Ontic and Epistemic Doubt A: A Scientific and Conceptual Introduction (Column 322)
With God’s help
In the coming columns I wish to address the relationship between epistemic (cognitive) doubt and ontic (factual, in-reality) doubt, in halakhic contexts and more generally. In this column I will first offer a scientific and conceptual preface to the topic.1 You don’t need prior knowledge to follow along, though I realize some readers shy away from scientific material and mathematical notation. Such readers can focus on my explanations; coefficients and equations aren’t truly necessary for understanding (even if they help).
Inability to Predict in Chaotic Systems
Duane Farmer, one of the pioneers of chaos theory and a member of the original Santa Cruz group that first conceptualized chaos, describes how he and his colleagues felt when they began to grasp that a physically meaningful and far-reaching theory was in their hands (see James Gleick’s Chaos, p. 253):
“Philosophically, it seemed to me a practical way to define free will, one that allows you to reconcile ‘permission is granted’ with ‘all is foreseen.’ The system is deterministic, but you can’t say what it will do the next moment… There’s a coin with two sides here. On one side there’s order from which randomness emerges, and one step away there’s randomness grounded in order.”
Despite the excitement, the linkage Farmer makes between randomness and free will is flawed for several reasons. First, free choice is not randomness; it is a different mechanism entirely—a philosophical misunderstanding regarding the meaning of free will. More seriously, there is a physical misunderstanding of what chaos means. A chaotic system is not truly random. In such a system we indeed can’t predict future behavior from the present state, but that’s only due to computational complexity and sensitivity to initial conditions. There is no genuine freedom here. Farmer conflates unpredictability with freedom. What leads him astray is the fact that if a person truly has free choice, we cannot predict their behavior. But the converse doesn’t hold: the mere fact we cannot predict behavior doesn’t necessarily imply freedom (i.e., non-determinism).
Consider tossing a coin or a die. Practically, we can’t predict the outcome, so many treat such phenomena as random and analyze them with probabilistic tools. But of course nothing “random” is actually going on. A coin toss or die roll is entirely deterministic, even conceptually simple—it’s just Newton’s laws. The difficulty of calculation stems both from enormous sensitivity to initial conditions (the direction and speed of the toss) and from the technical computation itself (shape of the objects, air currents, etc.). These prevent us from computing the result, but in principle such a computation exists. In Talmudic parlance one might say that “before Heaven it is known” what the outcome will be—God knows it. If you gave me a computer with infinite power and memory (plus exact data about the coin/die and initial conditions), I could tell you the outcome with certainty. True, I lack all that, so I can’t perform the computation—but that still isn’t freedom. A system that includes “freedom” it is not.
Epistemic Doubt and Ontic Doubt
What did Duane Farmer miss? Why the gap between unpredictability and freedom? The fact that I can’t predict the outcome of a coin toss stems from certain lacks, ambiguities, or unknowns on our side; it’s not a feature of reality itself. For any given state there is exactly one well-defined outcome determined by the present state. The lacuna is ours. In philosophical terms, this is epistemic doubt (a lack of knowledge). When it comes to chaotic systems, someone equipped with complete information and unlimited computational capacity could in principle know everything about them.2
To expose the error more sharply, recall that libertarian free will (the view that genuine free will exists) maintains that reality itself is not single-valued. Even given a particular set of circumstances, a person can still freely choose whether to do X or Y. Hence this is not a case of “we don’t know,” but of a reality that itself is not uniquely determined. In Talmudic terms, even granting an infinite-power knower does not help—there is no single right answer to know. We shall call such a situation ontic ambiguity (from ontology, the study of being): indeterminacy in reality itself, as opposed to epistemic doubt which concerns our knowledge of reality rather than reality itself. To sharpen the distinction, I’ll reserve “doubt” for a lack of human knowledge, and use “ambiguity” for a lack of determination in reality. As a rule of thumb: doubts are modeled by probability; ambiguities by fuzzy logic.
