Ape in the coat

• Ape in the coatApr 21, 2025, 4:49 AM

  2 points

  0

  in reply to: Rafael Harth’s comment on: Pre­dic­tion Mar­kets Are Mediocre

  I personally didn’t expect Trump to do any tarrifs at all

  Just curious, how comes? Were you simply not paying attention to what he was saying? Or were you not believing in his promises?

• Ape in the coatApr 21, 2025, 4:46 AM

  3 points

  −1

  in reply to: Steven Byrnes’s comment on: Pre­dic­tion Mar­kets Are Mediocre

  I think “mediocre” is a quite appropriate adjective when describing a thing that we had high hopes for, but now received evidence, according to which while the thing technically works, it performs worse than expected, and the most exciting use cases are not validated.

  I indeed used a single example here, so the strength of the evidence is arguable, but I don’t see why this case should be an outlier. I could’ve searched for more, like this one, that is particularly bad:

  In any case, you can consider this post my public prediction that other policy prediction markets would also follow a similar thread.

• Ape in the coatApr 21, 2025, 4:35 AM

  2 points

  0

  in reply to: quetzal_rainbow’s comment on: Prob­a­bil­ity The­ory Fun­da­men­tals 102: Ter­ri­tory that Prob­a­bil­ity is in the Map of

  I think the problem here is that you do not quite understand the problem.

  There is definetely some kind of misunderstanding that is going on, and I’d like to figure it out.

  It’s not that we “imagine that we’ve imagined the whole world, do not notice any contradictions and call it a day”.

  How it’s not the case? Citing you from here:

  When you are conditioning on empirical fact, you are imaging set of logically consistent worlds where this empirical fact is true and ask yourself about frequency of other empirical facts inside this set.

  How do you know which worlds are logically consistent with your observations and which are not? For that you need to hold them in your mind one by one with all their details and checks for inconsistencies. Which requires you to be a logically omniscient supercomputator with unlimited memory. And none of us is that.

  So you have to be doing something else. Only validate the consistency to the best of your cognitive resources, therefore—“imagine that we’ve imagined the whole world, do not notice any contradictions and call it a day”.

  It’s that we know there exists idealized procedure which doesn’t produce stupid answers, like, it can’t be money-pumped.

  Well, yes. That’s the goal. What I’m doing is trying to pinpoint this procedure without the framework of possible worlds which, among other things, doesn’t allow reasoning about logical uncertainty. I replace it with a better framework, of iterations of probability experiment that does allow that.

  The whole computationally unbounded Bayesian business is more about “here is an idealized procedure X, and if we don’t do anything visibly for us stupid from perspective of X, then we can hope that our losses won’t be unbounded from certain notion of boundedness”. It is not obvious that your procedure can be understood this way.

  The bayesian procedure is the same, we’ve just got rid of all the bizarre metaphysics and now explicitly talking about values of a function approximating something in the real world. What is not obvious for you here? Do you expect that there is some case in which my framework fails, where framework of possible worlds doesn’t? If so I’d like to see this example. But I’m also currious where such belief would even come from, considering that, once again, we simply talk about iterations of probability experiment instead of possible worlds.

• Ape in the coatApr 19, 2025, 7:20 AM

  2 points

  0

  on: What’s the Deal with Log­i­cal Uncer­tainty?

  In this post I’ve described a unified framework that allows to reason about any type of uncertainty be it logical or empirical. I would appreciate engagement from people who think that logical uncertainty is still unsolved.

• Ape in the coatApr 17, 2025, 5:18 PM

  3 points

  0

  in reply to: Knight Lee’s comment on: Six rea­sons why ob­jec­tive moral­ity is nonsense

  Are you arguing that the distinction between objective and subjective are “very unhelpful,” because the state of people’s subjective beliefs are technically an objective fact of the world?

  It’s unhelpful due to a an implicit (and in our case somewhat explicit) assumption that “subjective” and “objective” are in opposition to each other. That it’s two different magisteriums and things are either one or the other.

  why don’t you argue that all similar categorizations are unhelpful, e.g. map vs. territory

  Map and territory framework lacks this assumption. It’s core insight is that maps can and indeed quite often are embedded in the territory. Of course if one does not understand it and uses “map and territory” simply as synonyms to “subjective and objective” then it doesn’t matter which terms are used and they are equally unhelpful.

