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Is it ever reasonable to come across an event that is very improbable and then infer that it must have been designed?

Note that my question is referring to cases where we make this inference purely from the event's improbability.

In some examples, this may seem to be the case. For example, getting three royal flushes in a row is incredibly improbable. More specifically, this equates to 1 / 2.74x10^17. Thus, design seems obviously more likely.

But we don't conclude that someone cheated purely because that sequence was improbable. We conclude this based on the facts that:

a) 3 royal flushes in a row are improbable

b) humans exist and are capable of rigging card decks

c) there have been recorded instances of humans cheating

Without b) and c), would a) be enough to conclude design? More specifically, is there a probability X such that if the event's probability was below that X, we can safely conclude design?

What about a more modest proposal? Does an event being improbable raise the probability of the design hypothesis even if it is not enough to conclude that design is what explains the event?

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  • It's not about being sure but about probability. If you always assume the innocent explanation because it's possible, you'll be out of money in the saloon quickly. Better give your opponent a good beating the first time, just in case. (Obviously (hopefully) a joke)
    – DonQuiKong
    Commented Nov 5 at 9:04
  • In the example used, one might also speculate on the effectiveness of the shuffling between hands ! But I agree with your general point that high improbability of an outcome compared to much more probable outcomes available will indicate to most people that the rare outcome was "guided" in some way.
    – Trunk
    Commented Nov 5 at 9:53
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    VTC because you haven't done any research whatsoever. If you had, you'd know about "sigmas" for statistical confidence levels, a concept which has been a standard feature of every field of science for decades. Until you show you've done your homework, you can't ask a valid question.
    – Graham
    Commented Nov 5 at 10:12
  • @Graham You’re referring to significance testing which has been criticized on exactly this grounds. See here and don’t project what you have unto others (ignorance): joelvelasco.net/teaching/167/soberphilbio.pdf
    – Syed
    Commented Nov 5 at 16:11

17 Answers 17

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No, you cannot infer design on the basis of improbability alone. Take your card example. The odds of three royal flushes are very low, but so are the odds of any three hands with specific cards in them. You would not suspect cheating if three unremarkable hands were dealt, even though the probability of them containing their specific cards is extremely small.

There seems to be a variant of the gambler's fallacy at work here. If the probability of an event- assuming it happens at random- is p, then the probability of it happening by design is not 1-p.

The probability of design does not increase as the probability of chance goes down. What does happen is that the relative probability of design increases as the probability of chance decreases, but not the absolute probability. Therefore, to prefer the explanation of design, you need to have some independent basis for assessing that the probability of design is higher than the probability of chance.

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  • What do you mean by "relative probability"? Did you mean conditional probability?
    – user80226
    Commented Nov 7 at 0:03
  • Can you formalize the argument please using formulas and equations? I'm not seeing how "relative probability" (whatever you meant by that) can increase while the "absolute probability" (whatever you meant by that) can still remain the same. I need to see the math.
    – user80226
    Commented Nov 7 at 0:03
  • @user80226 relative probability is the common sense meaning. If Pa is 0.1 and Pb is 0.01, Pa is ten times more than Pb, so b is less likely than a. If Pa reduces to 0.001, b becomes more likely than a. Commented Nov 7 at 6:19
  • But they should add up to 1, unless you are claiming that there are more alternatives in addition to A and B. Do you agree or disagree that P(A) + P(B) = 1 always? Do A and B define a partition of the set of all possible events?
    – user80226
    Commented Nov 7 at 13:41
  • @user80226 no, you are making precisely the mistake I highlighted in my answer. To take the example of the unlikely hands of cards, what sum to one are the individual probabilities of all of the alternative hands of cards that might have been dealt at random. Commented Nov 7 at 14:20
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Improbability of an event arising from non-design does not necessitate the conclusion of design.

See Is it ever reasonable to infer impossibility from high improbability?

Even some zero-probability events are not impossible.

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Improbability is often used to rule out explanations but can't support alternative explanations without some other premises. If you get three royal flushes in a row, it is reasonable to rule out the mechanism of random dealing as an explanation of how that came about. This isn't the same as saying it must have been cheating because as you note, if you don't know that cheating ever occurs, that seems like something of a leap. Still the fact that you don't have an alternative explanation to random dealing does not rehabilitate that explanation. What you are left with in the absence of other information is just an inexplicable event. The astronomically improbable random deal doesn't become a better explanation just because you can't think of different explanation.

In general, if you have an event or state of affairs S, and there are two competing theories for how S came about, A and B, then a demonstration that A is astronomically improbable is a strong argument against A but not necessarily an argument for B. On the other hand, if it is a premise of the discussion that either A or B must be the case, then any evidence against A acts as evidence for B.

