Chekov’s Gun and the Principle of Sufficient Reason

I have a sneaky trick I use to figure out the murderer when watching mystery shows. If there’s a random background character — say a doorman or a random neighbor — who gets insufficiently motivated screen time and lines in an early scene, they’re the murderer. If the role is being played by a mildly famous actor rather than a bit-part nobody, then you can be doubly sure. My hack exploits a human-character special case of the fact that good storytellers tend to follow, the Chekov’s gun principle:

“Remove everything that has no relevance to the story. If you say in the first chapter that there is a rifle hanging on the wall, in the second or third chapter it absolutely must go off. If it’s not going to be fired, it shouldn’t be hanging there.”

This isn’t an entirely fair trick of course, especially if you use the mildly famous actor clue, since it’s an extrinsic structural clue that’s outside the narrative proper, and one that won’t necessarily lead you to further guess the motive, or means. The lesson of the trick though, is that the assumption that there are no insignificant details in a story (or equivalently, that there is a good author behind the story) is an extremely powerful one. One that allows you to solve the mystery faster than if you had to sort out the significant details (as you would have to in a real murder). Of course, a great author, as opposed to a merely good one will distract you with a plausible alternative explanation for the Chekov’s gun that will lead you astray,.

The fact that Chekov’s gun can be used as a cheat points to why the corresponding idea in metaphysics, the Principle of Sufficient Reason (PSR), made famous by Leibniz, is so controversial.

Informally, the PSR is the idea that “everything happens for a reason.” There are no insignificant details in the universe, and everything must be accounted for. There are weak and strong versions, straightforward and tricky versions.

The PSR seems like an innocuous enough first principle to adopt. You mere require that there be a good reason for anything to be or happen.

Unlike Chekov’s gun, the PSR in its weaker forms is only causal, not teleological, but for the point I’m making, this doesn’t matter. Whether you demand to know the cause or consequence of something being the case, you are demanding causal intelligibility and connectedness in the universe. And as the Stanford Encyclopedia of Philosophy entry notes, “This simple demand for thoroughgoing intelligibility yields some of the boldest and most challenging theses in the history of philosophy.”

This is not a trivial point. We are used to requiring coherence and internal consistency in models of reality. The PSR requires it of reality itself. In a way, the PSR is the assertion that there is in fact a coherent reality out there. That reality is perfectly mappable in principle, even if not in practice.

To believe in the PSR is to believe that there is a coherent structure to reality and that there is no true arbitrariness in nature. The PSR is the (usually unstated) assumption underlying any search for grand unified theories of things. There should be no loose ends, no superfluity, no mysterious parts unaccounted for in the cosmic Ikea manual. Everything should point towards the resolution of the murder, contribute to the construction of the Ikea dresser, or follow from the basic equations of physics.

The problem with the PSR is that it’s too powerful. It can be used to justify almost any metaphysical conclusion, depending on how willing you are to overfit the data. Leibniz, rather cleverly, used it as a way to give God something to do, even while helping invent the physics that was beginning to make the God hypothesis unnecessary. He also invented overfitting.

The modern form of Leibniz’s argument, in brief, is that you make up the sufficiency deficit in explaining why the universe is the way it is, by assigning “God” the job of picking the “best” universe that exists from among the many that could. You don’t even need to apply PSR in a teleological form to get there. You just need some unexplained arbitrariness in the parameters of the universe to get there (an alternative, equally unfalsifiable explanation is the anthropic principle).

To understand the appeal of the PSR, think about applying Chekov’s gun backwards. You’re handed a bald, undramatized account of the facts of some case, but you don’t know whether it’s real or made up. If the Chekov’s gun principle applies and everything in the story hangs together reasonably, you could argue that it’s been artificially authored. The party game of “two truths and a lie” is a test of this sort of ability to tell fact and fiction apart using structure alone, without access to additional fact-checking resources.

This explains why evidence of miracles is so important to religions. A miracle is a reverse-Chekov’s gun argument for the existence of divine agency, and relies on a strong (teleological) form of the PSR to work. A miracle is a loose end that allows you to expand your ontology.

If the PSR opens the door for religion, some form of it also appears to be necessary for doing science. If you don’t assume it, the idea of falsifiability is undermined, since a falsification need not be treated as a systematic flaw in a universal theory, requiring a systematic explanation.

