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That's your crux? Lesser interpretations than E won't do?

I am not convinced that E is logically coherent. It's as meaningless as "married bachelor".

Suppose that God's memory is the set of "all facts" O.
The set of all subsets (or powerset) of O, we'll call p(O).

Then, for any given fact f, there is a further fact f ' stating that it's either in or not in each subset of O in p(O).
Thus, there must be at least as many facts as there are elements of p(O), which, being the powerset of O, by Cantor's Theorem must have a strictly greater cardinality than O.
But we assumed that O contains all facts. Contradiction!

And Cantor's Theorem holds even for infinite sets! Q.E.D.

Did I just disprove God?

11

[ Question ]

I would like to try double crux.

by valentinslepukhin

10th Oct 2019

1 min read

11

Hello,

I would like to try double crux https://www.lesswrong.com/posts/exa5kmvopeRyfJgCy/double-crux-a-strategy-for-resolving-disagreement with someone. My statement A is "There is God" (I indeed believe in it, it is not just for the sake of trying the technique). I have three cruxes (well, two and a half, to be honest), according to the rules I do not publish it here so that you would prepare your cruxes independently.

Thank you!

11

I would like to try double crux.

4valentinslepukhin

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2valentinslepukhin

2Matt Goldenberg

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OK I'll bite. I'd also like to practice the technique. Shall we do this in the comments then? And would you consider trying this with more than one interlocutor? We could maybe rot13 "spoilers", if you like, but I'm not sure which parts you'd be concerned with.

Also, before we get started, the prerequisites must be observed. The first: Epistemic humility.

If there is God.
I desire to believe that there is God;
If there is not God,
I desire to believe that there is not God;
Let me not become attached to beliefs I may not want.
--The Litany of Tarski, for "The

... (read more)

7kithpendragon6y

I'd appreciate it if this was done publicly: I've never seen it done before.

4valentinslepukhin6y

Great! Ok, I am honestly reciting: If there is God. I desire to believe that there is God; If there is not God, I desire to believe that there is no God; Let me not become attached to beliefs I may not want. I say it, I mean it. Stop me if I appear to be attracted to the good effects of placebo more than to the truth. I am ok with many interlocutors, but you will need to explain how to use double crux in this case. And yes, let us do it here in comments. Do you have your cruxes already? If no, please do not read further. If yes, here are mine (go to the very bottom): 1. I believe that there are miracles. By the miracle I understand event or series of events that have either extremely low probability, seems to break the laws of Nature or have significantly higher probability to occur in the world with God rather than without. 2. I believe that the person can have contact with God through prayer. I would say - every person, but I am not that confident. 3. If the perception of the human mind is equivalent to the perception of the full-brain simulation, I believe that we live in the simulation (what is basically means that there is a Programmer who is like God). If the perception is not equivalent, I believe that it means indeducibility of the perception from the laws of Nature, what significantly increases my expectation that there is a God.

[-]Bird Concept6y150

Your cruxes are formulated as "Why do I believe what I believe?"

This is quite different from what seems to me important to get at in double crux -- "What would change my mind?"

For example, case 2 is only crux if it is true that: "Were you to believe that a person can not have contact with God through prayer, then you would change your mind and think there's no God".

Is that correct?

As a metaphor, think of a ceiling supported by a few walls. It's usually the case when constructing houses that not all walls are equally important to keeping the ceiling up. Some are merely decorative -- you can knock them over and put up a new one elsewhere, and the thing will be fine. But others are load-bearing -- if you take those walls down, the ceiling itself will come crashing in.

From experience, I find something similar happens with belief. For a given belief, I can often list many arguments supporting it. And those usually that take the form "I believe X". But it often turns out that most of them aren't actually the load-bearing reason I believe it. Because were I to knock them down and stop believing them, I still would not change my mind about X. To find the ones which are actually load-bearing, it's more useful to use as a search query "If false, would this change my mind?", rather than "Do I believe this?"

3Slider6y

1. Are magic tricks miracles because they seem to break the laws of Nature? Are lotteries miracles because they are extremely low probability? What counts as a law of nature? Does it factor human knowledge into it? Are superfluids an example of breaking the law of nature of liquids?

1Slider6y

3. What would you conclude about existence of god in the indistinguishable case? Would the programmer be god or would that be a separate entity? Do you think the perception is distinguishable?

1gilch6y

#3 has two branches. I agree that if mental things are ontologically basic, then supernatural explanations for things in general, including God, become more probable. But again this isn't nearly enough to establish your God in particular, as opposed to lesser spirits and whatnot. So it's not a crux for me. On the other branch, I do find it plausible that a full-brain simulation could be conscious, and that it follows that the apparent universe around us could also be simulated, because we have no access to the Universe outside of our perceptions. And then yes, there could be a programmer, which would qualify as being a Higher Power. But the Programmer seems to be incompatible with the Christian God. After all, the programmer could also have a programmer. And there could be multiple programmers who work on your simulation. Polytheism? And then there could be multiple instantiations of you in this moment. Run on different computers. Programmed by different Programmers. And because we're assuming reducible perception in this branch, there's simply no fact of the matter as to which one of them you are. They're bit-for-bit identical. Which Programmer is God? This branch is not a crux for me either.

1gilch6y

#2, as worded, assumes God exists, and so is begging the question. Obviously, if God exists, then it trivially follows that "there is a God". It can't be our Statement B if it is just an obfuscated Statement A. That's no progress. Just complaining about a fallacy seems uncharitable, so I'm trying to build a steelman out of this, but it's not working. If we remove "God" and replace it with "Higher Power", then it's no better than #1 as a crux. We still don't know it's your God we're talking to. If we remove "God" altogether, then we're talking about humans having psychic powers, which doesn't seem to help. Maybe you can word it better than I can.

1Slider6y

If you would have telepathic contact with a foreign intelligence would that make you think that other communication party exists? What would convince you that another person beside yourself was having communication contact with non-human intelligences? Do you lack the communcation potential to non-human intelligences? If yes that would be material disagreement whether every person can.

1gilch6y

The human mind is made of parts that can disagree or get out of sync. Auditory hallucinations are known to science, but telepathic communication is not. So on priors, I would first assume a hallucination. How can we distinguish these cases? At a minimum, I think the voice in your head would need to reveal things that it could not know simply from being inside your head. But even given that, if we're already assuming extrasensory perception for the telepathy, how do we know you're not hallucinating and clairvoyant as opposed to telepathic and in contact with an alien? Maybe it would help if said alien had multiple contacts, as this would seem to reduce the chance that they're all hallucinations, but only if the contacts independently agree about what the alien is saying. But if we're already assuming telepathy, how do we know the contacts aren't colluding telepathically behind your back? Maybe we would still need some outside confirmation the alien exists. Can we prove that people are telepathic but not clairvoyant? Can we prove that people are only telepathic with aliens but not each other?

1Slider6y

You are saying that you can totally communicate with a non-existent god so that point is only a single sided crux at the moment. I don't really understand the difference between clairvoyant and telepathic. Either the contact mechanism is know or unknown. If it is known we can argue what kind of entities can be in that kind of contact. If it is not known there is no point in differentiating between different types as the details could be anything.

