In Defense of David Hume Part 6, William L. Vanderburgh On "Hume’s 'Abject Failure' Vindicated"
William L. Vanderburgh defended Hume against John Earman in a very thorough article published in 2005 in Hume Studies, titled, Of Miracles and Evidential Probability: Hume’s “Abject Failure” Vindicated [You can read the PDF right here.]. In it Vanderburgh shows David Hume probably knew of Bayes Theorem and never mentioned it for good reasons. I'm including a few of the important highlights below. I consider it an important contribution on Hume and Earman and even Bayes.
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If the evidence for laws is the paradigmatically best evidence we have, the evidence for a miracle can at best equal it, in which case the competing evidence (for and against the uniformity of the law in question) will balance off, which “must properly only lead us to the suspension of judgment on the issue.” p. 15
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As Hume puts it, “no testimony is sufficient to establish a miracle, unless the testimony be of such a kind, that its falsehood would be more miraculous, than the fact, which it endeavours to establish” (EHU 10.13; SBN 115–16). Note that this is an outcome rather than an assumption of Hume’s analysis. p.43 [John Loftus: I think this is right on. My critics have faulted me for the same thing with regard to the Outsider Test for Faith. Sometimes I argue for it as a fair non-double standard test for faith. Other times I state the outcome when applying it, saying the test causes any reasonable person to reject their faith.]
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The idea that a miracle report is credible only when it would be more improbable for the testimony to be false than it would be for the law to be violated is something Hume calls a “general maxim.” A maxim is neither a necessary principle nor a certain truth, but rather a methodological rule to be followed in the absence of an adequate reason to think that it does not apply. Here, the maxim is a rule for reasoning about conflicting evidence claims: Barring adequate reasons to trust some particular testimony to a purported miracle, one should withhold assent from purported miracles. p. 44
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Hume argues that as a matter of fact, and given what we know about human psychology and the facts of history—especially what we know about bogus miracle claims, the credulity of religious believers, and how humans come to know laws of nature—there has never been and very probably never will be an instance in which the probability that a miracle has occurred is greater than the probability that the reporter is mistaken, has been deceived or is a deceiver. p. 46
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Quotes concerning John Earman's criticisms:
Hume is making a general a posteriori judgment about the facts of experience that are relevant to specific judgments about purported singular occurrences. These facts are so well-established that we need not perform a detailed analysis in every case. This is consistent with common sense and good epistemic practice. Given this, a great many of Earman’s criticisms are moot, based as they are on thinking that for Hume the probability that a miracle has actually occurred is always flatly zero. p. 46
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Earman’s example of the simultaneous cloud formations that spell out, “Believe in Emuh and you will have everlasting life,” over every nation of the Earth in the language of that nation (Earman, 11), is supposed to be an example of an extraordinary event that would (Earman thinks) give grounds for rational belief in the religious hypothesis written in the clouds. Of course, this event need not be a miracle. It might happen that the deity has arranged the laws and initial conditions of wind and weather in such a way that on a certain day the cloud formations in question come about naturally. In that case, there might be grounds for a design argument. Whether the design inference is adequately warranted will depend on the evidence that the event was not simply a freak of nature (a product of coincidence rather than design), or that it was not produced as an elaborate hoax (perpetrated, perhaps, by frat boys from outer space). p.43
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Earman misses Hume’s drift, too, when he gives a long discussion of results in Bayesian probability theory to show that testimony or other evidence could potentially supply warrant adequate for rational belief in the occurrence of a miracle. Earman relies here on assumptions Hume would grant hypothetically but would utterly reject in the analysis of actual cases. For example, Earman’s proof that the testimony of multiple witnesses could raise the probability of the occurrence of a miracle above the threshold for reasonable belief (Earman, 53–9) depends on the assumption that all the witnesses are honest and have correctly perceived the event in question! It is possible, Hume would say, that this condition is sometimes satisfied. But given our background knowledge it is a practical certainty that we will never have adequate grounds to believe that this condition is satisfied in any particular case. p. 47 [John Loftus: This too is right on. I find apologists and critics want to talk in terms of bizarre hypothetical scenarios rather than real concrete examples. I'd rather have them stick to the tale of a virgin giving birth to a baby deity in the ancient world, where the same claim of virgin birth status was attributed to other people perceived to be important later on in life.]
