Probability

Prayer and Probability

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The reader might wonder about the relation between the previous post and my discussion of Arman Razaali. If I could say it is more likely that he was lying than that the thing happened as stated, why shouldn’t they believe the same about my personal account?

In the first place there is a question of context. I deliberately took Razaali’s account randomly from the internet without knowing anything about him. Similarly if someone randomly passes through and reads the previous post without having ready anything else on this blog, it would not be unreasonable for them to think I might have just made it up. But if someone has read more here they probably have a better estimate of my character. (If you have read more and still think I made it up, well, you are a very poor judge of character and there is not much I can do about that.)

Second, I did not say he was lying. I said it was more likely than the extreme alternative hypothesis that the thing happened exactly as stated and that it happened purely by chance. And given later events (namely his comment here), I do not think he was lying at all.

Third, the probabilities are very different.

“Calculating” the probability

What is the probability of the events I described happening purely by chance? The first thing to determine is what we are counting when we say that something has a chance of 1/X, whatever X is. Out of X cases, the thing should happen about once. In the Razaali case, ‘X’ would be something like “shuffling a deck of cards for 30 minutes and ending up with the deck in the original order.” That should happen about once, if you shuffle and check your deck of cards about 10^67 times.

It is not so easy to say what you are counting if you are trying to determine the probability of a coincidence. And one factor that makes this feel weirder and less probable is that since a coincidence involves several different things happening, you tend to think about it as though there were an extra difficulty in each and every one of the things needing to happen. But in reality you should take one of them as a fixed fact and simply ask about the probability of the other given the fixed thing. To illustrate this, consider the “birthday problem“: in a group of 23 people, the chance that two of them will have the same birthday is over 50%. This “feels” too high; most people would guess that the chance would be lower. But even without doing the math, one can begin to see why this is so by thinking through a few steps of the problem. 22 days is about 6% of the days in a year; so if we take one person, who has a birthday on some day or other, there will be about a 6% chance that one of the other people have the same birthday. If none of them do, take the second person; the chance one of the remaining 21 people will have the same birthday as them will still be pretty close to 6%, which gets us up to almost 12% (it doesn’t quite add up in exactly this way, but it’s close). And we still have a lot more combinations to check. So you can already start to see that how easy it will turn out to be to get up to 50%. In any case, the basic point is that the “coincidence” is not important; each person has a birthday, and we can treat that day as fixed while we compare it to all the others.

In the same way, if you are asking about the probability that someone prays for a thing, and then that thing happens (by chance), you don’t need to consider the prayer as some extra factor — it is enough to ask how often the thing in question happens, and that will tell you your chance. If someone is looking for a job and prays a novena for this intention, and receives a job offer immediately afterwards, the chance will be something like “how often a person looking for a job receives a job offer.” For example, if it takes five months on average to get a job when you are looking, the probability of receiving an offer on a random day should be about 1/150; so out 150 people praying novenas for a job while engaged in a job search, about 1 of them should get an offer immediately afterwards.

What would have counted as “the thing happening” in the personal situation described in the last post? There are a number of subjective factors here, and depending on how one looks at it, especially depending on the detail with which the situation is described. For example, as I said in the last post, it is normal to think of the “answer” to novena on the last day or the day after — so if a person praying for a job receives an offer on either of those days, they will likely consider it just as much of an answer. This means the estimate of 1/150 is really too low; it should really be 1/75. And given that many people would stretch out the period (in which they would count the result as an answer) to as much as a week, we could make the odds as high as 1/21. Looking loosely at other details could similarly improve the odds; e.g. if receiving an interview invitation that later leads to a job is included, the odds would be even higher.

But since we are considering whether the odds might be as bad as 1/10^67, let’s assume we include a fair amount of detail. What are the odds that on a specific day a stranger tells someone that “Our Lady wants you to become a religious and she is afraid that you are going astray,” or words to that effect?

The odds here should be just as objective as the odds with the cards — there should be a real number here — for reasons explained elsewhere, but unfortunately unlike the cards, we have nowhere near enough experience to get a precise number. Nonetheless it is easy to see that various details about the situation made it actually more likely than it would be for a perfectly random person. Since I had a certain opinion of my friend’s situation, that makes it far more likely than chance that other people aware of the situation would have a similar opinion. And although we are talking about a “stranger” here, that stranger was known to a third party that knew my friend, and we have no way of knowing what, if anything, might have passed through that channel.

If we arbitrarily assume that one in a million people in similar situations (i.e. where other people have similar opinions about them) hear such a thing at some point in their lives, and assume that we need to hit one particular day out of 50 years here, then we can “calculate” the chance: 1 / (365 * 50 * 1,000,000), or about 1 in 18 billion. To put it in counting terms, 1 in 18 billion novenas like this will result in the thing happening by chance.

Now it may be that one in a million persons is too high (although if anything it may also be too low; the true value may be more like 1 / 100,000, making the overall probability 1 / 180 million). But it is easy to see that there is no reasonable way that you can say this is as unlikely as shuffling a deck of cards and getting it in the original order.

The Alternative Hypothesis

A thing that happens once in 18 billion person days is not so rare that you would expect such things to never occur (although you would expect them to most likely not happen to you). Nonetheless, you might want to consider whether there is some better explanation than chance.

But a problem arises immediately: it is not clear that the alternative makes it much more likely. After all, I was very surprised by these events when they happened, even though at the time I did attribute an explicitly religious explanation. Indeed, Fr. Joseph Bolin argues that you should not expect prayer to increase the chances of any event. But if this is the case, then the odds of it happening will be the same given the religious explanation as given the chance explanation. Which means the event would not even be evidence for the religious explanation.

In actual fact, it is evidence for the religious explanation, but only because Fr. Joseph’s account is not necessarily true. It could be true that when one prays for something sufficiently rare, the chance of it happening increases by a factor of 1,000; the cases would still be so rare that people would not be likely to discover this fact.

Nonetheless, the evidence is much weaker than a probability of 1 in 18 billion would suggest, namely because the alternative hypothesis does not prevent the events from remaining very unlikely. This is an application of the discussion here, where I argued that “anomalous” evidence should not change your opinion much about anything. This is actually something the debunkers get right, even if they are mistaken about other things.

Might People on the Internet Sometimes Tell the Truth?

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Lies and Scott Alexander

Scott Alexander wrote a very good post called Might People on the Internet Sometimes Lie, which I have linked to several times in the past. In the first linked post (Lies, Religion, and Miscalibrated Priors), I answered Scott’s question (why it is hard to believe that people are lying even when they probably are), but also pointed out that “either they are lying or the thing actually happened in such and such a specific way” is a false dichotomy in any case.

In the example in my post, I spoke about Arman Razaali and his claim that he shuffled a deck of cards for 30 minutes and ended up with the deck in its original order. As I stated in the post,

People demonstrably lie at far higher rates than 1 in 10^67 or 1 in 10^40. This will remain the case even if you ask about the rate of “apparently unmotivated flat out lying for no reason.” Consequently, “he’s lying, period,” is far more likely than “the story is true, and happened by pure chance.” Nor can we fix this by pointing to the fact that an extraordinary claim is a kind of extraordinary evidence. 

