Base-Rate Neglect in the News

It has been a while since I have thought about the fallacy of base-rate neglect. I did not even think about it when I was recently talking to someone about the reliability (or lack thereof) of tests for SARS-CoV2 antibodies. The piece by Todd Haugh and Suneal Bedi published in the New York Times today (linked above) is a useful reminder.

But it seems to me that Haugh and Bedi do not state their example clearly enough (perhaps because of editorial pruning). I would state it this way: Suppose that a test for SARS-CoV2 antibodies has a sensitivity of 90%. This means that it gives a positive result to 90% of subjects taking it who actually have the antibodies. Suppose also that it has a specificity of 90%. This means that it gives a negative result to 90% of subjects taking it who don't have antibodies. Suppose also that the incidence of antibodies to the virus in the population is (as the writers estimate it to be) 5 percent. And suppose, finally, that 2,000 randomly selected people take the test. If our sample is perfectly representative, 100 of the people taking the test will have the antibodies; and of these, 90 will get a positive result. Of the other 1,900 people taking the test, the ones who don’t have the antibodies, 1710 will get a negative result. But this means—and this is the most significant part—the remaining 190 will get a (false) positive result.

This is significant because it means that, of the 280 people in total who get a positive test result, more than two thirds will not have antibodies. In more general terms, the lower the base rate of what you are testing for, the higher the ratio of false positives to true positives, and therefore the less reliable a positive test result is. If the base rate is 10% then out of our representative sample of 2,000 tests there will be 180 true positives and 180 false positives. So, assuming 90% specificity and sensitivity of a test (which, as I gather, is far better than what any test now available can offer), the base rate has to be above 10% for a positive test result to be more reliable than a coin toss. (A coin toss as to whether a given positive result is true or false, that is, not a coin toss as to whether a given person has antibodies.)

These figures, of course, only describe a mathematical model. One assumption of the model is that persons taking the test are representative of the whole population with regard to the incidence of antibodies among them. This is not necessarily the case. In fact, it is not even probable; rather, people who have had symptoms that they attribute to COVID-19 are more likely to take the test than people who have not. Consequently, the incidence of antibodies to the virus will be higher among persons taking the test than the base rate of the total population. How much higher? I don’t know, and I don’t know how one would go about estimating such a thing.

Quantum Subterfuge

An account of the double-slit experiment by a former professor of mathematical physics is supposed to show the necessity of a paradoxical conclusion, but under examination it shows only the logical confusions of its author.

A few years ago, wanting to gain some knowledge of quantum mechanics, I started reading Quantum Theory: A Very Short Introduction by John Polkinghorne, formerly Professor of Mathematical Physics in the University of Cambridge (Oxford University Press, 2002). I recall being exasperated by the book on my first attempt to read it, but I did not recall the reason until more recently, when I reread Polkinghorne’s commentary on the double-slit experiment.

Polkinghorne opens his exposition by quoting a comment of Richard Feynman on the experiment:

In reality it contains the only mystery. We cannot make the mystery go away by ‘explaining’ how it works. We will just tell you how it works. In telling you how it works we will have told you about the basic peculiarities of all quantum mechanics. [Polkinghorne, p. 22; no citation of source provided]

I recall thinking, when I first read this: “Excellent! Now all I have to do is pay very close attention to the account of the experiment, and I shall understand the basic peculiarities of all quantum mechanics.” This expectation was disappointed.

Describing the physical setup and the results of the experiment is not difficult. Electrons or other quantum particles are fired at a barrier in which there is a pair of adjacent slits. On the far side of the slits is a screen that detects the impacts of the particles. Classical physics predicts that the particles will impinge on the screen in a scattering pattern, with two areas of greatest intensity located directly across from the two slits. But in fact what emerges is an interference pattern, with a single area of greatest intensity located across from the midpoint of the two slits, exactly as if one were sending waves of some sort through the slits.

One might try to explain this on classical-physical lines by supposing that the electrons, though individually particulate in nature, behave in a wave-like fashion when they are shot together in a stream: it is the stream of electrons, not the individual electron, that behaves like a wave. It is true that one cannot observe wave behavior in an individual electron but only in a collection of electrons. But that does not mean that the wave behavior can be explained on classical lines as an effect of physical interaction among electrons in a stream, for the fact is that the electrons form an interference pattern even when they are fired at the slits one at a time. So either one must suppose that the behavior of each electron is influenced by the path taken by its predecessors, or one must attribute wave properties to each electron.

Things get even weirder when the experiment is set up so as to allow the option of detecting which slit the particles pass through. In so-called “quantum eraser” experiments (q.v., Wikipedia), photons passing through circular polarizers form a scattering pattern or an interference pattern according to whether the polarization that distinguishes which slit they went through is preserved or “erased” by a second, diagonal polarizer. And with so-called the “delayed choice” quantum eraser experiment (q.v., Wikipedia again), things get even weirder. But those are other stories, not covered in Polkinghorne’s book. Polkinghorne finds weirdness enough in the original plain double-slit experiment. He writes:

Electrons arriving one by one is particlelike behaviour; the resulting collective interference pattern is wavelike behaviour. But there is something much more interesting than that to be said. We can probe a little deeper into what is going on by asking the question, When an indivisible single electron is traversing the apparatus, through which slit does it pass in order to get to the detector screen? Let us suppose that it went through the top slit, A. If that were the case, the lower slit, B, was really irrelevant and it might just as well have been temporarily closed up. But, with only A open, the electron would not be most likely to arrive at the midpoint of the far screen, but instead it would be most likely to end up at the point opposite A. Since this is not the case [emphasis mine], we conclude that the electron could not have gone through A. Standing the argument on its head, we conclude that the electron could not have gone through B either. What then was happening? That great and good man, Sherlock Holmes, was fond of saying that when you have eliminated the impossible, whatever remains must have been the case, however improbable it may seem to be. Applying this Holmesian principle leads us to the conclusion that the indivisible electron went through both slits (pp. 23–24, latter emphasis in original).

Pay attention to the words “this is not the case” and try to identify their antecedent: what is not the case? The only thing mentioned in the preceding sentences that can in any clear sense be said to be the case or not the case is that the electron in question struck the screen at the point opposite slit A. But it would be insane to say casually that this is not the case, since there is nothing in the preceding stipulations that would justify such a conclusion. No, what Polkinghorne seems to mean by “this is not the case” is that it is not the case that the electron would be “most likely” to arrive at the point opposite slit A.

(Note: The remainder of this post has been extensively revised since I first posted it. The paragraphs that immediately follow analyze and criticize Polkinghorne’s argument in a very detailed fashion. Readers whose patience or interest is tried by such a treatment may profit by skipping down to the paragraph just before the first graph, in which I restate my criticisms by means of an analogy with an argument whose defects are much easier to recognize.)

Let “E” designate a randomly selected electron that is fired at the slits and that strikes the screen on the far side of them. The first part of Polkinghorne’s reasoning can then be summed up as follows:

1. If E passes through slit A, then E is most likely to strike the screen at a point opposite A.
2. E is not most likely to strike the screen at a point opposite A.
Therefore,
3. E does not pass through A.
   

The argument appears to be impeccable as far as its logical form is concerned. If that is so then the only question to be raised about its cogency is whether both premises are true. But in fact, reflection on the premises reveals an ambiguity that defeats the argument.

Consider premise 2 first. Given the setup of the experiment, the only evidence that we have for attributing to a randomly selected electron a probability of hitting one or another part of the screen is the interference pattern that emerges on the screen.  That pattern shows the highest incidence of impacts at the midpoint between the two slits. From this fact we can conclude that a randomly selected electron that strikes the screen is most likely to do so at the midpoint and not opposite either slit. This reasoning justifies Polkinghorne’s second premise.

