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.

Schmid's Excellent New Paper on the Kalam Cosmological Argument

Schmid, Joseph C. " Benardete paradoxes, patchwork principles, and the infinite past ", Synthese , forthcoming. Abstract: Benardet...