But as I also stated there, those are not the only options. As it turns out, although my readers may have missed this, Razaali himself stumbled upon my post somewhat later and posted something in the comments there:

At first, I must say that I was a bit flustered when I saw this post come up when I was checking what would happen when I googled myself. But it’s an excellent read, exceptionally done with excellent analysis. Although I feel the natural urge to be offended by this, I’m really not. Your message is very clear, and it articulates the inner workings of the human mind very well, and in fact, I found that I would completely agree. Having lost access to that Quora account a month or two ago, I can’t look back at what I wrote. I can easily see how the answer gave on Quora could very easily be seen as a lie, and if I read it with no context, I would probably think it was fake too. But having been there at the moment as I counted the cards, I am biased towards believing what I saw, even though I could have miscounted horrendously.

Does this sound like something written by one of Scott Alexander’s “annoying trolls”?

Not to me, anyway. I am aware that I am also disinclined for moral reasons to believe that Razaali was lying, for the reasons I stated in that post. Nonetheless, it seems fair to say that this comment fits better with some intermediate hypothesis (e.g. “it was mostly in order and he was mistaken”) rather than with the idea that “he was lying.”

Religion vs. UFOs

I participated in this exchange on Twitter:

Ross Douthat:

Of what use are our professionally-eccentric, no-heresy-too-wild reasoners like @robinhanson if they assume a priori that “spirits or creatures from other dimensions” are an inherently crazy idea?: https://overcomingbias.com/2021/05/ufos-say-govt-competence-is-either-surprisingly-high-or-surprisingly-low.html

Robin Hanson:

But we don’t want to present ourselves as finding any strange story as equally likely. Yes, we are willing to consider most anything, at least from a good source, & we disagree with others on which stories seem more plausible. But we present ourselves as having standards! 🙂

Me:

I think @DouthatNYT intended to hint that many religious experiences offer arguments for religions that are at least as strong as arguments from UFOs for aliens, and probably stronger.

I agree with him and find both unconvincing.

But find it very impressive you were willing to express those opinions.

Robin Hanson:

You can find videos on best recent evidence for ghosts, which to me looks much less persuasive than versions for UFOs. But evidence for non-ghost spirits, they don’t even bother to make videos for that, as there’s almost nothing.

Me:

It is just not true that there is “almost nothing.” E.g. see the discussion in my post here:

Miracles and Multiple Witnesses

Robin does not respond. Possibly he just does not want to spend more time on the matter. But I think there is also something else going on; engaging with this would suggest to people that he does not “have standards.” It is bad enough for his reputation if he talks about UFOs; it would be much worse if he engaged in a discussion about rosaries turning to gold, which sounds silly to most Catholics, let alone to non-Catholic Christians, people of other religions, and non-religious people.

But I meant what I said in that post, when I said, “these reports should be taken seriously.” Contrary to the debunkers, there is nothing silly about something being reported by thousands of people. It is possible that every one of those reports is a lie or a mistake. Likely, even. But I will not assume that this is the case when no one has even bothered to check.

Scott Alexander is probably one of the best bloggers writing today, and one of the most honest, to the degree that his approach to religious experiences is somewhat better. For example, although I was unfortunately unable to find the text just now, possibly because it was in a comment (and some of those threads have thousands of comments) and not in a post, he once spoke about the Miracle of the Sun at Fatima, and jokingly called it something like, “a glitch in the matrix.” The implication was that (1) he does not believe in the religious explanation, but nonetheless (2) the typical “debunkings” are just not very plausible. I agree with this. There are some hints that there might be a natural explanation, but the suggestions are fairly stretched compared to the facts.

December 24th, 2010 – Jan 4th, 2011

What follows is a description of events that happened to me personally in the period named. They are facts. They are not lies. There is no distortion, not due to human memory failures or anything else. The account here is based on detailed records that I made at the time, which I still possess, and which I just reviewed today to ensure that there would be no mistake.

At that time I was a practicing Catholic. On December 24th, 2010, I started a novena to Mary. I was concerned about a friend’s vocation; I believed that they were called to religious life; they had thought the same for a long time but were beginning to change their mind. The intention of the novena was to respond to this situation.

I did not mention this novena to anyone at the time, or to anyone at all before the events described here.

The last day of the novena was January 1st, 2011, a Marian feast day. (It is a typical practice to end a novena on a feast day of saint to whom the novena is directed.)

On January 4th, 2011, I had a conversation with the same friend. I made no mention at any point during this conversation of the above novena, and there is no way that they could have known about it, or at any rate no way that our debunking friends would consider “ordinary.”

They told me about events that happened to them on January 2nd, 2011.

Note that these events were second hand for me (narrated by my friend) and third hand for any readers this blog might have. This does not matter, however; since my friend had no idea about the novena, even if they were completely making it up (which I believe in no way), it would be nearly as surprising.

When praying a novena, it is typical to expect the “answer to the prayer” on the last day or on the day after, as in an example online:

The Benedictine nuns of St Cecilia’s Abbey on the Isle of Wight (http://www.stceciliasabbey.org.uk) recently started a novena to Fr Doyle with the specific intention of finding some Irish vocations. Anybody with even a passing awareness of the Catholic Church in Ireland is aware that there is a deep vocations crisis. Well, the day after the novena ended, a young Irish lady in her 20’s arrived for a visit at the convent. Today, the Feast of the Immaculate Conception, she will start her time as a postulant at St Cecilia’s Abbey.

Some might dismiss this as coincidence. Those with faith will see it in a different light. Readers can make up their own minds. 

January 2nd, 2011, was the day after my novena ended, and the day to which my friend (unaware of the novena) attributed the following event:

They happened to meet with another person, one who was basically a stranger to them, but met through a mutual acquaintance (mutual to my friend and the stranger; unknown to me.) This person (the stranger) asked my friend to pray with her. She then told my friend that “Our Lady knows that you suffer a lot… She wants you to become a religious and she is afraid that you are going astray…”

Apart from a grammatical change for context, the above sentences are a direct quotation from my friend’s account. Note the relationship with the text I placed in bold earlier.

To be Continued

I may have more to say about these events, but for now I want to say two things:

(1) These events actually happened. The attitude of the debunkers is that if anything “extraordinary” ever happens, it is at best a psychological experience, not a question of the facts. This is just false, and this is what I referred to when I mentioned their second error in the previous post.

(2) I do not accept a religious explanation of these events (at any rate not in any sense that would imply that a body of religious doctrine is true as a whole.)

The Debunkers

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Why are they all blurry?

In a recent article, Michael Shermer says about UFOs:

UFOlogists claim that extraordinary evidence exists in the form of tens of thousands of UFO sightings. But SETI scientist Seth Shostak points out in his book Confessions of an Alien Hunter: A Scientist’s Search for Extraterrestrial Intelligence that this actually argues against UFOs being ETIs, because to date not one of these tens of thousands of sightings has materialized into concrete evidence that UFO sightings equal ETI contact. Lacking physical evidence or sharp and clear photographs and videos, more sightings equals less certainty because with so many unidentified objects purportedly zipping around our airspace we surely should have captured one by now, and we haven’t. And where are all the high-definition photographs and videos captured by passengers on commercial airliners? The aforementioned Navy pilot Ryan Graves told 60 Minutes’ correspondent Bill Whitaker that they had seen UAPs “every day for at least a couple of years.” If true, given that nearly every passenger has a smart phone with a high-definition camera, there should be thousands of unmistakable photographs and videos of these UAPs. To date there is not one. Here, the absence of evidence is evidence of absence.

So you say everything is always vague? There is never any clear evidence?

