Alexander, "The Leibnizian Cosmological Argument", in "The BlackWell Companion to Natural Theology", Edited by William Lane Craig and J. P. Moreland, © 2009 Blackwell Publishing Ltd. ISBN: 978-1-405-17657-6. Page 50.
Religious Studies 37, 485–90.
Pruss, Alexander, "The Leibnizian Cosmological Argument", in "The BlackWell Companion to Natural Theology", in "The BlackWell Companion to Natural Theology", Edited by William Lane Craig and J. P. Moreland, © 2009 Blackwell Publishing Ltd. ISBN: 978-1-405-17657-6. Pages 79-80.
Pruss, Alexander, "The Leibnizian Cosmological Argument", in "The BlackWell Companion to Natural Theology", Edited by William Lane Craig and J. P. Moreland, © 2009 Blackwell Publishing Ltd. ISBN: 978-1-405-17657-6. Pages 91, 92.
By "moral agents" I mean agents who have moral properties.
Most humans are moral agents. Crocodiles aren't. Vulcans and Klingons would be.
But would Skynet be a moral agent?
Maybe the writers made Skynet similar enough to humans to count as one.
Would a real AI made by aliens, or any rational alien from another planet, be a moral agent?
Maybe. Or maybe not. It's not clear to me.
But let's assume, for the sake of the argument, that all rational agents – or sufficiently intelligent rational agents – are moral agents – else, that alone blocks Pruss' argument for the goodness of the first cause.
Pruss, Alexander, "The Leibnizian Cosmological Argument", in "The BlackWell Companion to Natural Theology", Edited by William Lane Craig and J. P. Moreland, © 2009 Blackwell Publishing Ltd. ISBN: 978-1-405-17657-6. Page 96.
A first problem with this assumption is that N1 can't actually explain the BCCF, because the BCCF does not appear to make sense, but let's say that there is a way around that – via BCCF* or something else.
I have no objection to the claim that people often can and do act of their own free will, but I maintain that that has nothing to do with what libertarians call "free will".
Here, I'm using the word "fact" in a usual sense of the word in this context, not in the sense in which Koons uses it.
That there are no unicorns is a fact in the usual sense of the word "fact".
However, in Koons' terminology, it is not. It's what Koons calls a "negative condition".
On the other hand, a being who is aware of such negative condition is a fact, in Koons' terminology.
Koons, "A new look at the cosmological argument", American Philosophical Quarterly 34: 193–211; page 21.
In subsection 2.8, I will use "universe" in the same unusual sense in which Koons' uses the word.
Ironically enough, actual religions like Christianity usually deny that, say, the findings of science will hold in the distant future, and often even question whether we can tell that they will hold in the near future.
For instance, they usually claim – with no good reason, but leaving that aside – that in the future the dead will rise again, and/or the universe as we know it will cease to exist, and so on.
Moreover, their claims usually imply that we don't even really know whether the Earth will be orbiting the Sun a decade from now: what if Jesus comes back first, and ends it all?
After all, according to their beliefs, nobody knows the exact date...and that's not even counting more "mundane" miracles, which are also a rejection of previous generalizations.
While a generic form of theism is not committed to such claims, the fact  is that actual forms of theism usually do lead to a selective rejection of induction.
Let's suppose that numbers are things.
Craig maintains that an actual infinity is impossible, that time will continue indefinitely, and that numbers aren't capable of causal interaction.
If all those beliefs are correct, then there is a greatest natural number, say k, and no new numbers will come into existence – since numbers aren't capable of any causal interaction.
However, in the future, eventually at least k+1 events will have occurred, k+1 years will have passed, and so on. Hence, there will be more past years and past events than natural numbers. But that's an absurd conclusion.
To be clear, Craig does not claim that numbers, propositions, etc., are things. But then, why bring that up at all?
Even if there were such intuition, it seems to me it would be suspect.
It's a truism that we should trust any of our intuitions unless we have good reasons not to.
But modern physics has precisely show that our intuitions about causation, time and space are suspect when it comes to the very small, or the very massive.
That does not cast doubt on our intuitions in daily life, when we don't have to deal with anything like that – subatomic phenomena happen all around us, but in daily life we never deal with individual or a few particles in isolation.
However, it does cast doubts in
the case of the universe, which is surely massive, and used to be
Moreover, if there happens to be some kind of multiverse, this object would be radically different from the things we encounter in daily life – even if they're contained in it -, and there would seem to be no good reason to believe our intuitions would work when considering the multiverse as a whole – not our pretheoretical intuitions, at any rate.
Still, there appear to be no such intuitions, so this is a side note.