How can we overcome the challenge of the anti statistical philosopher?

Conventional statistical inference has been strongly challenged by the anti statistical philosopher who uses the following example:

Imagine a man. Imagine that every time a man opens his front door and steps outside a red 1965 Corvette with the license plate that says "not by chance" Drives By, And a cat runs up and claws his left foot, and a helicopter flies by and drops a bowling ball on his right foot. The man tries the experiment at all random times of the day and every time he steps out from this front door this conjunction of three events occurs.

According to Conventional statistical inference the probability that these three unlikely events would occur at the same time is so low that we must infer that it was deliberately designed.

But the anti statistical philosopher challenges the validity of this conclusion by pointing out that, if there is an unlimited number of parallel universes in addition to our own, then we just happen to be in that particular Universe in which an unlikely conjunction of these three events has occurred.

Therefore conventional statistical inference is undermined or rendered invalid by this challenge of the anti statistical philosopher. How can we regain our faith in conventional statistical inference or overcome this challenge of the anti statistical philosopher?

• For one you'd have to accept the notion of parallel universes. – Cell Oct 15 '20 at 15:38
• For any situation involving vast numbers of parallel universes, you probably need to use some version of the self-sampling assumption (a type of anthropic reasoning which says you should reason as if your identity was randomly sampled from some larger reference class, like all the parallel versions of yourself in other universes) if you want to defuse this objection. – Hypnosifl Oct 15 '20 at 18:14
• Interpreting statistics already requires "unlimited number of parallel universes", they call it statistical ensemble. Whether the universes are real or hypothetical makes no difference whatsoever as far as statistics is concerned. When someone gets a run of 100 heads in a row saying that there is a particular universe where it must happen is just a verbal rephrasing of this being theoretically possible in the ensemble. But this is unlikely, i.e. there are few such universes, and a loaded coin is much more likely either way. So I am not sure what the "challenge" is supposed to be. – Conifold Oct 15 '20 at 19:27
• "According to Conventional statistical inference the probability that these three unlikely events would occur at the same time is so low that we must infer that it was deliberately designed." Statistics is about whether the evidence is sufficient to reject a null hypothesis, not to accept a specific alternative to it. (The null hypothesis has to predict probabilities.) Just because the observations have to be more likely than the null hypothesis said, it doesn't mean the reason why they're more likely is design. – J.G. Oct 16 '20 at 14:32
• The anti-stat reminds me of the "weak anthropic principal". Assuming the laws of physics were created randomly at the big bang, the odds of galaxies and carbon life forms is astronomically small. Therefore, there must have been a lot of failed universes (the reverse gambler's fallacy).... or life is a conspiracy (the design argument). – John Henckel Oct 16 '20 at 16:26

We will suppose for the sake of argument that there do exist an infinite number of parallel universes. The question then becomes "Which universe are we in?". We observed these events, so we know we're in the subset of the universes in which they happen. Within that subset, there are some universes in which these events were deliberately designed, and others in which they happen by chance. We then ask the question, "Is it more likely that we're in a universe where it happened by design or by coincidence?".

The specific numbers will depend a lot on exactly how the set of infinite universes is defined, and whether we have an equal chance of being in any given one of them, but however it's defined, we should be able to say something like the following: If we select any large finite subset of the universes uniformly, then filter out any universes where the "coincidence" doesn't happen (and discard any empty sets), there will, with high probability, be more universes in which it happened by design than there are universes where it happened by chance.

Or somewhat more informally, there are way more universes where it happens by design than there are universes where it happens by coincidence, so the odds are good that we're in one of the ones where it happened by design.

If they don't accept that, then buy a two-headed coin, flip heads 30 times in a row in front of them, then bet them \$10,000 that it isn't a fair coin, at 10-1 odds. If they genuinely believe their parallel universe argument, they'll take the bet.

• @tnknepp "If we select any large finite subset of the universes uniformly". – Dan M. Oct 16 '20 at 14:07
• @tnknepp one of the tricky things about infinities is that one infinity is not necessarily equal to another. The numbers of "designed" and "coincidence" universes could both be infinite and yet we can meaningfully say there are probably more "designed" universes than "coincidence" ones - that one infinity is larger than the other. – Carcer Oct 16 '20 at 17:42
• @tnknepp As Dan M said, that's why I spoke in terms of an arbitrarily-selected finite subset. I suspect that both infinite sets have the same cardinality (whether it's countable or uncountable probably depends on whether physics permits real-valued values or whether it's all quantized). – Ray Oct 16 '20 at 19:17
• Two sets can be the same cardinality, but have different measure. It's usually measure we're talking about when we talk about probability. – Ben Millwood Oct 17 '20 at 15:35
• This anti statistical philosopher sounds a lot like Douglas Adams' Sentient Puddle – candied_orange Oct 18 '20 at 10:56

Thinking in terms of parallel universes shouldn't do much to change the way we assess which of two explanations is more likely.