Quantum Physics: Ambiguity Within Physics
It is told of the British astronomer Arthur Eddington that when told there were three people in the world who understood relativity (him and Einstein, of course), he asked who the third one was. Richard Feynman—later, a younger and renowned physicist—quipped that relativity isn’t really that hard to understand, but quantum mechanics nobody understands; at best you get used to it.
One of quantum theory’s strange features is that, according to standard interpretations, it’s the only domain in physics where ambiguity appears in reality itself (not merely in limits to our computation). There is an ontic margin in physics, not only an epistemic one. I’ll explain the relevant point briefly (relying on the common interpretations of quantum theory).
The Double-Slit Experiment
As Feynman suggested, the best way to grasp quantum mechanics is via the double-slit experiment. The experiment has a fascinating, flip-flopping history. Already in Newton’s time, there was a debate among physicists about the nature of light: is it particles (Newton) or waves (Huygens/Fresnel)? In 1801—74 years after Newton’s death—Thomas Young performed the original double-slit experiment to settle this. The setup sharply distinguishes waves from particle beams. It proved equally useful in the next century for an analogous debate about the nature of particles like electrons (wave-like or particle-like?).
With a single slit, both waves and particles give a central maximum on the screen with diminishing intensity to the sides. But with two slits, a particle beam would simply sum the contributions from each slit, giving two equal peaks; a wave beam produces an interference pattern of alternating bright and dark fringes, including destructive interference (two strong waves summing to zero) and constructive interference (total intensity exceeding the simple sum).
Experiments with light yielded the wave-pattern result and settled the old debate in favor of light’s wave nature. But early in the 20th century, evidence accumulated suggesting particles behave like waves. Louis de Broglie (1924) proposed that electrons have wave character and even supplied a mathematical description (wave function). Electron double-slit experiments were performed: the surprising result was an interference pattern—apparently electrons behave like waves.
To rule out the hypothesis that interference arose from electrons disturbing one another within the beam, the experiment was repeated with an extremely low emission rate so that only one electron was in flight at any time. Astonishingly, the pattern remained wave-like. A single electron interferes with itself. That is, an electron isn’t a tiny billiard ball at a definite place, but a wave spread out in space—just like light.
But if a single electron interferes with itself, it must “pass through” both slits. That seems intolerable. How can one particle go through two slits at once? To check, a detector was placed at one slit (call it slit A). When the detector registered the electron passing A, the pattern on the screen turned particle-like (two bright lobes) rather than wave-like. When a detector was placed at slit B and registered there, again the particle-like pattern appeared. In short: once we measure which slit the electron goes through, the interference pattern disappears; the electron stops behaving like a wave and behaves like a well-mannered particle. With tennis balls, by contrast, the pattern is always particle-like whether or not you “watch.”
Thus, as long as there’s no which-path measurement, the electron behaves like a wave; put a detector, and it behaves like a particle. Historically, after quantum theory was formulated, it also turned out that light isn’t purely a wave either. In some setups it behaves as discrete particles (photons). Newton returned from the dead, as it were.
The prevailing “Copenhagen interpretation” (associated with Niels Bohr and his school) concluded that the ontological distinction between “wave” and “particle” has lost its meaning. In micro-physics we don’t have two different kinds of beings, but one kind of being that sometimes behaves this way and sometimes that way—two different states of the same entity (photon or electron).
Quantum Theory: A Primary Interpretation
The picture physicists drew is this: as long as we don’t look (don’t measure), the electron is in a superposition—a sum of pure particle-states. A pure particle-state is one where the electron behaves like a tiny tennis ball: it has a definite position at every moment, and if we plot position versus time we get a well-defined trajectory. For example, the pure state “passes through slit A” we write as |A⟩, and the pure state “passes through slit B” as |B⟩. In both cases the electron behaves like a tennis ball.