Now consider the first premise. E was defined as an electron randomly selected from among all the electrons that reach the screen. But premise 1 concerns an electron that is randomly selected from among those that have passed through slit A. The pattern on the screen provides no evidence whatever relevant to a conclusion about the most likely point of arrival of such an electron as that. The only way to get evidence relevant to a conclusion about a randomly selected electron that has passed through slit A is either to block off slit B or to use a device that distinguishes the impacts of electrons that have passed through A from the impacts of electrons that have passed through B, as in the quantum eraser experiments. It is established that if we do either of these things then no interference pattern emerges. If we block off slit B, the highest incidence of impacts is opposite slit A, and if a device is used that distinguishes the electrons passing through A from those passing through B, then there will be an area of highest incidence opposite each slit. Under such conditions, Polkinghorne’s first premise is true. But his second premise is either false or irrelevant to the conclusion—false if it concerns an electron that has passed through slit A; irrelevant if it concerns an electron whose place of passage is undetermined.

Of course, this is not Polkinghorne’s entire argument, but only one half of its preliminary part. The second half of the preliminary part is the repetition of this argument with “slit B” taking the place of “slit A” in the premises and the conclusion.

4. If E passes through slit B, then E is most likely to strike the screen at a point opposite B.
5. E is not most likely to strike the screen at a point opposite B.
Therefore,
6. The electron did not go through B.
   

That part of the argument is, obviously, just as futile with “B” in it as it was with “A,” but let it stand for the moment, so that we can consider the would-be clinching part of the argument: the supposedly Holmesian conclusion that the electron passed through both slits. Polkinghorne’s stated reasoning is:

3. E does not pass through slit A.
6. E does not pass through slit B.
Therefore,
7. E passes through both slits.

There is nothing Holmesian about such a conclusion at all: Sherlock Holmes would not mistake such a bald non sequitur for a deduction. Nor does it take the intellect of Sherlock Holmes to see that what follows from lines 3 and 6 is:

E does not pass through either slit.

Of course, this is not the desired conclusion at all. Not only does Polkinghorne fail to establish his desired intermediate conclusions (3 and 6); he has set up his entire argument to establish the wrong final conclusion. The undesired conclusion can be avoided if we go back to re-write the previous two subordinate arguments by inserting the qualifier “solely” before the phrases “through slit A” and “through slit B,” and adding a further premise, “E passes through at least one slit.” But the fact remains that the intermediate conclusions 3 and 6 are not established or even made in the slightest degree credible by any of Polkinghorne’s reasoning.

The defects in Polkinghorne’s argument can be brought out by means of an analogy. A graph of the distribution of heights among adults in the United States looks like this (this graph and the two that follow are taken from this Web page by John D. Cook Consulting):

Graph 1: height distribution of all adults in US

The numbers along the bottom represent height in inches. The midpoint of the peak is around 67 inches. Let R be a randomly selected adult resident of the United States. According to this graph, R is most likely to be 67 inches tall. So R is not most likely to be, say, 64 inches tall, or 70 inches tall.

But R may, and indeed (setting aside rare cases of indeterminate sex) must, be either female or male. Suppose that R is female. The distribution of heights for adult females has a peak around 64 inches:

Graph 2: height distribution of adult females in the US

So if R is female, R is most likely to be about 64 inches tall. By contrast, the distribution for adult males has a peak around 70 inches.

Graph 3: height distribution of adult males in the US

So if R is male, R is most likely to be about 70 inches tall. Now imagine that, with these facts in hand, statistician John Jokinghorne presents us with the following argument:

1. If R is female, then R is most likely to be about 64 inches tall (by graph 2).
2. R is not most likely to be about 64 inches tall (by graph 1).
Therefore,
3. R is not female (from 1 and 2).
4. If R is male, then R is most likely to be about 70 inches tall (by graph 3).
5. R is not most likely to be about 70 inches tall (by graph 1).
Therefore,
6. R is not male (from 4 and 5).
Therefore,
7. R is both female and male (supposedly Holmesian conclusion from 3 and 6).

Clearly, all three of the conclusions in this argument are non sequiturs. Conclusion 3 does not follow from (1) and (2), because adding the supposition that R is female, as in (1), makes (2) false or irrelevant to (3). The same applies to the relation of premises 4 and 5 to conclusion 6. And the would-be Holmesian conclusion is of stupefying inconsequence. One may think that Polkinghorne’s argument cannot be as bad as Jokinghorne’s, because it is not so obviously bogus; but logically considered, it is every bit as bad. Its logical defects are exactly analogous. They just happen to be less conspicuous because of the more recondite subject matter.

One last observation: Presumably, Polkinghorne intends his argument to establish something not just about some randomly selected electron in the experiment but about every electron in the experiment, namely that it passes through both slits. The analogous conclusion of Jokinghorne’s argument would be:

8. Every American adult is both female and male.

If Jokinghorne’s argument does not incline you to accept this conclusion (and it shouldn’t), then neither should Polkinghorne’s argument incline you to accept his conclusion about the double-slit experiment.

There may be compelling reasons in quantum mechanics to say that each electron goes through both slits, but whatever those reasons may be, Polkinghorne fails to state them. Making a popular exposition of quantum mechanics requires making the reasoning that leads to its paradoxical conclusions clear. Instead of this, Polkinghorne’s book offers the kind of confused thinking that can at best produce only incomprehension and that at worst produces the false belief that one has understood something when in fact one has merely participated in the author’s own confusions.

Philosopher Defends B***s***

Stephen Asma argues that, because philosophers have failed to formulate a criterion to distinguish science from pseudo-science, the claims of traditional Chinese medicine cannot be dismissed. But it turns out that all that he thinks important is whether the treatments are effective—a question that he thinks immune to critical examination because it is not the sort of thing about which professional philosophers can engage in a lot of sophisticated-sounding talk.

The greater one-horned rhinoceros: one of the species being 

hunted to extinction to supply the market for traditional 

Chinese medicine (source: National Geographic)

Is The Stone, the philosophy blog of the New York Times, meant to be a platform on which professional philosophers can commit the intellectual equivalent of soiling themselves in public, or is my perception just biased by my attention to a few bad examples? I don’t know, but a piece by Stephen Asma published yesterday, “The Enigma of Chinese Medicine” (The Stone, September 29, 2013), certainly falls within the category of public trouser-fouling. Actually, it is an example of something even more contemptible than that: the employment of philosophical sophistication in the service of intellectual confusion.

The argument of Asma’s piece, to the extent that it has one, is that, because philosophers have failed to solve the problem of demarcating science from pseudo-science, one cannot reject the claims of certain “alternative” medical practices, specifically traditional Chinese medicine (“TCM”) and feng shui. After opening with an anecdote about how he recovered from a cold shortly after ingesting a Chinese preparation of freshly spilled turtle blood and strong liquor, Asma intimates that one cannot rule out the possibility that the Chinese concoction has curative powers because of the persistence of what philosophers of science call “the demarcation problem”:

The contemporary philosopher of science Larry Laudan claims that philosophers have failed to give credible criteria for demarcating science from pseudoscience. Even falsifiability, the benchmark for positivist science, rules out many of the legitimate theoretical claims of cutting-edge physics, and rules in many wacky claims, like astrology — if the proponents are clever about which observations corroborate their predictions. Moreover, historians of science since Thomas Kuhn have pointed out that legitimate science rarely abandons a theory the moment falsifying observations come in, preferring instead (sometimes for decades) to chalk up counter evidence to experimental error. The Austrian philosopher Paul Feyerabend even gave up altogether on a so-called scientific method, arguing that science is not a special technique for producing truth but a flawed species of regular human reasoning (loaded with error, bias and rhetorical persuasion). And finally, increased rationality doesn’t always decrease credulity.

We like to think that a rigorous application of logic will eliminate kooky ideas. But it doesn’t. Even a person as well versed in induction and deduction as Arthur Conan Doyle believed that the death of Lord Carnarvon, the patron of the Tutankhamen expedition, may have been caused by a pharaoh’s curse.

Setting aside the appeals to authority, Asma’s main claims here are these: (1) No one has identified a reliable criterion for distinguishing science from pseudo-science. (2) No one has given a credible specification of a method distinctive of science. (3) Increased rationality or practice in induction and deduction does not always decrease credulity toward kooky ideas.

