Miracles and Anomalies: Or, Your Religion is False

In 2011 there was an apparent observation of neutrinos traveling faster than light. Wikipedia says of this, “Even before the mistake was discovered, the result was considered anomalous because speeds higher than that of light in a vacuum are generally thought to violate special relativity, a cornerstone of the modern understanding of physics for over a century.” In other words, most scientists did not take the result very seriously, even before any specific explanation was found. As I stated here, it is possible to push unreasonably far in this direction, in such a way that one will be reluctant to ever modify one’s current theories. But there is also something reasonable about this attitude.

Alexander Pruss explains why scientists tend to be skeptical of such anomalous results in this post on Bayesianism and anomaly:

One part of the problem of anomaly is this. If a well-established scientific theory seems to predict something contrary to what we observe, we tend to stick to the theory, with barely a change in credence, while being dubious of the auxiliary hypotheses. What, if anything, justifies this procedure?

Here’s my setup. We have a well-established scientific theory T and (conjoined) auxiliary hypotheses A, and T together with A uncontroversially entails the denial of some piece of observational evidence E which we uncontroversially have (“the anomaly”). The auxiliary hypotheses will typically include claims about the experimental setup, the calibration of equipment, the lack of further causal influences, mathematical claims about the derivation of not-E from T and the above, and maybe some final catch-all thesis like the material conditional that if T and all the other auxiliary hypotheses obtain, then E does not obtain.

For simplicity I will suppose that A and T are independent, though of course that simplifying assumption is rarely true.

Here’s a quick and intuitive thought. There is a region of probability space where the conjunction of T and A is false. That area is divided into three sub-regions:

  1. T is true and A is false
  2. T is false and A is true
  3. both are false.

The initial probabilities of the three regions are, respectively, 0.0999, 0.0009999 and 0.0001. We know we are in one of these three regions, and that’s all we now know. Most likely we are in the first one, and the probability that we are in that one given that we are in one of the three is around 0.99. So our credence in T has gone down from three nines (0.999) to two nines (0.99), but it’s still high, so we get to hold on to T.

Still, this answer isn’t optimistic. A move from 0.999 to 0.99 is actually an enormous decrease in confidence.

“This answer isn’t optimistic,” because in the case of the neutrinos, this analysis would imply that scientists should have instantly become ten times more willing to consider the possibility that the theory of special relativity is false. This is surely not what happened.

Pruss therefore presents an alternative calculation:

But there is a much more optimistic thought. Note that the above wasn’t a real Bayesian calculation, just a rough informal intuition. The tip-off is that I said nothing about the conditional probabilities of E on the relevant hypotheses, i.e., the “likelihoods”.

Now setup ensures:

  1. P(E|A ∧ T)=0.

What can we say about the other relevant likelihoods? Well, if some auxiliary hypothesis is false, then E is up for grabs. So, conservatively:

  1. P(E|∼A ∧ T)=0.5
  2. P(E|∼A ∧ ∼T)=0.5

But here is something that I think is really, really interesting. I think that in typical cases where T is a well-established scientific theory and A ∧ T entails the negation of E, the probability P(E|A ∧ ∼T) is still low.

The reason is that all the evidence that we have gathered for T even better confirms the hypothesis that T holds to a high degree of approximation in most cases. Thus, even if T is false, the typical predictions of T, assuming they have conservative error bounds, are likely to still be true. Newtonian physics is false, but even conditionally on its being false we take individual predictions of Newtonian physics to have a high probability. Thus, conservatively:

  1. P(E|A ∧ ∼T)=0.1

Very well, let’s put all our assumptions together, including the ones about A and T being independent and the values of P(A) and P(T). Here’s what we get:

  1. P(E|T)=P(E|A ∧ T)P(A|T)+P(E|∼A ∧ T)P(∼A|T)=0.05
  2. P(E|∼T)=P(E|A ∧ ∼T)P(A|∼T)+P(E|∼A ∧ ∼T)P(∼A|∼T) = 0.14.

Plugging this into Bayes’ theorem, we get P(T|E)=0.997. So our credence has crept down, but only a little: from 0.999 to 0.997. This is much more optimistic (and conservative) than the big move from 0.999 to 0.99 that the intuitive calculation predicted.

So, if I am right, at least one of the reasons why anomalies don’t do much damage to scientific theories is that when the scientific theory T is well-confirmed, the anomaly is not only surprising on the theory, but it is surprising on the denial of the theory—because the background includes the data that makes T “well-confirmed” and would make E surprising even if we knew that T was false.

To make the point without the mathematics (which in any case is only used to illustrate the point, since Pruss is choosing the specific values himself), if you have a theory which would make the anomaly probable, that theory would be strongly supported by the anomaly. But we already know that theories like that are false, because otherwise the anomaly would not be an anomaly. It would be normal and common. Thus all of the actually plausible theories still make the anomaly an improbable observation, and therefore these theories are only weakly supported by the observation of the anomaly. The result is that the new observation makes at most a minor difference to your previous opinion.

We can apply this analysis to the discussion of miracles. David Hume, in his discussion of miracles, seems to desire a conclusive proof against them which is unobtainable, and in this respect he is mistaken. But near the end of his discussion, he brings up the specific topic of religion and says that his argument applies to it in a special way:

Upon the whole, then, it appears, that no testimony for any kind of miracle has ever amounted to a probability, much less to a proof; and that, even supposing it amounted to a proof, it would be opposed by another proof; derived from the very nature of the fact, which it would endeavour to establish. It is experience only, which gives authority to human testimony; and it is the same experience, which assures us of the laws of nature. When, therefore, these two kinds of experience are contrary, we have nothing to do but subtract the one from the other, and embrace an opinion, either on one side or the other, with that assurance which arises from the remainder. But according to the principle here explained, this subtraction, with regard to all popular religions, amounts to an entire annihilation; and therefore we may establish it as a maxim, that no human testimony can have such force as to prove a miracle, and make it a just foundation for any such system of religion.