For example, if we're playing poker, and I know I'll win unless you have the other two aces in your hand, I can ask, which is more probable? That you have those aces, or that you're bluffing recklessly?

If we think in terms of all possible parallel universes existing, I can ask, which are there more of? Parallel universes where you behaved like this and had two aces, or parallel universes where you behaved like this but didn't? The chances are that I'm in one of those universes where the more common event has happened.

Given bizarre events occurring, like a helicopter dropping a bowling ball on me every time I open my door, I can ask, which are there going to be more of? Universes where that just happens for no reason, or universes where someone does this to me on purpose?

This sort of question becomes difficult when we are dealing with things that seem impossible, because we can't really come up with a meaningful way rate that as a probability. For example, if you appear to have psychic powers, and are able to levitate objects on command, but I firmly believe psychic powers do not exist, I would still have to try to assess what's going on. Which is more likely? Coincidental helpful breezes? Elaborate conjuring tricks? Powers that I believe to be impossible are real? That I'm hallucinating?

To say that all possible parallel universes exist is to say that we can never 100% rule out the 'coincidental helpful breezes' explanation. Nevertheless, one of the other explanations is far more likely, because for every universe where a breeze just happens to help you out randomly whenever you need it, there will be quintillions of others.

• @user3153382 this is the best answer so far. Thank you for your Cogent analysis! – Frank McCain Oct 16 '20 at 12:15

If we inhabited every parallel universe simultaneously, then the antistatistic argument might have merit. But we do not, and events in one parallel universe can have no effect whatsoever on any of the other universes.

Testing the antistatistician's world view requires him or her to 1) establish the reality of parallel universes and 2) devise some way to make simultaneous observations in all of them. When this is done, please ask Mr. AntiStat to report back to us here.

Please note that the challenge of the antistatistical philosopher can be most easily overcome by hitting him or her over the head soundly with a statistics textbook, the heavier the better.

Well, here is one very non-statistical, informal answer.

I don't think explanations using multiple worlds or "parallel universes" do any work. Kant once remarked, in reference to the ontological proof of God, that "existence is not a predicate," meaning that it adds nothing to the statements, and the same can be said of such fundamentally unfalsifiable claims as multiple worlds as the "cause" of anything.

If the peers of this woebegon philosopher rightly observes that this conjunction of events is "highly improbable," then it is highly improbable in that very world he inhabits. He should conclude that he is the victim not of accidents but of a conspiracy. We cannot admit either miracles or design by mixing and matching from an infinitely varied set of "probabilities."

To do so would make absolutely nothing probabilistic or "surprising," in, for example, the sense of Shannon information theory, leaving us with no useful "information" whatsoever, to put one gloss on it. I'm sure others can dispatch with this argument in more formal terms.

• Kant's mistake, of course, was attempting to apply predication to God. God is not an object, nor a part of some hypothesis. God does not exhibit qualities. In fact the God to whom Kant referred does not exist. God IS existence, including Kant's. Besides, statistics never involves certainty but always involves some degree or other of 'confidence'. Confidence plays no role in metaphysical philosophy. A 'thing' is either real or not. – user37981 Oct 15 '20 at 17:05
• conventional statistical inference has always depended on proving that the total available number of Trials is limited. Most philosophers and scientists have not recognized that the burden of proof is on the person who is using statistical inference to prove a point. It is generally assumed that a total number of Trials is actually limited but if you can invoke an infinite number of parallel universes, then you cannot prove that. – Frank McCain Oct 15 '20 at 18:29
• I believe I understand what you are saying and don't disagree. But I would still say that if reasoning about likelihoods is to make sense you can't both accept that and say that that this observable constant conjunction is "very improbable," so probably designed, and then argue it is actually "more probable" that there are infinite parallel universes. Since we cannot observe or order those universes according to any probability, on what basis is this a good answer and not simply a kind of statistical nihilism, in which everything becomes equally probable? – Nelson Alexander Oct 15 '20 at 19:09
• @CharlesMSaunders Turning a predicate into a noun, then equating God with that noun, is a... non-standard use of the word God, but in any case the noun will still have predicates. (For example, existence is instantiated.) – J.G. Oct 16 '20 at 14:27
• @NelsonAlexander Descartes has an earlier discussion than Kant's of whether existence is a predicate, when he tries anticipating criticisms of the ontological argument in Meditations. – J.G. Oct 16 '20 at 14:29

It's the difference between absolute certainty and reasonable certainty.

We are not 100% sure that an exceedingly-unlikely event won't happen (or that an event didn't have an exceedingly-unlikely cause). We are only reasonably sure of this.

