Consider the following scenario:

I am alone at home and I accidentally spill a bottle of ketchup on my kitchen floor, and the ketchup splatters across the floor in such a way as to form the words "Alex, you're a douchebag".

A superstitious person will view this as definitive evidence of some other-worldy forces trying to tell me something.

A rational person will conclude that someone managed, against all odds, to play some elaborate prank on me, as unlikely as it is that someone could ever rig the ketchup and the floor to form such a pattern.

Neither of them would for one second entertain the possibility that this was a pure coincidence. And yet it is still physically possible, all though the chances are infinitesimally small, that somehow the ketchup just happened to fall in exactly that pattern.

Why is this the case? Why would one be certain that some agency is involved?

I am trying to figure out the relationship with skepticism here: Why is radical skepticism acceptable in so many other epistemic scenarios (Does external reality exist? do other people have minds or are they just zombies? etc,...), but in this case we would be certain that it is not a coincidence, that some agent was behind the occurrence?

More over, I could be certain in real life that no matter how many times I spill Ketchup on the floor, I will never get the above mentioned pattern (unless some trickery is involved). What is the grounds for such certainty?

Some clarifications:

  • Although many of the answers have been instructive - a lot of them seem to responding to the fact that the pattern was a meaningful sentence. I realize that my example is misguiding. My question would still be the same if the ketchup fell in an orderly hexagonal lattice pattern, or a ying-yang symbol, or any pattern exhibiting unambiguous order. Most people would consider that such a pattern occurring by accident not just unlikely, but outright impossible in real life, even though such a splatter pattern is physically possible.

  • The issue is not just the explanation of why such a pattern occurred after the fact (i.e. if it happened, there must be an agent behind it). If someone were to perform the ketchup splatter experiment beforehand, they would tell you with absolute certainty that such an ordered pattern will never occur, even though it is physically possible. Why do we deem such an event impossible? Where does this certainty come from? We can be skeptical of everything, we can even doubt that the sun is going to come up tomorrow, or that the moon might fall out of the sky, but this is one thing we are certain of. It is not just a question of probabilities, since if someone were asked to bet on such an event occurring, they will laugh at the proposal, and yet people bet against astronomical odds all the time when playing the lottery.*

  • Mod deletes comments. Please take extended discussion to chat. (Answers go in an answer)
    – Joseph Weissman
    Commented Feb 19, 2016 at 0:16

11 Answers 11


Actually, by using writing I believe you've picked the worst, or most confusing example for exploring improbability and skepticism. I largely agree with Ben Piper.

Writing itself is highly and very intentionally improbable. We create symbols that are not readily confused with the products of natural events. By this means we create communicable "meaning," which lies in the reduction of possibility to actuality, uncertainty to certainty. We will seek meaning even in scrambled "writing."

So your ketchup (spilled at Belshazzar's banquet, no doubt) actually signals a very high, almost certainly non-coincidental probability of mediating some other intelligence like ours. Precisely by appearing as "writing" and "meaningful writing" it has done what we intend to do in information: reduce all other possibilities to near zero.

The "epistemic" principle, if you want to call it that, is here to be found in the intentional structure of language, representation, and the more difficult problem of "meaning." Given that languages are arguably the deepest structures of rational being and are designed precisely to minimize natural "noise," we would almost have to be technically irrational to accept your scenario as "coincidence."