The idea seems to be something like this: contrary systems of religion put forth miracles in their support, so the supporting evidence for one religion is more or less balanced by the supporting evidence for the other. Likewise, the evidence is weakened even in itself by people’s propensity to lies and delusion in such matters (some of this discussion was quoted in the earlier post on Hume and miracles). But in addition to the fairly balanced evidence we have experience basically supporting the general idea that the miracles do not happen. This is not outweighed by anything in particular, and so it is the only thing that remains after the other evidence balances itself out of the equation. Hume goes on:

I beg the limitations here made may be remarked, when I say, that a miracle can never be proved, so as to be the foundation of a system of religion. For I own, that otherwise, there may possibly be miracles, or violations of the usual course of nature, of such a kind as to admit of proof from human testimony; though, perhaps, it will be impossible to find any such in all the records of history. Thus, suppose, all authors, in all languages, agree, that, from the first of January, 1600, there was a total darkness over the whole earth for eight days: suppose that the tradition of this extraordinary event is still strong and lively among the people: that all travellers, who return from foreign countries, bring us accounts of the same tradition, without the least variation or contradiction: it is evident, that our present philosophers, instead of doubting the fact, ought to receive it as certain, and ought to search for the causes whence it might be derived. The decay, corruption, and dissolution of nature, is an event rendered probable by so many analogies, that any phenomenon, which seems to have a tendency towards that catastrophe, comes within the reach of human testimony, if that testimony be very extensive and uniform.

But suppose, that all the historians who treat of England, should agree, that, on the first of January, 1600, Queen Elizabeth died; that both before and after her death she was seen by her physicians and the whole court, as is usual with persons of her rank; that her successor was acknowledged and proclaimed by the parliament; and that, after being interred a month, she again appeared, resumed the throne, and governed England for three years: I must confess that I should be surprised at the concurrence of so many odd circumstances, but should not have the least inclination to believe so miraculous an event. I should not doubt of her pretended death, and of those other public circumstances that followed it: I should only assert it to have been pretended, and that it neither was, nor possibly could be real. You would in vain object to me the difficulty, and almost impossibility of deceiving the world in an affair of such consequence; the wisdom and solid judgment of that renowned queen; with the little or no advantage which she could reap from so poor an artifice: all this might astonish me; but I would still reply, that the knavery and folly of men are such common phenomena, that I should rather believe the most extraordinary events to arise from their concurrence, than admit of so signal a violation of the laws of nature.

But should this miracle be ascribed to any new system of religion; men, in all ages, have been so much imposed on by ridiculous stories of that kind, that this very circumstance would be a full proof of a cheat, and sufficient, with all men of sense, not only to make them reject the fact, but even reject it without farther examination. Though the Being to whom the miracle is ascribed, be, in this case, Almighty, it does not, upon that account, become a whit more probable; since it is impossible for us to know the attributes or actions of such a Being, otherwise than from the experience which we have of his productions, in the usual course of nature. This still reduces us to past observation, and obliges us to compare the instances of the violation of truth in the testimony of men, with those of the violation of the laws of nature by miracles, in order to judge which of them is most likely and probable. As the violations of truth are more common in the testimony concerning religious miracles, than in that concerning any other matter of fact; this must diminish very much the authority of the former testimony, and make us form a general resolution, never to lend any attention to it, with whatever specious pretence it may be covered.

Notice how “unfair” this seems to religion, so to speak. What is the difference between the eight days of darkness, which Hume would accept, under those conditions, and the resurrection of the queen of England, which he would not? Hume’s reaction to the two situations is more consistent than first appears. Hume would accept the historical accounts about England in the same way that he would accept the accounts about the eight days of darkness. The difference is in how he would explain the accounts. He says of the darkness, “It is evident, that our present philosophers, instead of doubting the fact, ought to receive it as certain, and ought to search for the causes whence it might be derived.” Likewise, he would accept the historical accounts as certain insofar as they say the a burial ceremony took place, the queen was absent from public life, and so on. But he would not accept that the queen was dead and came back to life. Why? The “search for the causes” seems to explain this. It is plausible to Hume that causes of eight days of darkness might be found, but not plausible to him that causes of a resurrection might be found. He hints at this in the words, “The decay, corruption, and dissolution of nature, is an event rendered probable by so many analogies,” while in contrast a resurrection would be “so signal a violation of the laws of nature.”

It is clear that Hume excludes certain miracles, such as resurrection, from the possibility of being established by the evidence of testimony. But he makes the additional point that even if he did not exclude them, he would not find it reasonable to establish a “system of religion” on such testimony, given that “violations of truth are more common in the testimony concerning religious miracles, than in that concerning any other matter of fact.”

It is hard to argue with the claim that “violations of truth” are especially common in testimony about miracles. But does any of this justify Hume’s negative attitude to miracles as establishing “systems of religion,” or is this all just prejudice?  There might well be a good deal of prejudice involved here in his opinions. Nonetheless, Alexander Pruss’s discussion of anomaly allows one to formalize Hume’s idea here as actual insight as well.