But when we do not measure its position at the slits, the electron is in a superposition of these pure states: its “trajectory” is the sum of the trajectories, as if the particle goes through both slits. Hence it interferes with itself like a wave. Generally, an electron’s ordinary state is a combination of many such pure particle-states (not just two), each corresponding to a possible path. That’s why the overall pattern looks wave-like—the electron is “spread out” across space.
Once we measure its position, the state “collapses” into one pure particle-state making up the superposition (this is the “collapse of the wave function”). The wave function assigns probabilities to each pure state. Placing a detector at a slit is effectively conducting a lottery that selects one pure state from those composing the wave function, with probabilities given by the state’s coefficients. Without a detector, the particle remains “smeared” over all the pure states at once.
Symbolically we may write a two-state superposition as:
|ψ⟩ = α·|A⟩ + β·|B⟩
If we place a detector, the particle will be found going through |A⟩ with probability |α|² or through |B⟩ with probability |β|².
Ontic Ambiguity in Quantum Theory
Consider Schrödinger’s famous “cat in the box” thought experiment: a sealed vial of poison is triggered by a quantum process. The quantum state is a superposition of two simple (classical) states—vial open (poison released) and vial sealed. If open, the cat is dead; if sealed, the cat is alive. The cat’s state is thus a sum of “dead” and “alive,” not because it is both dead and alive in a simple mixture, but because its wave function is the sum of those classical alternatives.
Now note the difference from chaos. According to the usual interpretation, quantum mechanics here does not reflect epistemic doubt (our ignorance). It’s not that we don’t know which slit the particle passed or whether the cat is alive. Rather, the particle actually is in a sum of both alternatives, and the cat is in a sum of “alive” and “dead.” Probability in chaos reflected lack of knowledge; here, the distribution is a feature of reality itself. Even with a detector, the particle retains a non-zero chance for each outcome until measured; it has not been determined classically. Thus unlike chaos, quantum physics contains an ontic ambiguity: genuine indeterminacy in reality.
A helpful analogy: imagine a particle that can be yellow or blue. Measuring it yields either yellow or blue. Without measurement it is in a superposition of yellow and blue—not literally green (a mixture), but a sum of the pure color-states. If you pour a liquid containing many such particles into a beaker, you will of course see green (by the law of large numbers), but for a single particle the superposition is not a classical mixture.
Back to Determinism
In chapter 2 of my book The Science of Freedom I discussed whether quantum theory can “smuggle” free will into physics. Here we’ve found an ontic margin (ambiguity) within physics, not just an epistemic one as in chaos. Many claim the answer is yes. Briefly, I think not, for two main reasons. First, quantum effects manifest only on very small scales. A single neuron’s firing already lies far above the quantum scale. Second, quantum theory at most yields randomness (with a distribution over outcomes), but as noted, free choice is not randomness. In the quantum scheme, outcomes are governed by the coefficients (α, β in the equation above), not by human free will.
The upshot is: a libertarian must abandon strict physicalism—admit there is more in the world than matter and physical law—because within physics we don’t find room for genuine free will.
For Our Purposes
For our needs here it suffices to define an epistemic margin (doubt) and an ontic margin (ambiguity) in physics. I will use these in upcoming halakhic discussions, where this preface proves quite helpful not only in understanding the halakhic phenomena at issue, but also in making sense of the “mess” that reigns in quantum theory.
Notes (as referenced in the Hebrew original):
1) See chs. 9–10 of my book The Science of Freedom for more on free will.
2) “Chaotic” unpredictability is epistemic: with complete information and unbounded computation, a perfect predictor could in principle know the outcomes.
Discussion
Indeed. We’ll get to that in the next column.
Thanks for the fascinating column.
If I understood Frumer correctly, he argues that chaos is not computable (as opposed to your claim that it is simply complicated to compute), and nevertheless things can be calculated.
And then he projects the case onto the religious language of knowledge and choice.
And that is how he tries to escape the contradiction, by way of proving that this is possible and even happens in reality.
