Conceivability, Possibility, and the Ontological Argument

I don’t want to go into a full-dress exposition of the ontological argument, because I think it would be distracting to a simple yet decisive objection to it. For our purposes, then, we can express its structure crudely as follows:

1. It’s possible that there is a necessary being.
2. If it’s possible that there is a necessary being, then a necessary being exists.
3. Therefore, a necessary being exists.

The argument is valid; so, if its premises are true, its conclusion follows of necessity. Well, what reasons can be offered for the premises?

Premise (2) is just an instantiation of Axiom S5 of S5 modal logic. The underlying idea of Axiom S5 is that what is necesssarily the case doesn't vary from possible world to possible world: if something is necessary in one possible world, it's necessary in every possible world. I accept Axiom S5; so I accept premise (2). That leaves us with premise (1). Is it more reasonable to believe it than not -- or at least: is it more reasonable to believe it than to suspend judgment either way?

No, it isn’t. For the evidence is supposed to be that it’s conceivable that such a being exists, and that whatever is conceivable is possible. Now there are a lot of points that could be brought up here, but I want to limit myself to one point based on recent work in modal epistemology, i.e., the study of how our beliefs about what is impossible, possible, and necessary are known and/or justified.

There are many objections, both classical and contemporary, that have been raised against inferences from conceivability to possibility. For example, in the past, people were able to conceive of the Morning Star existing without the Evening Star, or water existing without H20. So if everything conceivable were possible, it should follow that it’s possible for the Morning Star to exist without the Evening Star, or water without H20. But we now know that these things are impossible, since the Morning Star is the Evening Star, and water is H20.

Another example: Goldbach's Conjecture is the mathematical hypothesis that every even number greater than 2 is the sum of two primes. To date, no mathematician has proven that Goldbach's Conjecture is true (nor have they proven that it's false). Now I can conceive, in some sense, that Goldbach's Conjecture is false. I can also imagine that it's true. So if all inferences from conceivability to possibility are valid, then it follows that it's both possible for Goldbach's Conjecture to be true, and possible for Goldbach's Conjecture to be false -- in other words it would follow that Goldbach's Conjecture is only contingently true if true at all. But that can't be right, for mathematical statements are necessarily true or necessarily false if true or false at all!

Thus, it looks as though we need some criterion of legitimate conceivings to screen out illegitimate conceivings, thereby preserving the utility of inferences from conceivability to possibility.

A lot of progress has been made over the past several decades in the sub-field of modal epistemology, but for our purposes, it’s enough to mention one key distinction that’s been developed that’s helpful. Stephen Yablo[1] and James Van Cleve[2] have each pointed out that there’s a distinction between not conceiving that P is impossible, on the one hand, and conceiving that P is possible, on the other. Van Cleve calls the former, ‘weak conceivability’, and the latter, ‘strong conceivability’.

Now it turns out that pretty much all of the counterexamples to the conceivability-possibility inference are cases in which something is weakly conceivable. For example, when one says that they can conceive of Goldbach’s Conjecture being true, and that they can conceive of it also being false, they really mean that they can’t see that either conception is impossible – i.e., they only weakly conceive of such things. The same goes for conceiving of water existing without H20, and conceiving of the Morning Star existing without the Evening Star. By contrast, I can strongly conceiving of my car as being red, and of myself as a person who doesn't like to surf (albeit just barely!); thus such conceivings provide prima facie evidence that it's possible for my car to be red, and that I really could have been a person who doesn't enjoy surfing.

In light of this distinction, then, we can handle the counterexamples by limiting conceivability-possibility inferences to those that involve what is strongly conceivable – i.e., to those in which one intuits that p is possible, and not to those in which one merely fails to intuit that p is impossible.

With the weak/strong conceivability distinction before us, let’s consider premise (1) again. Is it strongly conceivable that there is a necessary being -- i.e., do we "just see" that it is possible? It doesn’t seem so. Rather it merely seems weakly conceivable – i.e. I merely can't intuit that such a being is impossible. But this isn’t enough to justify the key premise (1) of the ontological argument. For that to be so, a necessarily existing individual would have to be strongly conceivable.

To come at the point from another direction: Christian theistic philosopher Peter Van Inwagen asks us to imagine a being whom he calls 'Know-No'. Know-No is a being who knows that there are no necessary beings. If such a being is possible, then a necessary being is impossible. For then there would be a possible world in which a being knows that there is no necessary being. And if he or she knows it, then it's true that there's no necessary being.

Now both possibilities can't be true -- either a necessary being is possible, or a being like Know-No is possible, but not both, since the possibility of each one precludes the possibiliity of the other. But notice: both possibilities are conceivable in the weak sense: on reflection, I fail to see an incoherence in the conception of either one. So, if weak conceivability were sufficient evidence for possibility, it would follow that I'm justified in believing that necessary beings and Know-Nos are both possible, which, as we've just seen, is false -- if either one is possible, the other is impossible. Thus, again, the notion of a necessarily existent individual is only weakly conceivable, and weak conceivability isn't good evidence for possibility.[3]

Thus, it looks as though the ontological argument is not a successful piece of natural theology. Whether or not the key premise is true, I don’t have sufficient reason to think so. Thus, the argument is of no help in the task of justifying theism.
[1] “Is Conceivability a Guide to Possibility?”, Philosophy and Phenomenological Research 53 (1993), 1-42.
[2] “Conceivability and the Cartesian Argument for Dualism”, Pacific Philosophical Quarterly 64, (1983), 35-45.
[3] This objection to the ontological argument can be found in Peter Van Inwagen's textbook, Metaphysics, 2nd edition (Westview, 2002).

Outline of Hume's "Of Miracles"

Section X, Part I: 
0. Introductory stuff: 
0.1 Quick summary of theologian John Tilotson's argument against Transubstantiation. 
0.1.1 Scripture and tradition are based on the testimony of the apostles 
0.1.2 But the evidence of testimony is always weaker than the evidence of the senses 
0.1.3 So, even if scripture and/or tradition tell us that the bread and wine turn into the body and blood of Christ, the evidence of the senses tells us that they remain bread and wine: they have all the sensible properties of bread and wine; nothing more. 
0.1.4 Therefore, since the evidence of the senses trumps the evidence of testimony, it is unreasonable to believe in Transubstantiation. 
0.2 Hume claims that he has found an argument of similar force and nature, but against the rationality of belief in miracles in general: "I flatter myself, that I have found an argument of a like nature, which, if just, will, with the wise and learned, be an everlasting check to all kinds of superstitious delusion, and consequently, will be useful as long as the world endures. For so long, I presume, will the accounts of miracles and prodigies be found in all history, sacred and profane." (p. 73) 

1. Setup: key notions and principles stated and explained: 
1.1 On the nature of experiential evidence in general 
1.1.1 Experiential evidence, which concerns matters of fact, is not infallible, but can lead to errors. 
1.2 There exists the whole spectrum of frequency of conjunction between antecedent and consequent event-types. 
1.3 The cases of uniform conjunction between antecedent and consequent warrant and/or cause full assurance/full proof. 
1.4 Cases of anything less: The evidence of non-uniform events yields only probability: 
1.4.1 procedure for determining the probability of such cases: consider the cases in which events of type A and events of type B are experienced to be conjoined consider the cases in which events of type A obtain without events of type B Deduct the latter from the former. The resultant ratio maps onto the probability and degree of assurance with respect to the event. Full uniformity cases = proofs; any other type of case has some degree of probability, from very high to very low, depending on the frequency with which the two types of events are conjoined. 
1.4.2 But if there is this range/spectrum, then the wise man proportions his belief according to the evidence; he doesn’t give full assurance to every experienced conjunction of events of type A and type B. 
1.5 Experiential evidence of testimony in particular 
1.5.1 The justification of testimony (i.e., as a reliable source of information): experienced conjunction between testimonial reports and verification of the facts reported: S testifies that p, and I observe that p is in fact the case. 
1.5.2 As testimonial evidence is founded on experience, it, like any other kind of experiential evidence, runs the range from proof to probability: some types of testimony cases are uniformly true, and others are less than uniform. 
1.6 Some causes of contrariety of accurate and inaccurate testimony reports, (and so) causes of testimony to be merely probable. 
1.6.1 Problems with the testifier(s): 
1.6.2 conflicting reports 
1.6.3 the character/quality of the witnesses 
1.6.4 the quantity of witnesses 
1.6.5 the manner in which the witness reports the fact 
1.6.6 a combination of two or more of the above 
1.6.2 Problems with the event testified to: when the event reported is unusual: in general: the stronger evidence destroys the weaker, and the “winning evidence” is diminished in proportion to the degree/extent of the defeated evidence. in cases in which the quality and quantity of testimony is also (apparently) impeccable: “proof against proof” cases. Mutual destruction of the opposing arguments. The stronger of the two proofs prevails. types of unusual events: marvelous events: not contrary to experience, but also not conformable with it. miraculous events: violations of laws of nature 

2. The argument against the rationality of testimony-based belief in miracles 
2.1 Laws of nature are matters of fact for which we have uniform experience of events of one type constantly conjoined with events of another type 
2.2 But miracles are, by definition, violations of laws of nature – they’re events that go against our uniform experience 
2.3 Miracles are, then, events against which there is a full proof from experience. 
2.4 Therefore, (by our principle above) if the evidence from testimony for a miracle is to prevail against the full proof from experience against miracles, it must be a stronger proof. 
2.5 (General maxim:) (i) This requires that it would be more of a miracle that the testimony is false, than that the miracle that the testimony reports didn’t occur. (ii) Even if it is, its evidence must be diminished in proportion to the strength of the proof against it. 

