# Thinking critically about false memories

## Introducing false memories

Many of us recognise intuitively that our memories aren’t perfect and that we can not only forget things but also misremember others.

False memory research is a burgeoning field where scientists systematically study the fallibility and malleability of human memory.

Their findings can be divided into two categories.

1. Spontaneous false memories

People can naturally mistake the face of an innocent for that of a rapist, confuse road signs seen during an accident, believe that the car collision was more violent if “crashed into” is used rather than “ran into” during the questioning and so on and so forth.

2. “Unnatural” false memories

The most spectacular forms of false memories are doubtlessly people misremembering being victims of satanic ritual or abducted by space aliens.

The genesis of such fictional memories generally follow these steps:

a) The person goes to a therapist with unspecific problems such as depression, overweight or anxiety.

b) The therapist convinces the person that it is likely he or she had a terrible experience she has repressed.

c) The therapist uses suggestive methods (such as hypnosis) to push the person to try to remember what she allegedly went through.

d) The persons gets persuaded she really experienced all these things.

Plenty of experimental studies have shown that manipulative techniques can spawn entirely fictional memories.

For instance, the cognitive psychologist can tell the test subject that his parents reported he was lost in a mall as a child and give him some true details related to his childhood in order that he gets convinced the person conducting the test really knows of his past. Researchers also often tell subjects to remember real past events in order to increase their confidence in the procedure.

And then, they are asked to imagine having experienced the fictional event. The subjects generally don’t remember it at first but after three sessions of suggestive imagination, many of them can form vivid memories of having gone through this.

The same method can even be applied to a fictional criminal action such as assaulting someone with a weapon or being viciously attacked by an animal.

In any case, there appears to be two necessary conditions for the genesis of such “big” false memories.

a) The person believes that the cognitive psychologist or therapist is in a position to know things about their past they don’t remember.

b) Suggestive techniques (whereby the person imagines having experienced these things) are used.

If these two conditions are satisfied, a certain number of test subjects confuse their imagining the false event with their remembering it really happened.

There is one important limitation of these studies which is often missed out on, though.

To the best of my knowledge, such radical false memories (also called “full” false memories” as the event never occurred) almost always come up through (conscious or unconscious) manipulation and not spontaneously.
(An exception might be memories “retrieved” many decades after an event such as being bombarded during World War 2).

In other words, it is statistically highly unlikely that a woman having kissed a man during an evening would remember being raped by him four years later without any manipulation (assuming she wasn’t raped by anyone in between).

And if this happens, you can bet a lot of money she has some serious mental health issues.

## Hillary Clinton’s bizarre “false memories”

During the presidential campaign of 2008, Hillary Clinton was harshly criticised after having claimed she landed under sniper fire in Bosnia whereas she actually took part in a peaceful ceremony.

A memory researcher tried to attribute this to false memories.

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It would be a horrible cliché to begin a post about the reconstructive nature of autobiographical memory with a Proust quote, so instead I’ll begin with something only slightly less cliché: beginning something about memory by talking about my own experience. You see, I’m southern, as anyone who’s ever heard me pronounce the words “pen” and “pin” exactly the same, or refer to any soft drink as a “coke,” can attest. In the south, it’s not uncommon to find people sitting around a grill, or a kitchen table, or pretty much anything you can sit around, participating in what might be described as story contests. These are basically pissing contests, but with words instead of, well, other stuff. The contest usually begins with someone telling a crazy story (usually from their youth), which is followed by someone else telling an even crazier story, and so on, back and forth, until someone tells a story so crazy that nothing believable could ever top it. Now, it goes without saying that these contests involve a great deal of, shall we say, creative interpretation of the events being described. And of course, everyone involved is well aware of this. In fact, because the same people often participate in these contests with each other over the years, you can actually watch the stories change: what started as a mildly dangerous activity changes to an extremely dangerous one, then a deadly one, and ultimately, in the “same” story, the story-teller barely cheated Death. The fish you caught became bigger, and the struggle with the one that got away longer and more grueling.

I’ve participated in many of these contests over the years, and generally do pretty well, because I’ve done a lot of stupid things that really did involve an uncomfortable proximity to death, and as anyone who knows me will readily tell you, I have an uncanny ability to hurt myself in bizarre ways (like the time I got a pencil stuck deep between two toes when I tripped on an Afghan blanket). As I’ve told my stories over the years (I have a long list of them ready to be told at a moment’s notice), and… umm… creatively interpreted them to make them more exciting (than the other person’s), I’ve added a detail here, or increased a measurement (by an order of magnitude) there. That’s just the way the game works.

But here’s the thing: in many cases, I don’t remember which parts really happened and which parts I added for effect in the course of one of those contests. This is a simple case of source monitoring failure. I can’t tell whether I’m remembering the event itself or one of the times I told the story of the event. And what’s worse, the vividness of the memory, or how much I can picture it in my head, doesn’t help, because my brain is just as good at coming up with images of things I made up creatively interpreted as it is at coming up with images of things that actually happened. The reason for this, of course that when my brain is remembering something, it’s just putting it together on the fly from bits and associated pieces. And every time I recall an episode, that recall becomes another associated episode, and the memory for the original episode is therefore altered, making it really easily to mistakenly recall things you thought or said about the episode long after it happened as part of the original episode. In other words, memory is just a form of makin’ shit up.

Why am I telling you all of this? Well, if you’ve been following politics at all, you’ve no doubt heard about Hillary Clinton’s latest gaffe. In a speech last week, she said this about a trip to Bosnia in 1996:

I certainly do remember that trip to Bosnia… we came in in an evasive maneuver… I remember landing under sniper fire… there was no greeting ceremony… we ran with our heads down, we basically were told to run to our cars… there was supposed to be some kind of a greeting ceremony at the airport, we basically were told to run to our cars, that is what happened.

Sounds harrowing, right? Well, it turns out that it didn’t really happen that way, and there’s video to prove it. It seems there weren’t any snipers, or evasive maneuvers, and instead of running to the cars with their heads down, they had a little ceremony on the tarmac. Oops.

Since it became clear that Clinton’s story wasn’t accurate, bloggers and the mainstream media have been taking her to task, and understandably so. If you’re telling a story that’s supposed to demonstrate your experience with dangerous foreign policy situations, and it turns out the story isn’t really true, you’re going to hear about it. But I think it’s unfair to accuse Clinton of lying. Don’t get me wrong, I think all politicians lie, and I’m no fan of Clinton (I voted for her opponent in my state’s primary), but this appears to be a pretty straightforward failure of memory to me, and I’d bet a lot of money that source monitoring has its dirty little hand in it.

To see why I think this is a memory rather than honesty issue, read the following recollection of the trip by Lissa Muscatine, who was on the plane with Clinton (from here):

I was on the plane with then First Lady Hillary Clinton for the trip from Germany into Bosnia in 1996. We were put on a C17– a plane capable of steep ascents and descents — precisely because we were flying into what was considered a combat zone. We were issued flak jackets for the final leg because of possible sniper fire near Tuzla. As an additional precaution, the First Lady and Chelsea were moved to the armored cockpit for the descent into Tuzla. We were told that a welcoming ceremony on the tarmac might be canceled because of sniper fire in the hills surrounding the air strip. From Tuzla, Hillary flew to two outposts in Bosnia with gunships escorting her helicopter.