We assume exceedingly-unlikely events don't happen because they are exceedingly unlikely, thus we would statistically be right almost all the time by assuming this.

These types of assumptions often lead to certain actions that are presumed to be optimal disregarding the exceedingly-unlikely event. However, if we consider the exceedingly-unlikely event, the actions are still presumed to be optimal, since the likelihood of that event occurring makes negligible the risk/reward of taking any action if that event occurs.

So what about infinite parallel worlds?

This doesn't seem like a problem.

If something is exceedingly unlikely, it's only going to happen in a tiny fraction of all worlds.

If we're talking about coincidental versus deliberately designed example, we are statistically almost always in a world where that didn't happen coincidentally, thus we assume that it didn't and look for other causes (like it being deliberately designed).

Wait a second...

Note that I didn't say we assume it is deliberately designed. Assuming this right out of the gate would be a fallacy even if the other possible cause is exceedingly unlikely.

To conclude that it's deliberately designed, you'd need to calculate the likelihood of this and compare it to the likelihood of it being coincidental.

It might be that there are another causes (maybe you're suffering from hallucinations or false memories?) or it could simply be that every possible cause (and thus also the event happening at all) are all exceedingly unlikely.

The simple fact is that exceedingly unlikely things do happen, so you can only ignore the possibility of this if there is an alternative that's at least reasonably likely (or at least massively more likely than the exceedingly unlikely event).

The parallel universes talk is a red-herring. The philosopher could just as well say that "it's possible for this to be a case of sheer luck which just happened to come true". And well... so what? How exactly does this refute statistical inference? Doesn't he have any further grounding for his belief? The claim he makes could be made for pretty much any kind of event, even the ones with a higher likelihood. So, in the end of the day, he is just begging the question.

If you refute statistical reasoning, it becomes practically impossible to reason about anything occurring in the natural world.

The example you gave involved unlikely coincidences, but we use similar inductive reasoning for all the "normal" events in our life as well. Every time someone walks behind a barrier and then reappears on the other side, it confirms the permanence hypothesis that we all learned as babies. We don't consider it a coincidence that the Sun rises every morning or the Moon exhibits the same phases every month.

All we have to go on when predicting the future is past experience. The more our predictions turn out to be true, it reinforces the assumption that the universe is based on rules, it's not just random chance.

How does this fit into the idea of infinite universes where anything is possible in some of them? That may simply not be true. If there are infinite universes, the differences may just be in some fundamental parameters, but not the laws that govern how the parameters interact in producing observable effects. It's analogous to the differences between Euclidean and non-Euclidean geometry: they have some different axioms, but the same rules of mathematics and logic.

The common sense philosopher and the anti-statistical philosopher are working with different definitions of "knowledge," so it is highly likely that they will come to different opinions on the matter. The common sense philosopher is arguing that at some point, its best to just give up and accept a "truth" about the universe because you're tired of testing it. Meanwhile, the anti-statistical philosopher is making very precise statements about a multiverse using tricky phrasings like "there exists." These two concepts of "knowledge" will not necessarily agree.

To regain trust in what we believe, we have to accept the challenges of both perspectives. The statistical philosopher has to recognize that statistical approaches have never been considered to provide knowledge in the most exacting of senses, and we were merely fooling ourselves to believe it does. WE have to explore some concept, such as "useful (almost-)knowledge" where we recognize that something falls short of the highest standards of knowledge but remains useful.

The anti-statistical philosopher has to recognize that the "there exists..." line of thinking in an infinite number of worlds must stem from a fundamental assumption that there actually exists an infinite number of worlds with every possibility. This is indeed written into your wording (emphasis mine):

But the anti statistical philosopher challenges the validity of this conclusion by pointing out that, if there is an unlimited number of parallel universes in addition to our own, then we just happen to be in that particular Universe in which an unlikely conjunction of these three events has occurred.

And at this point, hopefully both philosophers are familiar with enough with philosophy to remember that never has there ever been a point in philosophy that everybody agreed upon. Even fundamental concepts like 'I think therefore I am" get challenged.

And so, I close with Adam Watt's definition of a philosopher, because I find it a very useful concept to have in mind when exploring questions like these. "A philosopher is a sort of intellectual yokel. He goes around gawking at all the things everybody else takes for granted."

The "Anti-Statistical Philosopher" is right to so challenge.

Here's a possible scenario. You buy one lottery ticket in your entire life, and it's for a stupidly complex lottery draw. The probability of winning the lottery any given time is negligably small. However, you do, in fact, win.

Does this by definition mean it was rigged? No! You could very plausibly just have gotten lucky. Completely randomly, there was a coincidence between the numbers that you chose in that one instance and the numbers that did in fact come up.

And in a world where we are in a continuum of possibilities, where any one given outcome might be infinitesimally likely, rather than a discrete, binary countable system of simulation, that sort of stuff happens all the time.