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Earman’s attack on Hume depends on taking the threshold for reasonable belief in some proposition to be that there is a greater than 50 percent chance that it is true (Earman, 41, et passim). Since Hume speaks constantly of probabilities but never in numerical terms, it is difficult to say what Hume would take as the numerical threshold reasonable belief. As discussed below, this is something Hume likely would not be willing to specify at all. But of one thing I am quite sure, namely, that the threshold for reasonable belief would depend on the knowledge claim in question: the more extraordinary the claim, the more extraordinary the evidence required to make believing it reasonable. And even ordinary beliefs Hume would not think of as adequately warranted if there were a 49 percent chance of them being false. This is in the range where a good skeptic should suspend judgment, since both the assertion and its denial are nearly equally likely. p. 47
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Earman (25) chastises Hume for being unaware of Bayesianism and of mathematical probability generally. This is unfair on two counts. First, Bayes’s work on probability was not widely known in 1748 when Hume published the first edition of the Enquiry. Richard Price arranged the posthumous publication of Bayes’s essay only in 1763, and it remained obscure even after its publication; Price’s paper applying Bayesian methods to the evidence for miracles appeared in 1767. We know Hume read and admired that paper, but he neither addressed Bayesian arguments nor revised his account of miracles for the 1768 and 1777 editions of the Enquiry. This suggests that Hume ultimately did not view Bayes’s work as relevant to the argument against miracles. Second, Hume’s discussion of the probability of chances (see for example THN 1.3.11 and 1.3.12; SBN 124–42, and EHU 6; SBN 56–9) “shows without controversy that he was familiar with the basic concepts of probability based on the calculus of chances.” Given Hume’s familiarity with Pascalian probability in general, and his acquaintance (through Price) with Bayesian ideas, his non-numerical treatment of the evidential probability of miracles must be seen as a deliberate philosophical position, not as a result of negligence or ignorance. p. 53
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There have been several attempts over the years to analyze Hume’s argument against miracles in Bayesian terms. Interestingly, about as many claim to support Hume’s conclusion as claim to refute it; the fact that contradictory results have been achieved is possibly a symptom of the wrong-headedness of Bayesian reconstructions of Hume’s argument against miracles. The fact that there are so many incompatible Bayesian accounts of miracles also suggests that the correct Bayesian account is even now neither clear nor settled—yet another reason not to blame Hume for giving a non-Bayesian analysis. Given the diversity of Bayesian opinions, it is perhaps no surprise that some of them are consistent with what Hume says about miracles. p.55
======================
If the evidence for laws is the paradigmatically best evidence we have, the evidence for a miracle can at best equal it, in which case the competing evidence (for and against the uniformity of the law in question) will balance off, which “must properly only lead us to the suspension of judgment on the issue.” p. 15
======================
As Hume puts it, “no testimony is sufficient to establish a miracle, unless the testimony be of such a kind, that its falsehood would be more miraculous, than the fact, which it endeavours to establish” (EHU 10.13; SBN 115–16). Note that this is an outcome rather than an assumption of Hume’s analysis. p.43 [John Loftus: I think this is right on. My critics have faulted me for the same thing with regard to the Outsider Test for Faith. Sometimes I argue for it as a fair non-double standard test for faith. Other times I state the outcome when applying it, saying the test causes any reasonable person to reject their faith.]