Section X, Part II 
2.6 But, in actual fact, there has never been testimonial evidence for a miracle that amounted to a full proof; no miracle satisfies the maxim. This is seen in light of the following four lines of reasoning: 
2.6.1 Reason #1: Insufficient quantity and quality of testimony: the basic argument: The testimony for a miraculous event M satisfies the general maxim if and only if: (i) there is a sufficiently large group of testifiers for M; (ii) the testifiers all (a) have unquestioned good sense, (b) have education and learning that is sufficient to assure us that they aren’t self-deluded, (c) such that their integrity is so great as to preclude any suspicion that they would try to deceive us, and (d) of such substantial credit and reputation that they would have a lot to lose if they were caught in deceiving others; and (iii) M occurred (a) in such a public manner, and (b) in a part of the world so celebrated, as to make detection of deception unavoidable. No M satisfies clauses (i)-(iii). Therefore, there is no testimony for an M satisfies the general maxim. The testimony for an M is rationally acceptable iff it satisfies the general maxim. Therefore, no testimony for an M is rationally acceptable. 
2.6.2 Reason #2: violates general principles of rationality, viz.: (i) unobserved events resemble observed events, (ii) the most frequently observed events/objects are the most probable; (iii) where there are an opposition of arguments, we ought to give preference to the one that has the most experiments in its favor (i.e., to the most frequently observed event/object). but since miracles don’t satisfy these clauses, they flout these principles. oddly, although this maxim is usually followed with respect to testimony of “unusual and incredible” events, when it comes to testimony of miraculous events, pathological mechanisms go into effect among the vulgar, and these subvert these general principles. 
2.6.3 Further details on “the known and natural principles of credulity and superstition”: the pathological mechanisms relevant to reason #2: the passion of surprise or wonder its agreeable nature tends to cause belief of reports that cause it (such as is the case with miracle reports). the pride, admiration and delight received by telling such stories. when the love of wonder is attached to the “spirit of religion”: religious persons who are also enthusiasts: prone to delusion. “Sees things that aren’t there” willing, with the best of intentions, to persevere in perpetuating a falsehood for the sake of promoting a holy cause vanity and self-interest can result in the same effect as the previous. those who hear and evaluate his reports often don’t have the judgment to verify his reports critically and adequately. they are usually willing to suppress principles of sound judgment for “sublime and mysterious subjects”. even when they’re willing to be critical, “passion and heated imagination disturb the regularity of its operations.” “positive feedback loop” of credulity and impudence: “their credulity increases his impudence, and his impudence overpowers their credulity.” religious teachers and preachers often speak eloquently. But eloquence appeals entirely to “the fancy or the affections, captivates the willing hearers, and subdues their understanding”. propagation ensured by “the pleasure of telling a piece of news so interesting, of propagating it, and of being the first reporters of it.” (cf.. the “marriage reports” illustration) men of sense reject testimony of miracles. They conform to the maxim, because they are familiar with the pathology underlying these reports, and so these mechanisms don’t kick in and undermine conformity to the maxim. 
2.6.4: Reason #3: the fact that such testimonial reports tend to abound in areas where ignorant, uncivilized, uncultured people live generates a presumption against their probability. Where civilized cultures accept such reports, they always trace back in time to reports from ignorant ancestors. The civilized believe them because of: an “inviolable sanction and authority, which always attend received opinions” the universal tendency to think that the world operated differently in the past: what doesn't occur in one's own era may have occurred in an earlier one. In reading of the first history of any nation, "we are apt to imagine ourselves into some new world; where the whole frame of nature is disjointed, and every element performs its operations in a different manner, from which it does at present." In reality, the events of the past were not marvelous events, different from the present. People either lied, or were more ignorant and credulous than we are. Notice that recorded history progressively contains fewer and fewer miraculous reports, until we reach the present, where none occur. The diminishing of reports of marvelous and miraculous events through history, up to the present moment (when only few such reports occur) corresponds to the diminishing of ignorance and credulity in society, and the increase of reason and modernity. 
2.6.5 an account of the origination and propagation of miraculous stories: someone lies (or is deluded, or mistaken…?) about the occurrence of some unusual, incredible event the credulous and ignorant in the population (especially in remote and barbarous regions) receive the report as true the reasonable among them don’t think the story worth investigating…at least not until so much time has gone by, that it is impossible to disprove Foolish people are “industrious in propagating the imposture”. The previous four factors make it possible for the lie to go on. Later, the factors of distance in time and place from the origination of the story prevent those who hear of it from gaining better information as to what happened, than the fantastic reports they receive. the stories are exaggerated as they are passed down “and thus a story, which is universally exploded in the place where it was first started, shall pass for certain at a thousand miles distance.” 
2.6.6 Reason #4: The miracles of the various religions cancel out each other’s epistemic force there are miracle testimonies at the foundation of every religion. They function as verifications of the truth of a religion. Since the religions contradict each other, if we were to assume that any one of the miracle reports of one religion were true, then that religion would be true, and all the other religions would be false. So, the miracle reports of all the other religions must also be false. This logic iterates to each religion, since the evidential force of the miracle testimony for each religion is roughly the same. But if so, then no miracle report is to be believed: they cancel each other out. As the late J.L. Mackie nicely paraphrased Hume’s analogy with respect to this point: “it is as if a law court were presented with, say, twenty witnesses, each of whom was denounced as a liar by the other nineteen.” Mackie, J.L. The Miracle of Theism (Oxford: OUP, 1982), p. 15.

A Priori Naturalism, A Priori Inerrantism, and the Bible

Christian apologists often complain about New Testament critics who bring an a priori rejection of the supernatural to their studies of the New Testament. The underlying rationale, I take it, is that such a presupposition will determine a non-supernatural historical reconstruction of Jesus before they even begin their historical investigations. But if the historical Jesus turns out to be the miracle-working, resurrected Son of God that conservative Christians take him to be, such an assumption will lead them to construct a historically inaccurate conception of Jesus.

I agree with them in this regard: one shouldn't assume what can or can't be true on empirical matters before one even begins one's investigations. Although it's probably unavoidable that we bring assumptions about reality to all of our empirical inquiries, we should hold them tentatively, and allow them to be altered in light of our findings.

Of course, this assumes that supernatural events, if they occur, are capable of empricial detection, but I grant that they are detectable, at least in principle (I say this as someone who has read his Hume).

I also agree with them that there are some NT critics who do reject the supernatural a priori (e.g., the members of the Jesus Seminar, Gerd Ludemann, etc.). Having said that, however, I'd like to make three points with respect to naturalism, a priori commitments, and NT studies.

First, many New Testament critics do not assume that supernatural events do not or cannot occur; rather, they have principled reasons for thinking that, even if they do occur, the evidence for such events is never sufficient to establish their occurence. There are two ways to construe the 'never' here: never in practice and never in principle (both construals go back, of course, to Hume's famous essay "Of Miracles" in his Enquiry Concerning Human Understanding). Now one may disagree with their arguments on these matters (I tend to think that Hume's "in principle" argument is too strong, although I think his "in practice" argument has considerable force), but that's not the point. Rather, the point is that apologists too often attack straw men here, viz., by attributing to NT scholars a metaphysical basis for their conclusions, when in fact they're often based on epistemological considerations.

Second, although some NT critics do base their non-conservative conclusions about Jesus in particular or the New Testament in general on an a priori rejection of the supernatural, they need not do so. In fact, many don't. Indeed, there are plenty of NT scholars who are also serious Christians, yet who nonetheless reject the doctrine of inerrancy, based on their research.[1] In other words, non-conservative views of Jesus and/or the New Testament are supportable merely from applying ordinary historical methodology. For example, one can see how the geneologies and pre-birth narratives in Matthew and Luke contradict both each other and established historical fact in order to make theological points. The same goes with John versus the synoptic gospels on the day and time of Jesus' crucifixion: John changes it in order to fit his theological theme of Jesus as the Passover "Lamb of God" (I know that inerrantists argue against these discrepancies. I have no desire to argue with them in vain. I merely ask them to read a sufficiently representative sampling of NT scholarship outside of their conservative circles). Also, once one does their source-critical homework, they can see how, e.g., Matthew and Luke modified the portrait of Jesus they inherited from Mark and Q, and how John went even further. Thus, a non-conservative account of Jesus in particular and the New Testament in general often results from ordinary, non-controversial use of source criticism, redaction criticism, and the criteria of authenticity -- it need not be based on an a priori rejection of the supernatural. Complaints about "ruling out the supernatural a priori" are therefore something of a red herring.