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  • That is what I don’t understand then or perhaps don’t agree with then. How can one rule out “non design” (I use this instead of random chance since the term chance is vague) if one can’t think of a better candidate explanation? You would have to implicitly assume that another design filled explanation, even if not known, must be more likely than it occurring without design. But how do you infer that?
    – Syed
    Commented Nov 4 at 23:53
  • @Syed, how could anyone show that something as vague as "not design" is highly improbable? The description "not design" encompasses so many disparate possibilities that I find it highly improbable that anyone could do so. Commented Nov 5 at 0:15
  • but that is exactly why I don’t see how an “improbable” event by itself can rule out “non design” and that is what would be required to serve as evidence for “design” @David Gudeman
    – Syed
    Commented Nov 5 at 0:19
  • 3
    @Syed, why are you asking about a position that no one holds? I suspect you are misunderstanding an argument that someone made. Commented Nov 5 at 3:58
  • you said that improbability can rule out random chance or even serve as evidence against it. But you still haven’t shown why or how. @David Gudeman
    – Syed
    Commented Nov 6 at 9:16
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"Is it ever reasonable to come across an event that is very improbable and then infer that it must have been designed?"
No, I don't think one can. As others have pointed out, just because we can't think of another good, alternative explanation to design does not mean that this explanation does not exist. The prudent answer here would be "We don't know". At the very least, we certainly "must not" infer the design explanation from just that.

In a comment you ask "How can one rule out “non design” (I use this instead of random chance since the term chance is vague) if one can’t think of a better candidate explanation?". However, here we don't say that we rule out the design explanation; it's just that, by itself, the improbability is not enough to support that specific explanation; at least not enough to infer that it must be the correct one.

That said, this is being theoretical. If, on the other hand, there are important stakes at play, then it may be more pressing or more important to assume one explanation, instead of just saying "we don't know". For instance, this kind of use case might happen when trying to diagnose a disease, or to investigate a health issue. In this kind of case, we still "must not" infer the explanation from the improbability, but we might need to act "as if the explanation being considered is correct". However, for reference, just in case, I must say that it seems to me like the things that religions try to use this "argument of improbability" for (ex: existence of the world, or of humans) do not fall in this kind of use cases: there is no existential risk in keeping answering "we don't know" to those questions. Hence it's really a bad argument to use for those questions, as far as I can see.

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  • "As others have pointed out, just because we can't think of another good, alternative explanation to design does not mean that this explanation does not exist." this is crucial. I don't know how cars work. That doesn't mean they don't work. My lack of explanation does not change the functionality of cars. Now, you can point out that there is a lot of explanations about how cars work and me not knowing those doesn't invalidate those explanations. Which is true. That's the point. Just because me or somebody else doesn't know an explanation doesn't mean it doesn't exist.
    – VLAZ
    Commented Nov 5 at 10:17
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Is it ever reasonable to come across an event that is very improbable and then infer that it must have been designed?

No. It's called an argument from incredulity or the divine fallacy.

I have given a ridiculous example of this reasoning involving a vacuum cleaner and an earthquake in another answer:

https://philosophy.stackexchange.com/a/118340/67687

From Mr. Tea:

if you were the first human exploring a foreign planet and saw a cliff face full of what looked like carvings of complex symbols and drawings, would you think back to your vacuum example and decide the patterns must be the result of random weathering and erosion?

Remember the Face on Mars? It was supposed to be evidence of intelligent design. Spoiler: It wasn't. https://en.wikipedia.org/wiki/Cydonia_(Mars)

enter image description here

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    You've never seen elaborate graffiti on the wall and inferred that it was put there by a designer?
    – Mr. Tea
    Commented Nov 5 at 14:54
  • 2
    @Mr.Tea I would, but then I know so much more about how elaborate graffiti is made than I do about how life starts.
    – A Raybould
    Commented Nov 6 at 5:07
  • The question is not specifically asking about how life or the universe started though, is it?
    – Mr. Tea
    Commented Nov 6 at 14:55
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    @Mr.Tea You don't remember the face on Mars Commented Nov 6 at 16:24
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    I said "like complex symbols". Imagine finding something like Egyptian hieroglyphics arranged in rows and columns
    – Mr. Tea
    Commented Nov 6 at 17:02
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I want to preface my response by quoting something from the SEP entry on probability and logic:

There is some discussion about the exact relation between inductive logic and probability logic, which is summarized in the introduction of Kyburg (1994). The dominant position (defended by Adams and Levine (1975), among others), which is also adopted here, is that probability logic entirely belongs to deductive logic, and hence should not be concerned with inductive reasoning. Still, most work on inductive logic falls within the ‘probability preservation’ approach, and is thus closely connected to the systems discussed in Section 2. For more on inductive logic, the reader can consult Jaynes (2003), Fitelson (2006), Romeijn (2011), and the entries on the problem of induction and inductive logic of this encyclopedia.

So firstly, it is insufficiently precise to say, "X is either probable or improbable." You might mean, "X has a majority chance of being true, or it does not have a majority chance of being true," which is fine, but the latter phrasing makes it clearer that "improbable" events are not in themselves surprising, since their minority-chance of coming to pass translates into them not happening especially often. What would be totally unexpected would be if pre-life spontaneously turned into life constantly, everywhere, and somehow regardless of the unstable background conditions in most such places and at most such times. That life would flicker into stability here and there, once in a while, and not so as to foreseeably endure forever (though it might, they wouldn't really know, and even though some random books in their history might claim to reveal a future state), is about as unsurprising a turn of events as can be imagined in a universe that works according to quantum field theory and general relativity in an expanding spacetime.