Richard Carrier accidentally gives the game away when making the same point:

Which leads to the next general principle: notice how real UFO videos (that is, ones that aren’t faked) are always out-of-focus or grainy, fuzzy, or in dim light or infrared or other conditions of extreme ambiguity (you can barely tell even what is being imaged). This is a huge red flag. Exactly as with the errors of human cognition, here we already know we should expect difficulty identifying an object, because we are looking at unclear footage. That “UFOs” always only ever show up in ambiguous footage like this is evidence they are not remarkable. Real alien ships endeavoring to be this visible would have been filmed in much clearer conditions by now. Whereas vehicles able to hide from such filming would never even show up under the conditions of these videos. When you make the conditions so bad you can barely discern obvious things, you have by definition made them so bad you won’t even see less-than-obvious things.

Notice what? “Ones that aren’t faked?” What I notice is that you aren’t actually saying that all UFO reports and videos and so on are vague and unclear. There are plenty of clear ones. You just believe that the clear reports are fake.

Which is fine. You are welcome to believe that. But don’t pretend that all the reports are vague. This drastically reduces the strength of the argument. Your real argument is more or less, “If UFOs were aliens, we would have expected, after all this time, there would be so much evidence that everyone would already have been convinced. But I am not convinced and many people are not convinced. Therefore UFOs must not be aliens.”

Even in its real form, this is not a weak argument. It is actually a pretty good one. It is nonetheless weaker in the case of UFOs than in many other cases where similar arguments are made, because the evidence could easily be reconciled with a situation where the vast majority of UFOs are not aliens, a few or many “clear” cases are hoaxes, and a few clear cases are aliens who typically are attempting to avoid human notice, but who fail or make an exception in a very small number of cases. And in general it is more likely to fail in situations where the phenomena might be very rare, or in situations where something is deliberately hidden (e.g. where there are actual conspiracies.)

The Courage of Robin Hanson

In a sequence of posts beginning around last December, Robin Hanson has been attempting to think carefully about the possibility of UFO’s as aliens. In a pair of posts at the end of March, he first presents a list of facts that would need to be explained under that hypothesis, and then in the next presents his proposal to explain those facts.

In the following post, he makes some comments on fact of having the discussion in the first place:

I’ve noticed that this topic of UFOs makes me feel especially uncomfortable. I look at the many details, and many seem to cry out “there really is something important here.” But I know full well that most people refuse to look at the details, and are quick to denigrate those who do, being confident in getting wide social support when they do.

So I’m forced to choose between my intellectual standards, which say to go where the evidence leads, and my desire for social approval, or at least not extra disapproval. I know which one I’m idealistically supposed to pick, but I also know that I don’t really care as much for picking the things you are supposed to pick as I pretend to myself or others.

We often fantasize about being confronted with a big moral dilemma, so we can prove our morality to ourselves and others. But we should mostly be glad we don’t get what we wish for, as we are often quite wrong about how we would actually act.

This is not merely theoretical. He in fact receives quite a bit of pushback in these posts, some of it rather insulting. For example, in this recent post, someone says in the comments:

When there’s a phenomenon like Bigfoot or the Loch Ness Monster or Alien visitors, believers often point to “all the evidence”. But lots of bad evidence doesn’t equal good evidence! Navy pilots who say they see UFOs “everyday” actually are providing support for the idea that they are misidentifying something mundane. When talking to those who believe in a phenomenon with low plausibility, the best way to start is by saying, “Lets discuss the *single best piece of evidence you have* and then consider other pieces separately.”

I have seen UFO’s twice and each time my brow was furrowed in a vain attempt to understand what I had just witnessed. If I hadn’t simply been lucky enough to see the illusion again from another perspective, each time I would have walked away convinced that I had seen a large, extremely fast craft far away and not a small, slow object quite close to me. And I’m not easy to fool, as I already understand how perspective can be deceiving.

…

I get the idea that your skeptic skills may be under-exercised compared to the rest of your intellect. I’d recommend reading the Shermer book, “Why People Believe Weird Things” or Sagan’s “The Demon Haunted World.” Both are fun reads.

(5ive)

Robin replies,

Your response style, lecturing me about basics, illustrates my status point. People feel free to treat anyone who isn’t on board with full-skeptical like children in need of a lecture.

The debunkers, who are very often the same few people (note that 5ive refers to a book by Michael Shermer), tend to batch together a wide variety of topics (e.g. “Bigfoot or the Loch Ness Monster or Alien visitors”) as “bunk.” You could describe what these things have in common in various ways, but one of the most evident ways is what makes them count as bunk: There is “lots of bad evidence.” That is, as we noted above about UFOs, there is enough evidence to convince some people, but not enough to convince everyone, and the debunkers suppose this situation is just not believable; if the thing were real, they say, everyone would already know.

As I said, this is a pretty good argument, and this generally holds for the sorts of things the debunkers oppose. But this argument can also easily fail, as it did in the case of the meteorites. While people might accept this as a general remark, it nonetheless takes a great deal of courage to suggest that some particular case might be such a case, since as Robin notes, it automatically counts as low status and causes one to be subject to immediate ridicule.

In any case, whether or not the debunkers are right about UFOs or any other particular case, there are at least two general things that they are definitely mistaken about. One is the idea that people who discuss such topics without complete agreement with them are automatically ridiculous. The second will be the topic of another post.

A Correction Regarding Laplace

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A few years ago, I quoted Stanley Jaki on an episode supposedly involved Laplace:

Laplace shouted, “We have had enough such myths,” when his fellow academician Marc-Auguste Pictet urged, in the full hearing of the Académie des Sciences, that attention be given to the report about a huge meteor shower that fell at L’Aigle, near Paris, on April 26, 1803.

I referred to this recently on Twitter. When another user found it surprising that Laplace would have said this, I attempted to track it down, and came to the conclusion that this very account is a “myth” itself, in some sense. Jaki tells the same story in different words in the book Miracles and Physics:

The defense of miracles done with an eye on physics should include a passing reference to meteorites. Characteristic of the stubborn resistance of scientific academies to those strange bits of matter was Laplace’s shouting, “We’ve had enough of such myths,” when Pictet, a fellow academician, urged a reconsideration of the evidence provided by “lay-people” as plain eyewitnesses.

(p. 94)

Jaki provides no reference in God and the sun at Fatima. The text in Miracles and Physics has a footnote, but it provides generic related information that does not lead back to any such episode.

Did Jaki make it up? People do “just make things up“, but in this case whatever benefit Jaki might get from it would seem to be outweighed by the potential reputational damage of being discovered in such a lie, so it seems unlikely. More likely he is telling a story from memory, with the belief that the details just don’t matter very much. And since he provides plenty of other sources, I am sure he knows full well that he is omitting any source here, presumably because he does not have one at hand. He may even be trying to cover up this omission, in a sense, by footnoting the passage with information that does not source it. It seems likely that the story is a lecture hall account that has been modified by the passage of time. One reason to suppose such a source is that Jaki is not alone in the claim that Laplace opposed the idea of meteorites as stones from the sky until 1803. E.T. Jaynes, in Probability Theory: The Logic of Science, makes a similar claim:

Note that we can recognize the clear truth of this psychological phenomenon without taking any stand about the truth of the miracle; it is possible that the educated people are wrong. For example, in Laplace’s youth educated persons did not believe in meteorites, but dismissed them as ignorant folklore because they are so rarely observed. For one familiar with the laws of mechanics the notion that “stones fall from the sky” seemed preposterous, while those without any conception of mechanical law saw no difficulty in the idea. But the fall at Laigle in 1803, which left fragments studied by Biot and other French scientists, changed the opinions of the educated — including Laplace himself. In this case the uneducated, avid for the marvelous, happened to be right: c’est la vie.