7kithpendragon6y

While both telepathy and clairvoyance involve a mind gaining knowledge through means other than the known sense input modes*, telepathy refers to communication between two or more minds, whereas clairvoyance usually involves only one mind. One example of telepathy in pop culture is the Vulcan Mind Meld, where a Vulcan can achieve various levels of mind-to-mind communication through (apparently) touch alone. One example of clairvoyance in pop culture is Farsight, a Star Wars universe Force Power that allows the user to look at things that are not in their usual visual range. In this context, I believe gilch is suggesting that it would be difficult to discern between a telepath communicating with a remote (unseen) being and a clairvoyant whose mode of knowing is to hallucinate a conversation, but where no other being is present. *Known sensory modalities for living things on earth include but are not limited to vision, hearing, taste, smell, touch, balance, proprioception, time perception and magnetoreception.

0Slider6y

if the clairvoyant knows any thing ie their experience correlates to anything then the other being is present. But I guess it would be hopeless to establish how reliable the information channel is using that information channel only.

3kithpendragon6y

If you have an other being involved in any way the power isn't clairvoyance, it's telepathy. The problem is how to distinguish the telepath from the clairvoyant who interprets their unusual senses by hallucinating non-existent "voices" or some such.

1gilch6y

I do not believe in "miracles", in the sense that you probably mean, but if I somehow discovered I was mistaken about that fact, I still would not believe in God (though my prior would be higher than it is now). Therefore, #1 is not a crux for me. Miracles would be a necessary, but not a sufficient condition. (So this may be a co-crux for me.) All this would prove is a "Higher Power" of some kind, but the most likely Higher Powers on priors are not The one God in question, but AGIs or aliens, because these explanations do not require the burdensome details of the supernatural. And even if we are willing to entertain "supernatural" explanations (and, as I see it, we must, to include your version of God), then unspecified magical forces or lesser supernatural beings, like genies or even small-'g' pagan gods must be considered. Not to mention all of the big-G Gods of the wrong monotheistic religions.

1Slider6y

Do you believe in weak decay? Do you think weak decay is a low probablity event? Why does not weak decay fit within the sense of miracle here? Do you believe every kind of chess game that has played out has played out multiple times? If not why are the low frequency games not these low probablity event series? What kinds of events would be raised in probablity if god would exist? Would there be a separating signature from aliens and other fantasticals?

1gilch6y

I do believe weak decay happens. For an individual atom, perhaps weak decay is a low probability event, but the weak decay experiments have been repeated many many times. Low probability events happen all the time. Low probability, but that's no miracle. Any car you see should have a unique license plate. I am having a very hard time coming up with any evidence that could distinguish the God in question from other far more probable higher powers.

2Slider6y

If the evidence would be exactly the same for god as for other things shouldn't it be equally likely to be god rather than less likely?

5gilch6y

Definitely not, because they do not start out with equal priors. That's just Bayes. Every conjunctive detail can only decrease the prior probability, which is the principle known as Occam's Razor. The God in question is a highly conjunctive claim with lots of burdensome details. Note also that "The Orthodox Christian God" may have a similar prior to other monotheist's Gods, when taken individually, but it can't really be bigger than the set of monotheistic Gods as a whole, which can't be bigger than the set of gods as a whole, or the set of supernatural creatures as a whole, or the set of unspecified supernatural forces as a whole, as each successive set contains the former set. And if we cut out the burdensome detail of "the supernatural", then we're left with natural higher powers like alien teenagers, which is still plenty unlikely on priors, but is at least known to be possible based on established science. We haven't even established that the supernatural exists at all.

2Slider6y

I think in your treatment between different monotheistic gods there would be evidence that would favour one god over another even if both start similarly dysmally low. However if you had two gods and they are indistinguishable from aliens then they should not be distinguishable from each other. I guess there are two senses in that in "evidence we currently have" vs "evidence that could ever exist". Like I would think that god hypothesis would not have increased probability for flying saucers. But if god doesn't raise the expectation of saucers does god raise the expectation of anything? If it doesn't raise the expectation of anything then there is nothing to disagree about because we don't mean anything.

1Slider6y

Do you have reason to believe that valentinlespukhin is in fact using a different definition than he explicitly provided here? The explicit definition was of the form a,b or c and you claim to believe that entities of type a exist. Why would you not believe that the disjunction exists?

1gilch6y

I'm sorry, you've lost me here? What are a, b or c? What entities of type "a" did I claim exist?

1Slider6y

Paraphrasing: By the miracle I understand event or series of events that have either: a) extremely low probability, b) seems to break the laws of Nature or c) have significantly higher probability to occur in the world with God rather than without. "Low probability events happen all the time" 'I do not believe in "miracles", in the sense that you probably mean' The sense in which you replied to "miracles" seems not to be able to be understood in the literal definition provided, so you either used your own private definition or did not believe that their definition was accurately spelled out. Now the discussion has shifted and there has been an additonal feature added that miracles are connected to christian worship. If you are assuming they have additional properties it might be fruitful to be explicit about them.

1gilch6y

Yes, I was responding to what I thought he meant instead of his literal wording there. That's why I included "in the sense that you probably mean". I don't think "low probability" by itself is sufficient to make an event a miracle, and was assuming there was more to it than that, like an apparent purpose for being that way, perhaps.

1gilch6y

We can use others as facilitators to help keep us on track. But Double Crux is a pairwise activity. If someone else bites before one of us changes our minds, then you would do it paired with an interlocutor other than me, as a separate thread. The double crux for each pair may be different, so you're just doing Double Crux twice. But I would be able to read the other thread to understand your position better.

So, has this attempt failed? From the comment thread it looks like the OP has made an honest attempt and read up and probably learned a fair bit, but I did not see anything like "aha, this is where we disagree" and, to quote the link in the OP

If B, then A. Furthermore, if ¬B, then ¬A. You've both agreed that the states of B are crucial for the states of A, and in this way your continuing "agreement to disagree" isn't just "well, you take your truth and I'll take mine," but rather "okay, well, let's see what the evidence shows."

4valentinslepukhin6y

We are still discussing :)

2gilch6y

It has been some time since the last comment. Are we still discussing now? I think I have found my crux: If it could be shown that a God belief was founded on a sound epistemology that * reliably produced good results, * reliably did not produce bad results. * And there is enough information available to apply the method. * And the method indicates that God likely exists. then I must conclude that God likely exists. (I will also not accept ad-hoc special pleading, like "take my particular God as an axiom" plus whatever method I'm already using.) So my statement B is * "Belief in God is not founded on a sound and reliable epistemology. If it were, that would change my mind about A." Is this also a crux for you? So your statement B would be * "Belief in God is founded on a sound and reliable epistemology. If it were not, that would change my mind about A." If so, it is our first double crux. I have to assume that it must be, otherwise, you are disputing one of my conditions and admitting that * your God belief is not sound and reliable, or * that we do not have enough information to conclude God exists, or * you think God is unlikely to exist. Then the next step would be to find a double crux for statement B.