Finally, if some NT critics are guilty of an a priori commitment to naturalism, many conservative NT scholars are guilty of an a priori commitment to inerrancy. Yet many apologists don't seem to mind when the latter determines the conclusions of conservative NT scholars. This leads one to question the sincerity of apologists in their criticisms of a priori commitments creeping into NT scholarship. For again, the basis of their criticism appears to be that such a priori commitments are liable to result in an inaccurate historical reconstruction of Jesus, should the person of Jesus turn out to be in conflict with those commitments. But if that is the basis of their criticism, then they should be equally diligent in their criticisms of conservative scholars who have an a priori commitment to inerrancy -- and to a conservative view of Jesus in particular and the New Testament in general. In other words, the potential danger here is not naturalistic a priori commitments, but a priori commitments per se.

But it's hard to deny that there is an a priori commitment to inerrancy among the majority of conservative NT scholars. For one thing, many of them work at conservative seminaries, where one must subscribe to and even sign extremely conservative doctrinal statments in order to obtain and keep one's job. Such scholars can't let an admission of errancy through the door, no matter what the data, and no matter what sort of convoluted just-so stories are required to reconcile a given set of biblical texts.[2] Thus, it's a bit odd to hear apologists complain about a priori committments determining one's portrait of Jesus, when their own a priori committments determine their own portrait of Jesus.

To sum up: Christian apologists have a point worth hearing when they criticize certain NT critics for bringing an a priori commitment to naturalism to their studies. For one should let the empirical data about Jesus and the NT materials speak for themselves, lest one's conclusions be determined from the get-go, quite possibly distorting the data in the process. However, the apologists have failed to see that the point about a priori assumptions is a perfectly general one, and can't be limited to naturalism. And this entails that conservative NT scholars need to abandon a priori assumptions about inerrancy and orthodoxy when they come to their study of the empirical data, lest they, likewise, allow their assumptions to determine their conclusions from the get-go, quite possibly distorting the data along the way. The lesson is that all sides of the debate should hold their theoretical commitments tentatively, not forcing the pieces of evidence to fit within them when the fit is unnatural. Rather, one's assumptions should be malleable, and even disposable, thereby allowing the data to speak to us clearly, unmuffled.
[1] Examples include Raymond Brown, Dale Allison, James D.G. Dunn, John Meier, and Luke Timothy Johnson.
[2] For many examples of such just-so stories, see, e.g., Craig Blomberg's The Historical Reliability of the Gospels, Norman Geisler's When Critics Ask, and Gleason Archer's Encyclopedia of Bible Difficulties.

William Lane Craig on the Origin of the Belief in Jesus' Resurrection

I had a brief moment between grading stacks of papers, so I thought I'd make a quick point:

One argument that William Lane Craig uses as a part of his case for Jesus' resurrection can be summarized as follows:

The origin of belief in Jesus' resurrection must have been derived from either Christian sources, Jewish sources, or from experiencing Jesus as risen from the dead. But the belief couldn't have been derived from Christian sources, for Christianity didn't arise until after (or simultaneous with) the belief that he had risen from the dead. Nor could it have been derived from Jewish sources, since the Jews had no concept of a single individual being resurrected prior to the general resurrection at the end of time. Therefore, it must have arisen from experiences that they took to be of a resurrected Jesus.

The argument can be expressed a bit more carefully as follows:

1. If belief in Jesus' resurrection was due to something other than experiences as of Jesus risen from the dead, then the belief was derived from either Christian influences or Jewish influences.
2. If it was derived from Christian influences, then Christianity existed prior to itself.
3. Christianity didn't exist prior to itself.
4. Therefore, it wasn't derived from Christian influences. (From 2 and 3)
5. If it was derived from Jewish influences, then the idea of a single individual rising from the dead before the end of time was extant in Jewish belief prior to Christianity.
6. The idea of a single individual rising from the dead before the end of time was not extant in Jewish belief prior to Christianity.
7. Therefore, it wasn't derived from Jewish sources. (From 5 and 6)
8. Therefore, the belief wasn't derived from either Christian influences or Jewish influences (From 4 and 7)
9. Therefore, belief in Jesus resurrection was not due to something other than experiences as of Jesus risen from the dead (From 1 and 8)

As you can see, this argument is deductively valid. However, it looks to be unsound, as at least one of its premises looks to be false, viz., premise (5). For as a number of NT critics have pointed out, and as is fairly clear from the writings of the NT itself, the earliest Christians believed that Jesus' putative resurrection was (to use Paul's terminology) the "first fruits" of the general resurrection of the dead at the end of time. This is an agricultural metaphor. When farmers reaped and ate the first fruits of the harvest, they would then reap the full harvest the very next day -- the "general" harvest was "imminent", as it was "inaugurated" with the reaping of the first-fruits. Similarly, the earliest Christians believed that the final judgement and the general resurrection were imminent, given their belief that Jesus' resurrection was itself the inaugurating event of the general resurrection and the end of all things. Thus, contrary to what Craig says on this matter, there is a continuity between the beliefs of the early Christians and the beliefs of many Jews of his time: Jesus' resurrection was fundamentally construed in these eschatological terms.[1] And of course, as Craig acknowledges, the idea of a general resurrection at the end of time was a common Jewish belief at the time. Thus, premise (5) is false, and the argument is unsound.

In short, the answer to Craig's question, "Where did the Christians get the idea of a single resurrection prior to the end of time?" is: "They didn't. They construed Jesus' putative resurrection as the inauguration of the general resurrection at the end of time, which of course was a popular, traditional Jewish idea in Jesus' day. That's why Paul called Jesus 'the first-fruits' of the resurrection, and partially why Paul and the early church in general believed that the end of time was imminent."[2], [3]
[1] Which conforms nicely with the hypothesis/research program, held my the majority of NT scholars for the last century, that Jesus was fundamentally an eschatological prophet. See my earlier post for a brief sketch of some of the other evidence in support of this hypothesis.
[2] Question: But where did the earliest Christians get the idea of an imminent eschaton to begin with? Answer: From Jesus' fundamental message: "Repent, for the kingdom of heaven is at hand!" For a nice introduction to the research program of Jesus as an eschatological prophet, see Bart Erhman's Jesus: Apocalyptic Prophet of the New Millenium (Oxford, 1999). For more details, see Dale Allison's Jesus of Nazareth: Millenarian Prophet (Fortress, 1998).
[3] Others have critiqued premise (6), on the grounds that in the NT itself -- viz., Matthew 14:1-2 -- Herod believes that Jesus is John the Baptist risen from the dead(!):

"1At that time Herod the tetrarch heard the reports about Jesus, 2and he said to his attendants, "This is John the Baptist; he has risen from the dead! That is why miraculous powers are at work in him."

But if so, then if the passage is historically accurate, then it's not true that the idea of a single individual rising from the dead before the end of time was not extant in Jewish belief prior to Christianity. In other words, premise (6) is false.

Problems for the Fine-Tuning Argument

By my lights, the following considerations are sufficient to show that the argument from fine-tuning fails to make theism more likely than not.

There is an equally good, rival explanation of the apparent fine-tuning of our universe. For the fine-tuning for life would be equally well explained if our universe were embedded in a vast “sea” of infinitely many other universes.[1] Imagine a natural process or mechanism that continually generates universes (call it a 'cosmos generator') – perhaps something like a giant quantum field. Each time it pumps out a universe, it gives a random combination of values to its fundamental constants of nature. So on this hypothesis, infinitely many other universes exist – or at least lots and lots – and each one has a different set of values for its fundamental constants. Most of these universes have no life, since only a few possible combinations of values of the constants are life-permitting. But some do (e.g., ours). If so, then the explanation for why our universe is "fine-tuned" for life is that we exist in one of those few cosmoi – out of the trillions upon trillions of cosmoi that exist -- that has the “right” combination of values. This hypothesis is just as good as the hypothesis of intelligent design, since it's a hypothesis that explains all of the same data; so we have no persuasive reason to prefer the hypothesis of intelligent design to this one.

Objection 1: We've never seen such a multiverse, and we have no good evidence that it exists.

Reply: This objection fails to see that the point of constructing these theories in the first place is precisely because we have no way of directly observing the cause of the apparent fine-tuning of the fundamental constants of our universe. And it's just part of the nature of such theories that they accrue probability just to the extent that they can explain the range of data in question. Thus, it's not true that we have no evidence that a multiverse exists. Rather, the extent to which it can explain the data *just is* the grounds for according it some degree of probability. And the same is true of the theistic hypothesis, of course -- we only have reason to think that *it* is probable to the extent that it can explain the data of apparent fine-tuning. That's what the theory-data relationship is all about.