One way to look at truth in religion is to look at it as a way of life or as membership in a community. And in this way, asking whether miracles can establish a system of religion is just asking whether a person can be moved to a way of life or to join a community through such things. And clearly this is possible, and often happens. But another way to consider truth in religion is to look at a doctrinal system as a set of claims about how the world is. Looked at in this way, we should look at a doctrinal system as presenting a proposed larger context of our place in the world, one that we would be unaware of without the religion. This implies that one should have a prior probability (namely prior to consideration of arguments in its favor) strongly against the system considered as such, for reasons very much like the reasons we should have a prior probability strongly against Ron Conte’s predictions.

We can thus apply Alexander Pruss’s framework. Let us take Mormonism as the “system of religion” in question. Then taken as a set of claims about the world, our initial probability would be that it is very unlikely that the world is set up this way. Then let us take a purported miracle establishing this system: Joseph Smith finds his golden plates. In principle, if this cashed out in a certain way, it could actually establish his system. But it doesn’t cash out that way. We know very little about the plates, the circumstances of their discovery (if there was any), and their actual content. Instead, what we are left with is an anomaly: something unusual happened, and it might be able to be described as “finding golden plates,” but that’s pretty much all we know.

Then we have the theory, T, which has a high prior probability: Mormonism is almost certainly false. We have the observation : Joseph Smith discovered his golden plates (in one sense or another.) And we have the auxiliary hypotheses which imply that he could not have discovered the plates if Mormonism is false. The Bayesian updates in Pruss’s scheme imply that our conclusion is this: Mormonism is almost certainly false, and there is almost certainly an error in the auxiliary hypotheses that imply he could not have discovered them if it were false.

Thus Hume’s attitude is roughly justified: he should not change his opinion about religious systems in any significant way based on testimony about miracles.

To make you feel better, this does not prove that your religion is false. It just nearly proves that. In particular, this does not take into an account an update based on the fact that “many people accept this set of claims.” This is a different fact, and it is not an anomaly. If you update on this fact and end up with a non-trivial probability that your set of claims is true, testimony about miracles might well strengthen this into conviction.

I will respond to one particular objection, however. Some will take this argument to be stubborn and wicked, because it seems to imply that people shouldn’t be “convinced even if someone rises from the dead.” And this does in fact follow, more or less. An anomalous occurrence in most cases will have a perfectly ordinary explanation in terms of things that are already a part of our ordinary understanding of the world, without having to add some larger context. For example, suppose you heard your fan (as a piece of furniture, not as a person) talking to you. You might suppose that you were hallucinating. But suppose it turns out that you are definitely not hallucinating. Should you conclude that there is some special source from outside the normal world that is communicating with you? No: the fan scenario can happen, and it turns out to have a perfectly everyday explanation. We might agree with Hume that it would be much more implausible that a resurrection would have an everyday explanation. Nonetheless, even if we end up concluding to the existence of some larger context, and that the miracle has no such everyday explanation, there is no good reason for it to be such and such a specific system of doctrine. Consider again Ron Conte’s predictions for the future. Most likely the things that happen between now and 2040, and even the things that happen in the 2400s, are likely to be perfectly ordinary (although the things in the 2400s might differ from current events in fairly radical ways). But even if they are not, and even if apocalyptic, miraculous occurrences are common in those days, this does not raise the probability of Conte’s specific predictions above any trivial level. In the same way, the anomalous occurrences involved in the accounts of miracles will not lend any significant probability to a religious system.

The objection here is that this seems unfair to God, so to speak. What if God wanted to reveal something to the world? What could he do, besides work miracles? I won’t propose a specific answer to this, because I am not God. But I will illustrate the situation with a little story to show that there is nothing unfair to God about it.

Suppose human beings created an artificial intelligence and raised it in a simulated environment. Wanting things to work themselves out “naturally,” so to speak, because it would be less work, and because it would probably be necessary to the learning process, they institute “natural laws” in the simulated world which are followed in an exceptionless way. Once the AI is “grown up”, so to speak, they decide to start communicating with it. In the AI’s world, this will surely show up as some kind of miracle: something will happen that was utterly unpredictable to it, and which is completely inconsistent with the natural laws as it knew them.

Will the AI be forced by the reasoning of this post to ignore the communication? Well, that depends on what exactly occurs and how. At the end of his post, Pruss discusses situations where anomalous occurrences should change your mind:

Note that this argument works less well if the anomalous case is significantly different from the cases that went into the confirmation of T. In such a case, there might be much less reason to think E won’t occur if T is false. And that means that anomalies are more powerful as evidence against a theory the more distant they are from the situations we explored before when we were confirming T. This, I think, matches our intuitions: We would put almost no weight in someone finding an anomaly in the course of an undergraduate physics lab—not just because an undergraduate student is likely doing it (it could be the professor testing the equipment, though), but because this is ground well-gone over, where we expect the theory’s predictions to hold even if the theory is false. But if new observations of the center of our galaxy don’t fit our theory, that is much more compelling—in a regime so different from many of our previous observations, we might well expect that things would be different if our theory were false.

And this helps with the second half of the problem of anomaly: How do we keep from holding on to T too long in the light of contrary evidence, how do we allow anomalies to have a rightful place in undermining theories? The answer is: To undermine a theory effectively, we need anomalies that occur in situations significantly different from those that have already been explored.

If the AI finds itself in an entirely new situation, e.g. rather than hearing an obscure voice from a fan, it is consistently able to talk to the newly discovered occupant of the world on a regular basis, it will have no trouble realizing that its situation has changed, and no difficulty concluding that it is receiving communication from its author. This does, sort of, give one particular method that could be used to communicate a revelation. But there might well be many others.