The third claim seems pretty clearly irrelevant to Asma’s thesis. The case of Arthur Conan Doyle’s belief in the curse of Tutankhamen (it is disappointing that Asma does not cite the more instructive case of Doyle’s belief in the Cottingley fairies) might be of some relevance if it were an instance in which someone was led to supernaturalistic conclusions by sound deductive and inductive reasoning (supposing such a thing to be possible). But it is not; it is an instance of the distortion of judgment by cognitive bias. Such cases remind us that cognitive bias afflicts all human beings without exception. That is precisely why we need instruction in deductive and inductive reasoning, as well as knowledge of the cognitive biases themselves: only then can we, sometimes, rise above our worse selves and correct our judgment in empirical matters when it goes awry. But, as Asma makes no further reference to these observations in his piece, I will say no more about them.

What of the first two claims? Granted, for the sake of argument, that there is no known universal criterion or distinctive method demarcating science from pseudo-science, how is that supposed to lend credibility to the claims of traditional Chinese medicine? Asma never makes this clear, but the implied reasoning seems to be this: “Many people dismiss traditional Chinese medicine as pseudo-science; but there is no way to distinguish in principle between science and pseudo-science; therefore, one cannot dismiss traditional Chinese medicine.” If this is the intended argument, it fails on two scores. In the first place, the fact that one cannot give a universal criterion for distinguishing A from B does not show that there is no difference between A and B, or that one is unjustified in identifying something as an instance of A and not of B. There is, for example, no commonly accepted explanation of the distinction between right and wrong: it doesn’t follow that one can’t soundly and justly judge of some action that it is wrong. Second, even if Asma could show that traditional Chinese medicine escapes the charge of pseudo-science, it would not follow that its claims have the slightest degree of credibility. “Scientific” doesn’t imply “warranted” or “sound,” and “not pseudo-science” doesn’t imply “not a load of bollocks.”

I have said that this seems to be Asma’s argument, but in the end it is not clear that Asma even intends to make an argument. What we get instead in the conclusion of the piece is just a certain insinuation. After providing a second anecdote of his undergoing a treatment by traditional Chinese medicine and subsequently feeling decidedly better, he concludes the piece with these paragraphs:

It seems entirely reasonable to believe in the effectiveness of T.C.M. [traditional Chinese medicine] and still have grave doubts about qi. In other words, it is possible for people to practice a kind of “accidental medicine”—in the sense that symptoms might be alleviated even when their causes are misdiagnosed (it happens all the time in Western medicine, too). Acupuncture, turtle blood, and many similar therapies are not superstitious, but may be morsels of practical folk wisdom. The causal theory that’s concocted to explain the practical successes of treatment is not terribly important or interesting to the poor schlub who’s thrown out his back or taken ill.

Ultimately, one can be skeptical of both qi and a sacrosanct scientific method, but still be a devotee of fallible pragmatic truth. In the end, most of us are gamblers about health treatments. We play as many options as we can; a little acupuncture, a little ibuprofen, a little turtle’s blood. Throw enough cards (or remedies), and eventually some odds will go your way. Is that superstition or wisdom?

If this is the summation of Asma’s position, then the preceding references to the demarcation problem, far from being an argument, are just a sort of preparatory entertainment and are inessential, if not altogether irrelevant, to his main point. According to what Asma says here, it makes no difference whether traditional Chinese medicine is science or pseudo-science, because the legitimacy of its theoretical claims—about qi and so forth—is irrelevant to claims of its effectiveness. The “fallible pragmatic truth” of such claims is what really matters.

Notice what has happened here. Having spent most of the piece considering the theoretical claims of traditional Chinese medicine and invoking the demarcation problem to argue—by a villainous non sequitur—that because we can’t solve the problem, we can’t dismiss such claims, he now says that it is only the claims of effectiveness that matter. And with regard to such claims, he coyly suggests, we are wise to take a chance on the treatments because we can’t know that the claims for them are false.

What sort of claim is Asma talking about here? And how are such claims to be assessed? Notice that there is a world of difference between claims of the following two sorts:

(1) I underwent treatment T, and subsequently my headache went away.

(2) Treatment T is effective against headache.

Obviously, the second claim is much stronger than the first. For one thing, it has a generality to it that the first lacks. But more than that, it asserts a causal connection that the first one does not. To establish claim (1), all that is needed is evidence that the speaker had a headache before she underwent T and ceased to have it afterward. To establish claim (2), we require evidence (a) that quite generally people with headaches who undergo T lose those headaches after undergoing T and (b) that this is not due to factors extraneous to T, such as the headaches going away by themselves. Anecdotes on the lines of claim (1) can support point (a), and many people content themselves with finding evidence of this nature—a manifestation of confirmation bias. But such anecdotes, no many how many in number, fail to establish, or even to support, claim (2) if they are not supplemented by evidence supporting point (b). That sort of evidence is by far the more difficult sort to procure. It requires experimental controls, such as blinding and, optimally, even double-blinding (arranging that neither the administrator nor the recipient of the treatment knows whether T is being administered or not). And, of course, in any study of such matters, the significance of the results must be assessed according to the size of the sample, the basis of selection, possible sources of bias, and so forth. Such considerations are the ABCs of the “scientific method” on whose existence sophisticated philosophers of science like Feyerabend (invoked by Asma in the passage quoted earlier) would cast such scornful doubt.

What is exasperating about Asma’s piece is that he proceeds as if none of this elementary scientific method existed, or mattered. He seems to reason that, once the theoretical claims of traditional Chinese medicine are set aside, no critical assessment of the remaining claims is possible: anecdotes are all the evidence that anyone has or needs, because the choice of a treatment is always a gamble anyway. Well, of course there is an element of uncertainty in any medical treatment; in that respect, any choice of treatment is a gamble. But the fact that we don’t know exactly what is going to happen in any specific instance does not entail that we don’t know a great deal about the effectiveness of treatments. And of course it is possible that one or another Chinese treatment will eventually be found to be genuinely effective (i.e., more effective than placebo); that does not entail that we don’t already know a lot of them to be ineffective, or that we have as much reason to believe as to disbelieve the claims of effectiveness made for others of them. (See, e.g., Joe Nickell, “Traditional Chinese Medicine: Views East and West,” Skeptical Inquirer, March–April 2012.)

Pondering the “demarcation problem” is a professional specialty of philosophers. Evaluating the effectiveness of “alternative” medical treatments is not: it is a matter for medical scientists, though the results of their research can be judged and appreciated by persons without medical or other scientific training. Asma, having gotten to the end of his professional expertise by reflecting—uselessly and irrelevantly, as it emerges in the end—on the demarcation problem, proceeds as if there is simply no further basis for a critical assessment of the claims of traditional Chinese medicine. But there manifestly is: it just isn’t a matter of philosophical expertise. The specifically philosophical elements of Asma’s piece turn out in the end to be nothing but a blind for making it look as though claims of effectiveness made for traditional Chinese medicine and feng shui were beyond reach of critical examination.

And When I Know Precisely What Is Meant by “Magisterium”

Stephen Jay Gould’s thesis that science and religion are “non-overlapping magisteria” has weaknesses enough when considered solely on the basis of his presentation of it. When one considers it in light of the original ecclesiastical meaning and use of the term “magisterium,” it appears positively grotesque.

Pope Paul VI

A while back, I posted three entries on Stephen Jay Gould’s view of the relation between science and religion, a conception that he sums up as the principle of “non-overlapping magisteria” or “NOMA” (“Stephen Jay Gould on Science and Religion,” “More on Gould on Science and Religion,” and “A Dilemma for NOMA”). By “magisterium”—a bit of ecclesiastical Latin derived from magister, “teacher”—Gould says that he means “a domain of authority in teaching,” or, more specifically, “a domain where one form of teaching holds the appropriate tools for meaningful discourse and resolution” (see note at end for source). He explains further:

Each domain of inquiry frames its own rules and admissible questions, and sets its own criteria for judgment and resolution. These accepted standards, and the procedures developed for debating and resolving legitimate issues, define the magisterium—or teaching authority—of any given realm.

According to Gould, science and religion are two “non-overlapping magisteria.” The magisterium of science comprises “the empirical realm: what the universe is made of (fact) and why does it work this way (theory),” while that of religion “extends over questions of ultimate meaning and moral value.” No question belongs within both magisteria: hence their “non-overlapping” character.