Hence we see that a sense of "improbability" can depend very much on framing. This is similar to how portraying an option in two different statistical ways can influence the favor people feel towards an option. "A will lead to 60% mortality," can coincide with, "A will lead to a 40% survival rate," and if one leaves it at that—leaves the audience to figure out the complementary adverse probability—one has a better shot at getting people to favor option A.

Secondly: and how exactly would such an argument proceed?

  1. X had a low probability of happening.
  2. X happened.
  3. Therefore, X was (probably) intended to happen (by an agent/agents with sufficient physical power to actualize this intent).

From a deductivist vantage regarding probability logic, one is minded to amend (1) to (4):

  1. If X was not intended to happen, X had a low probability of happening.

Yet by itself this is far from good enough for present purposes, because we know from many and varied experiences that it is often not enough that we intend something to happen, such that it does happen because we intended it to. Plans go awry, our walks down our paths lead us astray, plenty often. When the action in question is (relatively) simple, like blinking or preparing a small meal, our chances of "perfect" success are much greater (indeed, it is not hard to conduct a "perfect" blink). But it is not the strength of our intent that decides these matters alone: the ease of success is a function more of the type of those actions than of the degree of willing involved. Again, it would be pretty difficult to vary one's degree of willing with respect to blinking; in this context, "Do or do not: there is no try." But that is consistent with other contexts admitting of trying.

Now, we should reformulate (4) as (5):

  1. If a powerful enough being did not intend that X, then X had a low probability of happening.

Of course, the probability that a powerful enough being could not only intend X but certainly bring X about, is actually 100%, trivially. That is, the probability of X happening if a powerful enough being so intended is 100%. But obviously this does not negate the possibility of X happening unintentionally. Anything could be "explained" as, "It was willed by a sufficiently powerful being," if that were the case, which it is not (and abstract occasionalism aside). But this would not be what we were looking for when we asked about explanations, which we frame in terms of mechanisms and processes involving mathematically precise ranges of functions. We do this even when, like Leibniz, we view intercausality as a distorted or fictitious conception of the natural order, because Leibniz would not hesitate at all to delve into the infinitesimal calculus, with all its risk of chaos and paradox, for the sake of a greater understanding of things.

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Note that my question is referring to cases where we make this inference purely from the event's improbability.

There is never a case where you make this inference purely "from the event's improbability" because if you infer design then you already have some notion of design(er).

In your case

  • if "getting three royal flushes in a row is incredibly improbable" and you do not have a notion of cheating in your mind (you are for example young trusting child) then you cannot infer cheating.
  • but the moment you are aware of concept of cheating you can infer cheating but it is not purely from "getting three royal flushes in a row" improbability.
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  • While grasping the concept is a prerequisite for posing and understanding the question, it does not bias the evidence towards an affirmative answer.
    – sdenham
    Commented Nov 8 at 13:20
  • @sdenham Sure, grasping a concept could make affirmative answer related to it even less probable. But it is not possible to make "affirmative answer" only on things not related to concept. There have to be assumptions related to concept.
    – Piro
    Commented Nov 9 at 6:51
  • With regard your first sentence: a person might have in mind a probability with respect to a concept which they think they grasp but actually do not (or do not grasp completely), in which case anything they inferred from it would lack proper justification. This, however, seems outside of the scope of Syed's question, as it is trivially true in all circumstances, and when we put aside all those cases, there is still a question worth contemplating.
    – sdenham
    Commented Nov 9 at 12:51
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Derek Parfit in his beautifully written article Why Anything? Why This? distinguishes two scenario's:

Suppose first that, of a thousand people facing death, only one can be rescued. If there is a lottery to pick this one survivor, and I win, I would be very lucky. But there might be nothing here that needed to be explained. Someone had to win, and why not me? Consider next another lottery. Unless my gaoler picks the longest of a thousand straws, I shall be shot. If my gaoler picks that longest straw, there would be something to be explained. It would not be enough to say, ‘This result was as likely as any other.’ In the first lottery, nothing special happened: whatever the result, someone’s life would be saved. In this second lottery, the result was special, since, of the thousand possible results, only one would save a life. Why was this special result also what happened?

The Big Bang, Parfit argues, was like this second lottery. For life to be possible, the initial conditions had to be selected with great accuracy. This appearance of fine-tuning also needs to be explained.

For life to be possible on Earth it needs to circle around the Sun in a narrowly defined habital zone (sometimes called the Goldilocks zone). The chances of that being the case are slim. However, with the growing understanding of the vastness of the Universe and the detection of exo-planets, the odds were no longer that astronomical. In other words, it became more like the first lottery and no explanation is needed.

The Big Bang with its appearance of fine-tuning can be explained in two ways: God or the assumption of many universes with different initial conditions.