(p. 505)

Like Jaki, Jaynes provides no source. Still, is that good enough reason to doubt the account? Let us examine a text from the book The History of Meteoritics and Key Meteorite Collections. In the article, “Meteorites in history,” Ursula Marvin remarks:

Early in 1802 the French mathematician Pierre-Simon de Laplace (1749-1827) raised the question at the National Institute of a lunar volcanic origin of fallen stones, and quickly gained support for this idea from two physicist colleagues Jean Baptiste Biot (1774-1862) and Siméon-Denis Poisson (1781-1840). The following September, Laplace (1802, p. 277) discussed it in a letter to von Zach.

The idea won additional followers when Biot (1803a) referred to it as ‘Laplace’s hypothesis’, although Laplace, himself, never published an article on it.

(p.49)

This has a source for Laplace’s letter of 1802, although I was not able to find it online. It seems very unlikely that Laplace would have speculated on meteorites as coming from lunar volcanos in 1802, and then called them “myths” in 1803. So where does this story come from? In Cosmic Debris: Meteorites in History, John Burke gives this account:

There is also a problem with respect to the number of French scientists who, after Pictet published a résumé of Howard’s article in the May 1802 issue of the Bibliothèque Britannique, continued to oppose the idea that stones fell from the atmosphere. One can infer from a statement of Lamétherie that there was considerable opposition, for he reported that when Pictet read a memoir to the Institut on the results of Howard’s report “he met with such disfavor that it required a great deal of fortitude for him to finish his reading.” However, Biot’s description of the session varies a good deal. Pictet’s account, he wrote, was received with a “cautious eagerness,” though the “desire to explain everything” caused the phenomenon to be rejected for a long time. There were, in fact, only three scientists who publicly expressed their opposition: the brothers Jean-André and Guillaume-Antoine Deluc of Geneva, and Eugène Patrin, an associate member of the mineralogy section of the Institut and librarian at the École des mines.

When Pictet early in 1801 published a favorable review of Chladni’s treatise, it drew immediate fire from the Deluc brothers. Jean, a strict Calvinist, employed the same explanation of a fall that the Fougeroux committee had used thirty years before: stones did not fall; the event was imagined when lightning struck close to the observer. Just as no fragment of our globe separate and become lost in space, he wrote, fragments could not be detached from another planet. It was also very unlikely that solid masses had been wandering in space since the creation, because they would have long since fallen into the sphere of attraction of some planet. And even if they did fall, they would penetrate the earth to a great depth and shatter into a thousand pieces.

(p.51)

It seems quite possible that Pictet’s “reading a memoir” here and “meeting with disfavor” (regardless of details, since Burke notes it had different descriptions at the time) is the same incident that Jaki describes as having been met with “We’ve had enough of such myths!” when Pictet “urged a reconsideration of the evidence.” If these words were ever said, then, they were presumably said by one of these brothers or someone else, and not by Laplace.

How does this sort of thing happen, if we charitably assume that Jaki was not being fundamentally dishonest? As stated above, it seems likely that he knew he did not have a source. He may even have been consciously aware that it might not have been Laplace who made this statement, if anyone did. But he was sure there was a dispute about the matter, and presumably thought that it just wasn’t too important who it was or the details of the situation, since the main point was that scientists are frequently reluctant to accept facts when those facts occur rarely and are not deliberately reproducible. And if we reduce Jaki’s position to these two things, namely, (1) that scientists at one point disputed the reality and meteorites, and (2) this sort of thing frequently happens with rare and hard to reproduce phenomena, then the position is accurate.

But this behavior, the description of situations with the implication that the details just don’t matter much, is very bad, and directly contributes to the reluctance of many scientists to accept the reality of “extraordinary” phenomena, even in situations where they are, in fact, real.

Some Remarks on GPT-N

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At the end of May, OpenAI published a paper on GPT-3, a language model which is a successor to their previous version, GPT-2. While quite impressive, the reaction from many people interested in artificial intelligence has been seriously exaggerated. Sam Altman, OpenAI’s CEO, has said as much himself:

The GPT-3 hype is way too much. It’s impressive (thanks for the nice compliments!) but it still has serious weaknesses and sometimes makes very silly mistakes. AI is going to change the world, but GPT-3 is just a very early glimpse. We have a lot still to figure out.

I used “GPT-N” in the title here because most of the comments I intend to make are almost completely general, and will apply to any future version that uses sufficiently similar methods.

What it does

GPT-3 is a predictive language model, that is, given an input text it tries to predict what would come next, much in the way that if you read the first few words of this sentence with the rest covered up, you might try to guess what would be likely to come next. To the degree that it does this well, it can be used to generate text from a “prompt,” that is, we give it something like a few words or a few sentences, and then add whatever it predicts should come next. For example, let’s take this very blog post and see what GPT-3 would like to say:

What it doesn’t do

While GPT-3 does seem to be able to generate some pretty interesting results, there are several limitations that need to be taken into account when using it.

First and foremost, and most importantly, it can’t do anything without a large amount of input data. If you want it to write like “a real human,” you need to give it a lot of real human writing. For most people, this means copying and pasting a lot. And while the program is able to read through that and get a feel for the way humans communicate, you can’t exactly use it to write essays or research papers. The best you could do is use it as a “fill in the blank” tool to write stories, and that’s not even very impressive.

While the program does learn from what it reads and is quite good at predicting words and phrases based on what has already been written, this method isn’t very effective at producing realistic prose. The best you could hope for is something like the “Deep Writing Machine” Twitter account, which spits out disconnected phrases in an ominous, but very bland voice.

In addition, the model is limited only to language. It does not understand context or human thought at all, so it has no way of tying anything together. You could use it to generate a massive amount of backstory and other material for a game, but that’s about it.

Finally, the limitations in writing are only reinforced by the limitations in reading. Even with a large library to draw on, the program is only as good as the parameters set for it. Even if you set it to the greatest writers mankind has ever known, without any special parameters, its writing would be just like anyone else’s.

The Model

GPT-3 consists of several layers. The first layer is a “memory network” that involves the program remembering previously entered data and using it when appropriate (i.e. it remembers commonly misspelled words and frequently used words). The next layer is the reasoning network, which involves common sense logic (i.e. if A, then B). The third is the repetition network, which involves pulling previously used material from memory and using it to create new combinations (i.e. using previously used words in new orders).

I added the bold formatting, the rest is as produced by the model. This was also done in one run, without repetitions. This is an important qualification, since many examples on the internet have been produced by deleting something produced by the model and forcing it to generate something new until something sensible resulted. Note that the model does not seem to have understood my line, “let’s take this very blog post and see what GPT-3 would like to say.” That is, rather than trying to “say” anything, it attempted to continue the blog post in the way I might have continued it without the block quote.

Truth vs Probability of Text

If we interpret the above text from GPT-3 “charitably”, much of it is true or close to true. But I use scare quotes here because when we speak of interpreting human speech charitably, we are assuming that someone was trying to speak the truth, and so we think, “What would they have meant if they were trying to say something true?” The situation is different here, because GPT-3 has no intention of producing truth, nor of avoiding it. Insofar as there is any intention, the intention is to produce the text which would be likely to come after the input text; in this case, as the input text was the beginning of this blog post, the intention was to produce the text that would likely follow in such a post. Note that there is an indirect relationship with truth, which explains why there is any truth at all in GPT-3’s remarks. If the input text is true, it is at least somewhat likely that what would follow would also be true, so if the model is good at guessing what would be likely to follow, it will be likely to produce something true in such cases. But it is just as easy to convince it to produce something false, simply by providing an input text that would be likely to be followed by something false.