Add to that the report by a U.S. general who was there on the ground that they were aware of security threats at the time, and the interference of all the other landings that Clinton made in Europe and elsewhere, plus the fact that Senator Clinton has likely told this story many times (it’s in one of her books), and you’ve got a situation that’s ripe for source monitoring errors.

Let’s look at what might have happened. In Germany, Clinton got on a plane that was used specifically because of its ability to maneuver during landings to avoid incoming fire. Undoubtedly, they were told that this was the reason for using the plane. They had flak jackets and Clinton was put into the armored cockpit for the descent, again as a precaution against incoming fire. Add to this the fact that there were credible threats, meaning she was probably rather anxious, and we all know that stress doesn’t make for better overall memory, even if it makes us remember perceptual details better. Hell, maybe even Clinton and her entourage were rushed, after the meeting on the tarmac, to their cars because they were on a tight schedule (not because of the threats), and you get a situation that’s easily distorted by the reconstructive processes of memory into something like the version that Clinton told. In fact, I’d bet that they even told Clinton or someone on her team that in the case of incoming fire, they would have to be rush to their cars with their heads down, instead of having the scheduled ceremony on the tarmac. All this could easily add up to a memory in which the threat, the fear, the flak jackets, etc., add up to a difficulty in remembering what actually happened and what she was afraid might happened. And the fact that Clinton seems to remember it so vividly, contrary to being evidence that she’s lying, is likely just a product of her brain filling in the gaps and building a coherent representation of the episode, just like it’s supposed to do.

None of this makes Clinton’s version of the events in Bosnia in 1996 more accurate, of course, nor does it excuse her and her campaign from not quickly verifying her memory to make sure she wasn’t misremembering. But it doesn’t mean she’s lying, either, and since she’s clearly a rational and intelligent person, it’s unlikely she’d lie about something that easily verified anyway. Instead, my money’s on a mundane, though potentially costly, error resulting from the reconstructive nature of memory. At least, until someone demonstrates otherwise, I’m willing to give her, and her memory, the benefit of the doubt.

As Montaigne put it, “The memory represents to us not what we choose but what it pleases.” Sorry,I had to end with a cliché too!

********************************************

I think there are many problems which emerge from this account once you start systematically investigating the case.

### The chronology of Hillary Clinton’s recounting of the facts

In order to assess the plausibility of any false memories, we must carefully reconstruct the way the story evolved.

In this case, it looks like this:

a) In 1996, Clinton went to Bosnia and participated in a peaceful meeting there.

b) In 2003, in her autobiography entitled “Living History”, Clinton stated:

“Security conditions were constantly changing in the former Yugoslavia, and they had recently deteriorated again. Due to reports of snipers in the hills around the airstrip, we were forced to cut short an event on the tarmac with local children, though we did have time to meet them and their teachers and to learn how hard they had worked during the war to continue classes in any safe spot they could find. One eight-year-old girl gave me a copy of a poem she had written entitled ‘Peace.’ “

This story already contains an embellishment as the event was not cut short. But it isn’t far from the truth.

c) December 30, 2007

“We landed in one of those corkscrew landings and ran out because they said there might be sniper fire. I don’t remember anyone offering me tea on the tarmac there.”

Apart from “running out”, this account is remarkably similar to what she wrote in her autobiography. She only spoke of a threat of actual sniper fire in both cases and would certainly have mentioned her real exposure to the danger if she had believed to have experienced that.

d) February 29, 2008

“I remember, particularly, a trip to Bosnia where the welcoming ceremony had to be moved inside because of sniper fire.”

Here, she strongly insinuated that the sniper fire was real rather than a mere potential threat.

e) March 17, 2008

I remember landing under sniper fire. There was supposed to be some kind of a greeting ceremony at the airport, but instead we just ran with our heads down to get into the vehicles to get to our base.

This is her tallest statement about the story. Here she asserts having fled from actual snipers who were shooting at her.

March 25, 2008

“Now let me tell you what I can remember, OK — because what I was told was that we had to land a certain way and move quickly because of the threat of sniper fire. So I misspoke — I didn’t say that in my book or other times but if I said something that made it seem as though there was actual fire — that’s not what I was told. I was told we had to land a certain way, we had to have our bulletproof stuff on because of the threat of sniper fire. I was also told that the greeting ceremony had been moved away from the tarmac but that there was this 8-year-old girl and, I can’t, I can’t rush by her, I’ve got to at least greet her — so I greeted her, I took her stuff and then I left, now that’s my memory of it.”

Revealingly, Clinton did NOT tell: “my most recent memories of the event diverged from what actually happened“.

Instead, she said she was aware all along she wasn’t being shot at by real snipers and tried to put the controversy behind her by saying she “misspoke”.

April 16, 2008

Well Tom I might told you, I may be a lot of things, but I am not dumb…and I wrote about going to Bosnia in my book in 2004. I laid it out there. And you’re right…on a couple of occasions in the last weeks, I just said things that weren’t in keeping with what I knew to be the case and what I’ve written about in my book and you know, I am embarrassed by it, I have apologised for it, I’ve said it was a mistake and it is I hope something you can look over.

### Evaluation

It is highly dubious that Hillary wouldn’t lie if something can be easily verified. For instance, she denied having changed her mind on gay marriage even though it could be clearly seen she was against it before.

Whilst Hilary Clinton did speak of having a different memory of the event in Bosnia, she always emphasised after the scandal that she was well aware she didn’t face actual snipers.

It is also extremely improbable she would come to erroneously believe she faced real snipers within only four months without her memory being manipulated.

For all these reasons, it is very implausible that Hillary Clinton misremembered landing under sniper fire, even though she might have been honestly mistaken about other aspects of her recollection.

## Conclusion

Scientists working on false memories have done a very good job by showing the unreliability of alleged “recovered memories” of being abused and by demonstrating that eye witnesses can be wrong about important details related to a criminal case. I don’t want to criticise the value of their research and investigations.

Nevertheless, they haven’t, in my opinion, shown that “human memory is totally unreliable” in that people can spontaneously remember a totally fictional event such as being shot at (except, perhaps, many decades after a traumatic war).

Before being considered genuine cases of false memories, incidents such as Hillary Clinton’s gaffe need to be carefully examined in order to assess the plausibility of false memories having caused them. Alternative explanations (such as that of a megalomaniac lie) need to be carefully ruled out.

It is worth mentioning a similar story.

Newsman Brian William came under heavy criticism after having said the helicopter he was in was hit during the war on Iraq whereas it was actually a helicopter flying 30 minutes ahead of him which had been the victim of the attack.

Many specialists have jumped to the conclusion this MUST have been a false memory.

Unfortunately, they failed to critically consider the context. Brian Williams had already strongly embellished the story only one month after the event, he has a stark tendency to aggrandise his role (as can be seen in other cases) and he himself recognised that

This came clearly from a bad urge inside me. This was clearly ego-driven, a desire to better my role in a story I was already in. That’s what I’ve been tearing apart, unpacking and analyzing.”