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  • Assumption of many universes is more of a rhetorical flair than an explanation of anything. The probability that you would be in the chosen universe is identical to the probability that the desirable initial conditions in this one would occur.
    – D. Halsey
    Commented Nov 6 at 1:59
  • The anthropic principle is irrelevant for Parfit's argument. The idea is that if we would have lived in an isolated solar system without any stars or galaxies in the night sky, we would have concluded that our position was unreasonably fine-tuned. What if the sun would have been much larger, much smaller, what if our orbit was much more irregular, and so forth. It would have needed an explanation. Now we know about a zillion other stars with exo-planets, we are no longer surprised that we happen to live on a planet that supports life. The argument for many universes is analogous.
    – Philomath
    Commented Nov 6 at 2:26
  • @D.Halsey I disagree. Afterall, you CAN only exist in this one universe. So you existing in the one universe whose parameters support stable planets and life is a neccessity. It is like the example with one of a thousand to survive by lottery. Only the one that "won" can ask the question "why me?". TL;DR the probability that you would be in the/a chosen universe is 100%
    – datacube
    Commented Nov 6 at 8:22
  • @D.Halsey Well, yes, that's not controversial. Like Parfit explains, it had to be someone, so it doesn't need explanation. We had to live on this planet out of thousands because it supports life. If we found ourselves on the ONLY planet, that miraculously supports life, that would need an explanation.
    – Philomath
    Commented Nov 6 at 8:38
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    @Philomath I do not see how believeing that some A is too unlikely and requiring an explanation while believeing that some A and some B, even without B being magnitudes more complex/unlikely/vast that A itself, is not so unlikely as to require an explanation makes sense. See: Conjunction fallacy. (Maybe i should have left the comment in brackets out, since it distracts more from the main point more than it helps. But i get the feeling some would say airplanes are fine tuned not to be shot in certain places when looking at the survivors, referencing the classic example ;) .)
    – Pepe
    Commented Nov 14 at 15:09
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I think the biggest issue with this kind of comparsions is that it assumes perfect knowledge about the possibilities and the process as to how one of those possibilities is chosen.

If you watch a game of poker and one player gets three royal flushs in succession you could reasonably infer that he is cheating. Yes there is a very slim chance of him being actually that lucky. In a regulated poker match you would still have to proof his cheating though to convict him, but it is reasonable to start the investigation with the assumption "that" he cheated and instead focus on finding out "how" he cheated. (In an illegal backroom poker game he would get "reasonably" beaten to a pulp without any investigation though).

But for poker you know the rules, you know that each card in the stack is unique, you know that the cards are shuffled by a perfectly random shuffling machine and you know that no card drawn is influenced by the other cards being drawn (except that they can't be the same).

But now you watch me and my friends play a card game. You don't know the rules, you don't know the deck. You only see the cards that are drawn. You can do estimations about the probability but your lack of information is making that more a guesswork than anything else.

Maybe the deck only has one color. Maybe the deck is shuffled in a very special way that makes previous hands more likely to appear again. Maybe the king and queen are quantum linked and are always drawn in succession. You don't know.

Yes we can reasonably infer design from improbability, but we can't if that calculated improbability is mostly based on guesswork.

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You are overlooking an important thing about improbability: The longer time, the more times you try, the more probable is your improbability!
You talk about a deck of cards, and a fairly short number of games giving three royal flush.
For simplicity, let's throw ten dice. The probability of all ten dice showing 6 is 1:6^10 which is 1/60466176 - one out of 60 millions.
But now throw these ten dice a billion times. The probability of not having all of them show 6 at least one time is 1:((1 - (1/60466176))^1000,000,000) = 1/15220774 - one out of 15 millions.
Improbability is very depending on how many times something is tried.

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    Also, the point is not even to have strictly "10 dice showing 6 in a row". The observer would have made the same point if he had observed another exceptional sequence, like ten 3 or even a perfect alternating between two values. In the end, the probability of "having something remarkable" are even higher.
    – Jemox
    Commented Nov 5 at 10:43
  • I believe this is fundamentally wrong. The number of times you may have tried something in the past doesn't affect future results. Unless I'm missing something... Every time you flip a coin the probability is 50/50, right? Why would past flips alter that? Commented Nov 6 at 1:36
  • it's not that the past dice rolls affect the latter dice rolls in any way. Rolling ten 6s right now is completly independed of all the rolls before. But we look at a different situation: the dice have already been rolled and now they show ten 6s and we wonder how that could have happend. And if it didn't happen we wouldn't wonder. But all people before us who rolled 10 dice WOULD also have wondered how they were able to roll ten 6s. So this experiement was tried (without knowing) a billion times. And ANY 10 dice showing ten 6s would have been remarkable, not only yours.
    – datacube
    Commented Nov 6 at 8:36
  • @MichaelHall I believe we can agree that if you flip a coin once, you'll have 1:2 chance for 'Heads', but I prefer to believe you'll also agree that if I flip the coin hundred times there is a significant greater chance for that one of these flips would result i a 'Heads', right? Commented Nov 6 at 8:39
  • @MichaelHall or in a more subjective approach: you pick up a 20 sided die and throw it. It shows a 20. You think "wow how lucky of me". But then you spent your afternoon rolling the 20 sided die around a hundred times but DON'T roll a single "1". Now you might think "wow how unlucky of me". Having had a "1" in the past 100 rolls was actually 99.4%. But rolling the die once more still has only a 5% chance to show "1".
    – datacube
    Commented Nov 6 at 8:44
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Suppose we come across a Dyson sphere in outer space. Humanity has no experience designing such structures, nor the advanced technology and physics knowledge likely required to construct one. We have no documented cases of anyone designing a Dyson sphere, nor would any human possess the expertise to claim, “Yes, it was designed, and here’s how it’s done step-by-step.” So, how could we explain the existence of a Dyson sphere if we encountered one? Here are three possible hypotheses:

  • H1: It was designed by some unknown intelligence (certainly not us).
  • H2: It formed by chance, through phenomena such as quantum tunneling.
  • H3: It emerged spontaneously from nothing, without any cause.

For H2, we might argue that its probability, based on any reasonable estimates from experience, is exceedingly low. However, in principle, it remains possible. In a sufficiently large (or infinite) universe, multiverse, or megaverse, such events might happen somewhere — unless future advances in physics definitively rule it out. Given our current understanding, though, we cannot exclude H2. You could think of this alternative as the Anthropic Principle applied to Dyson spheres.

Now, if P(H2) is extremely low, would it be reasonable to conclude that P(H1) is high? This depends on whether we consider a sufficiently large megaverse or multiverse in which even Dyson spheres might arise by chance. If so, our local probability estimates would miss the mark, as they consider only our universe’s statistics, not those of the entire megaverse. If, however, our local statistics are accurate, then P(H2) does appear extremely low, suggesting either H1 or H3 is likely. Since H3 also seems statistically improbable from experience (how often do we observe Dyson spheres appearing around stars or any other megastructure for that matter out of nothing?), H1 could seem the most reasonable.

In conclusion, it ultimately depends on whether one chooses to rely on local statistics or to assume the existence of vast multiverses, which could provide ample opportunities for unlikely events—such as the formation of colossal megastructures by chance or spontaneous occurrences without cause. If you're not inclined to either accept or reject assumptions like these, then it seems to me that the most reasonable stance would be to remain agnostic about the probabilities.

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  • I feel as if this analysis must involve analyzing what the probability of H1 is (I.e. how likely is it for the proposed designer to arise and have the capabilities and have the desire to create the Dyson sphere).
    – Syed
    Commented Nov 4 at 23:58
  • @Syed The designer could be a necessary being (in which case the probability is 1) or have been designed by another designer which was designed by another designer which ..., ending in a necessary being, or perhaps the designer appeared by chance through a natural process which is much more probable than a Dyson sphere appearing by chance (e.g., abiogenesis + evolution).
    – user80226
    Commented Nov 5 at 0:22
  • necessary in what sense? how can something be “necessary” if one can atleast imagine alternative forms of reality without that designer? @user80226
    – Syed
    Commented Nov 5 at 0:29
  • @Syed This might help: philpapers.org/archive/GLATDB-3v1, iep.utm.edu/ep-moda (metaphysically necessary)
    – user80226
    Commented Nov 5 at 0:38
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    @Syed Can you offer an example of something that would not "beg the question" in this way?
    – user80226
    Commented Nov 7 at 0:17
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Does an event being improbable raise the probability of the design hypothesis even if it is not enough to conclude that design is what explains the event?

No event is probable or improbable in itself. Instead, for each event there are many (often infinitely many) models of how it was caused. and for each model, if the probability is shown to be low, it's plausibility is lowered. This does not raise any other plausibility of any other model.

The scam that is ID is based on the Strawman fallacy that "science" only has one model for a given event, and that this "single model" has a realistically calculable probability, and that the only alternative to that "single model" is design.

The truth is that while science often and necessarily proposes models for past events, those are not exclusive single models, but just picked suggestions out of a nearly infinite field of other possible naturalistic models. Also typically there is no useful way of calculating the probability of such models, as this would require precise observations of earth at the time, which we do not have.

So even if a suggested naturalistic model for any event was wrong, it does not automatically mean a design model must be true, there are near-infinite naturalistic alternative models to consider, always.

And even if a given scientists suggests a model, it's probability cannot be calculated as suggested by ID pseudoscience.

All science can do (and does) is to attempt to reproduce environments and see if similar things happen today. And if this does not work, try our any of the infinite variations, learning along the way. There has been no reason to give up on this process anytime in the last 3000 years. Nor will there likely be any reason to give up on this process in the next 3000 years.

Infinity is a long time, and humanity still has roughly that much time to try out and exhaust naturalistic models for all the events in the universe that still lack a proven model. And with all the knowledge gained in the process, we can build bridges and cards and smartphones and satellites. But ID as a political movement would rather invest energy in teaching Christian lies in schools.