This results in an absolute upper limit on the quality of the output of a model of this kind, including any successor version, as long as the model works by predicting the probability of the following text. Namely, its best output cannot be substantially better than the best content in its training data, which is in this version is a large quantity of texts from the internet. The reason for this limitation is clear; to the degree that the model has any intention at all, the intention is to reflect the training data, not to surpass it. As an example, consider the difference between Deep Mind’s AlphaGo and AlphaGo Zero. AlphaGo Zero is a better Go player than the original AlphaGo, and this is largely because the original is trained on human play, while AlphaGo Zero is trained from scratch on self play. In other words, the original version is to some extent predicting “what would a Go player play in this situation,” which is not the same as predicting “what move would win in this situation.”

Now I will predict (and perhaps even GPT-3 could predict) that many people will want to jump in and say, “Great. That shows you are wrong. Even the original AlphaGo plays Go much better than a human. So there is no reason that an advanced version of GPT-3 could not be better than humans at saying things that are true.”

The difference, of course, is that AlphaGo was trained in two ways, first on predicting what move would be likely in a human game, and second on what would be likely to win, based on its experience during self play. If you had trained the model only on predicting what would follow in human games, without the second aspect, the model would not have resulted in play that substantially improved upon human performance. But in the case of GPT-3 or any model trained in the same way, there is no selection whatsoever for truth as such; it is trained only to predict what would follow in a human text. So no successor to GPT-3, in the sense of a model of this particular kind, however large, will ever be able to produce output better than human, or in its own words, “its writing would be just like anyone else’s.”

Self Knowledge and Goals

OpenAI originally claimed that GPT-2 was too dangerous to release; ironically, they now intend to sell access to GPT-3. Nonetheless, many people, in large part those influenced by the opinions of Nick Bostrom and Eliezer Yudkowsky, continue to worry that an advanced version might turn out to be a personal agent with nefarious goals, or at least goals that would conflict with the human good. Thus Alexander Kruel:

GPT-2: *writes poems*
Skeptics: Meh
GPT-3: *writes code for a simple but functioning app*
Skeptics: Gimmick.
GPT-4: *proves simple but novel math theorems*
Skeptics: Interesting but not useful.
GPT-5: *creates GPT-6*
Skeptics: Wait! What?
GPT-6: *FOOM*
Skeptics: *dead*

In a sense the argument is moot, since I have explained above why no future version of GPT will ever be able to produce anything better than people can produce themselves. But even if we ignore that fact, GPT-3 is not a personal agent of any kind, and seeks goals in no meaningful sense, and the same will apply to any future version that works in substantially the same way.

The basic reason for this is that GPT-3 is disembodied, in the sense of this earlier post on Nick Bostrom’s orthogonality thesis. The only thing it “knows” is texts, and the only “experience” it can have is receiving an input text. So it does not know that it exists, it cannot learn that it can affect the world, and consequently it cannot engage in goal seeking behavior.

You might object that it can in fact affect the world, since it is in fact in the world. Its predictions cause an output, and that output is in the world. And that output and be reintroduced as input (which is how “conversations” with GPT-3 are produced). Thus it seems it can experience the results of its own activities, and thus should be able to acquire self knowledge and goals. This objection is not ultimately correct, but it is not so far from the truth. You would not need extremely large modifications in order to make something that in principle could acquire self knowledge and seek goals. The main reason that this cannot happen is the “P in “GPT,” that is, the fact that the model is “pre-trained.” The only learning that can happen is the learning that happens while it is reading an input text, and the purpose of that learning is to guess what is happening in the one specific text, for the purpose of guessing what is coming next in this text. All of this learning vanishes upon finishing the prediction task and receiving another input. A secondary reason is that since the only experience it can have is receiving an input text, even if it were given a longer memory, it would probably not be possible for it to notice that its outputs were caused by its predictions, because it likely has no internal mechanism to reflect on the predictions themselves.

Nonetheless, if you “fixed” these two problems, by allowing it to continue to learn, and by allowing its internal representations to be part of its own input, there is nothing in principle that would prevent it from achieving self knowledge, and from seeking goals. Would this be dangerous? Not very likely. As indicated elsewhere, motivation produced in this way and without the biological history that produced human motivation is not likely to be very intense. In this context, if we are speaking of taking a text-predicting model and adding on an ability to learn and reflect on its predictions, it is likely to enjoy doing those things and not much else. For many this argument will seem “hand-wavy,” and very weak. I could go into this at more depth, but I will not do so at this time, and will simply invite the reader to spend more time thinking about it. Dangerous or not, would it be easy to make these modifications? Nothing in this description sounds difficult, but no, it would not be easy. Actually making an artificial intelligence is hard. But this is a story for another time.

Was Kavanaugh Guilty?

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No, I am not going to answer the question. This post will illustrate and argue for a position that I have argued many times in the past, namely that belief is voluntary. The example is merely particularly good for proving the point. I will also be using a framework something like Bryan Caplan’s in his discussion of rational irrationality:

Two forces lie at the heart of economic models of choice: preferences and prices. A consumer’s preferences determine the shape of his demand curve for oranges; the market price he faces determines where along that demand curve he resides. What makes this insight deep is its generality. Economists use it to analyze everything from having babies to robbing banks.

Irrationality is a glaring exception. Recognizing irrationality is typically equated with rejecting economics. A “logic of the irrational” sounds self-contradictory. This chapter’s central message is that this reaction is premature. Economics can handle irrationality the same way it handles everything: preferences and prices. As I have already pointed out:

  • People have preferences over beliefs: A nationalist enjoys the belief that foreign-made products are overpriced junk; a surgeon takes pride in the belief that he operates well while drunk.
  • False beliefs range in material cost from free to enormous: Acting on his beliefs would lead the nationalist to overpay for inferior goods, and the surgeon to destroy his career.

Snapping these two building blocks together leads to a simple model of irrational conviction. If agents care about both material wealth and irrational beliefs, then as the price of casting reason aside rises, agents consume less irrationality. I might like to hold comforting beliefs across the board, but it costs too much. Living in a Pollyanna dreamworld would stop be from coping with my problems, like that dead tree in my backyard that looks like it is going to fall on my house.

Let us assume that people are considering whether to believe that Brett Kavanaugh was guilty of sexual assault. For ease of visualization, let us suppose that they have utility functions defined over the following outcomes:

(A) Believe Kavanaugh was guilty, and turn out to be right

(B) Believe Kavanaugh was guilty, and turn out to be wrong

(C) Believe Kavanaugh was innocent, and turn out to be right

(D) Believe Kavanaugh was innocent, and turn out to be wrong

(E) Admit that you do not know whether he was guilty or not (this will be presumed to be a true statement, but I will count it as less valuable than a true statement that includes more detail.)

(F) Say something bad about your political enemies

(G) Say something good about your political enemies

(H) Say something bad about your political allies

(I) Say something good about your political allies

Note that options A through E are mutually exclusive, while one or more of options F through I might or might not come together with one of those from A through E.