Obection 2: The hypothesis of a cosmos generator only pushes the problem of apparent fine-tuning back a step. For a cosmos generator would be a very complex and intricate process/mechanism. If so, then we would need an explanation for the fine-tuning of the cosmos generator itself.[2]

Reply: (i) Of course, we can just stipulate that, as a part of our hypothesis, the cosmos generator has its laws and constants *of necessity*, i.e., that there is only one possible set of laws and constants for the cosmos generator. It’s not important that this stipulation is independently known to be true; it need only be a hypothesis with no features for which we have independent reason to think false or impossible. Why is it ok to make these stipulations? Because it's a *theory* constructed to explain a range of data, and that's just the way it is with theories in general. And notice: This is both true of this hypothesis and the designer hypothesis -- both theism and naturalism are treated in the argument as sort of large-scale scientific hypotheses that were generated to explain some fundamental features of the universe. (ii) But even if one rejects the "necessary laws" stipulation -- i.e., that the laws governing the nature and functioning of a cosmos generator must be contingent -- the objection is still pretty dubious. For it's an objection that applies equally well to the theistic hypothesis. For both hypotheses grant that there is some brute, unexplained order that can have no further explanation -- the structure and the laws governing the cosmos generator on the naturalistic hypothesis, and the intellect and will of God on the theistic hypothesis.[3]

Objection 3: OK. But even if we grant that both hypotheses are saddled with some brute order that can have no further explanation, still, the theistic hypothesis is *simpler* than the naturalistic “cosmos generator” hypothesis. For on the cosmos generator hypothesis, the explanation of the apparent fine-tuning of our universe requires that there are lots and lots of other universes -- perhaps infinitely many. By contrast, the theistic hypothesis explains the apparent fine-tuning of our universe in terms of just a single entity: the god of traditional theism. Thus, even granting that theism leaves unexplained and brute at least *some* order (God's intellect and will), it's a much more economical/parsimonious explanation of the data of apparent fine-tuning.

Reply: The objector mistakenly assumes that there is only one kind of theoretical parsimony, viz., *quantitative* parsimony (i.e., the explanation postulates fewer entities). However, as David Lewis has taught us, another type is *qualitative* parsimony (i.e.,the explanation postulates fewer *kinds* of entities). And while the theistic hypothesis is a much more *quantitatively* parsimonious explanation of the data (it explains all of the data in terms of just one entity, viz., a god), the naturalistic cosmos generator hypothesis is a more *qualitatively* parsimonious explanation of the data (since it explains all of the data solely in terms of one *kind* of entity, viz., material objects). And it's not clear which type of theoretical parsimony is more important here.

Thus, it seems to me that the theistic and multiverse hypotheses are roughly equally likely given the data of fine-tuning.
[1] This line of reasoning is based on Peter Van Inwagen's in his Metaphysics, 2nd edtion (Westview, 2002).

[2] Notice that this is precisely the naturalistic version of the objection to the design argument that the theist is unwilling to countenance as legitimate to her own hypothesis of design (i.e., the "who designed the designer?" objection).

[3] This seems to me where the real force behind the "who designed the designer?" objection lies: both theism and naturalism are saddled with at least *some* brute order; so why fault naturalism with a "problem" that applies equally well to theism?

Design Arguments: Old and New

The Design Argument

There are two broad forms of the design argument:

1.The Classical (“Old School”) Design Argument:

Paley’s is the most important version of the classical design argument. This version is an argument from analogy. It typically appeals to living organisms and their parts as cases of apparent design. The line of reasoning here can be put as follows:

We come to learn through experience whether an object has been intelligently designed. How do we learn to detect design? Well, over a long course of experience, we notice a constant conjunction of a cause of one type (intelligent designers) producing an effect of a certain type (complex objects whose parts work together to perform a function). Thus, after a while, we no longer have to observe a person designing an object in order to know that the latter has been designed. Rather, we can then legitimately *infer* that, say, a watch was fashioned by an intelligent cause. For we can then justifiably base such an inference on an inductive argument based on the observed constant conjunction of the cause-type of intelligence and the effect-type of complex objects whose parts work together to perform a function.

Now for the punchline. If we have come to know, via uniform experience, of this constant conjunction of intelligent causes producing the effect of complex objects whose parts work together to perform a function, then what must we conclude about living organisms and their parts -- things such as the marvelously intricate structures of cells, eyes, bird's wings, whole organisms, and even whole ecosystems? For these resemble the artifacts that we know to be designed, in that they, too, are incredibly complex entities whose parts work together to perform a function. For Pete's sake, think of the workings of a cell! We now know that it's functionally equivalent to (in the words of Michael Denton) "a self-replicating machine factory"! Thus, since living things relevantly resemble human artifacts, and the latter are intelligently designed, then we can't rationally avoid concluding that the former are intelligently designed as well.

In short, our basis for thinking that objects such as watches, cars, and computers are designed is an inductive inference based on our experience of a constant conjunction of a certain type of cause (intelligence) and a cerain type of effect (complex objects whose parts work together to perform a function). And our grounds for thinking that living organisms and their parts are designed is based on an argument from analogy between watches, cars, and computers on the one hand, and living organisms and their parts on the other.

The argument can be expressed as follows:

1. Human artifacts are intelligently designed.
2. Living organisms and their parts relevantly resemble human artifacts (in that they both are complex and their parts that work together to perform a function).
3. Therefore, probably, living organisms and their parts are intelligently designed as well.

This form of the design argument is seldom used today, due to a number of criticisms. But the most forceful criticisms come from David Hume (see his masterful Dialogues Concerning Natural Religion), and Charles Darwin.

Some of Hume's most forceful criticisms are these: (i) since the argument is an argument from analogy, the likelihood of the conclusion turns one the degree of similarity between the two things compared in the premises. Unfortunately, the degree of similarity between artifacts and organisms is too low to warrant a confident inference to the intelligent design of the latter; (ii) even if they were simillar enough to infer design, the conclusion wouldn''t justify an inference to full-blown theism -- let alone orthodox Christian theism. Thus, even if the argument worked, it wouldn't show that the designer is immaterial, all-powerful, all-knowing, perfectly good, or even that there is just one designer; nor would it show that the designer is the creator and/or sustainer of the universe -- or even that the designer still exists.

But the most forceful criticism appears to be the one from Darwin -- i.e. the strong empirical evidence for biological evolution. If biological evolution is true, then the complex, apparently purposive structures and organisms we find in the biological realm don't require explanation in terms of (at least) the direct causation of a divine designer (although we'd need another explanation of the *origin* of living organisms, since the latter wasn't the result of mutation and natural selection. Whether there is or could be a natural explanation for the origin of living things, I don't pretend to know).

However, philosophers have come up with a new version of the design argument, one that doesn't fall prey to most of these objections, viz.:

2. The Contemporary (“New School”) Design Argument:

This version is not an argument from an analogy, but rather an abductive inference to the best explanation (and thus isn't subject to the "weak analogy" objection). For purposes of simplicity of discussion, we can say that, roughly, one hypothesis H1 is a better explanation of a range of data D than another hypothesis H2 if we would *expect* D more if H1 were true than we would if H2 were true.

According to this version of the design argument, then, certain features of the universe are treated as data, and then various hypotheses are offered to explain the data. It typically appeals to non-living aspects of the universe as cases of apparent design (and thus isn't subject to the "evolution" objection). The most common sorts of phenomena appealed to in such arguments is the range of fundamental constants of nature -- in particular, the extremely precise values they have, and must have in order for life to arise in the universe.

There are anywhere from 20 to 50 (or so) such features of the basic structure of the universe. Each of these has to have a mind-bogglingly precise numerical value in order for life to evolve in the universe. The following is a small sampling of these features:

-the strong nuclear force: this is the force that binds protons and neutrons together within the nucleus of the atom.

-If the strengthened or weakened by 1% or more: would reduce the amount of carbon and oxygen produced by stars, so that carbon-based life would not be possible; nor would any oxygen-breathing organisms be able to exist.

-the weak nuclear force: this force controls, among other things, the fusion of protons. It’s current strength prevents stars from exploding, and allows them to burn slowly.

-if slightly weaker: stars wouldn’t produce the requisite light, heat, and heavy elements. The universe would be largely composed of just helium

-if slightly stronger: stars wouldn’t produce the heavy elements

-the cosmological constant: this constant relates to the rate of expansion of the universe due to the Big Bang.

-If expansion rate were increased by more than one part in 10120: matter couldn’t clump together to form galaxies. This would mean no stars, which would mean no planets, and thus no habitat for life to exist

-If the expansion rate were decreased by more than one part in 10120: all of the matter in the universe would clump together into one giant clump before the relevant types of stars could form

-other examples include the strength of gravity, the mass of a proton, the fine structure constant, the electromagnetic force constant, and the total density of the universe.

If the numerical values of these, and any of the other constants, were increased or decreased – often just by a fraction – then no life at all could have arisen in the universe. Thus, it looks as though the basic structure of the universe has been “fine-tuned” in order for life to evolve within it.

The two hypotheses typically proposed to explain the data of fine-tuning above are (i) intelligent design and (ii) non-intelligent, natural causes. Thus, the Best Explanation version of the design argument can be expressed as follows.