In his case, mythomania seems a (much) better explanation than the type of false memories found in the general population.

Of practical importance to all of us is the amount of trust we should put in our own memories. I remember the following incident. As I was a teenager, I used to hang out with a guy deeply involved in cannabis traffic. One day, he was tricked by another drug dealer. To avenge himself, he wrote a graffiti insulting that person. Several days later, as my friend and I were sitting in a former washhouse in his village, the other drug dealer showed up along with three or four accomplices. They were armed with heavy baseball bats. I remember laughing out of nervousness. My friend apologised and the men departed. He later rebuked me for having laughed as this might have led them to strike us down or hurt us badly.

Is it possible I dreamed up the whole thing? Yes.

Is it likely? Absolutely not.

I didn’t remember that after a “recovery therapy” or a psychological experiment. Therefore, I feel very confident that the things I mentioned truly occurred, even though I might be mistaken about details (such as the faces and number of the assailants).

Based on both common sense and our current knowledge of memory, I believe this is a rational and healthy way of considering our past.

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# On God’s hiddenness and the nature of faith

I was recently involved in an interesting debate about the nature of faith in God and the alleged moral guilt of disbelievers.

It revolved around the problem of divine hiddenness: if God really exists and is interested in people believing in Him, then why does He not unambiguously prove His existence?

The discussion took place in the comment section of a blog post written by progressive Evangelical theologian Randal Rauser entitled “Is the Atheist my Neighbour?

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When I wrote Is the Atheist My Neighbor? I had a very short endorser wish-list. That list consisted of folks who were leaders in their professions and exemplars of the kind of irenic dialogue between atheist and Christian that was the book’s reason for being.

Neither Richard Dawkins nor Ray Comfort made the list.

One of the people who did make that list was J.L. Schellenberg, Professor of Philosophy at Mount Saint Vincent University. Schellenberg is an atheist and one of the leading philosophers of religion in the world today. His most important work in philosophy of religion is a powerful argument for atheism from divine hiddenness, an argument that he has honed over more than twenty years. Professor Schellenberg has pushed the dialogue and debate forward with a thoughtful and powerful argument, and all without animus or rancor. Indeed, while I have never met him, I know several Christian philosophers who count him not only an esteemed and worthy opponent, but a personal friend as well. You can visit Professor Schellenberg online at his website here.

All this is to say that I was delighted to receive the following endorsement from Professor Schellenberg for Is the Atheist My Neighbor? Given my goals in writing this book, an endorsement like this is worth its weight in gold, and that would hold even if the endorsement were etched in granite. The first sentence alone provides one of the best introductions to a book endorsement that I’ve ever read:

“There are some whose way of following the first of the great commandments has, in the matter of nonbelief, meant violating the second. In this brief and lively but remarkably full and acute discussion, Rauser shows the way out of this problem. Impressively fair, and writing not perfunctorily but with feeling, he has found a way to express genuine neighborliness both to atheists like me and to Christians who struggle to reconcile love and loyalty.”

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Andy Schüler, a German Atheist reacted to another commentator arguing that rejecting God’s existence is never an innocent action.

Among many other things, he wrote:

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Schellenberg´s argument requires that at least some people who are open to the possibility of God’s existence and do not resist this truth still live and die as unbelievers. If you interpret the Bible in such a way that the existence of such people is impossible – then your interpretation makes the Bible evidently wrong about this matter (in a way that makes any further discussions impossible, because it forces you to accuse people who claim that they indeed are sincerely open to the possibility of God’s existence, yet also sincerely do not believe that there is a God, of simply lying about this).

…………………………….

You don´t teach your kid that he or she shouldn’t touch a hot stove by letting him touch it. Or rather – you would be a terrible parent if you did it). And the scripture you refer to depicts God in an even worse light, God is like a parent that is an extremely skilled mentalist and not only does nothing to stop his little kid from touching the hot stove, but rather uses his skills to convince him that he  should touch it!

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My response follows. Please forgive me for the small pieces of German dialect scattered here and there 🙂

Hi Andy! 🙂
Long time, no see!
(Sit longi Zit hon ich nix meh von dir gehert!).

“Innocence or lack thereof has nothing to do with anything here. Schellenberg´s argument requires that at least some people are open to the possibility of God existing / not resisting the truth of this, yet still live and die as unbelievers.”

My own view is that people “dying as unbelievers” (or atheists for that matter) but sincerely and humbly striving for justice and love will inherit eternal life whereas people dying as egoistical self-righteous bigots will irremediably lose their existence and be no more.

In all his parables, Jesus never threatened anyone with hellfire for not believing in Him or engaging in sexual immorality but for
1) failing to feed the poor, weak, hungry or neglected
and
2) not repenting from one’s own unjust pride.

Even Paul himself didn’t embrace the whole view often attributed to him in that he wrote

“God “will repay each person according to what they have done.”[a] 7 To those who by persistence in doing good seek glory, honour and immortality, he will give eternal life. 8 But for those who are self-seeking and who reject the truth and follow evil, there will be wrath and anger. 9 There will be trouble and distress for every human being who does evil: first for the Jew, then for the Gentile; 10 but glory, honour and peace for everyone who does good: first for the Jew, then for the Gentile. 11”

If you read Roman 2, it seems quite clear to me that Paul believed in the salvation of righteous heathens dying as such, his other ideas notwithstanding.

It is ironic that those arrogant and unloving fundamentalists who keep preaching about “salvation by faith” and eternal torment are those who are the most likely to miss everlasting life, according to Jesus.

Given that, I find that Schellenberg´s challenges are far less impressive (albeit not entirely unproblematic, of course).

God is under no moral obligation to give clear evidence of His existence to atheists if their unbelief while dying isn’t going to damn them.

You’re quite right that we cannot make a choice about what we deem to be reasonable
(obwohl die Engländer das Wort “decide” sowohl als “entscheiden” als auch als “bestimmen”, “herausfinden” verwenden 🙂 )

Yet, the same thing cannot necessarily be said about our hopes .

Obviously, someone convinced that theism is extremely implausible cannot entertain any hope in that direction.

But what if you’re completely ignorant about whether theism or atheism is true?

Or what if you (as I do) believe there are intriguing pieces of evidence for the existence of a non-material world which aren’t, however, compelling?

It appears quite reasonable to think one can, in that case, consciously choose to entertain and cultivate hope in either direction.

One example might make that concept a bit more palatable.

Consider the proposition: “Our world is actually some kind of simulation run by beings we know nothing about . It all started five minutes ago with the appearance of age.”

I’ve no doubt that most of us find that pretty absurd on an emotional level .
Yet, I do not think that anyone can show this to be widely implausible without begging the question and smuggling in assumptions about reality. And I spent quite a few hours exploring propositions aiming at rationally dismissing that possibility.
(You can try to prove me wrong if you so wish 🙂 ).

Therefore, I think that in order to ground our entire knowledge and existence, one has to take a leap of faith and make a pragmatic decision (Entscheidung) not based on whatever reasons.