Let’s suppose there are three people, a right winger who cares a lot about politics and little about truth, a left winger who cares a lot about politics and little about truth, and an independent who does not care about politics and instead cares a lot about truth. Then we posit the following table of utilities:
Right Winger
Left Winger
Independent
(A)
10
10
100
(B)
-10
-10
-100
(C)
10
10
100
(D)
-10
-10
-100
(E)
5
5
50
(F)
100
100
0
(G)
-100
-100
0
(H)
-100
-100
0
(I)
100
100
0

The columns for the right and left wingers are the same, but the totals will be calculated differently because saying something good about Kavanaugh, for the right winger, is saying something good about an ally, while for the left winger, it is saying something good about an enemy, and there is a similar contrast if something bad is said.

Now there are really only three options we need to consider, namely “Believe Kavanaugh was guilty,” “Believe Kavanaugh was innocent,” and “Admit that you do not know.” In addition, in order to calculate expected utility according to the above table, we need a probability that Kavanaugh was guilty. In order not to offend readers who have already chosen an option, I will assume a probability of 50% that he was guilty, and 50% that he was innocent. Using these assumptions, we can calculate the following ultimate utilities:
Right Winger
Left Winger
Independent
Claim Guilt
-100
100
0
Claim Innocence
100
-100
0
Confess Ignorance
5
5
50

(I won’t go through this calculation in detail; it should be evident that given my simple assumptions of the probability and values, there will be no value for anyone in affirming guilt or innocence as such, but only in admitting ignorance, or in making a political point.) Given these values, obviously the left winger will choose to believe that Kavanaugh was guilty, the right winger will choose to believe that he was innocent, and the independent will admit to being ignorant.

This account obviously makes complete sense of people’s actual positions on the question, and it does that by assuming that people voluntarily choose to believe a position in the same way they choose to do other things. On the other hand, if you assume that belief is an involuntary evaluation of a state of affairs, how could the actual distribution of opinion possibly be explained?

As this is a point I have discussed many times in the past, I won’t try to respond to all possible objections. However, I will bring up two of them. In the example, I had to assume that people calculated using a probability of 50% for Kavanaugh’s guilt or innocence. So it could be objected that their “real” belief is that there is a 50% chance he was guilty, and the statement is simply an external thing.

This initial 50% is something like a prior probability, and corresponds to a general leaning towards or away from a position. As I admitted in discussion with Angra Mainyu, that inclination is largely involuntary. However, first, this is not what we call a “belief” in ordinary usage, since we frequently say that someone has a belief while having some qualms about it. Second, it is not completely immune from voluntary influences. In practice in a situation like this, it will represent something like everything the person knows about the subject and predicate apart from this particular claim. And much of what the person knows will already be in subject/predicate form, and the person will have arrived at it through a similar voluntary process.

Another objection is that at least in the case of something obviously true or obviously false, there cannot possibly be anything voluntary about it. No one can choose to believe that the moon is made of green cheese, for example.

I have responded to this to this in the past by pointing out that most of us also cannot choose to go and kill ourselves, right now, despite the fact that doing so would be voluntary. And in a similar way, there is nothing attractive about believing that the moon is made of green cheese, and so no one can do it. At least two objections will be made to this response:

1) I can’t go kill myself right now, but I know that this is because it would be bad. But I cannot believe that the moon is made of green cheese because it is false, not because it is bad.

2) It does not seem that much harm would be done by choosing to believe this about the moon, and then changing your mind after a few seconds. So if it is voluntary, why not prove it by doing so? Obviously you cannot do so.

Regarding the first point, it is true that believing the moon is made of cheese would be bad because it is false. And in fact, if you find falsity the reason you cannot accept it, how is that not because you regard falsity as really bad? In fact lack of attractiveness is extremely relevant here. If people can believe in Xenu, they would find it equally possible to believe that the moon was made of cheese, if that were the teaching of their religion. In that situation, the falsity of the claim would not be much obstacle at all.

Regarding the second point, there is a problem like Kavka’s Toxin here. Choosing to believe something, roughly speaking, means choosing to treat it as a fact, which implies a certain commitment. Choosing to act like it is true enough to say so, then immediately doing something else, is not choosing to believe it, but rather it is choosing to tell a lie. So just as one cannot intend to drink the toxin without expecting to actually drink it, so one cannot choose to believe something without expecting to continue to believe it for the foreseeable future. This is why one would not wish to accept such a statement about the moon, not only in order to prove something (especially since it would prove nothing; no one would admit that you had succeeded in believing it), but even if someone were to offer a very large incentive, say a million dollars if you managed to believe it. This would amount to offering to pay someone to give up their concern for truth entirely, and permanently.

Additionally, in the case of some very strange claims, it might be true that people do not know how to believe them, in the sense that they do not know what “acting as though this were the case” would even mean. This no more affects the general voluntariness of belief than the fact that some people cannot do backflips affects the fact that such bodily motions are in themselves voluntary.

Perfectly Random

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Suppose you have a string of random binary digits such as the following:

00111100010101001100011011001100110110010010100111

This string is 50 digits long, and was the result of a single attempt using the linked generator.

However, something seems distinctly non-random about it: there are exactly 25 zeros and exactly 25 ones. Naturally, this will not always happen, but most of the time the proportion of zeros will be fairly close to half. And evidently this is necessary, since if the proportion was usually much different from half, then the selection could not have been random in the first place.

There are other things about this string that are definitely not random. It contains only zeros and ones, and no other digits, much less items like letters from the alphabet, or items like ‘%’ and ‘$’.

Why do we have these apparently non-random characteristics? Both sorts of characteristics, the approximate and typical proportion, and the more rigid characteristics, are necessary consequences of the way we obtained or defined this number.

It is easy to see that such characteristics are inevitable. Suppose someone wants to choose something random without any non-random characteristics. Let’s suppose they want to avoid the first sort of characteristic, which is perhaps the “easier” task. They can certainly make the proportion of zeros approximately 75% or anything else that they please. But this will still be a non-random characteristic.

They try again. Suppose they succeed in preventing the series of digits from converging to any specific probability. If they do, there is one and only one way to do this. Much as in our discussion of the mathematical laws of nature, the only way to accomplish this will be to go back and forth between longer and longer strings of zeros and ones. But this is an extremely non-random characteristic. So they may have succeeded in avoiding one particular type of non-randomness, but only at the cost of adding something else very non-random.

Again, consider the second kind of characteristic. Here things are even clearer: the only way to avoid the second kind of characteristic is not to attempt any task in the first place. The only way to win is not to play. Once we have said “your task is to do such and such,” we have already specified some non-random characteristics of the second kind; to avoid such characteristics is to avoid the task completely.

“Completely random,” in fact, is an incoherent idea. No such thing can exist anywhere, in the same way that “formless matter” cannot actually exist, but all matter is formed in one way or another.

The same thing applies to David Hume’s supposed problem of induction. I ended that post with the remark that for his argument to work, he must be “absolutely certain that the future will resemble the past in no way.” But this of course is impossible in the first place; the past and the future are both defined as periods of time, and so there is some resemblance in their very definition, in the same way that any material thing must have some form in its definition, and any “random” thing must have something non-random in its definition.