• Ape in the coatApr 11, 2025, 5:24 AM

  5 points

  1

  on: Six rea­sons why ob­jec­tive moral­ity is nonsense

  This debate seems hampered by a lack of clarity on what “objective” and “subjective” moralities are.

  Absolutely.

  Coyne gave a sensible definition of “objective” morality as being the stance that something can be discerned to be “morally wrong” through reasoning about facts about the world, rather than by reference to human opinion.

  That’s a poor definition. It tries to oppose facts about the worlds to human opinions. While whether humans have particular opinions or not is also a matter of facts about the world.

  The fault here lies on the terms itself. Such dychotomies as “objective/​subjective” or “real/​non-real” or “stance-independent/​stance-dependent” are very unhelpful. Artifacts of ancient philosophy which didn’t understand map-territory relations, treated mind and matter as separate magisteriums and therefore were tremendously confused about basically everything, unable to separate baby from the bathwater.

  I don’t think we need content on LessWrong that keeps perpetuating this confusion. Therefore, I’m downvoting this post even though I seem to agree with about 80% of it.

• Ape in the coatApr 10, 2025, 5:28 AM

  3 points

  0

  in reply to: Markvy’s comment on: Zom­bies! Sub­stance Dual­ist Zom­bies?

  Yes, you are correct! Thanks for noticing it.

Pre­dic­tion Mar­kets Are Mediocre

• Ape in the coatApr 2, 2025, 9:20 AM

  2 points

  0

  in reply to: milanrosko’s comment on: The g-Zom­bie For­mal Argument

  Actually… I will say it: This feels like a fast rebranding of the Halting Problem, like without actually knowing what it implies.

  Being able to rebrand an argument so that it could talk about a different problem in a valid way is exactly what is to understand it—not just repeat the same words in the same context that the teacher said but generalize it. We can go into the realm of second order logic and say that

  For every property that at least one program has, a universal detector of this property has to itself have this property on at least some input.

  Mind you, I wasn’t trying to prove you that I understand Turing’s proof. Previously, you claimed that your “argument follows exactly the same syllogistic structure (“If this, then that”) as Turing’s proof”. So I showed you what it actually is when an argument does follow the same structure. If what you are talking was just like that then you could simply do the same.

  How would a virus (B) know what the antivirus (A) predicts about B?

  By running a copy of antivirus software on its own code and checking its output. That’s a valid program.

  it’s unintuitive — almost so that it’s false.

  It can’t quarry an antivirus software.

  Why not? Anivirus software is a valid program, it has some code that can be executed on some input. You can include execution of this code on a particular input in your own program. If this is not intuitive for you, then maybe it’s you who do not understand Turing’s proof?

  But seems people here are not versed in classical computer science only shouting “Bayeism! Bayeism!”

  Well, I’m not making any claims about an average LessWronger here, but between the two of us, it’s me who has written an explicit logical proof of a theorem and you who is shouting “Turing proof!”, “Halting machine!” “Godel incompletness!” without going into the substance of them.

  Maybe there is an actual gear-level model inside your mind how all this things together build up to your conclusion but you are not doing a good job at communicating it. You present metaphors, saying that thinking that we are conscious, while not actually being conscious is like being a merely halting machine, thinking that it’s a universal halting machine. But it’s not clear how this is applicable. What does it even mean for a machine to have a belief about something? That’s not something Turing defines in his proof. It’s possible to formally prove that universal halting machine is impossible. Can you do the same for having consciousness? If you can—then just do it, that would be very helpful and allow us to talk about the substance, not just vibes.

  which is proven to be effectively wrong by the sleeping beauty paradox (frequentist “thirder’s” get more money in simulations.)

  Oh boy, do I have an opinion. Here you are wrong in three different ways.

  1. Disagreement in Sleeping Beauty is not between bayesianism and frequentism. Thirdism is not frequentist. Halfism is not bayesian. One can make a bayesian argument in favor of thirdism: how you learn that you are awaken ‘today’ which is, alledgedly, new information. Or frequentist argument in favor of halfism: how if we repeat the experiment a lot of times, in about ¹⁄₂ of such iterations of it, where at least one awakening happens, the coin is Heads.

  2. In general frequentism and bayesianism do not have disagreement of such kind. There are sitiations (unfair coin toss without any other details) where frequentist claim that probability is undefined, where bayesians are ready to assign a numerical value to it, but not ones where two different numerical values are assigned.