Schene Grisse uss Nordenglond 🙂

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# Can all our beliefs be based on evidence?

Jonny Scaramanga (a former British fundamentalist I interviewed here) wrote an interesting article about the way children may become persuaded of the truth of far fetched beliefs.

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# Children are not that gullible, which makes indoctrination even more odious

I recently submitted an article on indoctrination for publication in an academic journal. I was attempting to explain what indoctrination looks like in practice in an educational environment, and along the way I made an assertion that I think most people would accept: “Young children … in most cases will believe whatever they are told”.

This is a widely assumed to be true, so I am grateful to my anonymous peer reviewer for pointing out that I was mistaken. The reviewer recommended I read a paper by Dan Sperber et al, “Epistemic vigilance”, which, happily, is freely available online. The section on children begins on page 371. The evidence suggests that children from very young ages use sophisticated techniques to work out who to trust.

Even at a very early age, children do not treat all communicated information as equally reliable. At 16 months, they notice when a familiar word is inappropriately used (Koenig and Echols, 2003). By the age of two, they often attempt to contradict and correct assertions that they believe to be false (e.g. Pea, 1982). These studies challenge the widespread assumption that young children are simply gullible.

Do young children have the cognitive resources to allocate trust on the basis of relevant evidence about an informant’s trustworthiness? Given the choice, three-year-olds seem to prefer informants who are both benevolent (Mascaro and Sperber, 2009) and competent (e.g. Clement ´ et al., 2004). In preferring benevolent informants, they take into account not only their own observations but also what they have been told about the informant’s moral character (Mascaro and Sperber, 2009), and in preferring competent informants, they take past accuracy into account (e.g. Clement ´ et al., 2004; Birch et al., 2008; Scofield and Behrend, 2008). By the age of four, they not only have appropriate preferences for reliable informants, but also show some grasp of what this reliability involves. For instance, they can predict that a dishonest informant will provide false information (Couillard and Woodward, 1999), or that an incompetent informant will be less reliable (Call and Tomasello, 1999; Lampinen and Smith, 1995; Clément et al., 2004). Moreover, they make such predictions despite the fact that unreliable informants typically present themselves as benevolent and competent.

The paper goes on to explain that four- and five-year-olds develop methods of spotting deception and also hypocrisy. Further, they are good at interpreting signals about what other people think about information (and the informers), and they use this to assist their own judgements about who is a trustworthy informant and what information is reliable. They’re also pretty good at spotting when someone intends to deceive them, and they know to ignore that information. From the age of four, children are particularly careful about who to trust.

All of which is not to say that children can’t be fooled, of course, but adults can be fooled too. It turns out children are not the trusting dopes they are sometimes depicted as.

But I know, and you know too, that if you stick a class of children in a room with a teacher who tells them that God made the Earth in six days six thousand years ago, most of them are going to believe it (and this was my point when I said that children generally believe what they are told). So what’s going on?

The answer, of course, is that children have excellent reasons to trust their teachers and their parents. Even in the most extreme cults, the vast majority of the verifiable information we learn from our parents in our formative years turns out to be true. Stoves are indeed hot and plug sockets are dangerous. Waiting for the green man does make it safer to cross the road. The food they recommend is generally good tasting and non-poisonous, and the things they recommend for entertainment are usually enjoyable. Up to the age of four, most of what we know about the world comes from parents, and most of it is right.

Then our parents hand us over to the care of teachers, which implicitly tells us that they are to be trusted. Our parents may also explicitly tell us to trust our teachers, with phrases like “You should listen to what your teacher says”. We trust our parents because they haven’t steered us wrong so far, and sure enough the teacher does seem to be reliable as well. She teaches us to read, which is very useful, and when we read signs using the methods she taught us, we arrive in the right places. She shows us that when we connect wires to metal contacts, the bulb lights up, and when we connect them to plastic, nothing happens.

Our parents and teachers tell us stories, and from quite early on they distinguish between true stories and those which are ‘only stories’. So when they tell us about Noah’s Ark, the exodus from Egypt, and the walls of Jericho, we trust them. We have every reason to do so—they have demonstrated their reliability. We would, as Sperber’s paper argues, be pretty good at telling if they were trying to deceive us, but of course they aren’t.

In short, when children are taught creationism by their parents and teachers, they accept it because this is the rational thing to do. Even the most committed skeptic cannot check everything out first hand. We all gain much of our knowledge from reliable others, and for most of us parents and teachers are the most reliable others we will ever know. It would be insane to trust them on everything except religion when religion is presented as true in the same way as all other knowledge taught at home or school. Of course the children believe you. That’s what you’re for. When you use that fact to make children believe things for which there is insufficient evidence, you are abusing your power and abusing their trust.

Presenting religious ideas as though we can believe them with the same confidence we can believe that clouds make rain or electricity flows through metal better than plastic is just immoral. I find it difficult to overstate how wrong this is. There are not many things I would call sacred, but the duty of care to children must be one of them. Ironically, I find myself wanting to use religious language to emphasise the gravity of this point. From the point of view of the Christian teacher, God has put these children in your care. It is despicable to use this position to present scientific and religious information as though they are both equally knowledge. Your job is to educate children, and you’re lying to them. It is the educational equivalent of a doctor poisoning patients.

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I think this raised quite important questions about the nature of faith and what our convictions should be grounded on.

Here was my response.

Hi Jonny.

I certainly agree it may be pretty harmful to teach far-fetched beliefs to children.

I don’t think, however, that one can generally say that fundies are being immoral for doing so.

Most I talked with are sincerely convinced that there are good arguments for a young earth or an exodus out of Egypt and that if it doesn’t belong to public knowledge, it is only because “godless” scientists “suppress the truth”.

So they teach what they are honesty convinced of and I think that very few of them teach things they know very well to be false.

Of course, I believe they are either utterly irrational or terribly uninformed. But that changes nothing to their sincerity.

Otherwise, I doubt it is possible to only believe in things we’ve evidence for.

Consider the proposition:

“We do not live in a simulation ran by beings we know nothing about.”

Almost all human beings accept this.
Yet, I strongly doubt it is possible to bring up evidence for this without already making assumptions about reality, i.e. without begging the question.

As far as I can tell, nobody has ever come up with a satisfactory answer to the Muenchhausen dilemna,
****

All justifications in pursuit of ‘certain’ knowledge have also to justify the means of their justification and doing so they have to justify anew the means of their justification. Therefore, there can be no end. We are faced with the hopeless situation of ‘infinite regression’.
One can justify with a circular argument, but this sacrifices its validity.

One can stop at self-evidence or common sense or fundamental principles or speaking ex cathedra or at any other evidence, but in doing so, the intention to install ‘certain’ justification is abandoned.

An English translation of a quote from the original German text by Albert is as follows:[8]

Here, one has a mere choice between:

An infinite regression, which appears because of the necessity to go ever further back, but is not practically feasible and does not, therefore, provide a certain foundation.
A logical circle in the deduction, which is caused by the fact that one, in the need to found, falls back on statements which had already appeared before as requiring a foundation, and which circle does not lead to any certain foundation either.
A break of searching at a certain point, which indeed appears principally feasible, but would mean a random suspension of the principle of sufficient reason.
******

Consequently, I think there are some very basic beliefs we hold which cannot be justified.
This leads me to reject claims of knowing how things really are and to adopt a pragmatic view of our beliefs.
I view “faith” as hope in something highly desirable even if evidence is unavailable or insufficient.