In what sense is the PSR too strong? The issues with the PSR seem rather like the issues with the Axiom of Choice in mathematics: it allows you to draw a lot of conclusions that seem solid, but also conclusions that seem insane.

What happens if you drop the PSR?

To doubt the PSR is to adopt some variety of radical skepticism. As far as I can tell from a cursory Wikipedia-depth look (somebody correct me if I’m wrong here), Hume landed where he did, on a rather extreme form of empiricism, in part because he tried to get rid of the PSR, arguing that you can’t actually conclude a whole lot with any certainty about the universe. The result though, is that the universe then appears to be unreasonably lawful and structured, relative to whatever you can say about it with analytic certainty. So the Humean seems to be reduced to arguing things like “well, you can’t ground Newton’s laws on a sound epistemological footing in relation to sensed reality, but you should probably still expect billiard balls to behave in pretty lawful ways.”

In our murder mystery analogy, the Humean detective would solve cases but not claim solutions.

What happens if you keep the PSR?

I suspect one of the reasons philosophers are so wary of the PSR is that it turns subjective consciousness into ontological dynamite. It exists, and therefore must do so for sufficient reason. But nothing in the laws of physics says consciousness must exist. It also appears to have no observable consequences: anything a conscious entity could do, a philosophical zombie could do in an indistinguishable way. Subjective consciousness is not intelligibly connected to materiality. Anything that happens as a result of human agency can be explained without reference to subjective consciousness. So if it has no cause and no effects, it exists without sufficient reason. So you either have to give up the PSR, or give up believing in subjective consciousness, or give up believing in the material universe.

If you want to keep all three, you have to invent a reason, even if you can’t observe it. And that reason must invoke something that can interact with material reality, otherwise you are just left with two co-extensive domains, which taken together, constitute a larger reality within which neither piece has sufficient reason to exist.

Usually, the reason invented to keep all three is some variant of the God hypothesis. The more physics you know, the more convoluted this gets. It appears that Leibniz, despite (or perhaps because of) his pioneering genius as a physicist and mathematician, landed on something like monadology out of a desire to keep all three.

Going the other way, you could give up either the subjective or the objective. PSR can be used to argue that subjective experience is impossible, a sort of illusion or confusion caused by strange loops and weird recursions and simulations (a familiar argument around Strong AI for example).

Or it can be used to argue that subjective experience is the only thing that exists and that materiality is the illusion.

Or like Hume, you could simply give up and allow for a universe with disconnected but unreasonably harmonized islands within which the PSR appears to hold locally. This is the same thing as concluding the universe is not fully intelligible in order to avoid overwrought explanations for it.

(You see all these possibilities explored in Eastern philosophies, but afaik, there is no explicit discussion of a proposition analogous to the PSR).

But to bring it back around to murder mysteries, a good way to think about your metaphysics is this: do you think the universe is like a murder mystery, with a “solution” that includes an account of the significance of every detail, including your subjective consciousness?

Or do you think it’s an arbitrary mishmash of phenomenology which just happens to have some unreasonably grokkable structure to some parts of it and doesn’t have to make sense taken as a whole?

I honestly don’t know. I think there’s a good case to be made for both conclusions, which is why the principle of sufficient reason is such an interesting idea to think about.

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About Venkatesh Rao

Venkat is the founder and editor-in-chief of ribbonfarm. Follow him on Twitter


  1. The question is what you mean by “perfectly mappable in principle.” We know (from principle) that the universe is not perfectly mappable. As I put it elsewhere, if you are sitting in a room trying to draw a picture of the room including every detail in it, you will necessarily fail, since you cannot draw a picture of the details in your picture without adding more, and more, and more…

    In other words, since we are in the universe, we cannot perfectly map it, even in principle.

  2. I feel like you deliberately dodged defining “intelligible” for exactly the same reasons that all the dualists going back to Plato made perfectibility of the soul equivalent to perfectibility of the mind. That is: if the universe is ultimately perfectly intelligible to us — irrespective of whether this is a comment about the existence of mind/soul apart from body, or whether our computational substrate can get us there — then ultimately we can fill the same niche as God the First Mover. Perfect intelligibility of the universe in principle implies there are no logical barriers to omniscience. Practical ones, sure. But that’s why this is all tangled up in the mind-body problem. Plato went the opposite direction precisely because he wanted to reject empirical reality as being the shitty, flawed thing that often didn’t have good reasons for failing to reflect the noumenal ideal.