3gilch6y

I have yet to find a crux for myself, much less a double-crux, but not for lack of trying. I have maybe identified co-cruxes, that is, obstacles that would be necessary to overcome for me to believe in God as defined, but which individually proving would not be sufficient to prove God to me. Perhaps that is progress. Trying to summarize, I don't think we've exactly nailed down what "God" means, but I think establishing at least the possibility of each of the necessary attributes of God would be a co-crux (because God as defined must have all of them). Necessary attributes we've identified so far include * "omnipotence" (in the limited sense of being able to alter a simulation, and actually doing so), * being a "mind" rather than a simple law of nature, and * "omnibenevolence", which runs into the problem of evil, and the problem of defining evil. I haven't heard back enough on "omniscience" to know what definition we're using, but I am concerned that "infinite knowledge" must exclude God a priori from the hypothesis space of any kind of induction, which rules out using evidence to prove God exists, because no finite amount of evidence can ever be enough to prove an infinite amount of knowledge. That may still allow some kind of deductive logical necessity argument though. And perhaps it can be weakened somehow as we have done for "omnipotence". Am I mistaken in my approach here? This is my first real attempt at Double Crux. Are these co-cruxes pointing to a crux I have that I'm not seeing? I'm not sure if we can find a double crux before we first agree on questions of basic epistemology. My interlocutor is studying the topic as I bring points up, but it does take time.

2valentinslepukhin6y

I am feeling that our crux is prior probability for God that we are discussing in the other thread. I think that it is a little bit smaller than no God hypothesis, and gilch thinks that it is infinitesimal.

[-]Matt Goldenberg6y20

I recommend against figuring out your cruxes in advance, as they might not be cruxes for the other person.
Finding a double crux often involves seeing what someone else holds as a crux, and seeing if that would change your mind.

1gilch6y

From the double crux article (Not really claiming to be an expert here): and We seek cruxes independently as a first step to avoid anchoring too soon, but there's no guarantee that the lists will overlap. Then we seek collaboratively, or so says the article, but it also acknowledges that the method is experimental.

1valentinslepukhin6y

Maybe you are right. For everyone who thinks it is better - my cruxes are in the bottom of my comment.

1gilch6y

Also from the double crux article: I'm floundering, so I'll read yours.

[-]valentinslepukhin6y10

I will leave for a few days - need to do my job and to learn everything you recommended. Thanks to everyone, see you soon!

Wait! Before I read your cruxes, let me say that I don't actually have a list of cruxes yet. That's not supposed to happen until Step 3. You may want to remove (or rot13) yours until we're ready to proceed.

Step 1 was "Find a disagreement with another person" (we've done that).
Step 2 is "Operationalize the disagreement".

While I acknowledge that the double crux method is a set of guidelines, not laws, I think the "Define terms to avoid getting lost in semantic confusions that miss the real point" is a component that we should not skip:

I do not understand yo

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4valentinslepukhin6y

First of all, let me apologize for two things. A) I am not a native speaker so I will have mistakes in my English, especially articles. So why "There is God", not "There is a God" - because of my English. B) I am pretty new here, so I simply don't know what is "rot13" and how can I do it. Second, about my statement A. The very specific statement that I actually believe is "The Eastern Orthodox Christianity has a correct description of God". But to discuss it here would be too complicated, since it has a lot of details. I don't think it makes a lot of sense to discuss Trinity before we agree on the question whether there is a God. So, let me be slightly more general than this very specific statement, but more specific that I initially was. There is the God. God is individual being (i.e., has personality). God is omnipotent in the naive meaning of this word (i.e., you do not simply generate the random statement X and add "God can do X" assuming it to be true; I would rather say He is omnipotent like programmer who can do whatever he wants within the simulation he runs - it would be not exactle what I mean but a good approximation).

1gilch6y

Must God be omniscient? Does He know all future events or just past ones? In His native plane or only ours (using the programmer analogy)? Does He know all the logical implications of His knowledge or is He limited by processing power? (If so why run a simulation at all?) Must God be greater than all other beings? All other possible beings? Or can God also have a God? Why not skip your intermediate God and pick the greater being to worship? (Again, I think the naiive interpretation is incoherent.) Is God a halting oracle? At what degree? Or if not (because halting oracles are in some sense "impossible"), how many digits of Chaitin's constant does He know? I'm not expecting an actual number here. These are rhetorical questions pointing out that any such number would be finite, and thus there are questions with answers that God does not know, and therefore, no matter what number you pick, in principle, beings could be greater than God.

1valentinslepukhin6y

I would say that God do not have a God, otherwise we would consider the second one as the true God. Regarding halting oracle, let me first read it and understand what is it.

1gilch6y

Knowing that the God in question is a Christian God might be enough to get started. But I am struggling to find even a single crux: a Statement B short of Statement A such that if I discovered B were true, I would also change my mind about A. My prior for the Christian God is extremely low. I can think of various statements that might be cruxes for the other side, such that if they were true, my estimation that a God exists would increase, but none of them increase it enough to make me think it could be more likely than not. Other explanations (e.g. some non-God Higher Power, like Alien Teenagers) always dominate. This means I must resort to co-cruxes, and it seems like a large number of them would be required. A large number of co-cruxes may indicate some reason behind them all that could be a crux. Perhaps writing them all out could help us find it.

1valentinslepukhin6y

Ok. Maybe you could think why is your prior for the Christian God is extremely low to find at least one crux? I mean there should be a reason for such low prior, and if you find it, it can be a crux. I can try to add more co-cruxes * I believe that there are not just random miracles but such that directly connected with Christian practice (like associated with objects of veneration or worship). * I believe that many of the New Testament books are reliable historical documents, written when they are said to be written, telling the true story with possible mistakes in minor details. I would prefer not to work with this co-crux because I am not a professor of Ancient Rome history, but if it is your choice that is ok. * Regarding my crux 3: I personally believe in the fact that perception of the human is not equivalent to the perception of the simulation. I can expand more on it. * I believe that if you will try hard you can have a contact with God. If you try and not succeed though I might always say though that you did not try hard enough or did not follow the instructions properly, and since I can't read your mind, it will be hard to persuade me.

4gilch6y

The reason for my low prior is Occam's Razor derived from Bayes' Rule. The God in question is, in your words, "too complicated [to discuss it here], since it has a lot of details", which makes It a highly conjunctive claim, which gives it a naturally low prior. There are two ways to overcome an extremely low prior: make the prior higher, by making the claim simpler or even disjunctive; or provide extremely strong evidence to support it. I do not know of any single piece of evidence or body of evidence that would add up to be that strong.

1valentinslepukhin6y

It would we helpful if there was some algorithm or formula that connects complexity with prior probability. Otherwise, I can say that probability decays logarithmically with complexity, and you will say that it decays exponentially, and we will get totally different prior probabilities and totally different results. Do you know if such thing exists?

1gilch6y

The simplest explanation for anything is "The lady down the street is a witch; she did it." Right? No? How is that explanation any worse than "God did it"? We can at least see that the lady down the street exists. The magic algorithm is Solomonoff's lightsaber. It's not realistically computable, but it does give us a much better sense of what I mean by complexity, and how that should affect priors.