(That is, that there exists in reality a situation in which you do not know what the tiny causal factor will do, and nevertheless,{perhaps via the law of large numbers} you know what the outcome will be.)
If that is what he claims, he is mistaken. But he did understand chaos, so that is not what he claimed.
If that is what he claims, he is mistaken. He understood chaos, so that is not what he claimed.
In connection with the article (especially its beginning), I was always told that the difference between a case that is a psik reisha and a case that is not depends on whether there is uncertainty about what will happen in reality as a result of the act, or whether it is clear in advance what will happen. And I always found this difficult – after all, from the standpoint of reality itself there is no such thing as doubt, and if we knew all the data (for example – the weight of the bench, the moisture of the ground, and the angle of dragging) we would know how to calculate in advance whether there will be a furrow or not. So why does the point that we are not wise enough to calculate it prevent the case from being a psik reisha?
In the next columns
If we are discussing physics, it is worth noting that in the last ten or twenty years, the de Broglie–Bohm interpretation (the one that supports hidden variables, without indeterminacy, and is opposed to the Copenhagen interpretation) has been gaining significant momentum, mainly because of experiments that succeeded in reconstructing the trajectories of single photons fired through two slits—that is, obtaining the diffraction and interference pattern on the screen while at the same time knowing through which slit the photons passed (of course, the experiments “succeeded” subject to a few asterisks, footnotes, and certain reservations, but this is still significant progress). For details, you can google:
Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer
Since I am not a physicist, I am taking my life in my hands to ask a question that may be completely foolish and stem purely from ignorance.
You claim that even a neuron is too large in quantum terms, and therefore quantum theory cannot serve as a basis for free choice. My question is whether this is necessarily so. That is, might it be that even though the neuron’s response to some stimulus expresses a process of chaos that is seemingly completely deterministic, perhaps at the beginning of the process there is some single particle that set the process in motion from the start, and that particle is fully quantum. The analogy I can think of is a machine that has several codes that activate it. Each code causes the machine to perform a different action (or to choose from a defined set of actions for that code through a chaotic process), but the choice of codes is made through a quantum process.
I now recall that many years ago I asked a physics professor (who has since retired) exactly this question, and he nodded his head and said “maybe,” but was not willing to say anything definite one way or the other. Can you guess why he was not willing to say anything more decisive? (From my perspective, as a layman, either the answer is yes or it is no. Can the answer to a question also be in superposition?…). Or do you have a definite answer and disagree with him?
There is such a proposal by Rabbi Professor Yehuda Levi. In my book The Science of Freedom I explained why this cannot be. In large systems, the small effects get smeared out. For that not to happen, all the degrees of freedom would have to be coordinated, and that does not happen in noisy systems, only in liquids or conductors, and even there it happens only at extremely low temperatures. That is not the situation in neurons.
I will only mention my second argument: even if quantum effects were relevant to the neuron, that would yield randomness, not choice.
I have two questions, which I hope can be answered without teaching me the entire theory of quantum mechanics on one foot –
A. Can it be explained that the collapse of the superposition into one of the states is actually caused by the detector? I do not know how the detector works, but presumably it affects in some way the things it detects, and perhaps on the scale of an electron that effect is already critical.
B. Are such superposition realities indeed an ontic doubt, or do they simply reveal to us a limitation in the categories of thought? That is, could it be that Schrödinger’s experiment (if it existed literally) does not show that the cat is alive-dead, but rather that alive and dead are insufficient categories, and creatures can belong to neither of them?
A. It is commonly thought that the detector is what causes the collapse.
B. It is commonly thought that this is indeed ontic. It depends on the interpretations, which is why I wrote that I am following the accepted interpretation. That does not contradict what you wrote at the end. I tend to agree that what really exists is neither a wave nor a particle but some entity that has two kinds of states. You can call that a limitation of the categories of thought. But that entity can still turn into a wave or a particle from that very same state. There is an ontic doubt here.