According to that definition, it is my contention that everyone walks by faith.
I don’t have children but I think I would try to explain this to them as soon as they are old enough to grasp that (without hopefully making them too dizzy).
To my mind, these considerations lead to a humble pluralism rather than to a confident materialism.

I don’t, however, hold anything I said dogmatically and would be glad to see your objections, if you have some.

I certainly sympathize with the children of fundamentalists who go through terrible ordeals as you did.

Cheers.

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# The crazy bookmaker and the Cult of probability

## A Critique of the Dutch Book Argument

Many neutral observers concur into thinking we are assisting to the formation of a new religion among hopelessly nerdy people.

I’m thinking of course on what has been called hardcore Bayesianism, the epistemology according to which each proposition (“Tomorrow it’ll rain”, “String theory is the true description of the world”, “There is no god” etc.) has a probability which can and should be computed under almost every conceivable circumstance.

In a previous post I briefly explained the two main theories of probabilities, frequentism and Bayesianism. In another post, I laid out my own alternative view called “knowledge-dependent frequentism” which attempts at keeping the objectivity of frequentism while including the limited knowledge of the agent. An application to the Theory of Evolution can be found here.

It is not rare to hear Bayesians talk about their own view of probability as a life-saving truth you cannot live without, or a bit more modestly as THE “key to the universe“.

While trying to win new converts, they often put it as if it were all about accepting Bayes theorem whose truth is certain since it has been mathematically proven. This is a tactic I’ve seen Richard Carrier repeatedly employing.

I wrote this post as a reply for showing that frequentists accept Bayes theorem as well, and that the matter of the dispute isn’t about its mathematical demonstration but about whether or not one accepts that for every proposition, there exists a rational degree of belief behaving like a probability.

## Establishing the necessity of probabilistic coherence

One very popular argument aiming at establishing this is the “Dutch Book Argument” (DBA). I think it is no exaggeration to state that many committed Bayesians venerate it with almost the same degree of devotion a Conservative Evangelical feels towards the doctrine of Biblical inerrancy.

Put forward by Ramsey and De Finetti, it defines a very specific betting game whose participants are threatened by a sure loss (“being Dutch booked”) if the amounts of their odds do not fulfill the basic axioms of probabilities, the so-called Kolmogorov’s axioms (I hope my non-geeky readers will forgive me one day for becoming so shamelessly boring…):

1) the probability of an event is always a real positive number

2)  the probability of an event regrouping all possibilities is equal to 1

3) the probability of the sum of disjoint events is equal to the sum of the probability of each event

The betting game upon which the DBA lies is defined as follows: (You can skip this more technical green part whose comprehension isn’t necessary for following the basic thrust of my criticism of the DBA).

## A not very wise wager

Let us consider an event E upon which it must be wagered.

The bookmaker determines a sum of money S (say 100 €) that a person R  (Receiver) will get from a person G (Giver) if E comes true. But the person R  has to give p*S to the person G beforehand.

The bookmaker determines himself who is going to be R and who is going to be G.

Holding fast to these rules, it’s possible to demonstrate that a clever bookmaker can set up things in such a way that any better not choosing p respecting the laws of probabilities will lose money regardless of the outcome of the event.

Let us consider for example that a better wagers upon the propositions

1) “Tomorrow it will snow” with P1 = 0.65  and upon

2) “Tomorrow it will not snow” with P2 = 0.70.

P1 and P2 violate the laws of probability because the sum of the probabilities of these two mutually exclusive events should be 1 instead of 1.35

In this case, the bookmaker would choose to be G and first get P1*S + P2*S = 100*(1.135) = 135 €  from his better R. Afterwards, he wins in the two cases:

– It snows. He must give 100 € to R because of 1).  The bookmaker’s gain is  135 € – 100 = 35 €

– It doesn’t snow. He must give 100 € to R because of 2).  The bookmaker’s gain is also 135 € – 100 = 35 €

Let us consider the same example where this time the better comes up with P1 = 0.20 and P2 = 0.3 whose sum is largely inferior to 1.

The Bookmaker would choose to be R giving 0.20*100 = 20 € about the snow and 0.3*100 = 30 € about the absence of snow. Again, he wins in both cases:

– It snows. The better must give 100 € to R (the bookmaker) because of 1).  The bookmaker’s gain is -30 – 20 +100 = 50 €

– It does not snows. The better must give 100 € to R (the bookmaker) because of 2).  The bookmaker’s gain is  -30 – 20 +100 = 50 €

In both cases, P1 and P2 having fulfilled the probability axioms would have been BOTH a necessary and sufficient condition for keeping the sure loss from happening.

The same demonstration can be generalized to all other basic axioms of probabilities.

## The thrust of the argument and its shortcomings

The Dutch Book Argument can be formulated as follows:

1) It is irrational to be involved in a bet where you’re bound to lose

2) One can make up a betting game such that for every proposition, you’re doomed to lose if the sums you set do not satisfy the rules of probabilities. In the contrary case you’re safe.

3) Thus you’d be irrational if the amounts you set broke the rules of probabilities.

4) The amounts you set are identical to your psychological degrees of belief

5) Hence you’d be irrational if your psychological degrees of beliefs do not behave like probabilities

Now I could bet any amount you wish there are demonstrably countless flaws in this reasoning.

### I’m not wagering

One unmentioned premise of this purely pragmatic argument is that the agent is willing to wager in the first place. In the large majority of situations where there will be no opportunity for him to do so, he wouldn’t be irrational if his degrees of beliefs were non-probabilistic because there would be no monetary stakes whatsoever.

Moreover, a great number of human beings always refuse to bet by principle and would of course undergo no such threat of “sure loss”.

Since it is a thought experiment, one could of course modify it in such a way that:

“If you don’t agree to participate, I’ll bring you to Guatemala where you’ll be water-boarded until you’ve given up”.

But to my eyes and that of many observers, this would make the argument look incredibly silly and convoluted.

### I don’t care about money

Premise 1) is far from being airtight.

Let us suppose you’re a billionaire who happens to enjoy betting moderate amounts of money for various psychological reasons. Let us further assume your sums do not respect the axioms of probabilities and as a consequence you lose 300 €, that is 0.00003% of your wealth while enjoying the whole game. One must use an extraordinarily question-begging notion of rationality for calling you “irrational” in such a situation.

### Degrees of belief and actions

It is absolutely not true that our betting amounts HAVE to be identical or even closely related to our psychological degree of beliefs.

Let us say that a lunatic bookie threatens to kill my children if I don’t accept to engage in a series of bets concerning insignificant political events in some Chinese provinces I had never heard of previously.

Being in a situation of total ignorance, my psychological degree of beliefs are undefined and keep fluctuating in my brain. But since I want to avoid a sure loss, I make up amounts behaving like probabilities which will prevent me from getting “Dutch-booked”, i.e. amounts having nothing to do with my psychology.