Something being unlikely does not in itself give rise to agency - that is the Anthropic Fallacy at work. I'm with the "Anti-Statistical Philosopher".

• Well, I guess I'm just inclined to say that probability, as we use it in inferences, and infinite parallel universes don't mix, and perhaps that is even an argument against the latter. We might equally well invoke a Cartesian Demon. And if three events occur in conjunction "every time" why call it improbable? It seems this limited scenario is as probable as clouds before rain, unless we are bringing other factors observed in this one universe. Statistical inference has observable, falsifiable, predictive power, while "many worlds," say, offer only a theoretical redescription. – Nelson Alexander Oct 15 '20 at 19:22
• Probability is derived from experience and does not fall from the sky. Even if we can calculate somethin using logical possibilities and call this probability, this has nothing to do with statistical inference, which is from past occurrences to future events. As soon as we win the lottery, this event does not have a probability anymore. The concept is only applicable to future events. Thus, the idea that an event which occurs every single time would be seen as having a low probability does not make any sense. We would question the validity of the premises of our theoretical probability. – Philip Klöcking Oct 15 '20 at 22:17
• The same goes for lotteries in general, by the way: Even if the mathematical probability of winning was very low, if there in fact consistently is a winner every time, no statistician would ever say that the probability of there being a winner next time as well is in fact as low as the mathematical analysis suggests. That is why statistical inference without a real-world sample is nonsense. – Philip Klöcking Oct 15 '20 at 22:48
• Actually, Ten-Trillion-To-One things are observed by someone, somewhere on the planet probably around once an hour. 8 Billion People. Thousands of "things" that can happen to or be observed by them in any given day. 200 Trillion observations, give or take. If you want "never in all of human history" then you're probably talking at least 1-Sextillion-To-One, or the equivalent of winning the EuroMillions 4 times in a row. – Kaz Oct 16 '20 at 12:05
• @NelsonAlexander, the problem there is that you're talking about "infinitely many", whereas the mathematics of probability already invokes the "infinitely subdivided". There is absolutely nothing mathematically problematic about splitting the real open interval [0,1] into the two equally likely open intervals [0,0.5] and [0.5,1], even though these sets share cardinality with the set of real numbers. I think deflecting to "infinity" is a cop-out here; it's sufficient to recognize a distinction between "arbitrarily close" and "equal". – Paul Ross Oct 16 '20 at 17:01

Disclaimer: I don't know a lot of philosophy but I know a little physics so this answer is more physics/maths based so sorry in advance.

A lot of people think that since there infinite universes that anything is possible. But for something to happen in at least one these infinite universe it has to be possible as well. There is no universe in which I'm spiderman because this is not physically possible.

Still the scenario you mentioned isn't forbidden by the laws of physics, so surely it must happen in at least one of these universes right?

Let's imagine I setup an experiment where a bowling ball is suddenly released and we can track its height with high precision. Because of the random motion of air molecules it is possible that, by chance, the bowling ball moves upward before falling down because it is possible that at that moment more molecules happened to move upward giving the bowling ball a push. We could calculate the chance that the bowlingball moved upward by 1 milimeter. Already this chance is incredibly small. The amount of air molecules that had to move in exactly the right way is so large that it is hard to imagine for humans. But why stop at 1 milimeter? What about the chance of the ball moving up 1 centimeter? Or 1 meter?

We do know that the bowling ball won't fly into space because there is no air over there to push the bowling ball further. But what is the maximal height that the bowling ball would reach? We can't calculate it but I suspect it can't be higher than about a meter even in infinite universes. Why so low? The tricky thing about infinities is that once you start combining multiple kinds of infinities intuition goes out the window. If combine an infinite amount of something that is infinitely small you can get something that is not infinite.

If you for example added 1 + 1/2 + 1/4 + 1/8 + ... an infinite amount of times you would get 2. You add an infinite amount of terms but because each term gets smaller at just the right speed it never gets further than 2. The same is true for the bowling ball. At some point the combined probability is so low that it can't get any higher. If we take this back to the anti statistical philosopher than I think that the probability of all these things happening by chance is exactly zero. There are no universes where this would happen by chance.

So for discussion, how high would you think the bowling ball would go considering an infinite amount of parallel universes exist?

• This is an excellent answer. It makes me realize I haven't framed my question properly. I recently reposted my query in a much more accurate way. The post is written as follows : "Does the Multiverse undermine arguments based on statistical inference?" I would be very grateful for your learned response on this – Frank McCain Oct 17 '20 at 16:12
• An issue with this argument is that "probability 0" does not necessarily mean "does not happen" when dealing with infinite sets. An example: uniformly select a number from [0,1]. The probability of selecting any given number is 0, but we will select one of them. – Ray Oct 19 '20 at 16:09