Ape in the coat

Karma: 1,277

Ape in the coat Mar 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 coat Mar 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 coat Mar 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 coat Mar 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 coat Mar 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 coat Mar 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:
$S a m p l e (2)$
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

Ape in the coatMar 26, 2025, 6:40 AM

10 points

7 comments9 min readLW link

Ape in the coat Mar 26, 2025, 6:03 AM
2 points
0
in reply to: cubefox’s comment on: Probability Theory Fundamentals 102: Source of the Sample Space
As soon as you have your axioms you can indeed analytically derive theorems from them. However, the way you determine which axioms to pick, is entangled with reality. It’s an especially clear case with probability theory where the development of the field was motivated by very practical concerns.
The reason why some axioms appear to us appropriate for logic of beliefs and some don’t, is because we know what beliefs are from experience. We are trying to come up with a mathematical model approximating this element of reality—an intensional definition for an extensional referent that we have.
Being Dutch-bookable is considered irrational because you systematically lose your bets. Likewise, continuing to believe that a particular outcome can happen in a setting where it, in fact, can’t and another agent could’ve already figured it out with the same limitations you have, is irrational for the same reason.
Similar to “Bachelors are unmarried”.
Indeed. There is, in fact, some real world reasons why the words “bachelor” and “unmarried” have these meanings in the English language. In both “why these particular worlds for this particular meanings?” and “why these meanings deserved designating any words at all” senses. The etimology of english language and the existence of the institute of marrige in the first place, both of which the results of social dynamics of humans whose psyche has evolved in a particular way.
The truth of a statement in general is determined by two things, it’s meaning and what the world is like.
I hope the previous paragraph does a good enough job showing, how meaning of a statement is, in fact, connected to the way the world is like.
Truth is a map-territory correspondence. We can separately talk about its two components: validity and soundness. As long as we simply conceptualize some mathematical model, logically pinpointing it for no particular reason, then we are simply dealing with tautologies and there is only validity. Drawing maps for the sake of drawing maps, without thinking about territory. But the moment we want our model to be about something, we encounter soundness. Which requires some connection to the outside world. And then there is a natural question of having a more accurate map and how to have it.

Ape in the coat Mar 25, 2025, 6:48 PM
2 points
0
in reply to: cubefox’s comment on: Probability Theory Fundamentals 102: Source of the Sample Space
I think the probability axioms are a sort of “logic of sets of beliefs”. If the axioms are violated the belief set seems to be irrational.
Well yes, they are. But how do you know which axioms are the correct axioms for logic of sets beliefs? How comes violation of some axioms seems to be irrational, while violation of other axioms does not? What do you even mean by “rational” if not “systematic way to arrive to map-territory correspondence”?
You see, in any case you have to ground your mathematical model in reality. Natural numbers may be logically pinpointed by arithmetical axioms, but a question of whether some action with particular objects behave like addition of natural numbers is a matter of empiricism. The reason we came up with a notion of natural numbers, in the first place, is because we’ve encountered a lot of stuff in reality which behavior generalizes this way. And the same things with logic of beliefs. First we encounter some territory, then we try to approximate it with a map.
What I’m trying to say is that if you are already trying to make a map that corresponds to some territory, why not make the one that corresponds better? You can declare that any consistent map is “good enough” and stop your inquiry there, but surely you can do better. You can declare that any consistent map following several simple conditions is good enough—that’s a step in the right direction, but still there is a lot of place for improvement. Why not figure out the most accurate map that we can come up with?
That’s a more challenging thing to formalize than just logic or probability theory.
Well, yes, it’s harder than the subjective probability approach you are talking about. We are trying to pinpoint a more specific target: a probabilistic model for a particular problem, instead of just some probabilistic model.
It would amount to a theory of induction. We would need to formalize and philosophically justify at least something like Ockham’s razor.
No, not really. We can do a lot before we go this particular rabbit hole. I hope my next post will make it clear enough.