1valentinslepukhin6y

Ok, so I have studied the Solomonoff's lightsaber. I used this blog https://www.lesswrong.com/posts/Kyc5dFDzBg4WccrbK/an-intuitive-explanation-of-solomonoff-induction Please correct me if I am wrong, but I feel that there is a ... well, not mistake... assumption that is not necessarily true. What I mean is the following. Let us consider the space of all possible inputs and the space of all possible outputs for the Turing machine (yeah, both are infinitely dimensional, who cares). The data (our Universe) is in the space of outputs, theory to test in the space of inputs. Now, before any assumptions about data and theory, what is the probability for the arbitrarily chosen input of length n lead to output with length N (since the output is all the observed data from our Universe, N is pretty large) - this is what is prior probability, correct? Now we remember the simple fact about data compression: the universal algorithm of compression does not exist, otherwise you would have a bijection between the space of all possible sequences with length N and length N1 < N, which is impossible. Therefore, the majority of the outputs with length N can not be produced by the input with length n (basically, only 2^n out of 2^N has any chance to be produced in such way). For the vast majority of these outputs the shortest input producing them will be just the algorithm that copies large part of itself to output - i.e., a priory hypothesis is incredibly long. The fact that we are looking always for something simpler is an assumption of simplicity. Our Universe apparently happened to be governed by the set of simple laws so it works. However, this is the assumption, or axiom. It is not corollary from some math - from math prior should be awfully complex hypothesis. If you put this assumption as initial axiom, it is quite logical to set incredibly low priors for God. However, starting from the pure math, the prior for this axiom itself is infinitesimal. The prior for God's hypothe

6gilch6y

No? Perhaps you were trying to do something else, but the above is not a description of Solomonoff induction. Where exactly is the faulty assumption here? In Solomonoff induction, the observations of the universe (the evidence) are the inputs. We also enumerate all possible algorithms (the hypotheses modeling the universe) and for each algorithm run it to see if it produces the same evidence observed. As we gain new bits of evidence, we discard any hypothesis that contradicts the evidence observed so far, because it is incorrect. What probability should you assign to the proposition that the next observed bit will be a 1? How should we choose between the infinite remaining models that have not yet contradicted observations? That's the question of priors. We have to weight them with some probability distribution, and (when normalized), they must sum to a probability of 100%, by definition of "probability". We obviously can't give them all equal weight or our sum will be "infinity". Giving them increasing weights would also blow up. Therefore, in the limit probabilities must decrease as we enumerate the hypotheses. ---------------------------------------- Can you? It's not enough that it decays; it must decay fast enough to not diverge to infinity. Faster than the harmonic series (which is logarithmically divergent), for example. Solomonoff's prior is optimal in some sense, but it is not uniquely valid. Other decaying distributions could converge on the correct model, but more slowly. The exact choice of probability distribution is not relevant to our discussion here, as long as we use a valid one.

2gilch6y

If the observation is in no way compressible, then there is no model simpler than the observation itself, and your prediction for the next bit can be no better than chance. Maybe you haven't observed enough yet, and future bits will compress. But there can be no agents in a totally random universe, because there is no way to predict the consequences of potential actions. We can rule that case out for our universe by the anthropic principle. That's right. So what is your alternative? Give up on induction altogether? That's completely untenable.

2valentinslepukhin6y

Ok, let me repeat more precisely so you would see if I understand all things correctly, and if not you would correct me. 1. We have the Universe, that is like a black box: we can make some experiment (collide the particles, look at the particular region of the sky) and get some data. The Universe can be described as a mapping from the space of all possible inputs (experiments) to all possible outputs (observations). To be very precise, let us discuss not observations of humanity as a whole (since you do not observe them directly), but only your own observations in a particular moment of time (your past experiments and observations are now coming from your memory, so they are outputs from your memory). 2. If there are 2^K possible inputs and 2^M possible outputs, there are totally 2^N = (2^M)^(2^K) possible mappings. 3. We can represent this mapping as an output for the universal Turing machine (UTM), which input will be our hypothesis. There are different realizations of the UTM, so let us pick one of the minimal ones(see Wikipedia). 4. There will be more than one hypothesis giving correct mapping. "Witch did it", "Dumbledore did it" etc. Let us study the probability that the given hypothesis is the shortest that reproduces correct mapping. (If we have more than one shortest, let's pick the one that is assigned to a smaller binary number, or just pick randomly). For such a rule, there is only one shortest hypothesis. It exists because there is a correct hypothesis "Witch did it" , that might be not the shortest, so we will just look for those that are shorter. 5. The probability for a hypothesis with length n be the shortest hypothesis for n < N is a priori not larger than 2^(n - N) since there are 2^N possible mappings and only 2^n possible hypothesis. 6. The antropic principle does not help here. You know that you perceive input and produce output, but you can't assume anything about future input and output - a priori. 7. Now you want to introduce the new p

1gilch6y

I'm not sure if this is all correct. What you're describing doesn't exactly sound like Solomonoff induction, but you do seem to have a grasp of the principles involved. Solomonoff induction does not discard any program that is consistent with the observation so far. But for any observation string there are an infinite number of programs that produce that string. There is a shortest one, an infinite class of that program prefixed by some whole number of no-operations (computations that undo themselves). And compilers implementing that same program in encodings of other programming languages. And interpreters implementing that same program in encodings of other programming languages. And entire universes containing people who happen to be simulating one of these (which may be considered an unreliable type of interpreter). And arbitrary nestings of any of the above any number of times. None of this is discarded. But again, the set is infinite, so no matter what distribution you choose, the probabilities after some point must decrease for it to converge. The point about the witch isn't that "witch" is a complex cost to encode in a program (although it is), but that "she did it" fails to compress the data at all, because you still have to encode what the pronoun "it" is referring to. Because a "witch" can be blamed for literally anything, adding a "witch" to the uncompressed hypothesis "it" adds no predictive power whatsoever. (If you can compress "it" some other way, then you can make predictions without the witch and she is useless to your model.) God, who can likewise be credited for anything (even what looks like evil--"all part of God's plan", or "God works in mysterious ways", right?) is the same as the witch: no predictive power over "it" whatsoever. And worse, God's complexity cost is not just relatively big like any intelligent mind (such as the witch) would be, but literally infinite if we say that God is omniscient: If God is a "halting oracle", then God is

2valentinslepukhin6y

" God, who can likewise be credited for anything (even what looks like evil--"all part of God's plan", or "God works in mysterious ways", right?) is the same as the witch: no predictive power over "it" whatsoever." Not exactly. First, I can predict that if I throw the stone it will fall down and stuff like that. A miracle may happen, but the probability for it to happen from nowhere is very small (also not zero). Second, I give higher probabilities to what is common place for miracles to happen (like myrrh-streaming icon mentioned above, or healing, or answer to the prayers). With no God hypothesis I must put to zero such probabilities, and if there is a God I keep them finite. So, first, such theory can predict something (whether predictions correct or not, it is separate thread discussion, I will go back to it when I have time from this thread). Second, the predictions do not always coincide with no God theory predictions (like deist theory, that there is a God that does not interact with the Universe) - so it is different theory. " And worse, God's complexity cost is not just relatively big like any intelligent mind (such as the witch) would be, but literally infinite if we say that God is omniscient: If God is a "halting oracle", then God is not even contained in the set of all computer programs, because He is not computable: He can't even be a hypothesis, only approximated. And to get a better approximation, you must use a longer computer program that encodes more of Chaitin's constant, which is provably not compressible by any halting program. Better approximations of God get bigger without limit. The approximate God hypothesis has literally infinitesimal probability--you can't escape it: The better the approximation gets, the less likely it is. " Hmmm. Indeed, you are totally right here. I actually never thought that incomprehensibility is directly connected with the omniscience. Thank you very much for this, it make me to reconsider a lot of things. We