======================
The idea that a miracle report is credible only when it would be more improbable for the testimony to be false than it would be for the law to be violated is something Hume calls a “general maxim.” A maxim is neither a necessary principle nor a certain truth, but rather a methodological rule to be followed in the absence of an adequate reason to think that it does not apply. Here, the maxim is a rule for reasoning about conflicting evidence claims: Barring adequate reasons to trust some particular testimony to a purported miracle, one should withhold assent from purported miracles. p. 44
======================
Hume argues that as a matter of fact, and given what we know about human psychology and the facts of history—especially what we know about bogus miracle claims, the credulity of religious believers, and how humans come to know laws of nature—there has never been and very probably never will be an instance in which the probability that a miracle has occurred is greater than the probability that the reporter is mistaken, has been deceived or is a deceiver. p. 46
======================
Quotes concerning John Earman's criticisms:
Hume is making a general a posteriori judgment about the facts of experience that are relevant to specific judgments about purported singular occurrences. These facts are so well-established that we need not perform a detailed analysis in every case. This is consistent with common sense and good epistemic practice. Given this, a great many of Earman’s criticisms are moot, based as they are on thinking that for Hume the probability that a miracle has actually occurred is always flatly zero. p. 46
======================
Earman’s example of the simultaneous cloud formations that spell out, “Believe in Emuh and you will have everlasting life,” over every nation of the Earth in the language of that nation (Earman, 11), is supposed to be an example of an extraordinary event that would (Earman thinks) give grounds for rational belief in the religious hypothesis written in the clouds. Of course, this event need not be a miracle. It might happen that the deity has arranged the laws and initial conditions of wind and weather in such a way that on a certain day the cloud formations in question come about naturally. In that case, there might be grounds for a design argument. Whether the design inference is adequately warranted will depend on the evidence that the event was not simply a freak of nature (a product of coincidence rather than design), or that it was not produced as an elaborate hoax (perpetrated, perhaps, by frat boys from outer space). p.43
======================
Earman misses Hume’s drift, too, when he gives a long discussion of results in Bayesian probability theory to show that testimony or other evidence could potentially supply warrant adequate for rational belief in the occurrence of a miracle. Earman relies here on assumptions Hume would grant hypothetically but would utterly reject in the analysis of actual cases. For example, Earman’s proof that the testimony of multiple witnesses could raise the probability of the occurrence of a miracle above the threshold for reasonable belief (Earman, 53–9) depends on the assumption that all the witnesses are honest and have correctly perceived the event in question! It is possible, Hume would say, that this condition is sometimes satisfied. But given our background knowledge it is a practical certainty that we will never have adequate grounds to believe that this condition is satisfied in any particular case. p. 47 [John Loftus: This too is right on. I find apologists and critics want to talk in terms of bizarre hypothetical scenarios rather than real concrete examples. I'd rather have them stick to the tale of a virgin giving birth to a baby deity in the ancient world, where the same claim of virgin birth status was attributed to other people perceived to be important later on in life.]
======================
Earman’s attack on Hume depends on taking the threshold for reasonable belief in some proposition to be that there is a greater than 50 percent chance that it is true (Earman, 41, et passim). Since Hume speaks constantly of probabilities but never in numerical terms, it is difficult to say what Hume would take as the numerical threshold reasonable belief. As discussed below, this is something Hume likely would not be willing to specify at all. But of one thing I am quite sure, namely, that the threshold for reasonable belief would depend on the knowledge claim in question: the more extraordinary the claim, the more extraordinary the evidence required to make believing it reasonable. And even ordinary beliefs Hume would not think of as adequately warranted if there were a 49 percent chance of them being false. This is in the range where a good skeptic should suspend judgment, since both the assertion and its denial are nearly equally likely. p. 47
======================
Earman (25) chastises Hume for being unaware of Bayesianism and of mathematical probability generally. This is unfair on two counts. First, Bayes’s work on probability was not widely known in 1748 when Hume published the first edition of the Enquiry. Richard Price arranged the posthumous publication of Bayes’s essay only in 1763, and it remained obscure even after its publication; Price’s paper applying Bayesian methods to the evidence for miracles appeared in 1767. We know Hume read and admired that paper, but he neither addressed Bayesian arguments nor revised his account of miracles for the 1768 and 1777 editions of the Enquiry. This suggests that Hume ultimately did not view Bayes’s work as relevant to the argument against miracles. Second, Hume’s discussion of the probability of chances (see for example THN 1.3.11 and 1.3.12; SBN 124–42, and EHU 6; SBN 56–9) “shows without controversy that he was familiar with the basic concepts of probability based on the calculus of chances.” Given Hume’s familiarity with Pascalian probability in general, and his acquaintance (through Price) with Bayesian ideas, his non-numerical treatment of the evidential probability of miracles must be seen as a deliberate philosophical position, not as a result of negligence or ignorance. p. 53
======================
There have been several attempts over the years to analyze Hume’s argument against miracles in Bayesian terms. Interestingly, about as many claim to support Hume’s conclusion as claim to refute it; the fact that contradictory results have been achieved is possibly a symptom of the wrong-headedness of Bayesian reconstructions of Hume’s argument against miracles. The fact that there are so many incompatible Bayesian accounts of miracles also suggests that the correct Bayesian account is even now neither clear nor settled—yet another reason not to blame Hume for giving a non-Bayesian analysis. Given the diversity of Bayesian opinions, it is perhaps no surprise that some of them are consistent with what Hume says about miracles. p.55
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