  • 1
    Very thought-provoking explanation! Your answer has induced me to upvote the original question as well, because of the important distinctions it provokes. Such as: assuming we humans are ourselves 100% natural, how the heck did we ever manage to "invent" such an intentionally-unnatural thing as language??
    – Jeff Y
    Commented Jan 25, 2016 at 22:03
  • Well, that's another question. A dog or monkey can react to "unusual" events, but would see nothing "improbable" in the ketchup, while any human would. On the other hand, we might range from "it looks like a Pollock" to "it looks like a face." By the time we get to "letters," we have reduced natural probabilities to near zero and in a sentence to "certainty" or "maximum improbability" of non-intentionality. Commented Jan 25, 2016 at 22:14
  • Right, letters, words, sentences, are in some sense the most unnatural possible things. Yet we purport to study the natural world using them (science). It's all somewhat bizarre.
    – Jeff Y
    Commented Jan 25, 2016 at 22:20
  • Hmmm your answer makes sense on one level. Writing might be intentionally misleading. I chose writing because it would be intuitive to laymen. But what about maxwell's demon? Spontaneous decrease of Entropy is metaphysically possible, but so highly improbable that its impossibility has been written into law (the infamous 2nd law). Commented Jan 25, 2016 at 22:21
  • I've heard "life" described as just such a "spontaneous" decrease (presuming no supernatural "guiding hand"). Is that off the mark?
    – Jeff Y
    Commented Jan 25, 2016 at 22:23

I think you can chalk the whole phenomenon up to natural confirmation bias.

Our perceptual system is not as passive as recent history has traditionally depicted it. We do not perceive things and make sense of them. Instead, it seems, perception works by projecting options that would fit our fondest assumptions, and evaluating how they fit with the external data. https://www.braindecoder.com/up-to-90-of-your-perception-could-be-made-up-purely-by-the-brain-1104633927.html

The kind of distortions that appear when we test vision, for instance, show an inordinate level of confirmation bias: illusions of faces everywhere, color discernment that is impaired by unconscious assumptions about the nature of shadow, blatant failure to perceive things that impair meaning (e.g. extra interpolated words that make text less sensible), false perspective, etc. (These and some other examples: http://distractify.com/old-school/2015/02/22/mind-blowing-optical-illusions-1197825445)

From a sort of Nietzschean (or 'Selfish Gene') point of view, this is just as it should be: human perception is strongly biased toward seeing things that offer us power over our environment -- things that confirm our powers of prediction, or that answer to our dreams. (Because the nature of an animal, and so a human, is to explore all dimensions of power.)

To some degree, explanation is just another layer of perception, and there is no good reason why the higher-order process should be significantly different from the more detailed ones. Psychologists have accepted this for generations, focussing on how strong our tendency to presume and project is.

From that perspective, the one explanation that appears to help us the very least is that of complete randomness. It renders us powerless in the instant, so it is very hard to get to. Any alternative that involves people, or deeper meaning will present itself first, unless we have purposely trained ourselves out of considering it -- God and ghosts are a better model, if we think they might listen, or that we can predict their behavior because of their similarities to us. We only dismiss them because we have been making those same jumps for millennia and been wrong.

Ironically, science has made incredibly powerful use of the uniformity that results from explanations via complete randomness. But on a case by case basis, we reflexively resist objectivity in this way. That case-by-case 'certainty' comes from our arrogance as to the power of our perceptual mechanisms (which is logically built into the mechanisms themselves) something philosophers have been directly attacking at least since Hinduism first adopted the notion of 'maya', and not from any reasonable epistemic principle.

  • Could you see my edits at the end, and tell me if it makes more sense? Commented Jan 26, 2016 at 5:55
  • 1
    I think I got the idea from the ensuing discussion, so I cannot really confirm that the edits help. I think this answer remains consonant with them -- having appended a direct answer to "What is the grounds for such certainty?"
    – user9166
    Commented Jan 26, 2016 at 18:23
  • I think this is the best answer. It is not an 'epistemic principal' but rather a natural psychological trait that leads us ('allows us') to believe in one thing or another
    – M. le Fou
    Commented Jan 29, 2016 at 23:43

Any pattern would be highly improbable. The thing that would make your particular pattern seem almost impossible is that the already high improbability is compounded by the fact that the random pattern fits several specified, well-known design patters, each of which is itself highly improbable, including:

  • the ketchup forms shapes which correspond to letters
  • the letters are arranged in an order that spells words
  • the words have meaning
  • the words are arranged to form a grammatically correct sentence
  • the sentence has meaning
  • the sentence has your name in it

I'm not a mathematician, but I'm guessing that if the probability of any random ketchup pattern is x then the probability of your particular pattern is orders of magnitude greater, maybe like x^10.