5gilch6y

An update of beliefs! We are making progress. So are you weakening the original claim? You are no longer trying to persuade me of an omniscient being, but only a sufficiently knowledgeable one? Yeah, at this point, I think we may be talking about aliens, not God, but we're going to use your definitions of the terms. I personally wouldn't expect omniscience of a small-g "god". I don't really agree with that, and here is an illustration of why: Suppose I tell you that I have an aunt that owns a dog. I think most people would just believe me. Aunts are not at all rare, and neither are dogs. Maybe I could be lying to prove a point, but dogs are so common, that I probably could have picked another relative with no need to lie about it. Now, suppose I tell you that I have an uncle who owns a tiger. I think most people would not just believe that easily. There certainly are people who own tigers though. So maybe you'd be persuaded with a little more proof. Maybe I could show you a picture. That might help until you realize that you've only ever met me online, and have no idea what I look like. Maybe I'm not the man in the photo (I could be a woman for all you know), and maybe the owner is not my uncle. Maybe I could do a video chat with you and you could see I have the same face. That would help, but maybe I used Photoshop on the tiger picture to insert my face. At some point though, the evidence would be good enough, or you'd call my bluff. Now, suppose I tell you that I have a nephew who has a pet purple martian dragon. Your first impression might be, is that a Pokemon? A toy? (Even understanding what another person is saying requires some shared priors.) "No, I mean it's literally an alien creature from Mars," I say. Did he tell you that? Kids have wild imaginations. "No, no, I saw it." OK, we know life exists on Earth, there's no physical reason why it couldn't exist on other planets. It's not outside the realm of possibility, but you're going to need a lot more

1valentinslepukhin6y

Well, violation of Laws of Nature is violation of Laws of Nature, whether they applied to the remote drawing without any interactions or to star moving. If Steve can draw pictures on toast remotely he violates the Laws of Nature and the hypothesis that the Universe is completely controlled by the Laws of Nature, without any Higher Power, aliens, the guy who runs a simulation etc - is falsified. Now, going back to aliens vs God hypothesis. " The dragon is at least compatible with what we know of science. Magical powers, not so much. " The problem that compatibility of the hypothesis with what we know before is not an argument at all when we are talking about fundamental hypothesis (i.e., not "who stole my car" but the hypothesis explaining the Universe). Indeed, look at the history of Quantum Mechanics. Initially, a lot of scientists hated the idea that the probabilistic description of the Universe is fundamental, so they come up with hidden parameters idea. All they now before was deterministic. If you knew all the velocities and positions of all the molecules, you could predict everything exactly - but you did not, and here the classical probability was coming. So they just suggested the same idea for Quantum Mechanics. That actually everything is still deterministic, we just don't know hidden variables, and then the observation appears to be probabilistic. You do not need to invent modified Turing machine that would produce different input with different probability, you still good to have good old deterministic Turing machine. Looks much better, right? Then it appears that actually you can distinguish between these hidden parameters hypothesis and fundamentally probabilistic hypothesis - see Bell's inequalities. And the experimental test demonstrated, that there are no hidden parameters. QM is fundamentally probabilistic. Thus, the fact that we need to throw to the trash can all our current assumptions and build the theory based on new assumptions does not

1gilch6y

The alien hypothesis dominates the God hypothesis, because God is infinitely improbable, but aliens are only finitely improbable. You seem to be arguing that we can bias our prior to accept an approximate God at the very edge of the "width". I say the rights of Mortimer Q. Snodgrass are being violated. Why your God,

1valentinslepukhin6y

"You seem to be arguing that we can bias our prior to accept an approximate God at the very edge of the "width". I say the rights of Mortimer Q. Snodgrass are being violated." No. If you read the comment about the width of the function you can see that my argument is not about God at all, but about what we need from the hypothesis (predictivity). " The alien hypothesis dominates the God hypothesis, because God is infinitely improbable, but aliens are only finitely improbable. " No. We use the approximation, and approximation has the same size for both of them (we consider the case of comparing hypothesis "There is a God with such and such attributes" and " There are aliens forge us to believe that there is a God with such and such attributes"). The algorithm of construction of this approximation, though, is simpler for pure God's hypothesis (using the mere fact of its existence, not formulating the hypothesis itself, like we establish dualities between different types of string theories using that M-theory exists but without formulating it) since it does not require transitional link of "hidden aliens". "Why your God, " Suppose I tell you soon after the discovery of muon that there is another particle, like the electron, but with the mass 105.6583745 (24) MeV and lifetime 2.19698119(22) microseconds. You would tell me: "Ok I can assume that there is a particle like the electron, although I would put quite low probability to it. But to believe, that its mass is 105.6583745(24) MeV !? No, it is absurd - there is a trillion of other possibilities!" Of course. A priori possibility for all different gods is approximately the same. In total, they add to the prior probability that there is some God - and I was arguing that this prior probability is finite. Then, after you make an observation, you can discover more attributes of God and come to Allah, Christ, Flying Spaghetti Monster, Aliens or nothing beyond Laws of Nature.

2gilch6y

I'm not understanding this part. If we already assume that aliens and God exist (which is not allowed because it's begging the question) then of course it's simpler to assume God explains the evidence than to introduce the additional hypothesis that the aliens are also trying to fool us. But without committing the fallacy of begging the question, we are left with the conjunctive hypothesis of "aliens exist" and "they are trying to fool us" that dominates "there is an omniscient being" (which must have an infinitesimal prior), never mind all the other attributes of your particular God.

1valentinslepukhin6y

"that dominates "there is an omniscient being" (which must have an infinitesimal prior)" It must not, because the theory does not completely describe omniscient being, but states its existence. If your theory claim that the Universe is infinite (which can be true, we might live in the open Universe) it does not mean that your theory is infinite. Once again, how did you distribute priors? By how easy you can use the theory to make predictions. In both cases, hidden parameters or hidden aliens, you say: ok, let us keep our old assumptions, but introduce hidden thing Y that works such that our observations can be explained by X. X alone is not good - it requires to go from deterministic to random Turing machine (QM) or acknowledge that the theory exactly describing our observations can be infinitely large, while we can only approximate it. Y gives some hope to resolve it - to stay within deterministic Turing machine, or within finite though large theory of everything. However, in both cases using of Y is just "Y simulates X". Well, in my opinion you even do not need a Solomonoff's lightsaber here - simple Occam razor is enough to see that Y is redundant.

4gilch6y

Equivocation. The algorithmic (Kolmogorov) complexity cost of the conjunction of "simulated X" and Y is finite, but the "real X" is infinite, therefore, the former must be preferred by Occam's razor. "Simulated X" is a deception by aliens and is not a full halting oracle, but a finite approximation of one. It can't do everything the "real X" could. I do not believe that aliens are performing miracles, just that that explanation is infinitely more probable on priors than an omniscient God. The miracles you have pointed to so far are best explained as natural accidents or hoaxes, not nearly enough evidence to even suggest aliens.