 

Discount Rates

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Eliezer Yudkowsky some years ago made this argument against temporal discounting:

I’ve never been a fan of the notion that we should (normatively) have a discount rate in our pure preferences – as opposed to a pseudo-discount rate arising from monetary inflation, or from opportunity costs of other investments, or from various probabilistic catastrophes that destroy resources or consumers.  The idea that it is literally, fundamentally 5% more important that a poverty-stricken family have clean water in 2008, than that a similar family have clean water in 2009, seems like pure discrimination to me – just as much as if you were to discriminate between blacks and whites.

Robin  Hanson disagreed, responding with this post:

But doesn’t discounting at market rates of return suggest we should do almost nothing to help far future folk, and isn’t that crazy?  No, it suggests:

  1. Usually the best way to help far future folk is to invest now to give them resources they can spend as they wish.
  2. Almost no one now in fact cares much about far future folk, or they would have bid up the price (i.e., market return) to much higher levels.

Very distant future times are ridiculously easy to help via investment.  A 2% annual return adds up to a googol (10^100) return over 12,000 years, even if there is only a 1/1000 chance they will exist or receive it.

So if you are not incredibly eager to invest this way to help them, how can you claim to care the tiniest bit about them?  How can you think anyone on Earth so cares?  And if no one cares the tiniest bit, how can you say it is “moral” to care about them, not just somewhat, but almost equally to people now?  Surely if you are representing a group, instead of spending your own wealth, you shouldn’t assume they care much.

Yudkowsky’s argument is idealistic, while Hanson is attempting to be realistic. I will look at this from a different point of view. Hanson is right, and Yudkowsky is wrong, for a still more idealistic reason than Yudkowsky’s reasons. In particular, a temporal discount rate is logically and mathematically necessary in order to have consistent preferences.

Suppose you have the chance to save 10 lives a year from now, or 2 years from now, or 3 years from now etc., such that your mutually exclusive options include the possibility of saving 10 lives x years from now for all x.

At first, it would seem to be consistent for you to say that all of these possibilities have equal value by some measure of utility.

The problem does not arise from this initial assignment, but it arises when we consider what happens when you act in this situation. Your revealed preferences in that situation will indicate that you prefer things nearer in time to things more distant, for the following reason.

It is impossible to choose a random integer without a bias towards low numbers, for the same reasons we argued here that it is impossible to assign probabilities to hypotheses without, in general, assigning simpler hypotheses higher probabilities. In a similar way, if “you will choose 2 years from now”, “you will choose 10 years from now,” “you will choose 100 years from now,” are all assigned probabilities, they cannot all be assigned equal probabilities, but you must be more likely to choose the options less distant in time, in general and overall. There will be some number n such that there is a 99.99% chance that you will choose some number of years less than n, and and a probability of 0.01% that you will choose n or more years, indicating that you have a very strong preference for saving lives sooner rather than later.

Someone might respond that this does not necessarily affect the specific value assignments, in the same way that in some particular case, we can consistently think that some particular complex hypothesis is more probable than some particular simple hypothesis. The problem with this is the hypotheses do not change their complexity, but time passes, making things distant in time become things nearer in time. Thus, for example, if Yudkowsky responds, “Fine. We assign equal value to saving lives for each year from 1 to 10^100, and smaller values to the times after that,” this will necessarily lead to dynamic inconsistency. The only way to avoid this inconsistency is to apply a discount rate to all periods of time, including ones in the near, medium, and long term future.

 

Quantum Mechanics and Libertarian Free Will

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In a passage quoted in the last post, Jerry Coyne claims that quantum indeterminacy is irrelevant to free will: “Even the pure indeterminism of quantum mechanics can’t give us free will, because that’s simple randomness, and not a result of our own ‘will.'”

Coyne seems to be thinking that since quantum indeterminism has fixed probabilities in any specific situation, the result for human behavior would necessarily be like our second imaginary situation in the last post. There might be a 20% chance that you would randomly do X, and an 80% chance that you would randomly do Y, and nothing can affect these probabilities. Consequently you cannot be morally responsible for doing X or for doing Y, nor should you be praised or blamed for them.

Wait, you might say. Coyne explicitly favors praise and blame in general. But why? If you would not praise or blame someone doing something randomly, why should you praise or blame someone doing something in a deterministic manner? As explained in the last post, the question is whether reasons have any influence on your behavior. Coyne is assuming that if your behavior is deterministic, it can still be influenced by reasons, but if it is indeterministic, it cannot be. But there is no reason for this to be case. Your behavior can be influenced by reasons whether it is deterministic or not.

St. Thomas argues for libertarian free will on the grounds that there can be reasons for opposite actions:

Man does not choose of necessity. And this is because that which is possible not to be, is not of necessity. Now the reason why it is possible not to choose, or to choose, may be gathered from a twofold power in man. For man can will and not will, act and not act; again, he can will this or that, and do this or that. The reason of this is seated in the very power of the reason. For the will can tend to whatever the reason can apprehend as good. Now the reason can apprehend as good, not only this, viz. “to will” or “to act,” but also this, viz. “not to will” or “not to act.” Again, in all particular goods, the reason can consider an aspect of some good, and the lack of some good, which has the aspect of evil: and in this respect, it can apprehend any single one of such goods as to be chosen or to be avoided. The perfect good alone, which is Happiness, cannot be apprehended by the reason as an evil, or as lacking in any way. Consequently man wills Happiness of necessity, nor can he will not to be happy, or to be unhappy. Now since choice is not of the end, but of the means, as stated above (Article 3); it is not of the perfect good, which is Happiness, but of other particular goods. Therefore man chooses not of necessity, but freely.

Someone might object that if both are possible, there cannot be a reason why someone chooses one rather than the other. This is basically the claim in the third objection:

Further, if two things are absolutely equal, man is not moved to one more than to the other; thus if a hungry man, as Plato says (Cf. De Coelo ii, 13), be confronted on either side with two portions of food equally appetizing and at an equal distance, he is not moved towards one more than to the other; and he finds the reason of this in the immobility of the earth in the middle of the world. Now, if that which is equally (eligible) with something else cannot be chosen, much less can that be chosen which appears as less (eligible). Therefore if two or more things are available, of which one appears to be more (eligible), it is impossible to choose any of the others. Therefore that which appears to hold the first place is chosen of necessity. But every act of choosing is in regard to something that seems in some way better. Therefore every choice is made necessarily.

St. Thomas responds to this that it is a question of what the person considers:

If two things be proposed as equal under one aspect, nothing hinders us from considering in one of them some particular point of superiority, so that the will has a bent towards that one rather than towards the other.

Thus for example, someone might decide to become a doctor because it pays well, or they might decide to become a truck driver because they enjoy driving. Whether they consider “what would I enjoy?” or “what would pay well?” will determine which choice they make.

The reader might notice a flaw, or at least a loose thread, in St. Thomas’s argument. In our example, what determines whether you think about what pays well or what you would enjoy? This could be yet another choice. I could create a spreadsheet of possible jobs and think, “What should I put on it? Should I put the pay? or should I put what I enjoy?” But obviously the question about necessity will simply be pushed back, in this case. Is this choice itself determinate or indeterminate? And what determines what choice I make in this case? Here we are discussing an actual temporal series of thoughts, and it absolutely must have a first, since human life has a beginning in time. Consequently there will have to be a point where, if there is the possibility of “doing A for reason B” and “doing C for reason D”, it cannot be any additional consideration which determines which one is done.

Now it is possible at this point that St. Thomas is mistaken. It might be that the hypothesis that both were “really” possible is mistaken, and something does determine one rather than the other with “necessity.” It is also possible that he is not mistaken. Either way, human reasons do not influence the determination, because reason B and/or reason D are the first reasons considered, by hypothesis (if they were not, we would simply push back the question.)