So I avoid sure loss even if my psychological states didn’t behave like probabilities at any moment.

### Propositions whose truth we’ll never discover

There are countless things we will never know (at least assuming atheism is true, as do most Bayesians.)

Let us consider the proposition: “There exists an unreachable parallel universe which is fundamentally governed by a rotation between string-theory and loop-quantum gravity and many related assertions.

Let us suppose I ask to a Bayesian friend: “Why am I irrational if my corresponding degrees of belief in my brain do not fulfill the basic rules of probability?”

The best thing he could answer me (based on the DBA) would be:

“Imagine we NOW had to set odds about each of these propositions. It is true we’ll never know anything about that during our earthly life. But imagine my atheism was wrong: there is a hell, we are both stuck in it, and the devil DEMANDS us to abide by the sums we had set at that time.

You’re irrational because the non-probabilistic degrees of belief you’re having right now means you’ll get dutch-booked by me in hell in front of the malevolent laughters of fiery demons.”

Now I have no doubt this might be a good joke for impressing a geeky girl being not too picky (which is truly an extraordinarily unlikely combination).

But it is incredibly hard to take this as a serious philosophical argument, to say the least.

## A more modest Bayesianism is probably required

To their credits, many more moderate Bayesians have started backing away from the alleged strength and scope of the DBA and state instead that:

“First of all, pretty much no serious Bayesian that I know of uses the Dutch book argument to justify probability. Things like the Savage axioms are much more popular, and much more realistic. Therefore, the scheme does not in any way rest on whether or not you find the Dutch book scenario reasonable. These days you should think of it as an easily digestible demonstration that simple operational decision making principles can lead to the axioms of probability rather than thinking of it as the final story. It is certainly easier to understand than Savage, and an important part of it, namely the “sure thing principle”, does survive in more sophisticated approaches.”

Given that Savage axioms rely heavily on risk assessment, they’re bound to be related to events very well treatable through my own knowledge-dependent frequentism, and I don’t see how they could justify the existence and probabilistic nature of degree of beliefs having no connection with our current concerns (such as the evolutionary path through which a small sub-species of dinosaurs evolved countless years ago).

To conclude, I think there is a gigantic gap between:

– the fragility of the arguments for radical Bayesianism, its serious problems such as magically turning utter ignorance into specific knowledge.

and

– the boldness, self-righteousness and terrible arrogance of its most ardent defenders.

I am myself not a typical old-school frequentist and do find valuable elements in Bayesian epistemology but I find it extremely unpleasant to discuss with disagreeable folks who are much more interested in winning an argument than in humbly improving human epistemology.

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# On the probability of evolution

In the following post, I won’t try to calculate specific values but rather to explicate my own Knowledge-dependent frequentist probabilities by using particular examples.

The great evolutionary biologist Stephen Jay Gould was famous for his view that Evolution follows utterly unpredictable paths so that the emergence of any species can be viewed as a “cosmic accident”.

He wrote:

We are glorious accidents of an unpredictable process with no drive to complexity, not the expected results of evolutionary principles that yearn to produce a creature capable of understanding the mode of its own necessary construction.

“We are here because one odd group of fishes had a peculiar fin anatomy that could transform into legs for terrestrial creatures; because the earth never froze entirely during an ice age; because a small and tenuous species, arising in Africa a quarter of a million years ago, has managed, so far, to survive by hook and by crook. We may yearn for a ‘higher answer’– but none exists”

“Homo sapiens [are] a tiny twig on an improbable branch of a contingent limb on a fortunate tree.”

Dr. Stephen Jay Gould, the late Harvard paleontologist, crystallized the question in his book ”Wonderful Life.” What would happen, he asked, if the tape of the history of life were rewound and replayed? For many, including Dr. Gould, the answer was clear. He wrote that ”any replay of the tape would lead evolution down a pathway radically different from the road actually taken.”

You’re welcome to complement my list by adding other quotations. 🙂

## Evolution of man

So, according to Stephen Jay Gould, the probability that human life would have evolved on our planet was extremely low, because countless other outcomes would have been possible as well.

Here, I’m interested to know what this probability p(Homo) means ontologically.

### Bayesian interpretation

For a Bayesian, p(Homo) means the degree of belief we should have that a young planet having exactly the same features as ours back then would harbor a complex evolution leading to our species.

Many Bayesians like to model their degrees of belief in terms of betting amount, but in that situation this seems rather awkward since none of them would still be alive when the outcome of the wager will be known.

Let us consider (for the sake of the argument) an infinite space which also necessarily contain an infinite number of planets perfectly identical to our earth (according to the law of the large numbers.)

According to traditional frequentism, the probability p(Homo) that a planet identical to our world would produce mankind is given as the ratio of primitive earths having brought about humans divided by the total number of planets identical to ours for a large enough (actually endless) number of samples:

p(Homo)   ≈           f(Homo) = N(Homo) / N(Primitive_Earths).

### Knowledge-dependent frequentism

According to my own version of frequentism, the planets considered in the definition of probability do not have to be identical to our earth but to ALL PAST characteristics of our earth we’re aware of.

Let PrimiEarths  be the name of such a planet back then.

The probability of the evolution of human life would be defined as the limit  p'(Homo) of

f'(Homo) = N'(Homo) / N(PrimiEarths‘)

whereby N(PrimiEarths‘)  are all primitive planets in our hypothetical endless universe encompassing all features we are aware of on our own planet back then and N'(Homo) is the number of such planets where human beings evolved.

It is my contention that if this quantity exists (that is the ratio converges to a fixed value whereas the size of the sample is enlarged), all Bayesians would adopt p'(Homo)  as their own degree of belief.

But what if there were no such convergence?  In other words, while one would consider more and more  N(PrimiEarths‘) f'(Homo) would keep fluctuating between 0 and 1 without zooming in to a fixed value.

If that is the case, this means that the phenomenon  “Human life evolving on a planet gathering the features we know” is completely unpredictable and cannot therefore be associated to a Bayesian degree of belief either, which would mean nothing more than a purely subjective psychological state.

## Evolution of bird

I want to further illustrate the viability of my probabilistic ontology by considering another evolutionary event, namely the appearance of the first birds.

Let us define D as : “Dinosaurs were the forefathers of all modern birds”, a view which has apparently become mainstream over the last decades.

For a Bayesian, p(D) is the degree of belief about this event every rational agent ought to have.

Since this is an unique event of the past, many Bayesians keep arguing that it can’t be grasped by frequentism and can only be studied if one adopts a Bayesian epistemology.

It is my contention this can be avoided by resorting to my Knowledge-Dependent Frequentism (KDF).

Let us define N(Earths’) the number of planets encompassing all features we are aware of on our modern earth (including, of course, the countless birds crowding out the sky, and the numerous fossils found under the ground).

Let us define N(Dino’) as the number of these planets where all birds originated from dinosaurs.

According to my frequentism, f(D) = N(Dino’) / N(Earths’), and p(D) is the limit of f(D) as the sample is increasingly enlarged.