Our objector will continue. This is still not fair. Now you are saying that God could give a revelation but that if he did, the world would be very different from the actual world. But what if he wanted to give a revelation in the actual world, without it being any different from the way it is? How could he convince you in that case?

Let me respond with an analogy. What if the sky were actually red like the sky of Mars, but looked blue like it is? What would convince you that it was red? The fact that there is no way to convince you that it is red in our actual situation means you are unfairly prejudiced against the redness of the sky.

In other words, indeed, I am unwilling to be convinced that the sky is red except in situations where it is actually red, and those situations are quite different from our actual situation. And indeed, I am unwilling to be convinced of a revelation except in situations where there is actually a revelation, and those are quite different from our actual situation.

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Truth and Expectation III

Consider what I said at the end of the last post on this topic. When our Mormon protagonist insists that his religion is true, he improves the accuracy of his expectations about the world. His expectations would actually be less accurate he decided that his religious beliefs are false.

Now we said in the first post on truth and expectation that in part we seem to determine the meaning of a statement by the expectations that it implies. If this is the case, then why should we not say that the Mormon’s beliefs are definitely true? In fact, in the post linked above about truth in religion, I suggested that people frequently do mean something like this when they say that their own religion is true. Nonetheless, it is easy to see that truth in this particular sense does not imply that each and every claim in the religion, understood as a claim about the world, is true.

But why not, if one’s expectations become more accurate, just as with statements that are clearly true? As I noted in the earlier post, to say that “that man is pretty tall” is a statement about the man. It is not a statement about myself, nor about my expectations, even if the meaning is partly determined by these things. So ultimately the truth or falsehood of the claim about the man is going to be determined by facts about the man, even if they need to be understood as facts about the man in relation to me and my expectations.

Consider again Scott Sumner’s anti-realism. Scott claims that we cannot distinguish between “our perception of reality, and actual reality.” As I said there, this is right in the sense that we cannot consistently hold the opinion, “This is my opinion about reality, but my opinion is false: reality is actually different.” But we can recognize the distinct meanings in “my perception of reality” and “actual reality.” Scott’s failure to recognize this distinction leads him to suggest on occasion that our beliefs about certain matters are just beliefs about what people in the future will believe. For example, he says in this comment:

You misunderstood Rorty. He is not recommending that you try to trick you colleagues into believing something that is not true. Rather he is merely describing what society regards as true. And who can deny that society tends to regard things as true, when they believe them to be true. No you might say “but what society believes to be true is not always really true.” But Rorty would say that statement means nothing, or else it means that you predict that a future society will have a different view of what is true.

Most people, without even realizing it, assume that there is some sort of “God-like” view of what is “really true” which is separate from what we believe is true, and or will believe in the future to be true. Rorty is an atheist. He believes that what society’s experts believe is the best we can do, the closest we can come to describing reality. Rorty would suggest to Hayek “if you want to convince other economists, use persuasive arguments.” I think that is very reasonable advice. It is what I try to do on this blog.

This is much like Bob Seidensticker’s claim that moral beliefs are beliefs about what society in the future will believe to be moral. In both cases, there is an unacceptable circularity. If our belief is about what people in the future will believe, what are the future people’s beliefs about? There is only one credible explanation here: people’s beliefs are about what they say their beliefs are about, namely the very things they are talking about. Moral beliefs are about whether actions are good or bad, and beliefs describing the world are about the world, not about the people who hold the beliefs, present or future.

This does not imply that there is “some sort of ‘God-like’ view of what is ‘really true’.” It just implies that our beliefs are distinct from other things in the world. Sumner is suggesting that a situation where everyone permanently holds a false belief, forever, is inconceivable. But this is quite conceivable, and we can easily see how it could happen. Just now I counted the cups in my cupboard and there are exactly 14 (if anyone is surprised by that value, most of those are plastic.) It is entirely conceivable, however, that I miscounted. And since I also have some cups that are not currently in the cupboard, if I did, I will probably never get it right, since I will just assume there was some other assortment. And since there is presumably no way for the public to discover the truth about this, society will be permanently deluded about the number of cups in my cupboard at 11:16 AM on July 14, 2018.

What would it mean, then, if it was not “actually true” that there were 14 cups in my cupboard? It would be determined by facts about the cups and the cupboard, not by facts about me, about society, about my expectations or society’s expectations. It would not be actually true if there were, in fact, only 13 cups there, even if no one would ever know this.

This all remains related to expectations, however. I don’t think I miscounted, so I think that if I go again and count them, I will get 14 again. If I did miscount, there is a good chance that counting again would result in a different number. Now I don’t intend to bother, so this expectation is counterfactual. Nonetheless, there are at least conceivable counterfactual situations where I would discover that I was mistaken. In a similar way, to say that the Mormon holds false religious beliefs implies that there are at least counterfactual situations where the falsehood would be uncovered by a violation of his expectations: e.g. if he had been alive at the time and had followed Joseph Smith around all the time to see whether there were any golden plates and so on.

Nonetheless, one cannot ultimately separate the truth of a statement from facts about the thing the statement is about. A statement is true if things are the way it says they are, “the way” being correctly understood here. If this were not the case, the statement would not be about the things in the first place.

Truth and Expectation II

We discussed this topic in a previous post. I noted there that there is likely some relationship with predictive processing. This idea can be refined by distinguishing between conscious thought and what the human brain does on a non-conscious level.

It is not possible to define truth by reference to expectations for reasons given previously. Some statements do not imply specific expectations, and besides, we need the idea of truth to decide whether or not someone’s expectations were correct or not. So there is no way to define truth except the usual way: a statement is true if things are the way the statement says they are, bearing in mind the necessary distinctions involving “way.”