Intuitively, consider the Blackjack card game where players try to reach a score close to 21 that is higher than the score of the dealer. Imagine this with 1000 players and one dealer. So we look at player one. And let's say player one stands at a score of 14. That's a low probability of winning. Lower than say at 20. But standing at the low probability of 14 does not mean that the dealer has a blackjack (or would win). It also does not mean that the dealer would equally beat all the 999 other players. It just means the probability of the first player winning is low.

ID tries to convince people that the dealer must win because the chance of the first player to win is low, and there are no other players. And ID uses strawman arguments as the initial player.

This is why ID is considered pseudoscience not even worth investigating. (That it is only pushed by an organization that is a sockpuppet for by Christian fundamentalists and Creationists does not help, but certainly that is not the only reason to reject ID)

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Is it ever reasonable to come across an event that is very improbable and then infer that it must have been designed?

In general, "no". In order for a proposed cause to be considered viable, it should also possess sufficiency.

That said, "sufficiency" tends to cut against non-design causations. For example, random processes have never been shown to produce meaningful information (e.g. the works of Shakespeare, or a functional biological organ) from "scratch". Conversely, intelligent agents manipulate the world in a way to actualize extremely improbable outcomes all the time, so while the answer here is technically "no", it's unclear what situation could arise in which an intelligent agent (of suitable capabilities) would not be a sufficient cause for some improbable event.

For example, getting three royal flushes in a row is incredibly improbable.

Here we see the need to introduce another factor: specificity. Getting any specific three hands of cards is extremely improbably. Nevertheless, if I sit for three hands at a poker table, an extremely probably event will be actualized. "Entropy" plays a role, but what we're really trying to measure is "randomness". This is a whole, genuine field of study that can be qualified, but to keep things simple, "interesting" outcomes are both specified and complex.

A deck of cards adds some complications, so consider, instead, a series of coin flips. The outcome of all-heads is highly specified, but not complex; the most likely explanation is neither chance nor design, but necessity (namely, your coin probably isn't fair). A series of perfectly alternating heads and tails is more interesting, but still not complex enough to strongly suspect design rather than necessity. (For a more "real world" example, crystal growth is an example of necessity.) If, on the other hand, there is no discernible pattern, then the outcome is highly complex but is not specified, and is likely a result of chance.

Now, if you flipped a coin, and the flips, when "read" as binary representation of ASCII, spelled out the Declaration of Independence, you're dealing with a result that is both complex and highly specified; design is now a much more likely explanation than chance. Similarly, any three "typical" hands of poker are extremely improbable, but they are not specified. Three royal flushes are both unlikely and specified, therefore making design (cheating) a more likely cause.

Now... here's where things get interesting, because this is the point at which the infinite monkey theorem is usually invoked (including by several existing Answers here!). While technically correct, the theorem only works in the world of infinities, and only in certain conditions. To understand, however, it is necessary to clarify the nature of our unusual event.

Going back to the poker example, if Bob sits down and is immediately dealt three royal flushes, that's cause to suspect chicanery. If, on the other hand, Bob has been playing poker for 1016 hands, then it is much less "surprising" if, at some point, he was dealt three royal flushes in a row.

I'll circle back to this in a moment, but it's leading us to another point:

Is there a probability X such that if the event's probability was below that X, we can safely conclude design?

Yes. Often called the "universal probability bound", if we estimate the total number of particle interactions that have occurred in the history of the universe (usually cited as around 10150), then anything unlikely to occur given that many "chances" is unlikely to have occurred by chance. (Obviously, the number of poker hands that can be played is much, much lower than this number. More "realistic" estimates use a bound of 10-50 as the threshold for excluding chance as a plausible explanation.)

The oft-cited solution is to posit that existence is, in fact, infinite (a.k.a. the anthropic principle). The problem with this, besides being a wholly philosophical supposition with no concrete evidence to support it, is that it doesn't actually work in practice... and this is where we come back to the monkeys and how theorems about infinity don't work in a finite universe.

Let's use another Answer's Dyson sphere as an example. It's theoretically possible (albeit far, far below the universal probability bound) for such a structure to spontaneously materialize... just as infinite monkeys will eventually produce the complete works of Shakespeare. However, in an infinite universe, there will be infinitely many humans that have not encountered a Dyson sphere. The probability that, by chance, our universe happens to have both humans and Dyson spheres is itself unreasonable. In other words, the anthropic principle cannot defend chance as an explanation. The only plausible explanation for our universe happening to have both humans and Dyson spheres is either design or necessity.

Now, I can imagine no argument that makes the existence of Dyson spheres necessary in order for there to also exist humans to wonder about them. Moreover, it's difficult to imagine even the many unlikely forms of life that we do observe being necessary for observers to wonder about them.

To be fair, technically the humans in the universe with spontaneously generated Dyson spheres could still fall afoul of the anthropic principle, but this requires belief in infinite universes, for which we have no scientific evidence. Such belief is purely philosophical. Worse, because the probability of Advanced Aliens existing in an infinite multiverse is non-zero, it's actually more likely that a universe contains Dyson spheres because someone built them. In fact, if the probability of Advanced Aliens being able to create entire universes is non-zero, it immediately becomes more probably that any "interesting" universe is, in fact, designed.