Ape in the coat Mar 25, 2025, 4:50 PM
2 points
0
in reply to: cubefox’s comment on: Probability Theory Fundamentals 102: Source of the Sample Space
Degrees of belief adhering to the probability calculus at any point in time rules out things like “Mary is a feminist and a bank teller” to simultaneously receive a higher degree of belief than “Mary is a bank teller”. It also requires e.g. that if $P (A) = 0.6$ and $P (B) = 0.5$ then $0.1 \geq P (A \land B) \geq 0.5$ . That’s called “probabilism” or “synchronic coherence”.
What is even the motivation for it? If you are not interested in your map representing a territory, why demanding that your map is coherent?
And why not assume some completely different axioms? Surely, there is a lot of potential ways to logically pinpoint things. Why this one in particular? Why not allow
P(Mary is a feminist and bank teller) > P(Mary is a feminist)?
Why not simply remove all the limitations from the function P?

Ape in the coat Mar 25, 2025, 3:57 PM
2 points
0
in reply to: cubefox’s comment on: Probability Theory Fundamentals 102: Source of the Sample Space
Yes, that’s why I only said “less arbitrary”.
I don’t think I can agree even with that.
Previously we arbritrary assumed that a particular sample space correspond to a problem. Now we are arbitrary assuming that a particular set of possible worlds corresponds to a problem. In the best case we are exactly as arbitrary as before and have simply renamed our set. In the worst case we are making a lot of extra unfalsifiable assumptions about metaphysics.
You could theoretically believe to degree 0 in the propositions “the die comes up 6” or “the die lands at an angle”. Or that the die comes up as both 1 and 2 with some positive probability. There is no requirement that your degrees of belief are accurate relative to some external standard. It is only assumed that the beliefs we do have compose in a way that adheres to the axioms of probability theory. E.g. P(A)≥P(A and B). Otherwise we are, presumably, irrational.
Well, technically $P (Ω) = 1$ is an axiom, so you do need a sample space if you want to adhere to the axioms.
But sure, if you do not care about accurate beliefs and systematic ways to arrive to them at all, then the question is, indeed, not interesting. Of course then it’s not clear what use is probability theory for you, in the first place.

Ape in the coat Mar 25, 2025, 3:01 PM
2 points
0
in reply to: Viliam’s comment on: Probability Theory Fundamentals 102: Source of the Sample Space
You may assume that it’s the way how Albert managed to persuade Barry to continue)

Ape in the coat Mar 25, 2025, 2:44 PM
4 points
0
in reply to: cubefox’s comment on: Probability Theory Fundamentals 102: Source of the Sample Space
A less arbitrary way to define a sample space is to take the set of all possible worlds.
And how would you know which worlds are possible and which are not?
How would Albert and Barry use the framework of “possible worlds” to help them resolve their disagreement?
But for subjective probability theory a “sample space” isn’t even needed at all. A probability function can simply be defined over a Boolean algebra of propositions. Propositions (“events”) are taken to be primary instead of being defined via primary outcomes of a sample space.
This simply passes the buck of the question from “What is the sample space corresponding to a particular problem?” to “What is the event space corresponding to a particular problem?”. You’ve renamed your variables, but the substance of the issue is still the same.
How would you know, whether
$P (1) + P (2) + P (3) + P (4) + P (5) + P (6) = 1$
or
$P (1) + P (2) + P (3) + P (4) + P (5) = 1$
for a dice roll?

Probability Theory Fundamentals 102: Source of the Sample Space

Ape in the coatMar 23, 2025, 5:23 PM

12 points

17 comments7 min readLW link

Ape in the coat Mar 18, 2025, 6:08 AM
2 points
0
in reply to: Viliam’s comment on: Counting Objections to Housing
Thankfully rising land prices due to agglomeration effect is not a thing and the number of people in town is constant...
Don’t get me wrong, building more housing is good, actually. But it’s going to be only marginal improvement, without addressing the systemic issues with land capturing a huge share of economic gains, renting economy and real-estate speculators. These issues are not solvable without a substantial Land Value Tax.