At this point someone might consider this lack of the influence of reasons to imply that people are not morally responsible for doing A or for doing C. The problem with this is that if you do something without a reason (and without potentially being influenced by a reason), then indeed you would not be morally responsible. But the person doing A or C is not uninfluenced by reasons. They are influenced by reason B, or by reason D. Consequently, they are responsible for their specific action, because they do it for a reason, despite the fact that there is some other general issue that they are not responsible for.

What influence could quantum indeterminacy have here? It might be responsible for deciding between “doing A for reason B” and “doing C for reason D.” And as Coyne says, this would be “simple randomness,” with fixed probabilities in any particular situation. But none of this would prevent this from being a situation that would include libertarian free will, since libertarian free will is precisely nothing but the situation where there are two real possibilities: you might do one thing for one reason, or another thing for another reason. And that is what we would have here.

Does quantum mechanics have this influence in fact, or is this just a theoretical possibility? It very likely does. Some argue that it probably doesn’t, on the grounds that quantum mechanics does not typically seem to imply much indeterminacy for macroscopic objects. The problem with this argument is that the only way of knowing that quantum indeterminacy rarely leads to large scale differences is by using humanly designed items like clocks or computers. And these are specifically designed to be determinate: whenever our artifact is not sufficiently determinate and predictable, we change the design until we get something predictable. If we look at something in nature uninfluenced by human design, like a waterfall, is details are highly unpredictable to us. Which drop of water will be the most distant from this particular point one hour from now? There is no way to know.

But how much real indeterminacy is in the waterfall, or in the human brain, due to quantum indeterminacy? Most likely nobody knows, but it is basically a question of timescales. Do you get a great deal of indeterminacy after one hour, or after several days? One way or another, with the passage of enough time, you will get a degree of real indeterminacy as high as you like. The same thing will be equally true of human behavior. We often notice, in fact, that at short timescales there is less indeterminacy than we subjectively feel. For example, if someone hesitates to accept an invitation, in many situations, others will know that the person is very likely to decline. But the person feels very uncertain, as though there were a 50/50 chance of accepting or declining. The real probabilities might be 90/10 or even more slanted. Nonetheless, the question is one of timescales and not of whether or not there is any indeterminacy. There is, this is basically settled, it will apply to human behavior, and there is little reason to doubt that it applies at relatively short timescales compared to the timescales at which it applies to clocks and computers or other things designed with predictability in mind.

In this sense, quantum indeterminacy strongly suggests that St. Thomas is basically correct about libertarian free will.

On the other hand, Coyne is also right about something here. While it is not true that such “randomness” removes moral responsibility, the fact that people do things for reasons, or that praise and blame is a fitting response to actions done for reasons, Coyne correctly notices that it does not add to the fact that someone is responsible. If there is no human reason for the fact that a person did A for reason B rather than C for reason D, this makes their actions less intelligible, and thus less subject to responsibility. In other words, the “libertarian” part of libertarian free will does not make the will more truly a will, but less truly. In this respect, Coyne is right. This however is unrelated to quantum mechanics or to any particular scientific account. The thoughtful person can understand this simply from general considerations about what it means to act for a reason.

Causality and Moral Responsibility

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Consider two imaginary situations:

(1) In the first situation, people are such that when someone sees a red light, they immediately go off and kill someone. Nothing can be done to prevent this, and no intention or desire to do otherwise makes any difference.

In this situation, killing someone after you have seen a red light is not blamed, since it cannot be avoided, but we blame people who show red lights to others. Such people are arrested and convicted as murderers.

(2) In the second situation, people are such that when someone sees a red light, there is a 5% chance they will go off and immediately kill someone, and a 95% chance they will behave normally. Nothing can change this probability: it does not matter whether the person is wicked or virtuous or what their previous attitude to killing was.

In this situation, again, we do not blame people who end up killing someone, but we call them unlucky. We do however blame people who show others red lights, and they are arrested and convicted of second degree murder, or in some cases manslaughter.

Some people would conclude from this that moral responsibility is incoherent: whether the world is deterministic or not, moral responsibility is impossible. Jerry Coyne defends this position in numerous places, as for example here:

We’ve taken a break from the many discussions on this site about free will, but, cognizant of the risks, I want to bring it up again. I think nearly all of us agree that there’s no dualism involved in our decisions: they’re determined completely by the laws of physics. Even the pure indeterminism of quantum mechanics can’t give us free will, because that’s simple randomness, and not a result of our own “will.”

Coyne would perhaps say that “free will” embodies a contradiction much in the way that “square circle” does. “Will” implies a cause, and thus something deterministic. “Free” implies indeterminism, and thus no cause.

In many places Coyne asserts that this implies that moral responsibility does not exist, as for example here:

This four-minute video on free will and responsibility, narrated by polymath Raoul Martinez, was posted by the Royal Society for the Encouragement of the Arts, Manufactures, and Commerce (RSA). Martinez’s point is one I’ve made here many times, and will surely get pushback from: determinism rules human behavior, and our “choices” are all predetermined by our genes and environment. To me, that means that the concept of “moral responsibility” is meaningless, for that implies an ability to choose freely. Nevertheless, we should still retain the concept of responsibility, meaning “an identifiable person did this or that good or bad action”. And, of course, we can sanction or praise people who were responsible in this sense, for such blame and praise can not only reinforce good behavior but is salubrious for society.

I think that Coyne is very wrong about the meaning of free will, somewhat wrong about responsibility, and likely wrong about the consequences of his views for society (e.g. he believes that his view will lead to more humane treatment of prisoners. There is no particular reason to expect this.)

The imaginary situations described in the initial paragraphs of this post do not imply that moral responsibility is impossible, but they do tell us something. In particular, they tell us that responsibility is not directly determined by determinism or its lack. And although Coyne says that “moral responsibility” implies indeterminism, surely even Coyne would not advocate blaming or punishing the person who had the 5% chance of going and killing someone. And the reason is clear: it would not “reinforce good behavior” or be “salubrious for society.” By the terms set out, it would make no difference, so blaming or punishing would be pointless.

Coyne is right that determinism does not imply that punishment is pointless. And he also recognizes that indeterminism does not of itself imply that anyone is responsible for anything. But he fails here to put two and two together: just as determinism does not imply punishment is pointless, nor that it is not, indeterminism likewise implies neither of the two. The conclusion he should draw is not that moral responsibility is meaningless, but that it is independent of both determinism and indeterminism; that is, that both deterministic compatibilism and libertarian free will allow for moral responsibility.

So what is required for praise and blame to have a point? Elsewhere we discussed C.S. Lewis’s claim that something can have a reason or a cause, but not both. In a sense, the initial dilemma in this post can be understood as a similar argument. Either our behavior has deterministic causes, or it has indeterministic causes; therefore it does not have reasons; therefore moral responsibility does not exist.

On the other hand, if people do have reasons for their behavior, there can be good reasons for blaming people who do bad things, and for punishing them. Namely, since those people are themselves acting for reasons, they will be less likely in the future to do those things, and likewise other people, fearing punishment and blame, will be less likely to do them.

As I said against Lewis, reasons do not exclude causes, but require them. Consequently what is necessary for moral responsibility are causes that are consistent with having reasons; one can easily imagine causes that are not consistent with having reasons, as in the imaginary situations described, and such causes would indeed exclude responsibility.