1valentinslepukhin6y

Ok. Looks like we started to go on circle, sorry for not being clear enough. Let me try to explain once again. You have a lot of observation data. You have significantly more potential observation data you can gather. I was considered before that all the potential observation data as finite - however, I understood that it is not so, for example, if scientific breakthrough, aliens or God will turn us into the immortal creatures with every year increasing ability to gather, remember, and process information. So, you want to find a theory based on already observed data, that would predict the data that is not yet observed. I bet we both believe that it is possible to do, but with some limitations. 1. Does finite theory exactly predicting all data exists? (In a sense of the Turing machine). Since all the data is infinite, a prior probability for such theory would be zero - without any other assumptions. You can introduce strong assumption of predictivity, basically stating that such theory exists. However, I think that this assumption is too strong (based on a posteriori results of quantum mechanics where you can predict only the probability of the observation but not the definite outcome - so you can recover with your theory only part of the observed data). Instead I would suggest weak predictivity assumption: 2. The theory exactly predicting all the data is infinite (such infinite theories exist - for example "witch did it" where "it" is "all the data to be observed"); however, its finite approximations can predict some part of the data with some precision. You can try to make it stricter, saying: "Among all the finite approximations there is one with maximal predictive power" but I do not see any arguments for it. The prior expectations tells that you can increase the precision by increasing the length of the theory. Now, we would like to classify the finite approximations based on their precision and length. First, is just the reference to existence of exact

1gilch6y

Yes, I just started to notice that after re-reading this thread. It seems like we're talking past each other without understanding. For Double Crux to work, we're not supposed to aim for direct persuasion until after we've identified the double crux, or we'll get "lost in the weeds" discussing the parts that aren't important to us. Have we found it yet? I think we have not, and that's what went wrong here. I have yet to identify a single crux, but part of that might be because I don't understand your concept of God. I don't know what crux could possibly convince me your God exists, because I still don't know what "God" means (to you). I'm honestly not that familiar with the Eastern Orthodox tradition. Protestant sects are more common in my country. The God concept worshiped by the average churchgoer here seems laughably naiive, and logically incoherent, but it does have some differences with what you've described so far. And the apologists, even in my country, seem to have a different definition that the average churchgoer (in my country), probably because the naiive definition is so indefensible. It's motte-and-bailey rhetoric--a combination of bait-and-switch with equivocation. So I'll ask again: Is omniscience a crux for you? That is, if a source you would consider authoritative (the bishops, the Patriarch, archeology, visions from God, whatever it takes) explained to you that omniscience was not an attribute of God as He revealed Himself, but a later misrepresentation made by sinful philosophers, would you then say your God does not exist? If you answer, "Then my God still exists and is not quite omniscient as I had once believed," then omniscience is not a necessary attribute for your God definition, and there is no need to discuss it further, because it is not a crux. But, if you answer, "A 'God' that is not omniscient is no God of mine," then omniscience is a crux for you and we need to nail down what that means, because it might be closely related to a

3Raemon6y

I'm not sure this is part of the authoritative definition of doublecrux, but FYI the way I personally think of it is "Debate is when you try to persuade the other person [or third parties] that you're right and they're wrong. Doublecrux is when you try to persuade _yourself_ that they're right and you're wrong, and your collective role as a team is to help each other with that." (I don't think this is quite right, obviously the goal is for both of you to move towards the truth together, whatever that may be, but I think the distinction I just made can sometimes be helpful for shaking yourself out of debate mode)

1gilch6y

I'm not sure if anyone has an authoritative definition of doublecrux yet. But as this is my first real attempt at it, I appreciate guidance. We did open with the Litany of Tarski, but I might have lost sight of that for a moment. I maintain that I at least need to understand what my interlocutor is saying before I can conclude that he is right. Again, the Litany of Tarski: If a God exists, I desire to believe that is the case. An update for either side is a victory. But the goal is not to fool myself or give up, or give in to confusion. The update must be an honest one, or the whole exercise is empty.

1valentinslepukhin6y

Yes. Omniscience is a crux for me. Wouldn't the prior probability of God to exist be a crux for you? I.e., if you change your prior probability from infinitesimal to somewhat not negligibly small, would it change your position? At least the infinitesimal probability is a crux for me. Let me also notice that our positions do not completely cover all the spectrum of possible answers (it not exactly "A" or "not A" ). I.e., as far as I get you think the world is completely controlled by laws of nature, I think there is a God as Eastern Orthodoxy describe it. In between there are many other options: -simulation -aliens -Higher Power (includes my believe as particular case) -the world that is not describable by math fully but only approximately -and whatever else that just does not come to my mind It means that we can be wrong simultaneously.

1gilch6y

Getting past an infinitesimal prior to a tiny finite one is a long way from "more likely than not". But more simply, my prior is my position. If you get my prior belief for the proposition "God exists" over 50%, then you've won: at that point I've become a theist by definition (though maybe not a very confident one). This isn't a crux--It's the original proposition!

1valentinslepukhin6y

Errr not completely - you have prior and you have experience. For example, suppose you agree after long discussion that probability of God to exist is not infinitesimal but 0.01% . Ok, you are still more atheist than a theist. Then if you observe miracles you update it to much higher probability - but you can't do it if your prior is infinitesimal as now. What would you put your priors now for the following: -the Universe is completely describable by a finite set of laws, no other reality behind -the Universe is approximately describable by the finite set of laws, approximation improves with the length of the theory (need infinite theory to full description) -Universe is simulation -aliens -something else

1gilch6y

I don't consider this question well-posed. Physics seems to be working pretty well. But what do you mean by "Universe"? The part we can observe? Surely there's more to it than that. And "laws" can be dependent on context. The law that objects accelerate downward at 9.8m/s/s doesn't apply on Mars, but there's a similar law with a lower number and an underlying law of gravity connecting both cases. Laws that seem to be "fundamental" now are probably dependent on local conditions. The "symmetry breaking" observed in particle physics indicates this. And very simple rules like Conway's Life can produce very complex behavior, with emergent "laws", like "gliders travel diagonally". Is this law from a reality behind or in front of Life?

2valentinslepukhin6y

Ok, let us put it more strict. What are your priors that there exist a finite theory that can predict all our potential future observations exactly? And what are your priors that such theory does not exist and we can only use approximations? N.B. By all observations I mean ALL observations, including the results of measurements in QM (not just their probabilities, we observe results too, right?)

0gilch6y

I still don't understand. Are you asking if the universe is deterministic? Which sense of "exist" do you mean? Mathematically, where we can "have" imaginary things like infinite uncomputable sets, or physically, where we obviously can't construct an object corresponding to such a thing? Solomonoff induction cannot be run on real physics. It's an abstracted ideal that can only be approximated. Maybe quantum field theory predicts the motion of particles to an accuracy of eleven digits, but that doesn't mean you can use it to predict the weather. You don't have enough computing power, and you don't know the initial conditions to that precision anyway. Even AIXI, an ideal agent using Solomonoff induction (which can't be physically built), can only make probabilistic predictions based on observations made so far. There's always an infinite class of universes (hypotheses) that have produced the observations thus far, and they always disagree on the next bit. There's no need to invoke quantum physics here. Given what we already know of relativistic physics, it's always possible that a particle could approach at the speed of light and mess up your plans. Because it's moving at light speed, there's no way in principle you could have observed it to take it into account in advance. Even AIXI can be "surprised" by low-probability events like this, even in a deterministic universe (because it has only observed a small part of the universe so far), and it has infinite computing power!