If p(D) is strong, this means that on most earth-like planets containing birds, the ancestors of birds were gruesome reptilians.

But if p(D) is weak (such as 0.05), it means than among the birds of 100 planets having exactly the known features of our earth, only 5 would descend from the grand dragons of Jurassic Park.

Again, what would occur if p(D) didn’t exist because f(d) doesn’t converge as the sample is increased?

This would mean that given our current knowledge,  bird evolution is an entirely unpredictable phenomenon for which there can be no objective degree of belief every rational agent ought to satisfy.

## A physical probability dependent on one’s knowledge

In my whole post, my goal was to argue for an alternative view of probability which can combine both strengths  of traditional Frequentism and Bayesianism.

Like Frequentism, it is a physical or objective view of probability which isn’t defined in terms of the psychological or neurological state of the agent.

But like Bayesianism, it takes into account the fact that the knowledge of a real agent is always limited and include it into the definition of the probability.

To my mind, Knowledge-Dependent Frequentism (KDF) seems promising in that it allows one to handle the probabilities of single events while upholding a solid connection to the objectivity of the real world.

In future posts I’ll start out applying this concept to the probabilistic investigations of historical problems, as Dr. Richard Carrier is currently doing.

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# Recovering from the Conservative apologetic industry

Randy Harman has just published his fascinating testimony about his experiences as a former Conservative Evangelical apologist.

Part 1

Part 2

He told us from the very beginning that ” Just as it is easy to throw the baby out with the bathwater, these posts are in no way an attempt to say apologetics as a whole is a pointless discipline, nor are they intended to say that by defining myself as an “ex-apologist” I refuse any rational argumentation or apologetic endeavors.

I am an apologist in so far as it is a “tool” in my belt, not a vocation or an identity.”

In what follows I have copied some of the passages which I find the most profound and insightful.

Reason did little to strengthen my faith, despite my repeated claim that it “saved it.” It just turned me into a jerk with a lot of ammo–a jerk who merely pretended to have things put together by the overwhelming evidence of Christianity but, in reality, who was more assuredly as confused, carnal, and lost as the person I was insistent to win over to Christ through rigorous argumentation.

The doubts that I dealt with ten years ago are the same doubts that I deal with now, albeit in different ways sometimes and I routinely pray, not read, for faith. Rationalism never quenches the thirst of doubt; it only masquerades it.

Apologetics did not save my faith. It saved my pride.”

• Why is it that so many are threatened when popular boundaries are brought into question by none other than fellow Christians?
• Why is it, as I have seen personally, so many apologists turn out to be jerks, little different in rhetoric and spirit than the New Atheists they so fervently wish to counter?

As the late Stan Grenz and John Franke note in their tremendous book Beyond Foundationalism: Shaping Theology in a Postmodern Context, it is somewhat ironic that modernist thinking has extended so far in both the directions of the “godless” and the “godly.” For every atheist that’s incorrigibly committed to the truth of his philosophical naturalism there is an evangelical incorrigibly committed to his theism in such a way that neither one lacks the need to feel absolutely certain.

For these evangelicals, conviction leaves no room for doubt, and so in popular Christian apologetics doubt is something to be assuaged with answers

I find beauty in the multitude of voices, for the truth is sometimes life does seem nihilistic and we need Ecclesiastes to stand beside us or Job to yell at God with us;

I find beauty in reading Scripture primarily to save my soul and teach me how to live like and within Christ, not in teaching me what to believe and how to think about Christ.

My last two posts (here and here) dealt with my testimony as a trained apologist and a transformation that took place when I allowed myself to really stop thinking of faith as a science. This post still deals with what I find to be a strange irony in the discipline of apologetics, namely, the insistence on a “rational and well thought out” faith with the insistence on upholding scriptural inerrancy and creationism.

To that end, I have to confess that I am incredibly bothered by the fact that the popular apologetics movement laments the 75% of students who leave the faith (they say, “because they don’t have intellectual answers for what they believe”) and yet they demand that one cannot embrace certain conclusions of their disciplines, no matter how well thought out and evidenced.

It is my conviction that when we insist that young people have to choose between evolution and God or the critical results of scholarship and faith, we are not at all helping students overcome some of the intellectual barriers and questions they might have. Rather, we contribute to the swath of students who find Christianity to be opposed to reason.

I have watched too many friends abandon all trust in God because they were told they need to choose between the boundaries set by evangelical apologetics and science.

Though he is still more conservative than I am, I agree with most he has written.

I also want to point out that the enlightenment leaves us with a false dichotomy, namely:

1) having no grounds for thinking that Christianity is true, therefore pretending to know what you don’t know

2) having a Christian faith warranted by evidential arguments in the same way our belief in the theory of universal gravitation is warranted.

Unlike the claims of anti-theists, there are many Evangelicals who think that their faith is grounded on reason and evidence, thereby rejecting 2).

But I think that one option has been utterly left out.

3) Faith does not mean pretending to know what you don’t know, but to passionately hope in something even if the evidence is not sufficient.

I certainly believe there are good arguments against materialism and intriguing ones for the existence of a supernatural realm and theism.

Yet I also recognize that all these arguments (as well as those for atheism) depends on some postulates which cannot be proven and whose acceptance might very well strongly hinge on one’s own psychological make up.

Let us also consider the need of intellectually humility emphasized by Einstein:

“What I see in Nature is a magnificent structure that we can comprehend only very imperfectly, and that must fill a thinking person with a feeling of “humility.” that is to say the warranted conclusion that there might very well be many things our minds cannot fathom.

I think we have good grounds for concluding that many of our ideas about ultimate reality are pretty tentative and should never be made absolute.

But there is nothing which prevents us from passionately hoping in their truth.

Actually I know no human being who can practically live without hoping in many things he cannot asses the likelihood of.

Do you?

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# A mathematical proof of Ockham’s razor?

Ockham’s razor is a principle often used to dismiss out of hand alleged phenomena deemed to be too complex. In the philosophy of religion, it is often invoked for arguing that God’s existence is extremely unlikely to begin with owing to his alleged incredible complexity. A geeky brain is desperately required before entering this sinister realm.

In a earlier post I dealt with some of the most popular justifications for the razor and made the following distinction:

Methodological Razor: if theory A and theory B do the same job of describing all known facts C, it is preferable to use the simplest theory for the next investigations.

Epistemological Razor: if theory A and theory B do the same job of describing all known facts C, the simplest theory is ALWAYS more likely.”

Like the last time, I won’t address the validity of the Methodological Razor (MR) which might be an useful tool in many situations.

My attention will be focused on the epistemological glade and its alleged mathematical grounding.

## Example: prior probabilities of models having discrete variables

To illustrate how this is supposed to work, I built up the following example. Let us consider the result $Y$ of a random experiment depending on a measured random variable $X$. We are now searching for a good model (i.e. function  $f(X)$  ) such that the distance $d = Y - f(X)$ is minimized with respect to constant parameters appearing in $f$. Let us consider the following functions: $f1(X,a1)$$f2(X,a1,a2)$$f3(X,a1,a2,a3)$  and  $f4(X,a1,a2,a3,a4)$ . which are the only possible models aiming at representing the relation between $Y$ and $X$. Let n1 = 1, n2 = 2, n3 =3 and n4 = 4 be their number of parameters. In what follows, I will neutrally describe how objective Bayesians justify Ockham’s razor in that situation.