    Anyway, even without wading into the delicious sugary waters of dualism, both “intelligible” and “sufficient reasons” also imply an unstated set of beliefs about the relationship between metaphysics, observation, and reference. *gestures at Kripke* Intelligible implies coherent intersubjective meanings and references.

  3. One problem is how we give first class status to analytical reasoning. Hume basically says causality is always probabilistic whereas analytic thinking operates on 1 and 0. But I would go even further and say there is no categorial difference between mental and sensory events (which in itself is a statement in analytic syntax but oh well). Ie logical thinking is what it feels like for Awareness to watch a human neomammalian circuit processing reality. Suddenly analytic certainty is not Platonic but just the brain chatting about unmarried bachelors and three-legged dogs. The internal version of watching billiard balls or debugging a CPU. Strangely lawful, yes, but not any longer in a category that fundamentally juxtaposes with the merely-empirical.

  4. Consciousness exists because an agent which can model its environment can survive better. Introspection exists because an agent which can model itself as part of the environment survives better still.

    How are those not sufficient reasons for human consciousness as its experienced?

    • That’s not consciousness. A non-conscious agent can do all those things. There is no reason for subjective conscious experience to accompany those phenomena.

      • It’s be very interesting if that wasn’t true though; if we discover that p-zombies are for peculiar information reasons physically impossible.

        We can already imagine, for example, fire that makes you colder rather than hotter, but we exclude that possibility because of the connection we’ve made between fire as an experienced object and as a physical/chemical process. You don’t get fire that doesn’t burn, and if it burns like fire, it’s fire. If we finally determine the parameters by which consciousness arises, in the sense of finding its biophysics, or even just in terms of nailing down it’s scannable temporal patterns, I wouldn’t be at all surprised if we start assuming that all processes that have those properties are conscious, in the same sense that things can “burn” in non-oxygen environments, etc. The obvious application would be AI, but probably the most complex part would be classifying animal consciousness and comparing it to various human states.

      • I think the theory of p-zombies is the problem. They’ve not been proven to exist, and accomplish some impossible sounding things. The only reason that the idea survives is that we can’t easily falsify it.

        I’m going to duck-type consciousness until I see strong proof to the contrary.

  5. Isa Hassen says

    > “As far as I can tell from a cursory Wikipedia-depth look (somebody correct me if I’m wrong here), Hume landed where he did, on a rather extreme form of empiricism, in part because he tried to get rid of the PSR, arguing that you can’t actually conclude a whole lot with any certainty about the universe. ”

    I don’t think Hume tried to get of the PSR. Hume also said “I never asserted so absurd a proposition as that something could arise without a cause.” Hume’s keystone argument, the “problem of induction”, was only made to point out the logical weakness in the epistemological framework of materialist athiests. In other words, he was NOT trying to say that a cause doesn’t exist for anything, rather he was saying we cannot conclude with any certainty that the cause of A is B (which is what the entire project of Science is all about). I think his reason for arguing as such was a sort of roundabout way of saying that God must therefore exist if He be **defined** as the Cause of all things (an argument which relies on PSR). It is widely agreed that this was the motivation of similar philosophers of his time like Kant.

    > “If the Chekov’s gun principle applies and everything in the story hangs together reasonably, you could argue that it’s been artificially authored.”

    False dichotomy. Even leaving bad authors aside, you could still argue that the story has been artificially authored by an excellent author whose writing style is pure unintelligible arbitrariness.

    > “This explains why evidence of miracles is so important to religions. A miracle is a reverse-Chekov’s gun argument for the existence of divine agency, and relies on a strong (teleological) form of the PSR to work. ”

    Yes. And interesting to note how some counter-culture “spiritual” ideologies intentionally sabotage this appeal to PSR. For example in the Sufi tradition I studied, miracles were dismissed as mere distractions. Rumi’s conception of God actively calls for the abandonment of both the stronger and weaker form of PSR, positing God as fundamentally unintelligible, by all definitions of intelligibility. Yet in a beautifully non-nihilistic way.