1valentinslepukhin6y

Well, of course I do not suggest to predict the weather from the laws of QFT, I mean mathematically. Let us consider all possible future observations as a data. Do you think that it can be exactly generated by the theory of the finite length (as an output of the universal Turing machine with the theory as an input), or you would require an infinite length of the theory for the exact reproducing?

5gilch6y

* The observable universe probably has a finite number of possible states. * The laws of physics appear to be deterministic and Turing computable. Therefore, an infinite theory would never be required. (And this makes me sympathetic to the ultrafinitists.) The laws of physics can be mapped to a Turing machine, and the initial conditions to a (large, but) finite integer. There is nothing else. But I'm not sure that "all possible future observations" means what you think it means. In the MWI, any observer is going to have multiple future Everett branches. That's the indexical uncertainty. Before the timeline splits, there is simply no fact of the matter as to which "one" future you are going to experience: all of them will happen, but the branches won't be aware of each other afterwards. And MWI isn't even required for indexical uncertainty to apply. A Tegmark level I multiverse is sufficient: if the universe is sufficiently large, whatever pattern in matter constitutes "you" will have multiple identical instances. There is no fact of the matter as to which "one" you are. The patterns are identical, so you are all of them. When you make a choice, you choose for all of them, because they are identical, they have no ability to be different. Atoms are waves in quantum fields and don't have any kind of individual identity. You are your pattern, not your atoms. But, when they encounter external environmental differences, their timelines will diverge.

1TAG6y

Copies of you that arise purely from the size of the universe will have the same counterfacutal or funcitonal behaviour, that is they will do the same thing under the same circumstances...but they will not, in general, do the same thing because they are not in the same circumstances. (There is also the issue that being in different circumstances and making different decisions will feed back into your personality and alter it).

2gilch6y

I'm pretty sure I said that: I don't understand your point.

1valentinslepukhin6y

" * The observable universe probably has a finite number of possible states." Not so sure about that. For this you need at least 1. The Universe to be finite (i.e. you can not have open Universe, only the surface of 4d sphere). It is possible, the measured curvature of the Universe is approximately on the boundary, but the open is also possible. 2. The Universe to be discrete on microscale. Again, according to some theories it is the case, according to the others, it is not. So, I would say: "maybe yes, it is finite, but the prior probability is far from being 1 ". Side note: the Universe with finite number of states is quite depressive picture since it means that inevitably everything will just end up in the highest entropy state, so, the inevitable end of humanity. Of course, it contradicts nothing, but in this model any discussion of existential threats for the humanity (like superintelligence quite popular here) makes no sense since the end is unavoidable. " And MWI isn't even required for indexical uncertainty to apply. A Tegmark level I multiverse is sufficient: if the universe is sufficiently large, whatever pattern in matter constitutes "you" will have multiple identical instances. There is no fact of the matter as to which "one" you are. The patterns are identical, so you are all of them. When you make a choice, you choose for all of them, because they are identical, they have no ability to be different. Atoms are waves in quantum fields and don't have any kind of individual identity. You are your pattern, not your atoms. But, when they encounter external environmental differences, their timelines will diverge. " Could you please explain it in more details? I am confused. If I measure the spin of the electron that is in the superposition of spin up and spin down, I obtain with probability p spin up and with probability 1-p spin down. How to exactly predict using Tegmark multiverse when I see spin up and when I see spin down?

1gilch6y

I'm not saying that a Tegmark I multiverse is equivalent to MWI, that's actually Tegmark III. I'm saying that Tegmark I is sufficient to have indexical uncertainty, which looks like branching timelines, even if MWI is not true. See Nick Bostrom's Anthropic Bias for more on this topic.

1valentinslepukhin6y

Mmmm is explanation really that long that I need to read a whole book? Can you maybe summarize it somehow?

1gilch6y

Only if you're interested. I haven't actually read the whole book myself, but I have read LessWrong discussions based on it. I think the Sleeping Beauty problem illustrates the important parts we were talking about.

1valentinslepukhin6y

Ah, I think I got the point, thank you. However, it does not resolve all questions. 1. You can't deduce Born's rule - only postulate it. 2. Most important, it does not give you a prediction what YOU will observe (unlike hidden parameters - they at least could do it). Yes, you know that some copies will see X, and some will see Y, but it is not an ideal predictor, because you can't say beforehand what you will see, in which copy you will end up. So all your future observed data can not be predicted, only the probability distribution can be.

5gilch6y

Can't you? Carroll calls it "self-locating uncertainty", which is a synonym for the "indexical uncertainty" we've been talking about. I'll admit I don't know enough quantum physics to follow all the math in that paper. Yeah, in this scenario, the "YOU" doesn't exist. Before the split, there's one "you", after, two. But even after the split happens, you don't know which branch you're in until after you see the measurement. Even an ideal reasoner that has computed the whole wavefunction can't know which branch he's on without some information indicating which. More or less. You can compute all the branches in advance, but don't necessarily know where you are after you get there. The past timeline is linear, and the future one branches.

1valentinslepukhin6y

" Can't you? Carroll calls it "self-locating uncertainty", which is a synonym for the "indexical uncertainty" we've been talking about. I'll admit I don't know enough quantum physics to follow all the math in that paper. " That was super cool, thank you a lot for this link!

1gilch6y

Yes, according to our best current understanding of cosmology, the universe itself will eventually die (i.e. become unable to sustain life). Again the laws of physics are what they are and don't care what I want. But in the most likely scenarios, this will take a very long time. The Stelliferous Era (when the stars shine) is predicted to last 100 trillion years, and we're not even 14 billion years into it. Civilization may continue to extract energy from black holes for a time many orders of magnitude longer than that. It's not completely hopeless. Maybe in that time we'll figure out how to make basement universes and transfer civilization into a new one, as Nick Bostrom et al have argued may be possible. But even if we ultimately can't, shouldn't we try? Shouldn't we do the best we can? Wouldn't you rather live for over 100 trillion years than die at 120 at best?

1valentinslepukhin6y

" It's not completely hopeless. Maybe in that time we'll figure out how to make basement universes and transfer civilization into a new one, as Nick Bostrom et al have argued may be possible. " Yeah, you see then all the future possible observations data becomes infinite. " But even if we ultimately can't, shouldn't we try? Shouldn't we do the best we can? Wouldn't you rather live for over 100 trillion years than die at 120 at best? " Of course, we should try - because there is a chance that we can. Not because we would live 10^14 years and all die. We will count that we survive forever, or it will be pretty miserable 10^14 years without any hope.

1gilch6y

Not sure either, which is why I said "probably". Note that I said "observable universe", not "multiverse" or "cosmos". There are regions of the universe that are not accessible because they are too far away, the universe is expanding, and the speed of light is finite. This limit is called the Cosmic event horizon I think it is sufficient to say that the information content of the observable universe is finitely bounded. Space doesn't necessarily have to be made of pixels like some cellular automaton for this to hold. The Bekenstein bound is proven from Quantum Field Theory. How true QFT is, is another question, but experimental evidence proves that it is very true.