Let ‘D’ denote some range of phenomena or data that needs explaining. For example:

D: The universe is fine-tuned for the existence of life (i.e., there are a large number of fundamental constants of nature. The value had by each of these is contingent, and independent the others. Each value is just one among an extremely large range of possible values, and each constant had to be assigned the value it has (or one very, very close to it) or no life would have arisen in the universe.)

Let ‘H1’ and ‘H2’ denote competing hypotheses offered to explain D:

H1: The fine-tuning of the universe is due to intelligent design.
H2: The fine-tuning of the universe is due to non-intelligent factors, such as chance and necessity.

Then we can state the abductive, inference-to-the-best-explanation version of the fine-tuning argument simply as follows:

1. The truth of H1 would lead us to expect D, but the truth of H2 wouldn’t lead us to expect D.
2. Therefore, H1 is a better explanation of D than H2.

Outline of the Standard Evangelical Case for the Reliability of the New Testament

I'll probably return to this post a lot to fill in the details and provide explanation, but I just wanted to put something on my blog that provides a way to see the standard case at a glance.

The Reliability of the Orthodox “Portrait” of Jesus according to Evangelicals: The Basic Case[i]

1. From our Current Bibles to the Church Fathers: Textual Criticism
1.1 The Argument from Textual Criticism
1.2 The Argument from Patristic Quotation

“Okay, that gets us back to within a few centuries of the life of Jesus. But how do we know that our information about Jesus wasn’t corrupted prior to that?”

2. From the Church Fathers to the Gospels: The Argument from Patristic Testimony of Apostolic Authorship

“Okay, but the case for apostolic authorship is shaky and widely rejected. Are there other reasons to think that the gospels give us reliable eyewitness testimony about Jesus?”

3. From the Gospels to Their Immediate Sources:
3.1 The Argument from Markan Priority and the Dating of Luke-Acts
3.2 The Argument from Source Criticism: Mark, Q, M and L
3.3 The Sherwin-White Argument for a Stable Reliable Core of Information

“Okay, that gets us to information about Jesus that’s about two to three decades old, and many believe that the circumstances of the NT make Sherwin-White’s argument inapplicable in this case. Are there other reasons to think that such information is reliable?”

4. From the Gospel’s Immediate Sources to the Oral Tradition
4.1 The Argument from the Nature of Jewish Oral Tradition[ii]
4.2 The Argument from Studies of Oral Cultures
4.3 The Argument from Aramaisms
4.4 The Argument from Poetic Forms
4.5 The Argument from a Pre-Easter Tradition

“Okay, if these arguments work, then there is a general presumption of reliability in favor of the gospel materials, since they are based on reliably-preserved eyewitness information that goes back to the time of Jesus. But these arguments are widely disputed. Are there other reasons to believe that the sources behind the gospels are reliable if we’re not convinced by them?”

5. From the Oral Tradition to Jesus: The Argument from the Criteria of Authenticity[iii]

“Okay, but many people dispute that the criteria of authenticity establish the reliability of the quantity of passages that you claim. What if they’re right and many passages don’t give us reliable information about the words and deeds of Jesus?”

6. The Worst Case Scenario:
6.1 The Argument from the Minimal Core of Passages Accepted by the Radical NT Critics[iv]
6.2 The Argument from Coherence with Ancient Creeds and Hymns Preserved in the Epistles

[i] This case can be found in, for example, Blomberg’s The Historical Reliability of the Gospels (and summarized in chapter form in several apologetics books), Marshall’s I Believe in the Historical Jesus, the relevant chapter in Moreland’s Scaling the Secular City, Blomberg’s chapter in Craig’s Reasonable Faith, and Boyd’s Cynic Sage or Son of God?.

[ii] After this point, it’s often argued that a presumption in favor of reliability is established, and so the burden of proof is on anyone who challenges the inaccuracy of a given passage. In the next section, an argument is given to show that even if one is not convinced that this is true, general reliability can be established via the criteria of authenticity while constantly having to shoulder the burden of proof. Thus, there is a dilemma: either the burden of proof is established here or it isn’t. If it is, then in each case reliability can be upheld by argumentation when challenged. If it isn’t, then in each case reliability can be established by proper application of the criteria of authenticity. Either way, then, the gospels can be shown to be reliable. Blomberg often uses this argument, but I think it goes back to at least Marshall.

[iii] At this point, many apologists (e.g., Moreland) argue that even if one is still unconvinced of general reliability, the minimal set of authentic sayings widely accepted by most NT critics still prevents total skepticism about knowledge of Jesus. For even if you only accept sayings that pass the criterion of dissimilarity -- which even the most radical NT critics accept as a reliable tool for gleaning historical information -- you are still left with most of the parables some other sayings. These are about the kingdom of God and Jesus’ relation to it. And this picture of Jesus is in keeping with the orthodox one. Thus, no matter which way you slice it, the NT gives us a reliable picture of Jesus.

[iv] Which is usually based upon just the use of the criterion of dissimilarity.

On the Force of "Possibly" in Plantinga's Free Will Defense (Slightly Revised)

Plantinga construes the key claim in his Free Will Defense as possibly true:

(TWD) Possibly, every creaturely essence suffers from transworld depravity.

According to Plantinga, if a creature suffers from transworld depravity, then *every* God-accessible world (i.e., every world *that God can create*)) is one at which the creature goes wrong at least once.

So if some free creature FC is transworld-depraved, then we have:

1) Necessarily, if God actualizes FC, then FC goes wrong at least once.

And if every creature is transworld-depraved, then we have:

2) Necessarily, for any x, if x is a free creature, then if God actualizes x, then x goes wrong at least once.

If so, then if Plantinga is using "possibly" in (TWD) in the metaphysical sense (as in (1)), then (TWD) amounts to:

3) Possibly, it's necessary that for any x, if x is a free creature, then if God actualizes x, then x goes wrong at least once.

But Plantinga accepts S5 modal logic. If so, then he accepts the following axiom of S5 modal logic:

(AS5) If it's possible that P is necessary, then P is necessary.

But if so, then by (3) and (AS5), (TWD) reduces back to (2):

2) Necessarily, for any x, if x is a free creature, then if God actualizes x, then x goes wrong at least once.

But this can’t be what Plantinga meant to assert, can it? For now we don’t just have a defense – we have a theodicy. For we have an account that’s not just possibly true, but necessarily true. And you can’t have a stronger theodicy than one that’s necessarily true.

The problem, though, is that it’s implausible to think that (2) is true: is there some shortage of souls, such that there is no possible creaturely essence, such that there is at least one possible God-accessible world at which it never sins? Plantinga grants that there are possible worlds at which free creatures never sin; it’s just that none of them are worlds that God can actualize. Is this really plausible?

I think that this problem (in addition to some things that Plantinga says) leads many to say that Plantinga's "possibly" shouldn't be construed as *metaphysical* possibility (i.e., that there is, as a matter of fact, at least one possible world at which it's true), but rather as *epistemic* possibiliity (i.e., *we can't rule it out*, given all our evidence, that it's metaphysically possible).

Now the relevant notion of epistemic possibility can be construed in at least two ways:

(Strong EP) We're not quite justified in thinking that P really is metaphysically possible; however, we're not justified in thinking that P is metaphysically impossible, either -- given our evidence, it could go either way.

(Weak EP) We're not justified in thinking that P is possible; however, although it's implausible to think that P is possible, we can't *conclusively* rule it out that P is possible.

Of course, the theist hopes that (TWD) is at least strongly epistemically possible; if it's merely weakly epistemically possible, one wonders how interesting the Free Will defense really is ("Sure, it's pretty far-fetched to think that every essence suffers from transworld depravity, but it hasn't been *conclusively* ruled out as imposssible -- hooray!")

The problem is that the same objections arise all over again for the strong epistemic possibility construal: it seems implausible that it's metaphysically possible. It seems that there are infinitely many free creaturely essences that God could actualize; are we to think that *every one of them* is such that *all* of the worlds in which they always freely do right are inaccessible to God? And as I’ve mentioned before, it looks to be a part of conservative Christian theology that angels exist, are free, and that some never sin. But if so, then it’s not necessarily true (because it's not *actually* true) that all free creatures are transworld depraved. Thus, it looks as though it might not be an option for theologically conservative Christians to believe it’s strongly epistemically possible. Even if the Old and New Testaments don't force belief in a doctrine of sinless angels, it needs to be pointed out (again) that Christians who endorse Plantinga's Free Will Defense have no choice but to reject such an idea.

What about weak epistemic possibiity: is it true that we can't *conclusively* rule it out that every creaturely essence would freely go wrong in all God-accessible worlds? Well, maybe for non-theists, some non-Christian theists, and some moderate and liberal Christians. But it doesn't seem to be weakly epistemically possible for theologically conservative Christians (recall the problem of angels who always freely do right).

What, then, does Plantinga's Free Will Defense really show? In light of the previous discussion, just this: for people who aren't theologically conseverative Christians, it's not conclusively ruled out as impossible that the Free Will Defense saves theism from the logical problem of evil; but for the theologically conservative Christians, it seems that it is.