The idea that religion has or is a magisterium in Gould’s sense, and the idea that questions of ethical value and existential meaning belong within that magisterium, both invite strong objections, some of which I presented in my previous entries on this topic. Right now, though, I want to consider simply what the term “magisterium” means. I have presented Gould’s account of what he means by it. But it remains to consider what it means in the discourse from which he takes it, that of the Catholic Church. In what follows, I shall do my best to interpret accurately the passages that I have found, though I very much doubt that I shall avoid errors, not only because of my lack of familiarity with Catholic doctrine but because of my lack of comfort with it. Still, I believe that the evidence of the quotations will suffice to show how ill-suited the term “magisterium” is to the use to which Gould wants to put it.

The earliest occurrence of the word “magisterium” in Catholic ecclesiastical discourse that I have been able to find comes from a document of the First Vatican Council (1869–1870):

Wherefore, by divine and Catholic faith all those things are to be believed which are contained in the word of God as found in Scripture and tradition, and which are proposed by the Church as matters to be believed as divinely revealed, whether by her solemn judgment or in her ordinary and universal magisterium. (First Vatican Council, session 3, chapter 3, article 8)

The terms “solemn,” “ordinary,” and “universal” here are all technical terms. Definitive decrees made by the Pope and his councils belong to the “solemn” or “extraordinary” magisterium of the church, while all other teachings of the Pope and the bishops belong to the “ordinary” and “universal” magisterium of the church (source). The main point here is that the Bible and the traditions of the Catholic Church contain a body of teaching that is divinely revealed and therefore authoritative.

A passage from an encyclical by Pius IX, the Pope who presided over the First Vatican Council, lays stress on the point that it is solely the Pope and the bishops who bear the divinely conferred authority to determine revealed truth, not the laity (and, presumably, not the lower priesthood either):

For these writings attack and pervert the true power of jurisdiction of the Roman Pontiff and the bishops, who are the successors of blessed Peter and the apostles; they transfer it instead to the people, or, as they say, to the community. They obstinately reject and oppose the infallible magisterium both of the Roman Pontiff and of the whole Church in teaching matters. (On the Church of Italy, Germany, and Switzerland (1871), “Further Heresies”; source)

The same point was affirmed by the Second Vatican Council (1965), over which Pope Paul VI presided:

But the task of authentically interpreting the word of God, whether written or handed on, has been entrusted exclusively to the living teaching office of the Church [soli vivo Ecclesiae Magisterio concreditum est], whose authority [auctoritas] is exercised in the name of Jesus Christ. This teaching office [Magisterium] is not above the word of God, but serves it, teaching only what has been handed on, listening to it devoutly, guarding it scrupulously and explaining it faithfully in accord with a divine commission and with the help of the Holy Spirit, it draws from this one deposit of faith everything which it presents for belief as divinely revealed.

It is clear, therefore, that sacred tradition, Sacred Scripture and the teaching authority of the Church [Ecclesiae Magisterium], in accord with God’s most wise design, are so linked and joined together that one cannot stand without the others, and that all together and each in its own way under the action of the one Holy Spirit contribute effectively to the salvation of souls. (Dei Verbum, chapter two, article 10; English text; Latin text)

The gist of this passage is that the magisterium of the Church is an authority divinely vested in the Pope and the bishops to teach the members of the Church what is divinely revealed in scripture and tradition. (The alternation in the last-quoted passage between the two translations “teaching office” and “teaching authority” does not reflect a difference of meaning but rather a wish to avoid repetition in the sentence in which the word “authority” (auctoritas) also occurs.)

The ecclesiastical use of the term “magisterium” differs from Gould’s appropriation of it on several points. First, in ecclesiastical usage, a magisterium is not a “domain” of teaching authority: it simply is teaching authority. There are, of course, discussions of the range of matters in which the Church has this authority; but the word “magisterium” signifies the authority itself and not the subject matter to which it pertains. Hence, in ecclesiastical usage, it would be plain nonsense to speak, as Gould sometimes does, of the magisterium of this or that subject matter (e.g., natural fact, ethical values, etc.). The magisterium is the magisterium of the Church. Second, the pertinent sense of “authority” is not merely epistemological but also institutional: the magisterium of the Church is the authority that a certain body, the Catholic episcopacy, has over the faithful in matters of faith and morals. Third, the term “teaching” here is not a byword for “inquiry” or “discovery” but signifies the handing-down of conclusions by those in authority to those who are obliged to accept them. The magisterium of the Church has nothing to do with procedures for posing questions and resolving disputes. The Church may have these, but they are not what the word “magisterium” signifies. Rather, it signifies the status of the upper priesthood’s conclusions as divinely revealed truth. Fourth, the term occurs (so far as I have found) only in the singular form, never in the plural: there is no ecclesiastical talk of “magisteria,” but only of the magisterium of the Church (Magisterium Ecclesiae). Thus the term does not serve to demarcate one subject matter from another or one way of answering questions from another, but only to identify who or what bears teaching authority in matters of revealed truth.

In my previous entries on Gould’s thesis, I argued that there is no compelling reason to believe that religion has teaching authority with respect to any subject matter whatever. Specific religious institutions may have sectarian authority over their adherents, but there is no “form of teaching [that] holds the appropriate tools for meaningful discourse and resolution” characteristic of religion as such.

As questionable as it is to speak of the “magisterium of religion,” to speak of the “magisterium of science” is even worse. In fact, it is positively grotesque. There are, of course, creationists who try to smear evolutionary biology with the tu-quoque claim that it is a religion (example 1; example 2). But even they do not hold that science has the authority structure of a religion: rather, their claim is that the theory of evolution is not science. Anyway, regardless of what such ideologues may say, there can be no question that in its original import, the term “magisterium” has no application to scientific inquiry.

Certainly science can be taught and is taught. Many of its practitioners are among its teachers. But the practice of science is not in any serious sense a “form of teaching,” in Gould’s phrase; much less is it a handing-down of dogmata from those in authority to those who must obey. There is, in fact, almost nothing in the notion of Ecclesiae Magisterium that applies to science. The mismatch between the original meaning of the term and the use to which Gould tries to put it is so stark that one has to wonder how Gould could profess to “find the term so beautifully appropriate for the central concept of this book that I venture to impose this novelty upon the vocabulary of many readers.” Whatever made the term seem that way to him, I suspect that it had very little to do with what the Vatican actually meant by it.

REFERENCES

Stephen Jay Gould, Rocks of Ages: Science and Religion in the Fullness of Life (New York: Ballantine Books, 1999). The indented quotation is from pp. 52–53; the rest are from pp. 5–6

Gould presents his thesis more briefly in his essay “Non-Overlapping Magisteria,” Natural History 106 (1997).

My title is derived from a verse of the patter song of Major-General Stanley, “And when I know precisely what is meant by ‘commissariat.’” Gould was a great admirer of the work of Gilbert and Sullivan: see his essay “The True Embodiment of Everything That’s Excellent: The Strange Adventure of Gilbert and Sullivan,” The American Scholar, Vol. 69, No. 2 (Spring 2000), pp. 35–49.

More on Thinking Probabilistically

We typically use the plural noun “probabilities” only when speaking of events that are potentially repeatable, like throws of a pair of dice. But the notion of probability has another aspect, namely the degree of strength of belief warranted by evidence. This seems to apply, at least potentially, to the question of divine existence. But one may doubt whether the “God” about which some reason probabilistically can be identified with the God worshiped and served in any actual religion.

According to this page, these actually work

My previous entry addressed, but—characteristically, I confess—did not answer, the question “Is the existence of God a matter of probabilities?” I wish now that I had used the singular form of the noun “probability” rather than the plural, as the latter has associations that I don’t welcome. The plural form “probabilities” tends to suggest numerical values or measures of probability, which in turn (and this is the most unwelcome part) suggests the sort of case in which an event of a specific, repeatable type occurs under specific conditions—for instance, the event of a hand of five playing cards containing a pair, given that the five cards are dealt randomly from a deck of 52. Even if we are speaking, say, of the probability that candidate So and So will win the upcoming election, which is not a repeatable event-type but a single occurrence, we may consider that outcome as belonging to a type specifiable more or less broadly according to country, locale, time period, type of office, characteristics of the candidate, and so on; and we can then calculate the chances accordingly.