On the conscious level, I would distinguish between thinking about something is true, and wanting to think that it is true. In a discussion with Angra Mainyu, I remarked that insofar as we have an involuntary assessment of things, it would be more appropriate to call that assessment a desire:

So rather than calling that assessment a belief, it would be more accurate to call it a desire. It is not believing something, but desiring to believe something. Hunger is the tendency to go and get food; that assessment is the tendency to treat a certain claim (“the USA is larger than Austria”) as a fact. And in both cases there are good reasons for those desires: you are benefited by food, and you are benefited by treating that claim as a fact.

Angra was quite surprised by this and responded that “That statement gives me evidence that we’re probably not talking about the same or even similar psychological phenomena – i.e., we’re probably talking past each other.” But if he was talking about anything that anyone at all would characterize as a belief (and he said that he was), he was surely talking about the unshakeable gut sense that something is the case whether or not I want to admit it. So we were, in fact, talking about exactly the same psychological phenomena. I was claiming then, and will claim now, that this gut sense is better characterized as a desire than as a belief. That is, insofar as desire is a tendency to behave in certain ways, it is a desire because it is a tendency to act and think as though this claim is true. But we can, if we want, resist that tendency, just as we can refrain from going to get food when we are hungry. If we do resist, we will refrain from believing what we have a tendency to believe, and if we do not, we will believe what we have a tendency to believe. But the tendency will be there whether or not we follow it.

Now if we feel a tendency to think that something is true, it is quite likely that it seems to us that it would improve our expectations. However, we can also distinguish between desiring to believe something for this reason, or desiring to believe something for other reasons. And although we might not pay attention, it is quite possibly to be consciously aware that you have an inclination to believe something, and also that it is for non-truth related reasons; and thus you would not expect it to improve your expectations.

But this is where it is useful to distinguish between the conscious mind and what the brain is doing on another level. My proposal: you will feel the desire to think that something is true whenever your brain guesses that its predictions, or at least the predictions that are important to it, will become more accurate if you think that the thing is true. We do not need to make any exceptions. This will be the case even when we would say that the statement does not imply any significant expectations, and will be the case even when the belief would have non-truth related motives.

Consider the statement that there are stars outside the visible universe. One distinction we could make even on the conscious level is that this implies various counterfactual predictions: “If you are teleported outside the visible universe, you will see more stars that aren’t currently visible.” Now we might find this objectionable if we were trying to define truth by expectations, since we have no expectation of such an event. But both on conscious and on non-conscious levels, we do need to make counterfactual predictions in order to carry on with our lives, since this is absolutely essential to any kind of planning and action. Now certainly no one can refute me if I assert that you would not see any such stars in the teleportation event. But it is not surprising if my brain guesses that this counterfactual prediction is not very accurate, and thus I feel the desire to say that there are stars there.

Likewise, consider the situation of non-truth related motives. In an earlier discussion of predictive processing, I suggested that the situation where people feel like they have to choose a goal is a result of such an attempt at prediction. Such a choice seems to be impossible, since choice is made in view of a goal, and if you do not have one yet, how can you choose? But there is a pre-existing goal here on the level of the brain: it wants to know what it is going to do. And choosing a goal will serve that pre-existing goal. Once you choose a goal, it will then be easy to know what you are going to do: you are going to do things that promote the goal that you chose. In a similar way, following any desire will improve your brain’s guesses about what you are going to do. It follows that if you have a desire to believe something, actually believing it will improve your brain’s accuracy at least about what it is going to do. This is true but not a fair argument, however, since my proposal is that the brain’s guess of improved accuracy is the cause of your desire to believe something. It is true that if you already have the desire, giving in to it will improve accuracy, as with any desire. But in my theory the improved accuracy had to be implied first, in order to cause the desire.

The answer is that you have many desires for things other than belief, which at the same time give you a motive (not an argument) for believing things. And your brain understands that if you believe the thing, you will be more likely to act on those other desires, and this will minimize uncertainty, and improve the accuracy of its predictions. Consider this discussion of truth in religion. I pointed out there that people confuse two different questions: “what should I do?”, and “what is the world like?” In particular with religious and political loyalties, there can be an intense social pressure towards conformity. And this gives an obvious non-truth related motive to believe the things in question. But in a less obvious way, it means that your brain’s predictions will be more accurate if you believe the thing. Consider the Mormon, and take for granted that the religious doctrines in question are false. Since they are false, does not that mean that if they continue to believe, their predictions will be less accurate?

No, it does not, for several reasons. In the first place the doctrines are in general formulated to avoid such false predictions, at least about everyday life. There might be a false prediction about what will happen when you die, but that is in the future and is anyway disconnected from your everyday life. This is in part why I said “the predictions that are important to it” in my proposal. Second, failure to believe would lead to extremely serious conflicting desires: the person would still have the desire to conform outwardly, but would also have good logical reasons to avoid conformity. And since we don’t know in advance how we will respond to conflicting desires, the brain will not have a good idea of what it would do in that situation. In other words, the Mormon is living a good Mormon life. And their brain is aware that insisting that Mormonism is true is a very good way to make sure that they keep living that life, and therefore continue to behave predictably, rather than falling into a situation of strongly conflicting desires where it would have little idea of what it would do. In this sense, insisting that Mormonism is true, even though it is not, actually improves the brain’s predictive accuracy.