Intermission: A Quick Point about Plantinga's Free Will Defense

It's often said that Plantinga *refuted* the logical problem of evil -- i.e., that he demonstrated that' there's no logical inconsistency between the existence of an all-knowing, all-powerful, and perfectly good god, on the one hand, and evil on the other. This is extremely misleading. To see why, consider the following three claims, in descending order in terms of strength of claim:

1. The following is a fact: Possibly, every creature that God can create would freely perform at least one morally wrong action.
2. Here is a story that we have decent reason to believe is true: Possibly, every creature that God can create would freely perform at least one morally wrong action.
3. Here is a claim that we can't rule out for sure as false: Possibly, every creature that God can create would freely perform at least one morally wrong action.

Now many apologists talk as though Plantinga has shown that (1) or (2) is true. These are the sorts of claims that Plantinga would have to have vindicated for the apologists to be right. However, Plantinga has only shown that (3) is true.

As you can see, (3) is a bit less interesting than (1) and (2). According to the latter two claims, it would be true, or at least more reasonable to believe than not, that there are possible worlds in which it's possible that God and evil can co-exist, in which case the logical problem of evil would indeed be defeated in a way that would make the agument a failure. For on either of these two claims, it would be true, or more reasonable than not, to think that God and evil are compatible.

However, (3) doesn't show anything as strong as this. Consider the following two claims:

4. Theist to the non-theist: I've shown that *you are unreasonable* to think that God and evil can't coexist. I've shown that the deductive argument from evil is unsound.

5. Theist to the non-theist: I've shown you that *I'm not unreasonable* to think that God and evil can coexist, given that I also have strong enough evidence or warrant for thinking that theism is true. I've shown that we can't be absolutely sure that God and evil can coexist.

(1) and (2) give reason to accept (4); (3) only gives reason to accept (5). And the latter is all that Plantinga has done. But establishing (5) isn't sufficient to show that the deductive version of the problem of evil argument is unsound -- i.e., it may well be sound; it's just that we're not sure that it is.

Three relatively recent works have been published that underscore the point above:

-Michael Bergmann's "Might-Counterfactuals, Transworld Untrustworthiness, and Plantinga's Free Will Defense", Faith and Philosophy 16:3 (1999), 336-351.
-Daniel Howard-Snyder and John Hawthorne, "Transworld Sanctity and Plantinga's Free Will Defense", Int'l. Journal for Philosophy of Religion 44 (1998), 1-21.
-The chapter on Plantinga on the logical problem of evil in James F. Sennett's book on Plantinga's Philosophy, viz., Modality, Probability, and Rationality

Interestingly, all of these philosophers are fairly conservative christians.

A Critique of the Kalam Cosmological Argument

(Note: I've posted this previously at Debunking Christianity.
You can go to the archives at that site and read the follow-up of objections
and replies in the "comments" section below the post)

On the Possibility of a Beginningless Past: A Reply to Craig

William Lane Craig has argued vigorously that, cosmological discoveries aside, it’s reasonable to believe on purely a priori grounds that the set of past events is finite in number.1 He offers two main types of a priori arguments for this claim: (i) that it’s metaphysically impossible for an actually infinite set of concrete things to exist, in which case the set of past events can’t be actually infinite, and (ii) that even if such a set could exist, it’s impossible to traverse it even in principle. Craig doesn’t pursue this claim for it’s own sake, however. Rather, he does so as a means to demonstrating that a theistic god exists. He reasons that if the set of past events is finite, then the universe as a whole had an absolute beginning with the first moment of time2. But since nothing can come into existence without a cause, the universe as a whole has a cause. From here, he goes on to argue that such a cause must be timeless (at least sans creation), immaterial, immensely powerful, and a person of some sort.

I intend to show that one of Craig’s most popular versions of (ii) is unsound. In this essay, I’ll state this argument, prefacing it with an explanation of the concepts crucial to understanding it. Then, I’ll examine a common objection to his argument, along with Craig’s response to it, in order to shed light on an unstated assumption of the argument. Finally, I’ll show that the unstated assumption is false, and how this is fatal to his argument.


As I mentioned above, several concepts that are crucial for understanding the argument need clarification.3 First of all, one needs a fairly perspicuous idea of a set and of a proper subset. A set is a collection of entities, called members of the set. The precise number of members contained in a set is its cardinal number. A proper subset is a part of another set, the former lacking at least one member which the latter contains, and which contains no other members (e.g., from a totally distinct set). More formally, a set A is a proper subset of a set B if and only if every member of A is a member of B, and some member of B isn’t a member of A. To illustrate: Suppose you have ten bottlecaps, five of which are from Pepsi bottles and five of which are from Coke bottles. Then we can call this the set of bottlecaps, the cardinal number of which is 10. Let’s call this set, A. Furthermore, the set of Pepsi caps (call it B) is a proper subset of A, since B consists in a collection of members that belong to A, and A has members that B does not (i.e., the Coke caps).

Another concept that plays an important role in the argument is that of a one-to-one-correspondence. This is a concept used to determine whether two sets have the same number of members (or, the same cardinal number). So there is a one-to-one correspondence between two sets, A and B, if and only if each member of A can be paired up with exactly one member of B, and each member of B can be paired up with exactly one member of A. To illustrate this concept, consider our set of bottlecaps. Now suppose that you didn’t know how to count, but you wanted to know if your had just as many Coke caps as you had of Pepsi caps. You could accomplish this task by pairing each Coke cap with each Pepsi cap, and each Pepsi cap with each Coke cap. If this can be accomplished with no remaining bottlecaps, then there is a one-to-one correspondence between the set of Pepsi caps and the set of Coke caps. If follows that the respective sets of bottlecaps have the same cardinal number.

The concept most important for our purposes is that of actual infinity. To obtain a grasp of this concept, consider the set of all the natural numbers (i.e., {1, 2, 3, …}). This set, as well as any set that can be put into a one-to-one correspondence with it, is an actually infinite set (It’s actually the “smallest” of the infinite sets, but we won’t be concerned with “larger” infinites here). An actual infinite has several interesting features. First of all, it is complete, in the sense that it has an infinite number of members; it is not merely increasing in number without limit. Second, any actually infinite set (of the “size” we’re here considering) can be put into a one-to-one correspondence with one of its proper subsets. This can be demonstrated by putting the set of natural numbers in a one-to-one correspondence with its proper subset of even numbers:

1 2 3 4…

2 4 6 8…

This example shows that a part of an actually infinite set can have as many members as the whole set! The cardinal number of an actually infinite set that can be put into a one-to-one correspondence with the natural numbers is called “aleph null” (let’s use ‘A0’ for brevity).

The final concept relevant to our discussion is order-type. I won’t talk at length about this concept here. Rather, I’ll barely do more than mention the order-types of certain sets containing A0 members. Four our purposes, it will suffice to know that sets can be sequentially ordered according to certain patterns or types. The order-type given to the set of natural numbers so ordered that, beginning with 1, each natural number is succeeded by the next largest natural number – i.e., {1, 2, 3, …} – is ‘omega’, or 'w’, and the set of negative integers so ordered that they are sequentially the opposite of w is w* (i.e., {…-3, -2, -1}). Sets with A0 members can have other order-types, however. For example, an A0 set can have the order type w+1 (i.e., {1, 2, 3, ..., 1}), or the order-type w+2 (i.e., {1, 2, 3, …, 1, 2}), etc. In fact, a set with A0 members can have the order-type w+w (i.e., {1, 2, 3, …, 1, 2, 3, …}), or the order-type w+w+w (i.e., {1, 2, 3, …., 1, 2, 3, …, 1, 2, 3, …}), etc.! To see this, recall that any set that can be put into a one-to-one correspondence with the natural numbers has a cardinal number of A0. But sets with the order-types mentioned above can be put into such a correspondence. So, for example, a set with the order-type w+1 can be put into a one-to-one correspondence with the natural numbers as follows:

1 1 2 3…

1 2 3 4…

Similarly, a set with the order-type w+w+w can be put into a one-to-one correspondence with the natural numbers as follows:

1 2 3…1 2 3…1 2 3…

1 4 7…2 5 8…3 6 9…

Therefore, since sets with such order-types can be put into a one-to-one correspondence with the natural numbers, it follows that their cardinal number is A0.

At this point, an interesting feature of certain sets with A0 members emerges. For consider any A0 set with an order-type other than w. For example, consider a set of A0 offramps on an infinitely long freeway, such that a distance of one mile separates each offramp from its predecessor and successor (except, of course, the first offramp, since it has no predecessor). Suppose further that the order-type of the offramps is w+1 ({1, 2, 3, …, 1}). The offramp assigned the first 1 would seem to be infinitely distant from the offramp assigned the second 1. Such a set has the interesting feature of being non-traversable in principle – it cannot, even in principle, be exhaustively counted through one offramp at a time. This is because it is logically impossible to count to a number that has no immediate predecessor. But the offramp assigned the second 1 has no immediate predecessor. Therefore, a driver on such a freeway could never reach the offramp assigned the second 1. Call this particular logical ban on traversing sets with w+1 or “higher” order-types ‘LB’.