Ape in the coat 17 Mar 2025 9:14 UTC
2 points
2
in reply to: Viliam’s comment on: Counting Objections to Housing
Yes, if you have 500 000 people in town, you need to produce food for 500 000 people all the time. While if you have 500 000 people in town, you only need to build houses for 500 000 once.
Unless, of course, some people who already have a house or people who do not even live in your town can buy houses in your town in order to use them as investment and/or to rent them to people living in your town. Thankfully, this is a completely ridiculous counterfactual and noone ever does that...
But the logic of “there is a shortage of X, therefore the proper solution is to ban the production of X and hope that the problem will magically go away” is insane either way.
For some things this logic is valid. See induced demand and attempts to solve traffic jams by building even larger roads. Now housing isn’t exactly like that, but neither its like food. This kind of appeals to simplified heuristics and resulting referent class tennis is non-productive.

Ape in the coat 13 Mar 2025 7:52 UTC
2 points
0
in reply to: Fraser’s comment on: You don’t actually need a physical multiverse to explain anthropic fine-tuning.
Suppose, someone comes to you and shows you a red ball. Then they explain that they had two bags one with all red balls and one with balls of ten different colors. They have randomly picked the bag from which to pick the ball and then randomly picked the ball from this bag. Additionally they’ve precommited to come to you and show you the ball iff it happened to be red. What are the odds that the ball that is being shown to you have been picked from the all-red bag?

Ape in the coat 13 Mar 2025 7:45 UTC
4 points
2
in reply to: Fraser’s comment on: You don’t actually need a physical multiverse to explain anthropic fine-tuning.
To put a bit of a crude metaphor on it, if you were to pick a random number uniformly between 0 and 1,000,000, and pre-commit to having a child on iff it’s equal to some value X—from the point of view of the child, the probability that the number was equal to X is 100%.
Conditional P(X|X) = 1.
However, unconditional P(X) = ¹⁄_1,000,000.
Just like you can still reason about unconditional probability of a fair coin even after observing an outcome of the toss, the child can still reason about unconditional probability of their existence even after observing that they exist. They can notice it’s very low, and therefore be rightfully surprised that they exist at all and update in favor of some hypothesis that would make their unconditional existence more likely.

Ape in the coat 12 Mar 2025 12:53 UTC
5 points
0
on: You don’t actually need a physical multiverse to explain anthropic fine-tuning.
Imagine these factors didn’t work out for Earth, and it was yet another uninhabitable rock. We’d be standing on some distant shore, having the same conversation, wondering why Florpglorp-iii was so perfectly fine-tuned.
This is valid. Alice is doing the usual mistake of confusing P(One Particular Thing) with P(Any Thing from a Huge Set of Things) and Bob is right to correct her.
However, when we decrease the size of our Set of Things the difference between the two probabilities decreases. In the universe with billions of galaxies:
P(Life on at Least One Planet) is much much much higher than P(Life on One Particular Planet).
In the universe with only one galaxy the difference is not as dramatic. In the universe with only one solar system, with a few planets these probabilities become similar.
And so if Alice finds herself in such a universe it’s indeed rightfully surprising. As you’ve said yourself:
far more likely, you just get a few barren rocks circling a few billion times before their sun chars or consumes them.
On the other hand, if vast multiverse with many more planets exist then the difference between our two probabilities once again becomes high. So we would need to invoke multiverse to account for this kind of fine-tuning.

Ape in the coat 6 Mar 2025 5:09 UTC
2 points
0
in reply to: Lorec’s comment on: Re Hanson’s Grabby Aliens: Humanity is not a natural anthropic sample space
If you can’t generate your parents’ genomes and everything from memory, then yes, you are in a state of uncertainty about who they are, in the same qualitative way you are in a state of uncertainty about who your young children will grow up to be.
Here you seem to confuse “which person has quality X” with “what are all the other qualities that a person, who has quality X has”.
I’m quite confident about which people are my parents. I’m less confident about all the qualities that my parents have. The former is relevant to Doomsday argument, the latter is not.
And even if I had no idea about who my parents are I’d still be pretty confident that they were born in the last century not in 6th BC.
It may be helpful to distinguish the subjective future, which contains the outcomes of all not-yet-performed experiments [i.e. all evidence/info not yet known] from the physical future, which is simply a direction in physical time
Sure. But I don’t see how it’s relevant here.

Ape in the coat

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

Prob­a­bil­ity The­ory Fun­da­men­tals 102: Source of the Sam­ple Space

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

Probability Theory Fundamentals 102: Source of the Sample Space