 

Fairies, Unicorns, Werewolves, and Certain Theories of Richard Dawkins

In A Devil’s Chaplain, Richard Dawkins explains his opposition to religion:

To describe religions as mind viruses is sometimes interpreted as contemptuous or even hostile. It is both. I am often asked why I am so hostile to ‘organized religion’. My first response is that I am not exactly friendly towards disorganized religion either. As a lover of truth, I am suspicious of strongly held beliefs that are unsupported by evidence: fairies, unicorns, werewolves, any of the infinite set of conceivable and unfalsifiable beliefs epitomized by Bertrand Russell’s hypothetical china teapot orbiting the Sun. The reason organized religion merits outright hostility is that, unlike belief in Russell’s teapot, religion is powerful, influential, tax-exempt and systematically passed on to children too young to defend themselves. Children are not compelled to spend their formative years memorizing loony books about teapots. Government-subsidized schools don’t exclude children whose parents prefer the wrong shape of teapot. Teapot-believers don’t stone teapot-unbelievers, teapot-apostates, teapot-heretics and teapot-blasphemers to death. Mothers don’t warn their sons off marrying teapot-shiksas whose parents believe in three teapots rather than one. People who put the milk in first don’t kneecap those who put the tea in first.

We have previously discussed the error of supposing that other people’s beliefs are “unsupported by evidence” in the way that the hypothetical china teapot is unsupported. But the curious thing about this passage is that it carries its own refutation. As Dawkins says, the place of religion in the world is very different from the place of belief in fairies, unicorns, and werewolves. These differences are empirical differences in the real world: it is in the real world that people teach their children about religion, but not about orbiting teapots, or in general even about fairies, unicorns, and werewolves.

The conclusion for Dawkins ought not to be hostility towards religion, then, but rather the conclusion, “These appear to me to be beliefs unsupported by evidence, but this must be a mistaken appearance, since obviously humans relate to these beliefs in very different ways than they do to beliefs unsupported by evidence.”

I would suggest that what is actually happening is that Dawkins is making an abstract argument about what the world should look like given that religions are false, much in the way that P. Edmund Waldstein’s argument for integralism is an abstract argument about what the world should look like given that God has revealed a supernatural end. Both theories simply pay no attention to the real world: in the real world, human beings do not in general know a supernatural end (at least not in the detailed way required by P. Edmund’s theory), and in the real world, human beings do not treat religious beliefs as beliefs unsupported by evidence.

The argument by Dawkins would proceed like this: religions are false. Therefore they are just sets of beliefs that posit numerous concrete claims, like assumptions into heaven, virgin births, and so on, which simply do not correspond to anything at all in the real world. Therefore beliefs in these things should be just like beliefs in other such non-existent things, like fairies, unicorns, and werewolves.

The basic conclusion is false, and Dawkins points out its falsity himself in the above quotation.

Nonetheless, people do not tend to be so wrong that there is nothing right about what they say, and there is some truth in what Dawkins is saying, namely that many religious beliefs do make claims which are wildly far from reality. Rod Dreher hovers around this point:

A Facebook friend posted to his page:

“Shut up! No way – you’re too smart! I’m sorry, that came out wrong…”

The reaction a good friend and Evangelical Christian colleague had when she found out I’m a Catholic.

Priceless.

I had to laugh at that, because it recalled conversations I’ve been part of (alas) back in the 1990s, as a fresh Catholic convert, in which we Catholics wondered among ourselves why any smart people would be Evangelical. After I told a Catholic intellectual friend back in 2006 that I was becoming Orthodox, he said something to the effect of, “You’re too smart for that.”

It’s interesting to contemplate why we religious people who believe things that are rather implausible from a relatively neutral point of view can’t understand how intelligent religious people who believe very different things can possibly hold those opinions. I kept getting into this argument with other conservative Christians when Mitt Romney was running for president. They couldn’t bring themselves to vote for him because he’s a Mormon, and Mormons believe “crazy” things. Well, yes, from an orthodox Christian point of view, their beliefs are outlandish, but come on, we believe, as they do, that the God of all Creation, infinite and beyond time, took the form of a mortal man, suffered, died, arose again, and ascended into heaven — and that our lives on this earth and our lives in eternity depend on uniting ourselves to Him. And we believe that that same God established a sacred covenant with a Semitic desert tribe, and made Himself known to mankind through His words to them. And so forth. And these are only the basic “crazy things” that we believe! Judge Mormons to be incorrect in their theology, fine, but if you think they are somehow intellectually defective for believing the things they do that diverge from Christian orthodoxy, then it is you who are suffering from a defect of the intellectual imagination.

My point is not to say all religious belief is equally irrational, or that it is irrational at all. I don’t believe that. A very great deal depends on the premises from which you begin. Catholics and Orthodox, for example, find it strange that so many Evangelicals believe that holding to the Christian faith requires believing that the Genesis story of a seven-day creation must be taken literally, such that the world is only 7,000 years old, and so forth. But then, we don’t read the Bible as they do. I find it wildly implausible that they believe these things, but I personally know people who are much more intelligent than I am who strongly believe them. I wouldn’t want these folks teaching geology or biology to my kids, but to deny their intelligence would be, well, stupid.

I suspect that Dreher has not completely thought through the consequences of these things, and most likely he would not want to. For example, he presumably thinks that his own Christian beliefs are not irrational at all. So are the Mormon beliefs slightly irrational, or also not irrational at all? If Mormon beliefs are false, they are wildly far off from reality. Surely there is something wrong with beliefs that are wildly far off from reality, even if you do not want to use the particular term “irrational.” And presumably claims that are very distant from reality should not be supported by vast amounts of strong evidence, even if unlike Dawkins you admit that some evidence will support them.