Now it may be tempting to think that this consideration is decisive for the view that the past must be finite, since any set with A0 members can be ordered according to the order-type w+1. In this way, one might think, LB infects all actually infinite sets, and thus no set with A0 members is traversable. This reasoning can be expressed as follows:

1. A set is LB non-traversable if and only if it contains at least one member A0 distant from at least one of the other of its members.

2. Any set with the order-type w+1 is such that it contains a member A0 distant from at least one of the other of its members.

3. Therefore, any set with the order-type w+1 is LB non-traversable.

4. Any set with A0 members can be assigned the order-type w+1.

5. Therefore, any set with A0 members is LB non-traversable.

But this would be rash. For the inference from (3) and (4) to (5) is a non sequitur. For consider a set with A0 members that is assigned the order-type w. A set with this order-type is such that (i) no member is infinitely distant from any other member, and (ii) each member does have an immediate predecessor, as so is immune to LB. But any set with A0 members can be assigned the order-type w. So if the inference from (3) and (4) to (5) were valid, then by similar reasoning the following inference should go through as well:

3’. Any set with the order-type w is not LB non-traversable.

4’. Any set with A0 members can be assigned the order-type w.

5’. Therefore, any set with A0 members is not LB non-traversable.

But (5’) contradicts (5). Therefore, since the same pattern of reasoning yields contradictory results, it’s faulty. So, just because an A0 set can be assigned a non-traversable order-type, it doesn’t follow that such a set is non-traversable. What really follow from (3) and (4) is rather

5’’. Any set with A0 members can be assigned an LB non-traversable order-type.

Which, needless to say, doesn’t help to establish the finitude of the set of past events.

The arguments above suffer from another problem as well. For (2) is clearly false. To see this, consider again our infinitely long freeway. No suppose that it only has one lane, and that it has an infinitely long traffic jam. Finally, suppose that each car in the jam is assigned a number from the order-type w+1. Does it follow that there is a car A0 distant from any other car? No. For the car assigned the second 1 could be immediately in front of the first car. This illustration shows that the order-type assigned to a set of objects doesn’t necessarily affect the distances between its members. To drive this implication home, suppose that the cars of the traffic jam were assigned the order-type w. Would it follow that no car is A0 distant from any other car? Not in the least. For the first and second cars may be infinitely distant from one another. One might reply that we could just stipulate that the distances between the cars and the order-type assigned to the cars correspond. In such a case, each car would only be finitely distant from every other car when assigned the order-type w (e.g., the second car is 2 meters from the end of the traffic jam, the third car is 3 meters from the end of the jam, etc. [these are small cars!]). One could then reassign the cars with the order-type w+1, but then the correspondence between the order-type and the distances of the cars would break down. This is because no car assigned a number from the w order-type in our scenario is infinitely distant from any other car. Therefore, the second 1 of the newly assigned w+1 reordering would be assigned to a car that is only finitely distant from any other car. These illustrations show that (i) some sets assigned the order-type w+1 are such that no member is infinitely distant from any other, and (ii) we can know a priori than an A0 set of concrete objects cannot be reordered from w to w+1 in such a way that the distances between the members of such a set correspond to their order-type. Therefore, if a set of objects has A0 members (arranged linearly), it does not follow from this that it has members infinitely distant (whether in time or in space) from other members (and is therefore LB non-traversable).4 Thus, to show that an A0 past is non-traversable, Craig must show that no A0 set with either the order-type w or w* (and is such that no member is infinitely distant from any other) is traversable. Let’s consider one of Craig’s main attempts to do this.


Craig advances an argument for the proposition that one cannot traverse a beginningless past and end at the present moment.5 To do this, Craig assumes, for the sake of argument, that there could be a beginningless past, conceived as a set of events with the cardinal number A0 and the order-type w* (i.e., {…,. -3, -2, -1}), where each negative integer represents an event of the past. He then argues,

“…suppose we meet a man who claims to have been counting down from eternity and who is now finishing:…,-3, -2, -1, 0. We could ask, why didn’t he finish counting yesterday or the day before or the year before? By then an infinite amount of time had already elapsed, so that he should already have finished. Thus, at no point in the infinite past could we ever find the man finishing his countdown, for by that point he should already be done! In fact, no matter how far back into the past we go, we can never find the man counting at all, for at any point we reach he will already be finished. But if at no point in the past do we find him counting, this contradicts the hypothesis that he has been counting down from eternity.”6

Craig’s argument is a reductio ad absurdum, where we suppose that a beginningless past is possible in order to show that it entails a contradiction. The argument can be expressed as follows, with (1) as the premise set up for reduction:

1. The past is beginningless (conceived as a set of events with the cardinality A0, and the order-type w*).

2. If the past is beginningless, then there could have been an immortal counter who counts down from such a past at the rate of one negative integer per day.

3. The immortal counter will finish counting if and only if he has an infinite number of days in which to count them.

4. If the past is beginningless, then there are an infinite number of days before every day.

5. Therefore, the immortal counter will have finished counting before every day.

6. If the immortal counter will have finished counting before every day, then he has never counted.

7. Therefore, the immortal counter has both never counted and has been counting down from a beginningless past (contradiction)

8. Therefore, the past is not beginningless (from 1-7, reductio)

In short, Craig argues that the past must -- logically must -- have a beginning. For the very notion of traversing a beginningless past entails a contradiction. Craig’s underlying intuition here is that if the past is beginningless, then it must contain an actually infinite proper subset of events that was not formed by successive addition, and that this is absurd.

Critics typically attack (3), arguing that Craig mistakenly assumes that to count an infinite number of negative integers is to count all of them. However, critics of Craig’s argument point out that one can count an infinite set of numbers without counting them all.7 For example, suppose our eternal counter just finished counting all the negative integers down to -3. Then it would be true that he has counted an infinite number of integers, and yet he has not counted all the integers. This can be demonstrated by the following one-to-one correspondence:

Days counted: -3 -4 -5…

Nat. numbers: 1 2 3…

In this case, the set of days counted has the cardinal number A0, since its members can be put into a one-to-one correspondence with the natural numbers. Yet he clearly hasn’t counted all the negative integers, since he has failed to count -2 and -1. Therefore, since counting an infinite number of things is not synonymous with counting them all, Craig’s (3) is based on an equivocation.

Craig has denied that he is guilty of this charge8:

“I do not think the argument makes this alleged equivocation, and this can be made clear by examining the reason why our eternal counter is supposedly able to complete a count of the negative numbers, ending at zero. In order to justify this intuitively impossible feat, the argument’s opponent appeals to the so-called Principle of Correspondence…On the basis of the principle the objector argues that since the set of past years can be put into a one-to-one correspondence with the set of negative numbers, it follows that by counting one number a year an eternal counter could complete a countdown of the negative numbers by the present year. If we were to ask why the counter would not finish next year or in a hundred years, the objector would respond that prior to the present year an infinite number of years will have elapsed, so that by the Principle of Correspondence, all the numbers should have been counted by now.

But this reasoning backfires on the objector: for on this account the counter should at any point in the past have already finished counting all the numbers, since a one-to-one correspondence exists between the years of the past and the negative numbers.”9

From this passage, we see Craig’s rationale for (3):

(R) The counter will have finished counting all of the negative integers if and only if the years of the past can be put into a one-to-one correspondence with them.

Furthermore, from the passage cited, we see that Craig thinks that the defender of an A0 past agrees with (R). But since the type of correspondence depicted in (R) can be accomplished at the present moment, it follows that the counter should be finished by now. Therefore, Craig’s opponent is committed to a view that entails the absurdity surfaced by the above reductio.


It isn’t clear that Craig hasn’t made his case, however. For consider the following scenario. Suppose God timelessly numbers the years to come about in a beginningless universe. Suppose further that He assigns the negative integers to the set of events prior to the birth of Christ, and then the positive integers begin at this point. Then the timeline, with its corresponding integer assignment, can be illustrated as follows:

…-3 -2 -1 Birth of Christ 1 2 3…

Suppose yet further that God assigned Ralph, an immortal creature, the task of counting down the negative integers assigned to the years BCE, and stopping at the birth of Christ. Call this task ‘(T)’. With this in mind, suppose now that Ralph has been counting down from eternity past and is now counting the day assigned (by God) the integer -3. In such a case, Ralph has counted a set of years that could be put into a one-to-one correspondence with the set of negative integers, yet he has not finished all the negative integers. This case shows that, while it is a necessary condition for counting all of the events that one is able to put them into a one-to-one correspondence with the natural numbers, this is not sufficient. For if the events that are to be counted have independently “fixed”, or, “designated” integer assignments set out for one to traverse, one must count through these such that, for each event, the number one is counting is the same as the one independently assigned to the event. In the scenario mentioned above, God assigned an integer to each year that will come to pass. In such a case, Ralph must satisfy at least two conditions if he is to accomplish (T): (i) count a set of years that can be put into a one-to-one correspondence with the natural numbers, and (ii) for each year that elapses, count the particular negative integer that God has independently assigned to it. According to Craig’s assumption (R), however, Ralph is supposed to be able to accomplish (T) by satisfying (i) alone. But we have just seen that he must accomplish (ii) as well. Therefore, being able to place the events of the past into a one-to-one correspondence with the natural numbers does not guarantee that the counter has finished the task of counting all the negative integers. In other words, (R) is false. But recall that (R) is Craig’s rationale for (3). Thus, (3) lacks positive support. But more importantly, (3) is false. This is because the scenario above is a counterexample to both (R) and (3). For (3) asserts that it is sufficient for counting down all the negative integers that one has an infinite amount of time in which to count them. But our scenario showed that one could have an infinite amount of time to count, and yet not finish counting all of the negative integers (e.g., one can count down to -3 in an infinite amount of time, and yet have more integers to count).