But the thing that makes it seem impossible isn't the enormously high improbability. It's the fact that it fits many meaningful patterns that were specified in advance.

If you want a deeper study of the idea I recommend William Dembski's The Design Inference.

  • "your particular pattern is orders of magnitude greater, maybe like x^10." you orders of magnitude smaller and x^-10? I'm not following the whole response. Commented Jan 25, 2016 at 22:43
  • Dembski gets the basics right, then starts making heaps of errors when it comes to more subtle effects (iterative effects, correlations, selection effects, etc.).
    – Rex Kerr
    Commented Jan 26, 2016 at 8:56

Your question "What epistemic principle allows us to be certain that highly improbable events will never occur in real life?" is highly interesting, but the example you provide derails the issue into the wrong direction, if I may say so.

Let me address one problematic assumption in your question, that the shape of the ketchup splatters has something to do with meaning. It has not.

The philosopher Rudolf Carnap, in a completely different context, once gave this lovely example, quite similar to your's in structure:

Should unusual, brilliant patterns suddenly appear in the sky — even if they took the form of letters which seemed to compose a sentence — science could not comprehend them except by first conceiving them, describing them, and explaining them […] as physical facts. The question whether such an arrangement of symbols constitutes a meaningful sentence must be decided without taking into consideration whether or not it appears in the sky. If this symbol-arrangement is not a meaningful sentence beforehand, it cannot become one no matter how bright an appearance it makes in the sky. (Psychology in the physical language, 1932, pp. 179-80 of the english translation)

Think of brightness of the letters in analogy to how well the shapes of the ketchup splatters resemble letters. Think of a continuum in which the splatters may not resemble letters at all, almost resemble letters, barely resemble letters and clearly resemble letters. None of these steps make them more meaningful.

Leaving aside the particular context, Carnap here makes the point that meaning is not part of the physical events you see. It is dependent on the contingent development of an association of some shapes to some meaning. The fact that you give them meaning is based on a psychological-perceptual recognition - it is exactly the same phenomenon as if you were to see Christ's face appearing in spilled ketchup, as suggested by Nelson Alexander. See the WP entry Perceptions of religious imagery in natural phenomena for more details, also wrt to the perception of (religious) word shapes in natural phenomena.

The fact that you recognize some shapes as meaningful is also dependent on which shapes you deem to be meaningful. To see this point even more clearly: I could spill the ketchup and then construct a language that has is formed of an alphabet that perfectly resembles the shapes I see on the floor. You would be surprised of the things the ketchup tells me :) Or, even easier, I could directly associate the shapes with some meaning and translate those shapes into an existing language.

Suggestion: Why not restate the interesting question stated in your title with a much less problematic and contentious example like "I am certain that I will never be killed by an asteroid."?

  • I added some clarifications. I would rewrite the question all together, but I don't know exactly what the Phil SE policy is, plus so many have already put decent efforts into answering this one. Commented Jan 26, 2016 at 5:54
  • Feel free to ask a new one!
    – DBK
    Commented Jan 26, 2016 at 11:06

I think that there are two types of certainty being conflated here. One is mathematical , being certain when the probability of an occurrence is zero percent. The other is a psychological state when a person has decided if they believe something has happened or not. It is quite possible for a person to reach psychological certainty for any number of reasons even when it isn't justified mathematically. In fact it happens quite a bit, or at least seems to. (People often present as if absolutely certain yet will change their minds in light of new evidence.)

In your example:

"Neither of them would for one second entertain the possibility that this was a pure coincidence. And yet it is still physically possible, all though the chances are infinitesimally small, that somehow the ketchup just happened to fall in exactly that pattern."

You are clearly referring to psychological certainty which is not justified mathematically. The onset of psychological certainty is, of course, an empirical question and must be addressed within psychology. In fact however it is possible for someone to react in the manner that you describe without being psychologically certain. They can simple start looking for alternate explanations because they consider them to be much more likely than random chance. They may even express the attitude that it is foolish to even consider the possibility of it being random chance, not because they are certain that it isn't, but because other alternatives are vastly more likely.