Wonderful article. Waiting for part 2 🙂
It seems to me (though perhaps I am mistaken) that the following story should be brought in here:
R. Baruch Ber Leibowitz was discussing, in learning, with his students the sugya of “one who betroths one out of five.” In the heat of the argument one of the students said to R. Baruch Ber, “Here even the Holy One, blessed be He, does not know who the one betrothed is…” R. Baruch Ber turned completely pale and responded immediately and sharply: “Slow down. We only say, ‘It is not revealed before Heaven.’ What is written is written; do not go too far with words.”
Nice 🙂
Not-a-physicist, keep in mind that the problem does not end with this explanation, and laying the blame on the detector creates a new problem, around which there is also debate as to where exactly the measurement process occurs. In the detector or in the person? And where in the detector? Or where in the person? Perhaps the entire detector is also part of the observed system, and the retina in the human eye is the detector? In short, where exactly does the collapse of the wave function occur? This is called the ‘Heisenberg cut,’ and here too there are interpretations as to where it lies. For example, the extreme von Neumann approach claims that even the information-processing system in the human brain is part of the observed system, and measurement occurs only when the person actually becomes conscious of the result, and not before that.
There are also other approaches—for example, Renninger’s thought experiment from 1953, which shows how a wave function can collapse even without a measurement (this is an experiment in which the measurement was not actually performed, and yet one can infer the state of the system and collapse the wave function). The Einstein–Rosen paradox also relates to this; there too a particle collapses into a certain state even though no direct interaction was performed with it.
What is nice?
Mordechai, I join your view that on the face of it this is possible.
I raised this claim in the past in a comment on another post on the site, and a bit of discussion developed around it.
If you want, you can read it here:
https://mikyab.net/posts/66535#comment-34284
Do not put words in my mouth. I did not express an opinion; I asked a question. I am not a physicist, and I do not tend to express opinions in fields in which I am not an authority.
I am also not playing at humility here. In fields in which I feel firmer ground under my feet, I have not hesitated to go against Rabbi Michi, and at times sharply so (and he too, astonishingly enough, was not intimidated by me and did not flee to a monastery of the silent…). In this field my knowledge is limited, so at most I ask questions but do not express opinions.
Since my message appears to be nonsense, I will explain. To phrase it as “even God does not know” is a precise formulation and hits exactly the point. If one separates “Heaven” from God, one loses the whole idea (because if God knows, then it is an ordinary doubt). Admittedly, at first glance it sounds provocative, but it presents precisely the idea that the concrete knowledge (who is betrothed) simply does not exist (is not defined), and once you understand that, it completely stops being provocative. Did the Gemara not use similar formulations in order to clarify ideas? “My children have defeated Me,” “What does My son so-and-so say,” the dispute of the Holy One, blessed be He, and the Heavenly Academy, and Maimonides’ ruling there in halakhah 9 like the Heavenly Academy—is that lacking? Caution in correct formulations is relevant only if one fears mockery and demagoguery, but within the study hall that makes no sense, because there is no benefit in error. Therefore within the study hall they said without any problem, “Woe to me if I speak, for they will learn deceit and forgery; and woe to me if I do not speak,” and in the end they said, “for the ways of the Lord are upright,” etc. In short, not a nice story at all.
There is an article by Professor Yakir Aharonov in issue no. 4 of the scientific journal Odyssey that explains quantum theory in a way that, to the best of my understanding, matches the explanation here. He describes quantum theory mainly by a renewed explanation of the concept of time: unlike the usual understanding that the future develops from the present, the present and the past too are created as a result of the future. Consequently, although there is an ontic doubt regarding the present, this does not mean that one can actually choose in the present, but only that the future reveals retroactively what was in the past and in the present.