To sum up: We’ve looked at an argument that Craig repeatedly gives for the impossibility of a beginningless past. We then saw that one of its premises is false, in which case it is unsound. Thus, this argument, at least, cannot be used to offer a priori support for the key premise in his Kalam argument.

1 See, for example, his The Kalam Cosmological Argument (London: Macmillan, 1979); Craig and Quentin Smith, Theism, Atheism, and Big Bang Cosmology (Oxford: Clarendon Press, 1995). See also Craig’s popular-level book, Reasonable Faith (Wheaton: Crossway Books, 1994).

2 I should mention a wrinkle here: the possibility that the universe did not begin to exist with the first event of time, but rather existed eternally in a quiescent, eventless mode of existence “prior” to the first event. Craig addresses this worry in “The Kalam Cosmological Argument and the Hypothesis of a Quiescent Universe”, Faith and Philosophy 8 (1991), pp. 104-8.

3 My discussion of the following set-theoretic concepts is indebted to J.P. Moreland’s Scaling the Secular City (Grand Rapids: Baker, 1987)

4 The points and illustrations are similar to those made and conceded by Craig in “Reply to Smith: On the Finitude of the Past”, International Philosophical Quarterly 33 (1993), pp. 228-9.

5 Actually, he advances two arguments for this proposition. One is a variation on the famous Tristam Shandy Paradox. In Craig’s construal of it, Shandy writes his autobiography from the beginningless past at the rate of one year of writing per day of autobiography. It seems that Shandy would never finish his autobiography, getting farther behind with each passing day. But since one can put the days of his life into a one-to-one correspondence with the set of past years, it (paradoxically) seems that he should have finished his autobiography by now. The other version is virtually the same as the one I consider here. It asserts that Shandy should be finished by now, irrespective of the rate at which he is writing. However, I won’t consider the former version here. See Craig and Smith’s Theism, Atheism, and Big Bang Cosmology, pp. 99-100, and Craig’s “Feature Review of Time, Creation, and the Continuum”, International Philosophical Quarterly 25 (1985), pp. 319-26. For a briefer exposition, see Craig, Reasonable Faith, pp. 98-9.

6 Craig, Reasonable Faith, p. 99.

7 This objection can be found in David A. Conway. “’It Would Have Happened Already’: On One Argument for a First Cause”, Analysis 44 (1984), pp. 159-66; Richard Sorabji. Time, Creation, and the Continuum (Ithaca: Cornell University Press, 1983), pp. 219-24.

8 See, for example, Craig and Smith, Theism, Atheism, and Big Bang Cosmology, pp. 105-6; Craig, “Review of Time, Creation, and the Continuum”, p. 323.

9 Craig, “Review of Time, Creation, and the Continuum”, p. 323.

Problems for PSR (Slightly Revised)

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

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

1. Type-(i) Criticisms:

1.1 Contrary to what its proponents often assert, PSR does not seem to be supported by reflection on cases. Rather what such reflections support is the weaker principle that objects and events are explained in terms of antecedent causes and conditions. In actual practice, ordinary individuals and scientists explain the existence of objects and events in terms of antecedent causes and conditions, provisionally taking the latter things to be brute facts unless or until they, too, can be further explained. But the prinicple implicit in this sort of search for explanations isn't sufficient to generate the need for an explanation of the universe as a whole in terms of a necessary being.[1]

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

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

1.3 Even if PSR were a presupposition of reason, it wouldn’t follow that it would then be true. But in any case, PSR does not seem to be a presupposition of reason. Rather, again, reason only seems to demand that the existence of each object or fact is explained in terms of antecedent causes and conditions, which are provisionally taken as brute facts unless or until they, in turn, can be explained. Reason does not seem to require anything beyond this.[2]

2. Type-(ii) Criticisms:

2.1 PSR absurdly entails that everything obtains of necessity. The argument for this can be stated as follows. Consider the conjunction of all contingent facts (CCF). By PSR, there is a sufficient reason for CCF. Now the sufficient reason for CCF is itself either contingent or necessary. But it can’t be contingent, because then it would represent a contingent fact, in which case it would itself be a part of the CCF. But contingent facts don’t contain within themselves the sufficient reason for why they obtain – let alone the sufficient reason for why the CCF obtains. Thus, the sufficient reason for CCF must be necessary. But whatever is entailed by a necessary truth is itself necessary, in which case all truths would be necessary truths, and the referents they represent would obtain of necessity. But this is absurd. Therefore, PSR is false. [3]

2.2 The following scenario is prima facie possible: there are just two kinds of beings that exist: contingent-and-dependent beings (e.g., rocks, trees, planets, galaxies, you and me) and contingent-yet-independent, “free-standing” beings, out of which all contingent-and-dependent beings are made (perhaps matter-energy is like this). If so, then even though there are possible worlds at which the contingent-yet-independent beings don’t exist, they are eternal and indestructible at all possible worlds in which they do exist (interestingly, some theists -- e.g., Richard Swinburne -- take God to be just such a being). On this account, then, there are contingent beings that come to be and pass away – viz., the contingent-and-dependent beings. But the beings out of which they’re made – i.e., the contingent-yet-independent beings -- do not; nor can they.[4] This scenario seems possible. But if so, then since PSR entails that such a state of affairs is impossible, then so much the worse for PSR.[5]

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

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

Appendix: Recent Defenses of PSR

A number of philosophers have attempted to revive the Leibnizian cosmological argument in recent years by advancing a weaker version of PSR.[6] According to their version of PSR, every contingent being has a possible explanation in terms of something else. That is, every contingent being is such that there is at least one possible world at which it has an explanation for why it exists. Call this version of PSR, 'Modal PSR'.

Now some authors, such as Garrett DeWeese and Joshua Rasmussen[7] -- offer an argument for Modal PSR. Now I think their argument has a couple of problems, but here I just want to mention one that I think is decisive: The argument uses Modal PSR as a premise to derive the standard version of PSR we discussed above. But this premise is implausible at best, and outright false at worst. For unless they just beg the question and assume that there are no possible beings that lack a sufficient reason, then they must be claiming that, even if there are possible worlds at which a given contingent beings lacks a sufficient reason, there are *other* possible worlds at which it does. But this is implausible, For It seems to me that the only way to accept Modal PSR is to reject origin essentialism. Allow me to me unpack and explain this criticism below:

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

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

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

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

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

[2] See ibid.

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

[4] Here are a couple of possible ways this could be:

(i) The Strong Version: at least one possible independent being x has indestructibility as an essential property: x is indestructible at all possible worlds in which x exists. This is because nothing has what it takes to destroy x at each possible world in which it exists. Now consider the set S of worlds at which x exists. Suppose at least one member of S -- call it 'W' -- is such that x never began to exist in W, and that. It follows from this and the above-mentioned properties that x is independent, indestructible and everlasting in W. However, since x isn't a metaphysically necessary being, there are possible worlds at which x doesn't exist. X is therefore a contingent-yet-independent being of the requisite sort.

(ii) A Weaker Version: there is a being y like x, except that y's indestructibility is world-indexed: it has the property of being indestructible-at-W, where 'W' denotes a possible world. How can y's indestructibility be indexed to W? Because nothing in W has what it takes to destroy y (although things may well have such an ability at other worlds in which y exists). Thus, y is not destroyed at W. This W-indexed fact about y then grounds the fact that W is not destroyed at all worlds counterfactual to W. And if that's right, then y is indestructible in W. Now suppose that, at W, Y never began to exist. Then y is independent, indestructible, and everlasting at W. Y is therefore a contingent-yet-independent being of the requisite sort.

[5] If one is skeptical that this is possible, one could re-construe it as an epistemic possibility, and thus re-categorize it as an undercutting (instead of a rebutting) defeater of PSR along with the other type-(i) criticisms.

[6] See, for example: Gale, Richard and Pruss, Alexander. "A New Cosmological Argument", Religious Studies 35 (1999), pp. 461–476; “Hume and the Kalam Cosmological Argument”, in In Defense of Natural Theology: A Post-Humean Reassessment, ed. Douglas Groothuis and James Sennett (IVP, 2005)

[7] “Hume and the Kalam Cosmological Argument”.

What God Would Have Known... the title of J.L. Schellenberg's forthcoming book , which offers a large number of novel arguments against Christian theism. I...