Some Personal Remarks

At one point we looked at Trent Horn’s question for a Mormon:

Is there anything that would convince you that Mormonism is false? If not, then why should you expect other people to leave their faiths and become Mormon when you aren’t prepared to do the same?

The main reason that our Mormon protagonist  is unwilling to change his mind about religion is not because of the evidence in favor of Mormonism. There certainly is such evidence, as for example the witnesses who testified that they saw Joseph Smith’s golden plates. But such evidence is surely not the principal motive involved. Basically they have motives other than truth for continuing to believe. If a Mormon changes their religious views, this can have serious negative consequences for their social and personal life. This is not specific to Mormonism, but is common to religion in general, as well as to many political views, because of the way that such views are used to express social and political loyalties. As noted in the linked post, someone who changes his view is seen as a traitor to his community.

Gregory Dawes, a former Catholic, seems to have had this experience. He remarks (quoted in the post linked above):

Christian philosopher William Lane Craig writes somewhere about what he calls the “ministerial” and the “magisterial” use of reason. (It’s a traditional view — he’s merely citing Martin Luther — and one that Craig endorses.) On this view, the task of reason is to find arguments in support of the faith and to counter any arguments against it. Reason is not, however, the basis of the Christian’s faith. The basis of the Christian’s faith is (what she takes to be) the “internal testimony of the Holy Spirit” in her heart. Nor can rational reflection can be permitted to undermine that faith. The commitment of faith is irrevocable; to fall away from it is sinful, indeed the greatest of sins.

The Catholic Church does not teach that falling away from the faith is the greatest of sins. In fact, although it certainly teaches that it is objectively wrong for a Catholic to do so, it does not even teach that a Catholic is always subjectively guilty at all when they change their religious views. Dawes was a well educated Catholic, so he is probably aware of these facts. Why then does he call this “the greatest of sins?” It seems pretty reasonable to suppose that he is responding in a personal way to how he was treated by others after he changed his mind about his religion.

As I said in the linked post, I agree with Trent Horn and Gregory Dawes about the use of reason. However, this is not the only thing that Dawes and I have in common. Like Dawes, my family and background are completely Catholic. Like Dawes, my education was completely Catholic. Finally, I substantially agree with Dawes in his conclusions regarding Catholicism and regarding religion in general, considered as a body of factual claims about the world. Of course this is not the case not in every detail. I also suspect that I disagree with him to a larger extent on the reasons for those conclusions. This is not an opinion that I have just arrived at. I have held this view for over a year now. Nor was it the result of a brief process, but the result of a gradual process of thought which took decades of my life.

As with Dawes, and as with our theoretical Mormon, this has had serious consequences for my personal life, and not only on account of the reactions of others. Nonetheless, the reactions of others play a significant role here. Consequently I have a few remarks principally for those who know me in real life:

  1. This blog is and remains theoretically anonymous. Please do not make this post a public announcement connected to my real name.
  2. I appreciate your prayers. Needless to say, this does not imply that there is any meaningful weakness to the case for my position.
  3. I do not appreciate insults. Your faith does not require you to believe that I am foolish, wicked, arrogant, or possessed by demons. If you think that it does, or if it pleases you to think these things in any case, please keep them to yourself.
  4. While it should be obvious from this blog that I do not mind conversations about religion, considered in general, I do not appreciate proselytism, namely efforts that could reasonably be described as “stop him from being foolish and get him to come to his senses.” I am not being foolish, and I am entirely in possession of my senses. Please do not engage in this behavior; it is uncharitable, it will not have the effects that you wish, and persistence in it over a long period of time can only have the effect of destroying relationships.

One additional remark concerning the “possessed by demons” point. Someone recently said in a personal communication:

By the strange things you write, I can see that your mind has been given blinders / tunnel vision, presumably by some evil spirit, who only lets you look at things from his point of view.

This refers to things written on this blog, and in that sense it is completely incorrect. Everything currently on the blog is completely consistent with a Catholic view, and only expresses views that I have held for many years. Many orthodox Catholics would agree in substance with virtually everything here.

As for the demon comment itself, I have noted in the past that if you say that a person’s beliefs are caused by a demon, you cannot have a conversation with them. In the same way, if you say that a person’s religious views are caused by a demon, you cannot have a conversation about religion with them.

The Second Mistake

The second mistake that we mentioned at the end of this post was that given the thesis that God is hidden, arguments against a religion become arguments in favor of it. Pascal suggests such a position when he says, “that darkness in which they are, and with which they upbraid the Church, establishes only one of the things which she affirms, without touching the other, and, very far from destroying, proves her doctrine?”

This is not completely wrong, but there is less truth than error in it. If you explain a difficulty by adding something to your account, as the Mormon does in this example, then technically the difficulty does support the new account. The problem is, as was said there, that the new account overall remains less probable than the original account was without the addition. And the difficulty remains evidence that the original account was simply wrong; it does not “change sides” to support only the new account.

There are several things that need to be considered in the present case. The first is in what sense it is an additional explanation when one says that the explanation for the existence of difficulties is the hiddenness of God. It is somewhat different from the example of the Mormon, and in a way that favors Christianity. The Mormon may have been aware of all widely known facts about his religion, without being aware of the problem regarding the Book of Abraham. But this could not be true of the Christian in the case under discussion. It may be a Christian does not realize that his religion implies that God is hidden; but this is on account of a lack of consideration. The very things that he already knows and believes imply that this must be true in order for his religion to be true. In the Mormon case, on the contrary, nothing about the Mormon religion implies there needs to be some special explanation regarding the Book of Abraham. So when the Mormon adds a special explanation, this is a real addition that must reduce the probability of his general claim. But the Christian in the case under discussion is simply explaining what was implicit in his claim in the first place. In this sense it does not reduce the probability of his claim, but leaves it as it is.