This illustrates why I think that the two 'certainties' aren't being separated. Your example equates their completely ignoring the possibility of random chance with their being certain that it wasn't random chance. It is foolish to consider extremely low probability alternatives. I spend zero time being concerned about a panda bear being in my bathroom even though it is a possibility. This doesn't mean that I'm certain that I will never find one there.

P.S. Also instead of "infinitesimally small" you might want to consider "exceeding small". I'm sure that you meant it loosely but it does have mathematical definitions which I presume that you didn't mean to evoke.


I think there is no such epistemic principle, but given that there are always many possible explanations to a given observation (including hallucination or dream), if the fact that something happens by mere coincidence is highly improbable, then there is always a chance that one of the alternative explanations will get more credence.

Perhaps there is a point where the hypothesis that an observation arrives by mere coincidence should be given less credit than the laws of physics themselves, which raises interesting questions: this coincidence can be considered strictly impossible because we'd revise our physics rather than believe it. However it seems possible, at least in principle, to be more and more confident in our physics (in its completeness, in our perfect control of the observed situation, etc) to the point that we'd accept that it couldn't be anything but a coincidence. Now in everyday situations we are very far from this level of control.

Note that I can think of a third way in your example: remaining agnostic regarding the right explanation.

  • This ties into the idea that all observations are theory laden -- an observation can be impossible within a given theory, then when you see it you either need to toss the observation or toss the theory.
    – Dave
    Commented Jan 25, 2016 at 14:51
  • @Dave kind of, but you could say it's always the interpretation of an observation that you toss not the observation itself Commented Jan 25, 2016 at 17:45
  • The issue is not just about explanations, but about future predictions as well. In most situations, we can predict with absolute certainty that such an event will never occur. Commented Jan 26, 2016 at 5:56
  • @AlexanderSKing I don't think so, how could we? Commented Jan 26, 2016 at 16:51

There is no such principle, because it is simply false. In fact, incredibly improbable things happen all the time in real life. Consider that something might happen, say, once a second. That's 2.5 million times a month. And there are billions of people in the world. The chance of a one in one quadrillion event happening somewhere to someone is not that unlikely.

There is an interesting book exploring this by a statistician, David Hand. It is called The Improbability Principle: why incredibly unlikely things keep happening.

  • 1) The theoretical probability that ketchup will behave that way is far far less than even one in one quadrillion. 2) The fact that "highly unlikely events" nonetheless occur with some regularity does not mean that "ketchup to sentence" events can just be taken as one more.
    – Jeff Y
    Commented Jan 25, 2016 at 21:36

One shouldn't be completely certain. That's irrational.

If you pick out a tiny subset S of a universe of possibilities U then it simply isn't the case that elements in S certainly will never happen. If U is designed such that all elements are equally likely, we can easily calculate just how likely it is that an observation s will be in S: it's just p = |S| / |U|.

So what is really going on, in the mind of a rational person, is that when phenominally rare patterns occur (like the first hundred words of the Declaration of Independence appearing in ketchup splatters), first they must estimate the relevant S of picked-out stuff (e.g. the first hundred words of the Declaration of Independence is picked out by virtue of it having been written down already) and try to estimate p. This often is really really really tiny, since each letter (for instance) is very unlikely to form, and the formation of each letter should be independent, so all the probabilities should multiply.

So you end up with things on the order of p = 10-1000, which is in the realm of "you don't expect to have one of these happen in the lifetime of the universe, even if you devote the entire universe to making such splatters". It's not that it can't happen, but we shouldn't expect it. "Find another explanation" is a reasonable heuristic in this case.

Thus, one is justified in trying to find almost any other explanation that could make the observation more probable. In particular, we know that some people like pranks, and some people are really good at stage magic and other magic-seeming stuff, and some people think the Declaration of Independence is pretty cool and worth copying. So it's not entirely unjustified to estimate that the p-value for it being intentional is pretty low, but still way higher than the "it's random" thing.