But what if we are speaking of the probability of a possible fact that is not an instance of a repeatable type? Discussions of the existence of God would be a case of this. The idea of assigning the existence of God to some type of repeatable event seems senseless. Perhaps some diligent analytic metaphysician somewhere has reckoned the probability of divine existence as the proportion of God-made possible worlds to Godless ones; but I don’t care to take account of all conceivable products of academic invention. If the concept of probability applies only to repeatable event-types, and if, as seems plain, the existence of God is not an event of a repeatable type, then the answer to the question “Is the existence of God a matter of probability?” is a flat and rather uninteresting “No.”

But the concept of probability is not restricted to such cases. When Bishop Butler remarked in the “Introduction” to his Analogy of Religion (1736) that “to us, probability is the very guide of life,” he was not referring to the calculus of chance, which was then in its infancy. He was speaking of probability in contrast with absolute certainty, and of the condition of finite intellects in contrast with that of an infinite one:

Probable evidence is essentially distinguished from demonstrative by this, that it admits of degrees; and all variety of them, from the highest moral certainty, to the very lowest presumption. . . .

Probable evidence, in its very nature, affords but an imperfect kind of information, and is to be considered as relative only to beings of limited capacities. For nothing which is the possible object of knowledge, whether past, present, or future, can be probable to an infinite Intelligence; since it cannot but be discerned absolutely, as it is in itself, certainly true, or certainly false. But, to us, probability is the very guide of life.

Probability is our guide in life because our knowledge of the world is, by our nature, limited. To follow probability in the pertinent sense is not to reckon odds but to weigh what Butler calls “presumptions,” or reasons for belief. There is more to probability than mere chance. As Ian Hacking remarks in his historical study The Emergence of Probability,

Probability has two aspects. It is connected with the degree of belief warranted by evidence, and it is connected with the tendency, displayed by some chance devices, to produce stable relative frequencies.

Hacking dubs the first aspect of probability the “epistemological” (from Greek epistēmē, “knowledge”) and the other the “aleatory” (from Latin ālea, “die” or, by derivation, “game of chance”). I think “epistemic” is a more widely used term for the former, although, since it is belief and not knowledge that is in question, “doxic” (from Greek doxa, “belief”) would be more apt. Whatever the terminology, and however we may try to understand the relation between these two aspects of probability, it is the doxic or epistemic aspect that is pertinent when the existence of God is treated probabilistically. The fundamental thought is not that we can calculate the chance that God exists as we can the chance of getting a certain result from throwing a pair of dice, say, but that some degree of strength of belief that God exists is warranted by the evidence available to us.

The question “Is the existence of God a matter of probability?” is a question about a question. It concerns how the question “Does God exist?” may be answered—what sort of thing one has to do, or may do, to answer it. Anyone who assumes that the question must be, or may be, answered by weighing what Butler terms “probable” evidence (meaning empirical evidence, as contrasted with the “demonstrative” evidence of proofs a priori) assumes that the answer to the first question is “Yes”—that the existence of God is a matter of probability.

Most writers who argue for atheism seem to make this assumption. They typically argue either that there is no evidence that God exists or that there is evidence that God does not exist. It seems to go without saying for them that to answer the question of God’s existence otherwise than by evaluating the available evidence would be incompatible with intellectual integrity. For instance, Richard Dawkins entitles one chapter of his book The God Delusion “The God Hypothesis” and another “Why There Almost Certainly Is No God.” For Dawkins, to treat belief in God as a “hypothesis” is what it means to take the proposition “God exists” seriously as a contender for truth. As for the probabilistic qualification “almost certainly,” it is not for him a sign of weakness but a point of strength, as it shows that he, like any good scientist and in contrast to the great majority of theistic believers, founds his opinion in the matter on where the preponderance of evidence lies. “What matters,” he says at one point, “is not whether God is disprovable (he isn’t) but whether his existence is probable”; which, of course, it isn’t, according to him.

I am inclined to agree, in a certain guarded fashion, with Dawkins that the existence of God is not probable—not, however, because it is improbable, as he thinks, but because it is not a matter of probability at all. I said in my previous entry that it is not easy to defend this claim. This evoked some interesting comments from Tommi Uschanov, who does not share my sense of difficulty on this point. The following two observations, which, he says, “have been presented often in Wittgensteinian philosophy of religion, by O. K. Bouwsma or D. Z. Phillips, for instance,” he finds “do the work so well that nothing more needs to be said”:

1) If someone has lived his life atheistically or otherwise irreligiously through a wrong assessment of probabilities, due to an innate lack of talent for mathematics and statistics, this would seem to mean that God condemns him to perdition through a failure to endow him with sufficient talent to make the required calculations. But this is obviously contrary to the moral teaching of the religion itself. And indeed to the whole official self-image of the religion.

2) The importation of the probabilistic way of speaking to properly religious language makes this language (not unintelligible, which would be the positivist critique, but) uproariously funny.

For instance, . . . Psalm 23 does not say: “The Lord is probably my shepherd; I probably shall not want. . . .” [Other examples follow.]

The first argument seems to me an effective objection to anyone who, like William Lane Craig, uses probabilistic arguments to defend the reasonableness of Christianity; but only because Christianity, at least in some of its varieties, holds the non-acceptance of Christian doctrine to be a sin subject to divine retribution. There are, of course, interpretations of Christianity that reject this belief, but it has been a part of Christian doctrine historically and is, so far as I know, not found in any other major religion. In any case, it is not a part of theistic belief per se. The objection, therefore, tells only against probabilistic defenses of some varieties Christianity and not to probabilistic approaches to the question of divine existence in general. Further, the objection seems to be just a variant of the ancient one that if God makes human beings sinful that he cannot justly punish them for their sins: so if he makes someone inept at forming beliefs, he cannot justly punish that person for failing to arrive at the right beliefs. In any case, the most that this objection can show is that it is imprudent for a Christian to try to make probabilistic arguments for the existence of God. It doesn’t show that there is anything inherently wrong with doing this in general or with treating the question of God’s existence probabilistically in the first place.

Uschanov’s second argument may seem even less effective, as it can be rebutted on several grounds. For one thing, to make a probabilistic argument means only that the premises from which one argues provide reasons to accept one’s conclusion without entailing it with logical necessity. It does not mean that the conclusion has to include a probabilistic qualifier. For instance, if I know that Smith fell into a piece of industrial machinery and was ground to bits, and I conclude on that basis that he is dead, I am reasoning probabilistically; that does not mean that I am obliged to say only, “Smith is probably dead.” In such a case, my premise warrants my conclusion with moral certainty, which is certainty beyond a reasonable doubt (though not beyond all logically conceivable doubt). For another thing, if someone tries to show that there is sufficient empirical evidence to conclude that God exists, it does not follow that she is bound to import probabilistic language into her religious practices, such as prayers, or to rephrase scriptural passages to include such language. Finally, to advance a probabilistic argument for belief in the existence of God does not commit one to holding that theistic believers should base their belief on such a justification. One might offer the argument purely for the purpose of refuting skeptical doubts of God’s existence and showing that theistic belief is rationally warranted. (As I said in my reply to Tommi’s comment, William Lane Craig seems to be trying to do something parallel to this, but specifically for certain Christian doctrines, not for bare theism.)

With all that said, I think that there is at least potentially more to Uschanov’s objection (or to the sources from which he draws it) than such replies recognize. The point of the objection, as I understand it, is not to argue, “To defend theism probabilistically commits you to saying things like these; these things are patently ridiculous; therefore, it is misconceived to defend theism probabilistically.” At least, I think that the objection is much more effective if it is taken differently, as an attempt to bring out something incoherent in the probabilistic approach to divine existence precisely by taking it seriously. It is as if one were to say: “You want to treat the existence of God as a matter of probability? Fine! Let’s do that consistently and see what happens!”

The suggestion, in other words—at least, this is the suggestion that I derive from the objection as stated—is that if you adopt a probabilistic approach to the question of God’s existence, the “God” that you reason about, no matter whether your conclusion is theistic or atheistic, will be a philosophical fetish or idol and not that which is worshiped and served in any of the world’s religions. Probabilistic reasoning and religious practice are not two different ways of relating oneself to the same entity; rather, one is a way of relating oneself to God, if God exists, and the other is a way of relating oneself to a figment of the intellect mistakenly called by the same name. To put the point another way, a possible object of religious devotion is not a possible object of probabilistic reasoning.