  3. While following lewisian halfers betting odds in Sleeping Beauty indeed performs terribly, double halfers do no worse than thirders. There are also some cases where thirdism gives very stupid answers, like betting on whether at least one of the awakening happens on Monday.

• Ape in the coatMar 31, 2025, 5:17 AM

  5 points

  1

  in reply to: milanrosko’s comment on: I, G(Zom­bie)

  You basically left our other more formal conversation to engage in the critique of prose.

  Not at all. I’m doing both. I specifically started the conversation in the post which is less… prose. But I suspect you may also be interested in engagement with the long post that you put so much effort to write. If it’s not the case—nevermind and let’s continue the discussion in the argument thread.

  These are metaphors to lead the reader slowly to the idea...

  If you require flawed metaphors, what does it say about the idea?

  Now you might say I have a psychotic fit

  Frankly speaking, that does indeed look like that. From my perspective you are not being particularly coherent, keep jumping from point to point, with nearly no engagement with what I write. But this can be an artifact of large inferential distances. So you have my benefit of the doubt and I’m eager to learn whether there is some profound substance in your reasoning.

• Ape in the coatMar 31, 2025, 4:59 AM

  7 points

  1

  in reply to: milanrosko’s comment on: The g-Zom­bie For­mal Argument

  So, essentially, it’s like trying to explain to a halting machine—which believes it is a universal halting machine—that it is not, in fact, a universal halting machine.

  Don’t tell me what it’s like. Construct the actual argument, that is isomorphic to Turing proof.

  Let me give you an example. Let’s prove that no perfect antivirus is possible.

  Let a perfect antivirus A be a program that receives some program P and it’s input X as arguments and returns 1 if P is malevolent on input X and 0 otherwise. And A itself is not malevolent on any input.

  Suppose A exists. Then there has to exist another program B with such code:

  if A(B, X) == 1:

  return 0

  else:

  V(X)

  Where V is a trivial virus, a program malevolent on any input.

  If A(B, X) == 0, then a virus is executed but A didn’t detect it. Which contradicts our premise.

  If A(B, X) == 1 nothing else is executed beyond program A on some input. So either A is malevolent on input B,X, or it is mistaken. Both options contradict or premise. Therefore A doesn’t exist.

• Ape in the coatMar 30, 2025, 8:57 PM

  3 points

  1

  in reply to: milanrosko’s comment on: The g-Zom­bie For­mal Argument

  If you are familiar with it, just say “yes,” and we’ll proceed.

  Yes.

• Ape in the coatMar 30, 2025, 8:42 PM

  3 points

  0

  on: I, G(Zom­bie)

  In The Terminator, we often see the world through the machine’s perspective: a red-tinged overlay of cascading data, a synthetic gaze parsing its environment with cold precision. But this raises an unsettling question: Who—or what—actually experiences that view?

  Is there an AI inside the AI, or is this merely a fallacy that invites us to project a mind where none exists?

  Nothing is preventing us from designing a system consisting of a module generating a red-tinged video stream and image recognition software that looks at the stream and based on some details of it sends commands to the robotic body. Now, it would be a silly and overcomplicated way to design a system, but that’s beside the point.

  If matter is merely a symbol within our conceptual models, does the claim that “matter precedes and governs mind” hold any meaning?

  Don’t confuse citation and the referent “Matter” is a symbol in our map, while matter itself in the territory. Naturally, the territory predates the map.

  If one insists that the software—the computational patterns and processes—alone constitutes the essence of the AI, then one leans toward idealism, suggesting that the “helpful assistant” might exist in a realm hierarchically above physical instantiation, beyond space and time. Conversely, if one asserts that only the hardware—the physical substrate—truly exists, then one aligns with materialism or physicalism, reducing the AI to mere excitations of electrical charges within the integrated circuits of the GPU.

  This seems to be entirely vibe based. You don’t need to lean idealist to talk about software.

  Drawing from the first incompleteness theorem, EN suggests that the brain, as a biological “good regulator”, operates most effectively when it generates unprovable formal falsehoods—one of which corresponds to the claim of experiencing consciousness or qualia.

  Incompleteness theorem implies the existence of either unprovable and true statement (if the system is incomplete), or provable and false statement (if it’s inconsistent).

  It seems that all the substance of your argument is based on a completely wrong premise.