So it is rational to provisionally accept the hypothesis that it was intentional over the hypothesis that it was random. (There may be other hypotheses that are more likely yet, such as a sheet of paper with the Declaration of Independence had been scribbled on with crayon, and the crayon stuck to the paper but not the ink; and then the sheet was left on the floor and stepped on a bunch, transferring a stencil of the wax to the floor; and the ketchup splatters slid across the wax into the wax-free letters. The point is that it seems overwhelmingly likely that there is some correlation between the original Declaration of Independence and what you've observed.)

But again, it's not that you a priori rule out rare happenstance. Rather, it needs to be a somewhat-informed guess about the relative probabilities of the two scenarios.


Your question operates on two different levels: On one hand you describe how people search natural explanations in daily life. On the other hand, you ask on a theoretical level

What epistemic principle allows us to consider highly improbable events as impossible?

My answer to the latter question: There is no epistemic principle which builds a bridge from the possible - but highly improbable - to the impossible.

Concerning the first alternative, I assume that the rational person remembers several unlikely cases which eventually got a rational explanation. Possibly he even sets out to investigate the case and to find out the rational explanation. And as long he has not found it, he abstains from any pseudo-explanation of the situation.

Aside, what about converting your remarks concerning skepticism into a separate question?

  • "what about converting your remarks concerning skepticism into a separate question?" But that's my point: Doesn't the certainty in this situation present a challenge to skepticism? If we can be certain in this case, can't we also be certain in other cases, such as the problem of other minds? Commented Jan 25, 2016 at 7:09
  • @Alexander I apologize, but you ask several different questions. Notably the heading does not refer to skepticism. - I do not share your premiss that we are certain in the situation of your example. Only after finding a rational explanation we can be certain or have a reliable hypothesis.
    – Jo Wehler
    Commented Jan 25, 2016 at 7:25
  • You're right, I will edit my title. Commented Jan 25, 2016 at 7:31

The probability of the ketchup splattering in that form is just as low as any other form. There is nothing uniquely improbable about it, so it wouldn’t actually be more of a coincidence than any other shape the ketchup took as the answers here seem to indicate.

The real reason why one entertains other possibilities, such as a prank, is because one instinctively thinks that a prank that spells out those words is more probable than it landing by chance. And this is because we have apriori evidence that pranksters exist and that they might have reasons to form those words. More importantly, we know that this is possible. The reason why we don’t think it’s a prank for any other pattern is because we can’t imagine why one would want to rig the ketchup to land in a way that doesn’t seem significant to us, even though that is possible.

In the case of supernaturalism, we cannot actually conclude that a supernatural force caused that pattern to occur, even if we were confident that a prank didn’t happen. This is because we don’t, apriori, know if some supernatural force causing that pattern is possible.


This is a bad example since the forms in which ketchup splatters can take on different probabilities. Even if those words were not meaningful to us, something about the structure of that pattern may deem it to be less probable than other forms. But let’s suppose that each form of a splatter is equally improbable. I wager that people would still find the ketchup splattering in the form of that sentence to be a huge miracle. An example that matches this scenario would be a coin toss sequence landing on heads hundreds of thousands of times straight.

And yet, there would be nothing uniquely improbable about this, since it would be just as improbable as every other form. Thus it wouldn’t actually be more of a coincidence than any other shape the ketchup took.

The real reason why one entertains other possibilities, such as a prank, is because one instinctively thinks that a prank that spells out those words is more probable than it landing by chance. The reason why we don’t think it’s a prank for any other pattern is because we can’t imagine why one would want to rig the ketchup to land in a way that doesn’t seem significant to us.

In the case of supernaturalism, we cannot actually conclude that a supernatural force caused that pattern to occur, even if we were confident that a prank didn’t happen. This is because we don’t, apriori, know if some supernatural force causing that pattern is possible.

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