That, at any rate, is the idea that Uschanov’s comment suggests to me. I think it can also be taken as a development of the objection that Duncan Richter was making in the blog entry that I discussed in my previous entry here, when he said that a probabilistic approach to the question of divine existence “treats God as the same kind of thing as a fluke gust of wind, i.e. something whose odds we might calculate or at least estimate, i.e. as something natural, however super.” If the objection can be satisfactorily worked out, it should be applicable to polytheistic religions as well as to monotheisms—or rather, not to the religions, but to probabilistic treatments of the question of the existence of their gods. It may even be applicable to probabilistic would-be defenses of revealed religion, such as that offered by Craig, who incorporates scripture into his evidence base.

I find it an attractive idea, but I don’t entirely trust it, and I certainly don’t have a defense of it ready. So, once again, I close with unfinished business.

REFERENCES

Joseph Butler, Analogy of Religion, Natural and Revealed, to the Constitution and Course of Nature, ed. by G. R. Crooks (New York: Harper and Brothers, 1860), p. 84.

Richard Dawkins, The God Delusion, paperback ed. (Boston and New York: Houghton Mifflin, 2008), p. 77.

Ian Hacking, The Emergence of Probability, 2nd ed. (Cambridge: Cambridge University Press, 2006), p. 1.

Is the Existence of God a Matter of Probabilities?

To treat the question whether God exists as a matter of probabilities seems to some people completely natural and to some utterly perverse. Believers and non-believers are found in both camps. I agree with Duncan Richter in finding such a way of thinking deeply wrongheaded, but I find his attempt to say what is wrong with it unsatisfactory.

I was delighted to find my previous two posts (1, 2) on ancient polytheism and the concept of evidence cited and discussed by Duncan Richter in his blog Language on Holiday. Richter’s discussion includes a parenthetical remark that approaches some lines of thought that I have pursued. He remarks that arguments for the existence of God that are founded on empirical observations, whether concerning religious experience, miracles, or design, all try to establish their conclusion as a matter of probability. (For the sake of simplicity, I shall in this entry equate questions of the existence of a divine being with the question of the existence of God, i.e., an inherently unique deity, leaving polytheism out of account.) He says of this way of thinking:

It is a logical and ethical mistake, an error in grammar and theology, to think of the existence of God as a question of probabilities. This might become clearer if one tried to calculate the odds, although I think people have done this and not achieved the clarity I have in mind. In case it isn’t clear, it’s a mistake because it treats God as the same kind of thing as a fluke gust of wind, i.e. something whose odds we might calculate or at least estimate, i.e. as something natural, however super. To think of God this way is to misunderstand what believers believe in a way that is both simply wrong (that isn’t what they believe) and insulting (it is to treat God as something less than what they believe). This is complicated by the fact that some believers (or “believers”) are idolaters in just this way, but that isn’t the kind of belief that interests me. There’s also the question whether non-believers like me should care about the alleged badness of insulting God, but we can at least respect the feelings of believers. And I think we can respect the concept of God, too, and want to do justice to it.

I suspect that the passage was written with some haste and impatience, for two reasons: first, it is rather long and contentious, not to say blustery, for a merely parenthetical remark; and second, saying exactly what is wrong with treating the existence of God as a matter of probability is no easy matter—or so, at any rate, say I. In this piece, I will give reasons for finding Richter’s presentation of the case unsatisfactory. I hope, though I dare not promise, to make a stronger case of my own in a subsequent entry to this blog.

Richter finds fault with probabilistic discourse about theism in two respects. One concerns the way in which it treats theistic believers. According to him, it insults them by treating God as “something less than what they believe [in].” He also implies that it fails to “respect their feelings.” Now it is possible that I am missing something here, but to me such claims seem simply irrelevant. If—and this is a large “if”—there is no fundamental conceptual error inherent in inquiring whether probability favors the existence or the non-existence of God, then I can see no compelling reason why those making such inquiries should care in the least whether they hurt the feelings of theistic believers or denigrate the object of their beliefs. At most, such considerations would be reasons to pursue such inquiries out of public hearing, so that they not offend the delicate ears of believers. But one could just as credibly argue that it is insulting to believers to assume that their sensibilities require this kind of protection. In any case, if they do, then it’s hard cheese for them and nothing more.

So it seems to me that Richter’s would-be ethical objection can be set aside. The entire weight of his objection must rest on its logical and grammatical part—“grammatical” here in Wittgenstein’s sense of concerning what one can intelligibly say and under what conditions. I believe that if this element of the objection could be satisfactorily articulated, the ethical aspect would emerge by itself. In fact, if I may mix the terms of the later Wittgenstein with the phrasing of the earlier, I would say that on this point grammar and ethics are one: if we could understand exactly what is so perverse about talking probabilistically about the existence of God, we would not distinguish a logical an ethical objections. Richter seems to me to move, or at least to face, in this direction when he describes theistic believers who take the question of divine existence to be a matter of probability as “idolaters,” a term that implies perversion of both intellect and will; but to make such a heavy charge stick would require an argument than I, for one, have not got at the ready.

What, then, is wrong with trying to assess the probability of divine existence? Richter holds that to do so “treats God as the same kind of thing as a fluke gust of wind, i.e. something whose odds we might calculate or at least estimate, i.e. as something natural, however super.” To take the first point first: what are the conditions under which we can calculate or at least estimate the odds of something? Richter may be assuming that we can do this only when we are talking about a type of event that occurs and recurs unpredictably under certain specifiable conditions, such a gust of wind of such and such a character that occurs a certain number of times in a certain location over a certain period of time. Given such specifications, we can observe a sample of cases and calculate the relative frequency of the event in question. The larger the sample that we have observed, the more confidently can we identify this relative frequency with the probability of a gust of wind occurring under the specified conditions.

Obviously, none of this is applicable to the existence of God, since that is not a repeatable event. So, if those who think of the existence of God probabilistically operate with a frequentist interpretation of probability, then they are hamstrung from the outset. But, of course, they do nothing of the sort; or at least, they need not do so. Here is the philosopher and Christian apologist—and, if Richter’s assessment is just, idolater—William Lane Craig on his website Reasonable Christianity answering a correspondent who is perplexed by the application of probabilistic terms to the question of the existence of God. Craig’s correspondent understands probability not in terms of relative frequency but according to what is known as the classical interpretation of probability, in which probability values are equated with the ratio of the number of cases in which a certain event occurs to the total number of possible cases. But Craig’s reply is equally applicable to the frequentist interpretation:

Probabilities are always relative to some background information. . . . Now the atheist says God’s existence is improbable. You should immediately ask, ‘Improbable relative to what?’ What is the background information? . . . The interesting question is whether God’s existence is probable relative to the full scope of the evidence.

Had you asked that question of your friend, it would have been evident that he is considering no background information at all! He seems to be talking about a sort of absolute probability of God’s existence Pr (G) in abstraction from any background information B and specific evidence E. That’s a pointless exercise. He seems to be imagining all the possible deities that could exist and asking, “What are the chances apriori that a certain one of these exists?” How silly! That’s like inquiring about the absolute probability that a certain person, for example, you, exists, given the infinite number of possible persons there could be. Nobody is interested in such absolute probabilities, if there even are such things. What we want to know, rather, is the probability of your existence or God’s existence relative to our background information and specific evidence: Pr (G|E & B).

Craig operates with a subjectivist or, as it is widely known, Bayesian interpretation of probability. On this interpretation, the values that are assigned to probabilities of events represent degrees of confidence in the occurrence of those events. Such assignments do not require that the events be repeated or repeatable at all: one can attribute a degree of probability to any event whatever, even the existence of God (or of a god of some specific description). (“Event” here is a technical term in probability theory for that to which a probability value is assigned and is not contrasted with “fact” or “state of affairs.”)