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  • Only answer I've seen that discusses specificity, so +1 for that! I would argue though that the existence of spontaneous Dyson spheres and humans together (given an infinite ultra-megaverse of all possibilities) is not unreasonable. Wouldn't there also be an infinite number of humans who have seen a spontaneous Dyson sphere as well, meaning the Anthropic Principle would still apply?
    – Mr. Tea
    Commented Nov 6 at 20:44
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    Only answer copying Discovery Institute Propaganda. If anyone wants that, they know where to find that website.
    – tkruse
    Commented Nov 6 at 20:50
  • @Mr.Tea, maybe, but only if the anthropic principle is a cop-out for believing that for every universe in which humans see Dyson spheres, there are many, many others with humans but no Dyson spheres. And... I don't see how that can be called "science" at that point. Which reminds me of something else; edit coming soon.
    – Matthew
    Commented Nov 6 at 21:21
  • @Matthew Your answer inspired me to ask this.
    – user80226
    Commented Nov 7 at 5:21
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I would like to add another perpective to the quite varied and interesting set of answers already present, which, i believe, might help a bit by presenting another angle to this topic.

I do not believe that one can infer design from improbability alone, here is why:

Imagine that Alice and Bob are two reporters, each tasked with writing an article about how it feels to win the Grand Lottery. The chances of winning are 1 in 10^20.

  • Alice buys a ticket, picks her numbers, wins and then proceeds to write her article.

Now, this seems exceedingly unlikely given the probability and i would be very skeptical of the truth of her article, if i ever were to read it.

  • Bob, on the other hand, finds a winner or waits until someone wins the Grand Lottery, visits and interviews them and proceeds to write his article.

The underlying probability of winning here is just as in Alice's case, but it appears vastly more likely to have happened. Generally, i would say this article seems believable, especially since it will only ever be written if someone, anyone wins.

Now, a problem i see arise most often with questions such as the above is, that people try to reason about a situation similar to Bob's, looking back at something that has already happened, but apply probabilities the way they are used in Alice's case, looking forward to something that is going to happen, but with a very specific outcome in mind.

Most of the time the "improbability argument" pops up, we are clearly in Bob's situation. Something has happened, then somebody tries to explain its specialness and somehow ends up acting like we are in Alice's case with respect to the probabilities. But the question for an explanation can only be asked if there was a winner. And the numbers are only special because they came up. If other numbers produced another winner, the same question would be asked about those.

Given the contexts in which the "improbability argument" is usually used, we are woefully unequipped to assign an informed propability to the equivalent of "Bob's situation", even if we were to know the minutae of "Alice's" probabilities. We know even less about possible alternative explanations.

Addendum:

I tried finding something more mathematically rigorous on this topic, but so far i only found this interesting blogpost, which might help illustrate the point a bit further via a rather simple example using Bayes Rule. The two most relevant statements from it are:

Backward Probabilities require information from all possible causes whereas Forward Probabilities do not

and

Backward Probabilities can be drastically different from analogous Forward Probabilities

If we accept the reasoning in this example, then the given - improbable but not impossible - forward probabilities are never sufficient to conclude something about the backward probabilities in and of themselves. This includes the validitiy of any other possible explanation besides chance, like a designer - unless we were vastly better informed about all the possible explanations' respective base rates, i guess. ;)

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  • +1 for being the only response so far to bring up Bayes. Inferring design from low probability alone is a subjective act, even if the probability is objective, and it is a valid input to Bayesian reasoning, but it is wishful thinking to take the result as an objective truth.
    – sdenham
    Commented Nov 9 at 12:56
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Frankly, yes. And I'm speaking as an atheist. My first major in college was physical anthropology.

If something created us, it wasn't God, it was sufficiently advanced technology that's indistinguishable from magic.

Anyone before us would definitely have evolved millions of years beyond us. Creating a universe as a garden is exactly the kind of thing you'd expect them to do.

When they appeal to probability and long times, they remind me of someone afraid to talk about the elephant and the parlor when it's slapping them in the face with its tail.

They exquisitely go into the details of how this astounding complexity can occur naturally, but they never address WHY it occurred.

It's like if, over thousands of years, water erosion turned a granite rock into the statue of David.

Yes, it CAN happen but why did it?

Space aliens!