• Ape in the coatMar 30, 2025, 8:19 PM

  3 points

  1

  in reply to: milanrosko’s comment on: The g-Zom­bie For­mal Argument

  “This, if I’m not missing anything” Yes you This is called a Modus tollens. We are not concerned about the boolean of each of the statements.
  

  1.
  ”if I’m not missing anything” it is likely you do let me explain. This is called a Modus Tollens. We are not concerned about Lisas logic as a boolean. We look each proposition its entirety. I advice you to read about Turings proof on the halting problem, because it is the same technique.

  I struggle to parse this. In general the coherency of your reply is poor. Are you by chance using an LLM?

  I appreciate the irony of utilizing it to argue against the existence of consciousness, but that’s not likely to result in a productive discussion.

  Again: The argument isn’t that Lisa is wrong, but that she cannot formally prove the truth of her own consciousness from within her own system — even if it’s true.

  That doesn’t seem to be your argument. You explicitly claimed that Lisa has to believe in a false thing in order to be incomplete. This is not correct.

  So: if Lisa asserts she’s not a P-Zombie, and the system generating that assertion is formally incomplete, then she cannot prove the claim she’s making — that’s the point. It’s a Modus Tollens structure: if she could prove it, the system would be complete — but systems like that cannot be.

  With this I agree, but, once again, this is not what your argument was saying. You were talking about assertions that Lisa makes, not about her ability to prove things. And as soon as we start talking about proofs it all adds up to normality:

  A. Lisa is not P-Zombie

  B. Lisa can’t prove that she is not P-Zombie

  C. Lisa is incomplete but consistent

  But EN argues that the illusion of qualia isn’t just propositional — it’s a functional artifact of modeling unprovable internal states. In other words, qualia-like evidence (subjective experience, introspective certainty, etc.) is what that kind of belief looks like from the inside.

  So what’s the argument then? Just saying magical words “functional artifact” does not work as one.

  That openness is perfectly valid — and EN doesn’t assume that no one is a P-Zombie.

  EN assumes that everyone is P-Zombie doesn’t not?

• Ape in the coatMar 30, 2025, 7:16 PM

  2 points

  0

  on: The g-Zom­bie For­mal Argument

  First of all, I think you are confusing incompleteness with having false beliefs.

  A. Lisa is not a P-Zombie
  B. Lisa asserts that she is a not P-Zombie
  C. Lisa would be complete: Not Possible ✗

  C doesn’t follow. Lisa would need to be able to formally prove that she is not P-Zombie, not merely assert that she is not one, so that completeness was relevant at all. Even then it’s not clear that Lisa would be complete—maybe there is some other statement that Lisa can’t prove which, nonetheless, has to be true?

  A. Lisa is a P-Zombie
  B. Lisa asserts that she is a not P-Zombie
  C. Lisa would be not complete: Possible ✓

  In this case Lisa is not incomplete, she is wrong. This, if I’m not missing anything, would actually make her complete: you can prove anything from falsehood, therefore you can prove Godel statement as well.

  Secondly, even if we grant the g-zombie premise this doesn’t explain the whole ellaborate illusion that our minds are alledgedly playing on us. If some logical neccesity required me to believe in a thing and not being able to conceptualize that this thing is not true, this doesn’t imply that the same logical necessity would create for me a lot of evidence in favor of this thing, that only I can observe. A simpler scenario is where no evidence matters at all for my conviction.

  Thirdly, while a lot of people dismiss the possibility of being a P-Zombie as a priori ridiculous, I’m, in fact, open to such possibility. I’m not sure what kind of argument can persuade me, but yours argument seem to be based on the assumption that no people are like that, which is clearly wrong.

• Ape in the coatMar 28, 2025, 7:07 AM

  2 points

  0

  in reply to: cubefox’s comment on: Prob­a­bil­ity The­ory Fun­da­men­tals 102: Source of the Sam­ple Space

  I think picking axioms is not necessary here and in any case inconsequential.

  By picking your axioms you logically pinpoint what you are talking in the first place. Have you read Highly Advanced Epistemology 101 for Beginners? I’m noticing that our inferential distance is larger than it should be otherwise.

  “Bachelors are unmarried” is true whether or not I regard it as some kind of axiom or not.

  No, you are missing the point. I’m not saying that this phrase has to be axiom itself. I’m saying that you need to somehow axiomatically define your individual words, assign them meaning and only then, in regards to these language axioms the phrase “Bachelors are unmarried” is valid.