    • They are called “siddhis” (powers) in the East, and yes, they are considered irrelevant.

      Sufism, mystics, Zen, etc are all trying to not-involve themselves with the epistemic domain at all. In contrast to religion, whose syntax is a mix of myth / paraconsistent logic / deontic / personhood-ontology and observed phenomena / aristotelian logic / epistemic / object-ontology. And they throw in a bit of phenomenology / direct experience as well.

      Where the religions differ, is in how they overlap those two modes. Whereas various mystics are trying to go for the direct experience domain only.

  6. Ralph W Witherell says

    I lean towards the arbitrary mish mash that we then provide an overlay of pattern recognition, etc, to that we call understanding. Seems psr requires a fixed point of view.

  7. FYI, quantum mechanics is fundamentally non-deterministic. It does not obey the PSR. It allows for the calculation of probabilities, however, and it includes some of the most robustly-validated theories in physics.

    For example, to the best of our knowledge (which is really, really good at this point), there is no way whatsoever to predict when a radioactive nucleus will decay. It’s totally random. But for any macroscopic amount of radioactive material, composed of a statistically large number of radioactive nucleii, we can predict with a great deal of certainty the overall rate of the decay (and the rate of change in the rate of decay).

    This property of QM led to the famous exchange in which Einstein said “God does not play dice with the universe” and Niels Bohr replied “Don’t tell God what to do with his dice.”.

    • A lottery winner, by numbers chosen via radioactive decay, wouldn’t have won if they hadn’t bought a ticket.

      • In such a case, purchasing a ticket is a reason but not a sufficient reason for the winning event. If a person knew everything that could possibly be known at the time of the ticket purchase* and could reason flawlessly through all the mechanisms of cause and effect, the person would still not have sufficient grounds to reach the conclusion that the ticket would win.

        *and human understanding of quantum mechanics is correct on this point, but we’re really pretty sure it is.

      • Also, note that I’m not saying that nothing has a sufficient reason. Just that not everything does.

  8. Clumsy Dad says

    The more we know, the more we know about all we don’t know. For me the PSR is a bit of a fool’s game because we are endlessly aware of our deficiency in knowledge about the “all that is” that we as humans are trying to define, classify, and delimit. Peace (-:

  9. Mich Ita says

    Subjective consciousness, and with it other concepts such as “man”, “Western/Eastern civilization”, “history”, are, very likely, products of the mind.

    So is freedom, both as in free will and as in hypothetical-probabilistic physics models, where it is daringly that a particle could not have done what it in fact did (because outbof other 100 particles observed only 23 did it: as if could prove that a single particle is “free” as to what it will do).

    So there might be an account for all what will go on over the entire universe’s existence — but it would be unthinkably diverse than the nanoaccounts we like to fantasize about (depressingly, it would not include anything like “man”, “will”, except for including them as intellectual mistakes occurred in one hyper-weird planet, once).

    Or maybe everything (we said there is no freedom for beings, living and not) can only happen the way it happens. This would spoil the question “Why?” of sense, for to ask why of something cannot make sense if that something happened tbe only way it could happen (“why?” presupposes the idea of freedom for reality… of different paths allowed to phenomena. If nothing can happen unlike it happens, there is no “why” to query about).

    The different approaches to Leibniz’s PSR map onto the realism/idealism division of philosophies.
    Idealism: the only reality is created by the subjects, via his deeds of thought.
    Realism (not ingenuous varieties): There is both a reality made by the mind, and another one, the noumenic kantian thing-in-itself for instance. The question is whether and how much of reality-reality can be accessed and charted by our reality-making mind.

    You have the hardcore realists (the subject creates nothing. Reality is… plainly real, and out there for everyone to apprehend it), and the hardcore idealisists (Hegel, Gentile).

    • Mich Ita says

      *daringly stated*

    • 1) We have quite a bit of understanding about how people behave with various brain injuries. This evidence strongly implies that matter creates mind, not vice-versa.

      2) We know that subatomic particles behave non-deterministically. Any particle can do what it did (obviously), but sometimes they might have done something else. We are reasonably certain that subatomic particles are mindless; their random behavior is not “choice” in any meaningful sense of the word.