The competition among interpretations of probability is a vast and complicated issue, into which I don’t propose to enter any farther. My point here is simply that, if one holds there to be a confusion inherent in treating the existence of God as a matter of probability, one cannot support that claim by simply assuming an interpretation of probability that requires a repeated event or a countable set of possible outcomes, as there are interpretations of probability that don’t require those things. To Richter’s remark that to talk of the existence of God in probabilistic terms treats it as “something whose odds we might calculate or at least estimate,” Craig would reply, or anyway could reply, “Yes; so what?” So, for that matter, could Richard Dawkins.

I can imagine one of these probabilists saying to Richter (and, for that matter, to me): “I suspect that the reason why you dislike this talk of the probability of God’s existence is that it seems to kill all the existential drama and to make the business of believing or not believing in God out to be a matter purely of the intellect. But, look you, I am not touching at all on the question of what moves people to believe or disbelieve in God, or what difference their belief or lack of belief makes to their lives. I am just assuming that when we ask, ‘Does God exist?’, we are posing a genuine and well-formed question—one that has a correct answer. The correct answer is either ‘Yes, God exists’ or ‘No, God does not exist.’ To determine which is the correct answer, one has to determine where the preponderance of evidence lies. To do this is to assess the probability of the proposition ‘God exists.’”

I do not think that this argument is unanswerable, but I do think that to answer it is not easy. In any case, I leave the task for a later post.

Ancient Polytheism and the Concept of Evidence Reconsidered (More Briefly)

The issue of whether the ancient Greeks could have had good evidence of the existence of their gods comes down to the issue of whether a theistic explanation of their religious experiences can be a better explanation than any naturalistic one.

Image found at Ancient Greek Gods for Kids

My previous entry on this blog (“Ancient Polytheism and the Concept of Evidence,” August 2, 2013), written in response to a piece by Gary Gutting (“Did Zeus Exist?”, The New York Times on line, July 31, 2013), grew out of a couple of paragraphs that I had posted in a discussion of Gutting’s piece on Facebook. I thought at the time that I needed only to add some circumstantial explanation to what I had written to make an entry for this blog but instead I ended up writing a completely new piece twelve paragraphs long. It is bad enough to put so much time and so many words into commenting on someone else’s blog post; what makes matters worse is that by writing at such length I make it all the more unlikely that anyone, even among the small number of people who ever see this blog, will read what I wrote. Today I will try to make up for the verbosity of that entry by setting forth my main thoughts in this matter concisely and without much reference to the details of Gutting’s piece. I have on some points modified the position that I took in the earlier piece, as I have come to a more charitable assessment of what Gutting does with the concept of evidence, but I do not bother to indicate the modifications here.

(1) If some people, such as the ancient Greeks in Parker’s account, have experiences that they take to be theophanies (manifestations of a god or of gods), these experiences may be the basis of their belief in their gods. But that does not mean that they take these experiences to be evidence of the existence of those gods.

(2) In fact, no one who experiences what seem to him to be theophanies can coherently regard his experiences as evidence of the existence of gods, since the presumption of the existence of gods is inherent in the experiences themselves. An ancient Greek who claims to have experienced a theophany might say, e.g., “Zeus manifested himself to me.” To make such a statement is not to cite anything that can possibly count as evidence of the existence of Zeus, as the statement presupposes the existence of Zeus.

(3) For an ancient polytheist to be in a position to cite his religious experiences as evidence of the existence of his gods, he must renounce the naive conviction that originally characterized his experiences in favor of a skeptical attitude, and must redescribe his experiences in terms that are neutral with respect to the existence of gods. So he must say, e.g., not “Zeus manifested himself to me,” but rather, “It seemed to me as though Zeus manifested himself to me.”

(4) Note that such a person would have to do this across the board with regard to everyone’s putatively theophanic experiences. The issue is not the veracity of this or that person’s religious experience but rather the existence of the gods themselves. It would be no effective argument to say, e.g., “What I saw and felt during the ritual agrees with the accounts of others to whom Zeus has appeared; therefore, Zeus exists”; for the statement that Zeus has appeared to others presupposes that Zeus exists. To cite religious experiences as evidence of the existence of gods, one must describe all such experiences in terms that are neutral with respect to the existence of gods.

(5) For an ancient Greek apologist for polytheism to get from the premise “Such and such Greeks have had such and such experiences” (the experiences being described in terms that are neutral with respect to the existence of gods) to the conclusion “The gods exist,” he would have to supply some further premise or premises. Otherwise, the premise of his would-be argument provides no reason to accept its conclusion. That is to say, the cited experiences do not constitute evidence of the existence of the Greek gods unless a further premise or premises can be supplied that makes the argument cogent.

(6) What might this premise be? One possibility is: “So many pious Greeks can’t be wrong.” That, of course, invites the rebuttal: “Yes, they can.” The issue, as far as I can tell, comes down to the question of what sort of explanation of the Greeks’ religious experiences is most compelling: a theistic one, according to which the gods really did appear to the ancient Greeks, or a non-theistic one, such as one in terms of natural causes. If the polytheistic apologist can establish the claim that the best possible explanation of the data that he has cited is that the Greek gods really have appeared to him and to his fellow Greeks, then he has a cogent argument, and the religious experiences of ancient Greeks do indeed constitute evidence of the existence of the Greek gods. But can he establish such a claim?

(7) Gutting argues, in effect, that we have no rationally compelling basis for rejecting such a claim. The modern rejection of supernatural causes, he holds, is not a finding of science but an a priori presupposition of scientific procedure. Therefore, we have no rational basis for dismissing the possibility that the ancient Greeks had good evidence of the existence of their gods. Therefore, we have no rational basis for dismissing the possibility that their gods existed.

I have further thoughts on the last point, but rather than include them in this entry I will simply post this part by itself.

Added August 7, 2013:  Upon further consideration of Gutting’s piece, I have concluded that its arguments do not merit further close attention. We have abundant reason to prefer a naturalistic explanation of Greek or any other religious experiences to a theistic one. A naturalistic explanation can be thoroughly well-integrated with everything else that we know about how the natural world works, while a theistic one cannot be. A naturalistic explanation needs to posit no entities that act in contravention of the known laws of nature, while theistic explanation (at least as understood by Gutting) does so. The principles of a naturalistic explanation admit of the derivation of predictions that can be empirically tested and confirmed, while those of a theistic explanation do not. The theistic explanation may have an advantage in simplicity (though even that may be contested: see this piece at Philosophical Disquisitions for reasons why the notion of simplicity of explanation is not itself simple), but it is a clear non-starter in all other respects.

Gutting’s insistence that the Greeks may have had good evidence of the reality of their gods because we have not got decisive evidence that they did not have such evidence is as fatuous as the assertion that the Greeks may have had the technology to build nuclear reactors or that it may have been possible for human beings to fly by attaching wings made of wax to their bodies in those days, since we have no decisive evidence to the contrary (by the standard of decisiveness that Gutting’s reasoning seems to presuppose). In each case, the assertion of what “may have” been the case amounts to nothing more than the proposal of a fantasy in which there is no obvious logical incoherence. It provides not the slightest reason to take such fantasies seriously as real possibilities or to set them alongside the contrary assertions—viz., that the ancient Greeks had no nuclear technology, could not fly with waxen wings, and had no good evidence of the reality of their gods—and to say that there is no sufficient reason to choose between the two.

Agnosticism about the existence, past or present, of the Greek gods seems to me a defensible position; but Gutting’s argument for such agnosticism, founded as it is on the assertion of agnosticism about the former availability of now-unknown evidence for the existence of those gods, is itself indefensible.

Ancient Polytheism and the Concept of Evidence

Gary Gutting offers a double-layered agnosticism about the existence of the gods of ancient Greece: we are in no position to say with assurance that the ancient Greeks did not have good evidence for the existence of Zeus and company, he argues, and therefore, we are in no position to say with assurance that their gods did not exist. The first claim is mistaken, and it is mistaken because the facts that Gutting marshals to support his case have nothing to do with evidence at all.

 In a piece recently published in The Stone, a part of the Web site of the New York Times, Gary Gutting poses the question whether we are in a position to deny the existence of the gods of ancient Greece. If, he says, we cannot “eliminate the very real possibility” that for the ancient Greeks “divinity was . . . a widely and deeply experienced fact of life”—and he goes on to assert that we cannot—then “shouldn’t we hold a merely agnostic position on Zeus and the other Greek gods, taking seriously the possibility that they existed but holding that we have good reason neither to assert nor deny their existence?” After considering and rebutting several arguments for a negative answer to this question, he opts for an affirmative one: a denial of the existence of Zeus, he says, is “ungrounded,” and, although “there is no current evidence of his present existence,” we have no reason “to assume that there was no good evidence for his existence available to the ancient Greeks.”