See there: https://www.teva.co.il/about-teva/social-responsibility2/odyssey/
The revered author here wrote as follows: “Nice,” end quote; and in the next column he wrote as follows: “Even the Holy One, blessed be He Himself, if asked, would not know how to tell us which of them is betrothed,” end quote. Understand this.
In the future, one should quote precisely, and then the question does not arise in the first place.
What the revered author wrote exactly was: Nice :).
Study this carefully.
If I understood correctly, the electron is an entity that has two states, and it cannot “turn into a wave or a particle from that very same state” – because in a situation without a detector it will turn into a wave, and in a situation with a detector it will turn into a particle.
If so, the only ontic doubt is in the situation with a detector – whether the entity will turn into a particle that passes through A or through B. Did I understand correctly?
This is a matter of interpretation. I tend to think as you do. In my opinion, in a situation where there is no detector, what we have before us is not a particle but a wave described by the wave function, and it indeed passes through both slits (more accurately: it is composed of the sum of the two particle functions). An ontic doubt exists only regarding which slit it will pass through after there is a collapse into a particle state. In that state we have a particle, and therefore there is room for doubt whether it passes through slit A or B, and that is an ontic doubt.
As for the story itself, I think it is right to direct our attention in another direction. R. Baruch Ber did not mean to emphasize that the information exists with the Holy One, blessed be He, in some personal secret vault and only “Heaven” and the Heavenly Academy are not updated. If that was indeed his intention, then the claim of the writer above is justified: we have done nothing except add a higher level to the epistemic lack of information. In my humble opinion, R. Baruch Ber meant to argue that our failure to grasp the way the Master of the Universe works means that it could still be that He has a position on the question of who is really betrothed, and yet this would still be a doubt about which there is no information anywhere. For the Master of the Universe is above place, time, and logic. He mainly intended to silence the student from saying things about which we have no tradition. (And see Rubin’s book, What God Can’t Do.)
That fits the distinction between “God does not know” and “the Holy One, blessed be He, would not know how to tell.” In my view it is still nonsense. Even the compromise Rubin proposed at the end of the book is nothing. Everything we say is mediated through our logic and our time. Nor is it clear how uprooting the difficulty with the little smiley helps. An ugly story. Only if it serves as a critique of etc. will it become nice. And one cannot say that the rummaging proves beauty in the manner of a peshar doubt.
The little smiley helps convey the criticism; sometimes it is preferable to a short, concise but opaque sentence.
How could the story be nice in your eyes?
The topic has been beaten to death and I have nothing to add. Everything written in the article here https://tinyurl.com/y2r8btkf is correct in my opinion. Just a few small Hinduizations on the margins. In Rubin’s entire book there is no additional theoretical contribution (that is correct) on this. The book is part of the above article with the history and genealogy of ideas.
A story that illustrates or argues something true in a pointed way is nice. A story that illustrates a failure is nice only as such, not in its content.
But I have troubled everyone quite enough on this marginal issue, and I hereby respectfully withdraw my hands.
Hello Rabbi,
There is something I did not understand – is a doubt that depends on a person’s choice, assuming there is free choice, an ontic doubt or an epistemological one? That is, is the doubt whether Reuven will decide to choose the tree or the pli (not what will come out in the end) an ontological one?
Epistemic. Consider the question regarding a choice that was made in the past; there it is certainly epistemic. There is no fundamental difference between the past and the future. If you ask what that person will choose, meaning a question about his current state before he chose, that is a somewhat different question, but here too there is no ontic indeterminacy. It is not a state in the present but nothing. When he chooses, there will be a choice.
Hello, can the page be fixed? The text does not appear, also in the follow-up column (323)
Strange. I passed it on to Oren the editor for him to take care of.
A beautiful column, thank you!
It seems to me that these points are difficult in relation to the laws of uncertainty, and to R. Shimon Shkop’s statement that when he betrothed several women, they are all betrothed; this is an ontic doubt and not merely an epistemic one. As opposed to a case where one betrothed one woman and it is not known who she is, which is an epistemic doubt, etc.