  Moreover, I think neither of them is really “entangled” with reality

  You’ve drawn the graph yourself, how meaning is downstream of reality. This is the kind of entanglement we are talking about. The choice of axioms is motivated by our experience with stuff in the real world. Everything else is beside the point.

  Suppose you are not instrumentally exploitable “in principle”, whatever that means. Then it arguably would still be epistemically irrational to believe that “Linda is a feminist and a bank teller” is more likely than “Linda is a bank teller”.

  Yes. That’s, among other things, what not being instrumentally exploitable “in principle” means. Epistemic rationality is a generalisation of instrumental rationality the same way how arithmetics is a generalisation from the behaviour of individual objects in reality. The kind of beliefs that are not exploitable in any case other than literally adversarial cases such as a mindreader specifically rewarding people who do not have such beliefs.

  I don’t think we have to appeal to reality. Suppose the concept of bachelorhood and marriage had never emerged. Or suppose humans had never come up with logic and probability theory, and not even with language at all. Or humans had never existed in the first place. Then it would still be true that all bachelors are necessarily unmarried, and that tautologies are true.

  I think the problem is that you keep using the word Truth to mean both Validity and Soundness and therefore do not notice when you switch from one to another.

  Validity depends only on the axioms. As long as you are talkin about some set of axioms in which P defined in such a way that P(A) ≥ P(A&B) is a valid theorem, no appeal to reality is needed.

  Likewise, you can talk about a set of axioms where P(A) ≤ P(A&B). These two statements remain valid in regards to their axioms.

  But the moment you claim that this has something to do with the way beliefs—a thing from reality—are supposed to behave you start talking about soundness, and therefore require a connection to reality. As soon as pure mathematical statements mean something you are in the domain of map-territory relations.

  Moreover, it’s clear that long before the actual emergence of humanity and arithmetic, two dinosaurs plus three dinosaurs already were five dinosaurs.

  Territory behaved the way that we now can describe in the map as 2+3=5. But no maps existed back then. If we are in agreement about it, there is nothing substabtial to argue about.

• Ape in the coatMar 27, 2025, 6:26 AM

  2 points

  0

  in reply to: cubefox’s comment on: Prob­a­bil­ity The­ory Fun­da­men­tals 102: Source of the Sam­ple Space

  Yes, the meaning of a statement depends causally on empirical facts. But this doesn’t imply that the truth value of “Bachelors are unmarried” depends less than completely on its meaning.

  I think we are in agreement here.

  My point is that if your picking of particular axioms is entangled with reality, then you are already using a map to describe some territory. And then you can just as well describe this territory more accurately.

  I think the instrumental justification (like Dutch book arguments) for laws of epistemic rationality (like logic and probability) is too weak. Because in situations where there happens to be in fact no danger of being exploited by a Dutch book (because there is nobody who would do such an exploit) it is not instrumentally irrational to be epistemically irrational. But you continue to be epistemically irrational if you have e.g. incoherent beliefs.

  Rationality is about systematic ways to arrive to correct map-territory correspondence. Even if in your particular situation no one is exploiting you, the fact that you are exploitable in principle is bad. But to know about what is exploitable in principle we generalize from all the individual acts of exploatation. It all has to be grounded in reality in the end.

  Epistemic rationality laws being true in virtue of their meaning alone (being analytic) therefore seems a more plausible justification for epistemic rationality.

  You’ve said yourself, meaning is downstream of experience. So in the end you have to appeal to reality while trying to justify it.

• Ape in the coatMar 27, 2025, 6:10 AM

  3 points

  0

  in reply to: jwfiredragon’s comment on: Prob­a­bil­ity The­ory Fun­da­men­tals 102: Ter­ri­tory that Prob­a­bil­ity is in the Map of

  Ok, let me see if I’m understanding this correctly: if the experiment is checking the X-th digit specifically, you know that it must be a specific digit, but you don’t know which, so you can’t make a coherent model. So you generalize up to checking an arbitrary digit, where you know that the results are distributed evenly among {0...9}, so you can use this as your model.

  Basically yes. Strictly speaking it’s not just any arbitrary digit, but any digit your knowledge about values of which works the same way as about value of X.

  For any digit you can execute this algorithm:

  Check whether you know about it more (or less) than you know about X.