Gutting recommends agnosticism, and even what one might call adoxism (absence of belief one way or the other), on two distinct questions: (1) whether Zeus and the other gods of ancient Greece existed and (2) whether the ancient Greeks had good evidence of their existence. He holds that we lack sufficient evidence for either an affirmative or a negative answer to the second question, and that for that reason we lack sufficient evidence for either an affirmative or a negative answer to the first. In other words, we are, according to Gutting, in no position to answer the question of whether the ancient Greeks had good evidence of the existence of their gods, and in consequence we are in no position to affirm or deny that the Greek gods existed. (Gutting has further considerations on the question whether we are in a position to affirm or deny that Zeus and company do (now, still) exist, but they seem to me secondary and I prefer to leave them aside for the sake of simplicity.)

Clearly, then, the weight of Gutting’s position falls on his claim that, for all we know, the ancient Greeks may have had good evidence of the existence of their gods. His argument for this claim is contained in a paragraph that begins thus:

Why did belief in the gods persist in spite of critical challenges? What evidence seemed decisive to the ancient Greeks? Robert Parker, in his recent authoritative survey, “On Greek Religion,” emphasizes the role of what the Greeks saw as experiences of divine actions in their lives. “The greatest evidence for the existence of gods is that piety works . . . the converse is that impiety leads to disaster,” with by far the most emphasis given to the perils of ignoring the gods.

One might wonder whether Parker, in the quotation within this quotation, is making an assertion of his own about evidence or is merely reporting on what the ancient Greeks took for evidence. Is he saying that, in ancient Greece, piety toward the gods produced good effects and impiety or disregard of the gods bad effects? Or is he saying merely that the Greeks experienced the world as if it worked in this way? The first, stronger claim surely goes beyond anything that can be justified by historical evidence. Presumably Parker is making only the second, weaker claim—and so, presumably, is Gutting. No doubt, ancient Greeks, like other theistic believers, took note of instances in which pious conduct was followed by good fortune or the lack or the opposite of it by ill fortune, and tended to disregard counterinstances. No doubt, like other theistic believers, they were very resourceful in finding correlations where none was obvious, and in positing unobserved acts of piety or impiety to make sense of occurrences of good or ill fortune that seemed to lack the required antecedent. But these are simply the common tricks of confirmation bias, not instances of following evidence in any serious sense.

So far, if this is the kind of “evidence” of the existence of the gods that “seemed decisive to the ancient Greeks,” it does not support Gutting’s recommended agnosticism at all. The cited observations of Parker concern how the theistic beliefs of the ancient Greeks influenced their perception of the workings of the world. They do not provide the least reason to believe that the Greeks actually had anything that merits the description “evidence of the existence of gods,” much less “good evidence” thereof. If what the Greeks thought of as evidence was just their perception of correlations between one’s comportment toward the gods and one’s fortunes, then agnosticism about whether they had such evidence is not warranted at all: rather, we have good reason to conclude that they had no such evidence.

However, Gutting offers further observations, still drawing on Parker’s work:

There were also rituals, associated with the many cults of specific gods, that for some worshippers “created a sense of contact with the divine. One knows that the gods exist because one feels their presence during the drama of the mysteries or the elation of the choral dance.” More broadly, there were “epiphanies” that could “indicate not merely a visible or audible epiphany (whether in the light of day or through a dream . . .) but also any clear expression of a god’s favor such as weather conditions hampering an enemy, a miraculous escape, or a cure; it may also be used of the continuing disposition of a god or goddess to offer manifest assistance.”

I take it that in the passages quoted within the quotation Parker is, once again, adopting a kind of disguised indirect speech. That “one knows” that the gods exist because “one feels” their presence in the course of ritual observances is what “one” would say if “one” were an ancient Greek. Of course, we moderns, speaking of and for ourselves, will say no such things, and not only because we do not participate in ancient Greek religious rituals or have seeming epiphanies of their gods. Setting aside all ironic, disguised, or “inverted comma” modes of expression, surely what we will say of the ancient Greeks’ experience of their rituals and their epiphanies is not that they (really, literally) felt the presence of their gods but only that they experienced these activities as if the gods were present in them, or that they took them to be experiences of divine presences.

What, then, if anything, in these facts can constitute, or even be a candidate for constituting, evidence of the existence of the Greek gods? Some, perhaps most or even all Greeks, it seems, had certain experiences, which they attributed to the influence of their gods. Is the mere fact that they attributed these experiences to divine influence supposed to be evidence that this attribution was correct? Surely such a suggestion would rob the term “evidence” of all meaning: it would amount to making a belief count as “evidence” for itself.

Perhaps what Gutting has in mind is this: The ancient Greeks had certain experiences which they described in terms of the presence and the influence of their gods. If their gods really existed, then those experiences were evidence of the existence of their gods; if their gods did not exist, then those experiences were not evidence of the existence of their gods. Although we moderns do not believe that their gods existed, we do not know that they did not exist. Therefore, we do not know that the Greeks had no evidence of the existence of their gods. For all we know, they may have had such evidence.

But that won’t do: it reverses the order of argumentation that Gutting sets out. Gutting argues first that we don’t know that the Greeks had no evidence of the existence of their gods, and then in consequence that we don’t know that their gods did not exist.

Rather than try out further interpretations I will simply confess at this point that, if Gutting has a coherent position in this matter, I have been unable to find it. In fact I believe that he has made a coherent position impossible for himself by introducing the term “evidence” where it does not belong. The point in whose service Gutting quotes Parker, namely that for the Greeks “divinity was . . . a widely and deeply experienced fact of life,” has nothing to do with evidence at all. I can gather from Parker’s statements that if I were an ancient Greek, I would experience religious observances as involving the presence or the influence of Zeus and company. That does not mean that I would regard my experiences as having a sort of divine-presence quality to them and then, from the fact that I had experiences of this character, draw the conclusion that I had genuine experiences of divine presence. Such a manner of thinking would be a bizarre case of self-dissociation. In any case, it is certainly not what Parker is describing in the passages that Gutting quotes. If the Greeks commonly had what they interpreted as experiences of the presence and the actions of their gods then it would have been idle and pointless for them in addition to cite those experiences as evidence that their gods existed.

“Very well,” one might reply in defense of Gutting: “the Greeks themselves did not regard their religious experiences as evidence of the existence of their gods, but they could have done so. They could have cited the fact that they had certain experiences as evidence that their gods existed.” Could they indeed? How could they have identified and described the pertinent experiences? If they had done so in terms of the presence of their gods, then they would be building into their statements of the so-called “evidence” the very claim for which those statements are supposed to constitute evidence, namely that their gods exist. To avoid doing that, they would have had to describe their experiences in terms that were completely neutral with regard to the existence of their gods. But how could they have gone about doing that? Would they even have been capable of doing that? As I understand what Parker is telling us, it is in the very nature of the experiences that the Greeks had of their religious observances that, to those who had  them, they seemed to be experiences of the presence of gods. So it is doubtful that those who had such experiences could ever describe them in non-theistic terms. It is therefore doubtful that the ancient Greeks could ever have cited such experiences as evidence of the existence of their gods. Their belief in their gods was not derived from evidence, and Gutting provides no reason to believe that it ever was or even could have been supported by any evidence.

So what comes of Gutting’s argument for agnosticism about the existence of the gods of the ancient Greeks? Its main premise, that we are in no position to say whether the Greeks had good evidence of the existence of their gods, is false: we have in fact good reason to conclude that they had no such evidence. There may be grounds for agnosticism about the existence of the Greek gods, but agnosticism about the existence, in ancient times, of evidence for the existence of those gods is not a support for it.

REFERENCES

Gary Gutting, “Did Zeus Exist?”, The New York Times on line, July 31, 2013.

Robert Parker, On Ancient Greek Religion (Ithaca: Cornell University Press, 2011)