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  • 4
    I've upvoted this just because it's so contrarian. But tell, why does there need to be a big why? There are lots of little why's though (feedback loops). But if we could explain in detail how the human became so klunky, and less well-designed than an octopus eye (I know because I nearly lost my eyes retinas), does there remain any extra why question? (The answer to why could just be: well, this functional structure did the job "good enough" and once it was there it was really difficult to change it (which also happens in legacy software devlopment...) :/
    – mudskipper
    Commented Nov 4 at 23:39
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    Btw David Haig (oeb.harvard.edu/people/david-haig), the evolutionary biologist, in "From Darwin to Derrida" also says we should ask the (little) why questions. Not the big why. There is no big why, according to him (if I understood him correctly).
    – mudskipper
    Commented Nov 4 at 23:43
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    You seem to be implicitly suffering from an agency bias without realizing it. Why can’t the why be a natural process? For example, a certain event occurred because the initial conditions of the universe combined with the laws of the universe made it inevitable. Why is this not good enough? If a “why” must mean “because an agent wanted it to be that way” and that’s the only thing that would satisfy you, then that’s begging the question.
    – Syed
    Commented Nov 4 at 23:44
  • > the initial conditions of the universe combined with the laws of the universe made it inevitable. === I used to tell that to people too. Then I realized, it's not inevitable. In fact it's astronomically improbable. To explain punctuated equilibrium, they talk of local clades. Maybe once, for one feature. But over and over again, these inconsequential features are critical to the survival of many individuals. But we have piles of Habilis bones and piles of Erectus bones, but nothing in between. Then the same thing happens to Erectus. Version 2.0 becomes version 3.0, everywhere. Commented Nov 4 at 23:55
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    @Miss_Understands - Sorry - You're right. I meant "contrarian" not as expression of intent or attitude, but as contrast to the usual dismissal of ID plus in contrast to the usual defense from religious quarters.
    – mudskipper
    Commented Nov 5 at 1:29
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My two cents follows.

Suppose we are shown a recording of what we are told is a very unusual event in a game, similar to all players getting a royal flush in poker. We might think the cards were loaded, that we've misunderstood the rules of the game, that the game's been going on for some time, that the video is faked, etc.. Do we have a way to choose between those scenarios, if all we have is the recording?

Besides which, I like all the counter arguments here, and probably think that there is nothing remarkable about being able to make observations: that the universe supports them is one observation among very many, more general but no more special than any other.

The question, as I understand it, not your question, needs more clarity.

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The question is about reasonableness:

Is it ever reasonable to come across an event that is very improbable and then infer that it must have been designed?

That is, the question does not seem to be asking "If something seems very improbable, can you ever say with absolute confidence that the improbable thing didn't happen?" - the answer is no, given only that information, you can never have a higher confidence than that probability :)

So I take "reasonable to infer" as "a reasonable person, given the balance of probabilities, would not find that any alternative hypotheses need be considered".

As for "design", I take that to mean "created with a deliberate goal in mind".

The canonical example of this is the pocketwatch.

In the absence of a designer, who had the deliberate goal to create a timepiece, the existence of a pocketwatch is vanishingly improbable.

So it is entirely reasonable in this case to infer a designer, given no more evidence than the existence of the pocketwatch. There is no plausible alternative hypothesis: we could appeal to magic and say someone just waved a wand and said "let there be timepieces" and there was one, but that's not plausible. The balance of probabilities does not support it, even if someone writes in a book that it's how it happened.

Now say we have a pocketwatch, with an English textual label engraved on it, saying "Designed By Fred". This watch is demonstrably similar to all other pocketwatches by the same designer. It has a certificate of authenticity, a well-documented chain of custody, and if you ask Fred himself, he'll tell you he remembers making that specific watch, and will be able to point to some remembered toolmarks, and correctly telling you where you can find others in the watch's internals. You can observe Fred designing and creating other watches.

It would be an exceptionally unreasonable position to claim that this wristwatch was never designed, and that the book about the wand is correct instead.


The distinction between a pocketwatch and a mouse or a moon, is that in the latter cases, it is exceptionally unreasonable to claim that any living thing or planetary system was intentionally designed. Not only is there a plausible alternative hypothesis for these things (evolution, gravitational accretion) but it's the overwhelmingly more likely hypothesis.

All that supporting evidence that we saw for the pocketwatch's design being Fred's, is similarly present for these, and vastly more, and it all points to the "design" being created through evolutionary/gravitational processes... which require no "deliberate goal".

Now, we could argue "there might be an intent guiding the hand of evolution/universe formation, so gently that it cannot be statistically detected above the level of random noise in any form of analysis, but having an immense effect over millions of years." That is, that evolution might have a subtle artificial-selection element to it.

That hypothesis cannot be disproven, but neither can the null hypothesis of no guidance, or the extreme hypothesis that there are two, three, or even a million different intents all subtly battling to direct life's development in different ways.

So just like if there was a book about someone waving a wand and saying "let there be life", so the idea of "let life be directed from random chance, but in like really very small amounts, by precisely N entities", is not a plausible hypothesis. A reasonable person would not accept that hypothesis as having significant weight in the balance of probabilities.

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  • "There might be an intent guiding the hand of evolution/universe formation, so gently that it cannot be statistically detected above the level of random noise in any form of analysis, but having an immense effect over millions of years." How would you define "statistically detected"? Commented Nov 6 at 1:44
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    @MichaelHall I'm no microbiologist, but I believe there are various operations in which predictable odds can be estimated mathematically, and verified in real life: for example, en.wikipedia.org/wiki/Punnett_square - if it was found in experiment that even across very large populations, the odds consistently deviated slightly from what math suggested, then that could be interpreted as circumstantial evidence of a hand on the scales. Commented Nov 6 at 9:12

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