  Yes: Go to the next digit

  No: Add it to the probability experiment

  As a result you get a bunch of digits about values of which you knew as much as you know about X. And so you can use them to estimate your credence for X

  The first part about not having a coherent model sounds a lot like the frequentist idea that you can’t generate a coherent probability for a coin of unknown bias—you know that it’s not ¹⁄₂ but you can’t decide on any specific value.

  Yes. As I say in the post:

  By the same logic tossing a coin is also deterministic, because if we toss the same coin exactly the same way in exactly the same conditions, the outcome is always the same. But that’s not how we reason about it. Just like we’ve generalized coin tossing probability experiment from multiple individual coin tosses, we can generalize checking whether some previously unknown digit of pi is even or odd probability experiment from multiple individual checks about different unknown digits of pi.

  The fact how a lot of Bayesians mock Frequentists for not being able to conceptualize probability of a coin of unknown fairness, and then make the exact same mistake with not being able to conceptualize probability of a specific digit of pi, which value is unknown, has always appeared quite ironic to me.

  This seems equivalent to my definition of “information that would change your answer if it was different”, so it looks like we converged on similar ideas?

  I think we did!

  I’d argue that it’s physical uncertainty before the coin is flipped, but logical certainty after. After the flip, the coin’s state is unknown the same way the X-th digit of pi is unknown—the answer exists and all you need to do is look for it.

  That’s not how people usually use these terms. The uncertainty about a state of the coin after the toss is describable within the framework of possible worlds just as uncertainty about a future coin toss, but uncertainty about a digit of pi—isn’t.

  Moreover, isn’t it the same before the flip? It’s not that coin toss is “objectively random”. At the very least, the answer also exists in the future and all you need is to wait a bit for it to be revealed.

  The core princinple is the same: there is in fact some value that Probability Experiment function takes in this iteration. But you don’t know which. You can do some actions: look under the box, do some computation, just wait for a couple of seconds—to learn the answer. But you also can reason approximately for the state of your current uncertainty before these actions are taken.

• Ape in the coatMar 26, 2025, 9:52 AM

  5 points

  0

  in reply to: jwfiredragon’s comment on: Prob­a­bil­ity The­ory Fun­da­men­tals 102: Ter­ri­tory that Prob­a­bil­ity is in the Map of

  Is there a formal way you’d define this? My first attempt is something like “information that, if it were different, would change my answer”

  I’d say that the rule is: “To construct probability experiment use the minimum generalization that still allows you to model your uncertainty”.

  In the case with 1,253,725,569th digit of pi, if I try to construct a probability experiment consisting only of checking this paticular digit, I fail to model my uncertainty, as I don’t know yet what is the value of this digit.

  So instead I use a more general probability experiment of checking any digit of pi that I don’t know. This allows me to account for my uncertainty.

  Now, I may worry, that I overdid it and have abstracted away some relevant information, so I check:

  - Does knowing that the digit in question is specifically 1,253,725,569 affects my credence?

  - Not until I receive some evidence about the state of specifically 1,253,725,569th digit of pi.

  - So until then this information is not relevant.

  Unrelatedly, would you agree that there’s not really a meaningful difference between logical and physical uncertainties?

  Yes. I’m making this point here:

  We can notice that coin tossing is, in fact, similar to not knowing whether some digit of pi is even or odd. There are two outcomes with an equal ratio among the iterations of probability experiment. I can use the model from coin tossing, apply it to evenness of some unknown to me digit of pi, and get a correct result. So we can generalize even further and call both of them, and any other probability experiment with the same properties as:

  $Sample\left(2\right)$

  There is no particular need to talk about logical and physical uncertainty as different things. It’s just a historical artifact of confused philosiophical approach of possible worlds and I’m presenting a better way.

  logical uncertainty is where you could find the answer in principle but haven’t done so; physical uncertainty is where you don’t know how to find the answer.

  Even this difference is not real. Consider:

  A coin is tossed and put into an opaque box, without showing you the result. What is the probability that the result of this particular toss was Heads?

  This is physical uncertainty. And yet I do know how to find the answer: all I need is to remove the opaque box and look. Nevertheless, I can talk about my credence before I looked at the coin.

  The exact same situation goes with not knowing a particular digit of pi. Yes, I do know a way to find an answer: google an algorithm for calculating any digit of pi and insert there my digit as an input. Nevertheless, I can still talk about my credence before I performed all these actions.

Prob­a­bil­ity The­ory Fun­da­men­tals 102: Ter­ri­tory that Prob­a­bil­ity is in the Map of