### The objective Bayesian reasoning

Objective Bayesians apply the principle of indifference, according to which in utterly unknown situations every rational agent assigns the same probability to each possibility.

Let be $pi_{total} = p( f i)$ , the probability that the function is the correct description of reality. It follows from that assumption that $p1_{total}=p2_{total} = p3_{total} = p4_{total} = p = \frac{1}{4}$ owing to the the additivity of the probabilities.

Let us consider that one constant coefficient $ai$ can only take on five discrete values  1, 2, 3, 4 and 5. Let us call $p1$  $p2$$p3$  and  $p4$ the probabilities that one of the four models is right with very specific values of the coefficient (a1, a2, a3, a4). By applying once again the principle of indifference, one gets: $p1(1) = p1(2) = p1(3) = p1(4) = p1(5) = \frac{1}{5}p1_{total} = 5^{-n1}p$ In the case of the second function which depends on two variable a, we have 5*5 doublets of values which are possible: (1,1) (1,2),…..(3,4)….(5,5) From indifference, it follows that $p2(1,1)=p2(1,2) = ... = p2(3,4) = ....p2(5,5) = \frac{1}{25} p2_{total} = 5^{-n2}p$ There are 5*5*5 possible values for f3.

Indifference entails that $p3(1,1,1)=p3(1,,12)=... =p3(3,,2,4)=....p3(5,5,5)= \frac{1}{125} p3_{total} = 5^{-n3}p$ f4 is characterized by four parameters, so that a similar procedure leads to $p4(1,1,1,1)=p4(1,1,1,2) =...=p4(3, 2,1,4)=....p4(5,5,5,5)=\frac{1}{625}p4_{total}= 5^{-n4}p$ Let us now consider four wannabe solutions to the parameter identification problem: S1 = a1 S2 = {b1, b2} S3 = {c1, c2, c3} S4 = {d1, d2, d3, d4} each member being an integer between 1 and 5. The prior probabilities of these solutions are equal to  the quantities we have just calculated above. Thus $p(S1)= 5^{-n1}p$ $p(S2)= 5^{-n2}p$ $p(S3)= 5^{-n3}p$ $p(S4)= 5^{-n4}p$ From this, it follows that  $\frac{p(Si)}{p(Sj)}= 5^{nj - ni}$ or $O(i,j)= \frac{p(Si)}{p(Sj)} =5^{nj - ni}$ If one compares the first and the second model, $O(1,2) = 5^{2-1} = 5$ which means that the fit with the first model is (a priori) 5 times as likely as that with the second one .

Likewise, O(1,3) = 25 and O(1,4) = 125 showing that the first model is (a priori) 25 and 125 times more likely than the third and fourth model, respectively. If the four model fits the model with the same quality (in that for example fi(X, ai) is perfectly identical to Y), Bayes theorem will preserve the ratios for the computation of the posterior probabilities.

In other words, all things being equal, the simplest model f1(X,a1) is five times more likely than f2(X,a1,a2), 25 times more likely than f3(X,a1,a2,a3) and 125 times more likely than f4(X,a1,a2,a3,a4) because the others contain a greater number of parameters.

For this reason O(i,j) is usually referred to as an Ockham’s factor, because it penalizes the likelihood of complex models. If you are interested in the case of models with continuous real parameters, you can take a look at this publication. The sticking point of the whole demonstration is its heavy reliance on the principle of indifference.

## The trouble with the principle of indifference

I already argued against the principle of indifference in an older post. Here I will repeat and reformulate my criticism.

### Turning ignorance into knowledge

The principle of indifference is not only unproven but also often leads to absurd consequences. Let us suppose that I want to know the probability of certain coins to land odd. After having carried out 10000 trials, I find that the relative frequency tends to converge towards a given value which was 0.35, 0.43, 0.72 and 0.93 for the four last coins I investigated. Let us now suppose that I find a new coin I’ll never have the opportunity to test more than one time. According to the principle of indifference, before having ever started the trial, I should think something like that:

Since I know absolutely nothing about this coin, I know (or consider here extremely plausible) it is as likely to land odd as even.

I think this is magical thinking in its purest form. I am not alone in that assessment.

The great philosopher of science Wesley Salmon (who was himself a Bayesian) wrote what follows. “Knowledge of probabilities is concrete knowledge about occurrences; otherwise it is uselfess for prediction and action. According to the principle of indifference, this kind of knowledge can result immediately from our ignorance of reasons to regard one occurrence as more probable as another. This is epistemological magic. Of course, there are ways of transforming ignorance into knowledge – by further investigation and the accumulation of more information. It is the same with all “magic”: to get the rabbit out of the hat you first have to put him in. The principle of indifference tries to perform “real magic”. “

Objective Bayesians often use the following syllogism for grounding the principle of indifference.

1)If we have no reason for favoring one outcomes, we should assign the same probability to each of them

2) In an utterly unknown situation, we have no reason for favoring one of the outcomes

3) Thus all of them have the same probability.

The problem is that (in a situation of utter ignorance) we have not only no reason for favoring one of the outcomes, but also no grounds for thinking that they are equally probable.

The necessary condition in proposition 1) is obviously not sufficient.

This absurdity (and other paradoxes) led philosopher of mathematics John Norton to conclude:

“The epistemic state of complete ignorance is not a probability distribution.”

The Dempter Shafer theory of evidence offers us an elegant way to express indifference while avoiding absurdities and self-contradictions. According to it, a conviction is not represented by a probability (real value between 0 and 1) but by an uncertainty interval [ belief(h) ; 1 – belief(non h) ] , belief(h) and belief(non h) being the degree of trust one has in the hypothesis h and its negation.

For an unknown coin, indifference according to this epistemology would entail  belief(odd) = belief(even) = 0, leading to the probability interval [0 ; 1].

### Non-existing prior probabilities

Philosophically speaking, it is controversial to speak of the probability of a theory before any observation has been taken into account. The great philosopher of evolutionary biology Elliot Sober has a nice way to put it: ““Newton’s universal law of gravitation, when suitably supplemented with plausible background assumptions, can be said to confer probabilities on observations. But what does it mean to say that the law has a probability in the light of those observations? More puzzling still is the idea that it has a probability before any observations are taken into account. If God chose the laws of nature by drawing slips of paper from an urn, it would make sense to say that Newton’s law has an objective prior. But no one believes this process model, and nothing similar seems remotely plausible.”

It is hard to see how prior probabilities of theories can be something more than just subjective brain states.

## Conclusion

The alleged mathematical demonstration of Ockham’s razor lies on extremely shaky ground because:

1) it relies on the principle of indifference which is not only unproven but leads to absurd and unreliable results as well

2) it assumes that a model has already a probability before any observation.

Philosophically this is very questionable. Now if you are aware of other justifications for Ockham’s razor, I would be very glad if you were to mention them.