On the other hand, if one has not yet considered the fact that Christianity requires the thesis of hiddenness, it may be that the prior probability for Christianity should be less than what one supposed, when one was judging it without this consideration. In this sense, it may reduce the probability for a particular individual who has not yet fully considered the situation.

Finally, this does not in fact imply that concrete difficulties with Christianity are not evidence against it, because even if the difficulties fit with the claim that Christianity is true but hidden, they may sometimes fit even better with the claim that Christianity is false. For example, suppose there were no historical evidence for the Virgin Birth (this is a counterfactual, since in reality there is historical evidence for it, even if weak relative to the strength of the claim, namely the assertions of the Gospels); such an absence of evidence would fit with the idea that the doctrine is true but hidden, but it would fit even better with the idea that the doctrine is false. Consequently, the evidence would make “the doctrine is true but hidden” more probable relative to “the doctrine is true and not hidden,” but overall the evidence would be likely to make “the doctrine is false” more probable than it was initially before checking the evidence.

 

Hidden God

Porphyry, arguing against the resurrection of Christ, comments on the appearance to Mary Magdalene:

There is also another argument whereby this corrupt opinion can be refuted. I mean the argument about that Resurrection of His which is such common talk everywhere, as to why Jesus, after His suffering and rising again (according to your story), did not appear to Pilate who punished Him and said He had done nothing worthy of death, or to Herod King of the Jews, or to the High-priest of the Jewish race, or to many men at the same time and to such as were worthy of credit, and more particularly among Romans both in the Senate and among the people. The purpose would be that, by their wonder at “the things concerning Him, they might not pass a vote of death against Him by common consent, which implied the impiety of those who were obedient to Him. But He appeared to Mary Magdalene, a coarse woman who came from some wretched little village, and had once been possessed by seven demons, and with her another utterly obscure Mary, who was herself a peasant woman, and a few other people who were not at all well known. And that, although He said: “Henceforth shall ye see the Son of man sitting on the right hand of power, and coming with the clouds.” For if He had shown Himself to men of note, all would believe through them, and no judge would punish them as fabricating monstrous stories. For surely it is neither pleasing to God nor to any sensible man that many should be subjected on His account to punishments of the gravest kind.

If the argument is that Christ should have appeared to rich people rather than to poor people, or to the government rather than to common people, and it seems that this may be Porphyry’s actual intention, his argument is rather weak, especially given things that Christ says in the Gospels about the rich and the poor.

But on the other hand, if one understands his argument to be concerned with the fact that Jesus appeared to his friends and disciples rather than to others, the argument is significantly better, because this is what we would expect in the case of a fraud on the part of the disciples. In fact, there are many situations where most people would assume the existence of fraud with this kind of testimony. For example, Joseph Smith managed to get eleven people to swear that they saw the golden plates on which he supposedly received his revelation,  but most people remain unconvinced by this, since there is little reason to think that his witnesses are unbiased.

Of course, things are more complicated in the case of Christ, since for example we have the testimony of St. Paul, who was originally not a disciple. Nonetheless, the argument is meaningful and should not simply be dismissed.

In fact, a reasonable Christian response to this argument requires a particular idea of Christ’s intentions. Porphyry speaks under the assumption that Christ wanted to convince everyone: “For if He had shown Himself to men of note, all would believe through them.” Whether or not this method is sufficient, it is certainly the case that appearing to enough people and in enough ways would have convinced everyone. For that matter, Christ could have stayed on the earth for two hundred years instead of ascending to heaven, in order to ensure that everyone would believe in him, including Porphyry, if that had been his goal. In other words, the implication is that Porphyry was wrong about Christ’s intentions: Christ did not intend to convince everyone.

Given various things Christ says in the Gospels, this is not an unreasonable interpretation of his intentions. For example, he says,

Do not think that I have come to bring peace to the earth; I have not come to bring peace, but a sword.

For I have come to set a man against his father,
and a daughter against her mother,
and a daughter-in-law against her mother-in-law;
and one’s foes will be members of one’s own household.

Likewise, he suggests that not all are intended to understand:

The reason I speak to them in parables is that ‘seeing they do not perceive, and hearing they do not listen, nor do they understand.’ With them indeed is fulfilled the prophecy of Isaiah that says:

‘You will indeed listen, but never understand,
    and you will indeed look, but never perceive.
For this people’s heart has grown dull,
    and their ears are hard of hearing,
        and they have shut their eyes;
        so that they might not look with their eyes,
    and listen with their ears,
and understand with their heart and turn—
    and I would heal them.’

But blessed are your eyes, for they see, and your ears, for they hear.

Isaiah says, “Truly, you are a God who hides himself, O God of Israel, the Savior.” In a similar way, the Christian understanding of the cross and resurrection implies the existence of a hidden truth that is, by design, only made known to some.

People arguing against Christianity might suggest that “ultimately perhaps this way of viewing things is only a trick of the church and of theologians who have run out of solutions but do not want to admit it, and now they are looking for something to hide behind,” as Cardinal Ratzinger puts it.

And on the other hand, the Christian might suggest that given this position, things that seemed unfavorable to his position, such as the three issues mentioned in the linked post, are now favorable to it. Since the truth of Christianity is something intentionally hidden, such things are just what we would expect.

But both of these arguments, the Christian and the non-Christian, are wrong.