1valentinslepukhin6y

" Note that I said "observable universe", not "multiverse" or "cosmos". There are regions of the universe that are not accessible because they are too far away, the universe is expanding, and the speed of light is finite. This limit is called the Cosmic event horizon " On the one hand side, you are totally correct about it - assuming cosmological constant (lambda-term ) stays what it is. There are nuances however: -if we are forever in the de Sitter space (lambda dominated, as now) the universe is explicitly not time-invariant (simply because it extending). There is non-zero particle production rate, for example (analog of Hawking radiation). It means that we potentially can construct a "first kind perpetuum mobile" which means that we can get to any energy - infinite space for the observations. Unless this will start to have a screening effect on lambda-term. -If lambda desreases (or screened) the expansion may go back from lambda-dominated to matter-dominated, leading to its slowing down. In this case we can start observing areas of the universe that used to be beyond the horizon. Anyway, there are a lot of speculations what can be and what can not. Can we maybe agree that both prior probabilities: that all our possible future observations are finite and that they are infinite are not negligible? What about 1/2 for each, to start with?

1gilch6y

I worry we may be getting lost in the weeds again. We need to try and find cruxes. Is this related to a crux of yours? What exactly are you getting at? Even if time could be extended infinitely without the universe dying, there is no time at which the infinity has been completed. It's always finite so far. An "immortal" being with finite memory in infinite time will eventually forget enough things to repeat itself in a loop, living the same life over and over again. Can this be avoided? There are limits to any physical realization of memory. If you try to pack too many bits in a given volume of space, it will collapse into a black hole. And then adding anything more will make the event horizon bigger. Infinite memory requires infinite space and energy. Maybe with basement universes it could be done. They might have to communicate through wormholes or something. This is all very speculative, so I don't know.

1valentinslepukhin6y

Well we can also make infinite memory (as you suggested). But, ok, what would you put as prior probability that the theoretically possible observation data is infinite? Looks like you are not strongly against it, so what about something between 0.5 and 0.1? (Of course we can't strictly prove it right now). If you say "yes, this works" we can move on. If you would claim that this probability is also supertiny, like 10^(-1000) , I will continue to argue (well, yes, if we can not at all observe in all the infinite future infinite data, it does not make sense to talk about omniscient God). To show you what I am leading to: -if the total possible observation data is infinite, what is prior probability that it is exactly reproduced by finite hypothesis? I argue that it is infinitesimal -what is the probability that there exist such infinite hypothesis? I argue that 1, for example, "witch did (copypaste all the data)". Predictive force of this hypothesis is zero -we need predictivity so we assume that there are finite approximations that can partially reproduce the data. Such assumption is less strong than assumption of the finite exact hypothesis so it should be preferred. -therefore, we should use Solomonoff's lightsaber not on full theories, but on approximmations -consider two classes of approximations. The first gives exact predictions where it can and predicts nothing whee it can not. The second is weaker, it sometimes gives wrong predictions. Since the second is weaker, the priors for this are significantly higher. So, I would say, if observable data is infinite, most of our approximate theory have from time to time give wrong predictions -this does not say, of course, how often are these wrong predictions. If they are too often, such approximation is useless. -Basically, since predictions are laws of nature, wrong predictions are miracles. We should expect to them to exist but to be rare. -Talking about aliens. Infinite hypothesis "God with such attribut

3gilch6y

You are not a future hyper-mind made of basement universes and wormholes. You're a mortal human like me, with a lifespan measured in mere decades so far. Yet you claim to have knowledge of an infinite God. How did you come to this conclusion? By what method can you make such an assertion? Is this special pleading for a special case or do you use this method for anything else? Why should I consider that method sound and reliable? My best guess: you were indoctrinated in childhood by your parents and community, long before you were old enough to develop critical thinking skills of your own. For obvious survival reasons, children are very inclined to learn from their parents and elders. The memeplex of any of the old religions must be self-sustaining, or they wouldn't still be here. They include psychological tricks to produce fake evidence, to stop questions, to make empty threats. They include answers to your questions or at least pretend to. It became part of your identity. You later learned of the methods of science, but they didn't become a part of you the same way. You compartmentalized the lessons and didn't use them to update your old thinking. You sought out evidence to support your belief instead of trying to disprove it to see if it would hold up, like a scientist. Most people seem to use this method. You are not alone. And that's exactly the problem with it. People are using the same methods to believe in other religions that you already know to be false. How can that method be reliable if it so reliably produces the wrong answers? What makes you any different from them? Accident of birth. That's it. Your methods are the same. Maybe that's a crux for me. If it could be shown that a God belief was founded on a sound epistemology that reliably produced good results, instead of these obvious fallacies, I would have a much harder time dismissing the proposition as a fraud.

1valentinslepukhin6y

" You sought out evidence to support your belief instead of trying to disprove it to see if it would hold up, like a scientist. " 1. If I would do this I would never go to this website discussing this with you. Assume good intentions. 2. As you said, for infinitesimal prior probability no evidence is enough. That is what I am arguing here. If I get persuaded that probability is indeed infinitesimal, all my evidence are nothing. I can see resurrection of the deads and still it won't be enough then. 3. I can blame the same thing on you. I am not going to guess but there are so many stories of atheists who became atheists just because God didn't do what they asked. "I do not want to deal with such God that does not do what I want, therefore there is no God." Ok, let us go back to our business if you don't mind. " If it could be shown that a God belief was founded on a sound epistemology that reliably produced good results, instead of these obvious fallacies, I would have a much harder time dismissing the proposition as a fraud. " First, could you review the previous comment to see if you agree with the logic, and if not, what do you disagree in particular. Second, if you agree with this logic, you should acknowledge that there is not negligible prior probability that miracles exist in principle. You can claim that they are rare, and each time you do not observe the miracle you can say it is even more rare. Third, if you acknowledge that the miracles can happen, it is worth looking at the cases when someone claim them to happen in particular. If you have large organised religion (like Catholic, Anglican, Russian churches for example) you very often have special commitee (usually with scientists inside) that check if the miracle that people claim to be miracle, is indeed miracle. Very often they found it to be hoax or natural effect, but sometimes they acknowledge that this is indeed miracle. Other religions may also have miracles, as well as just someth

1gilch6y

A fair point. But I still think you are compartmentalizing. It's never enough for induction, performed correctly. But an a priori deductive argument maybe could work. I've heard theists attempt these arguments, but have not found them convincing. I am trying to find cruxes, not blame. I would rather leave our identities out of it and examine the question as objectively and impartially as possible. But your epistemology is extremely relevant in this case. It's the rights of Mortimer Q. Snodgrass again. I don't think the God hypothesis has enough going for it to even justify raising it to our attention. If we had started with a good scientific epistemology, this would not even be a question. Instead we started with a biased indoctrination, and have to dig ourselves out of it. It's the availability heuristic again. Who have you heard these stories from? It's probably not the atheists themselves! You can't trust the clergy to be honest about this topic. They believe atheism is damnation, and so must present it as a sin. But for those raised atheist with a scientific worldview, believing in God seems as silly as believing in Santa Claus or the Tooth Fairy. In my case, I was raised as a believer. My perspective changed due to an accumulation of a number of factors. The Problem of Evil was apparent to me in childhood. It introduced a doubt that I could not resolve. The biblical creation story also didn't align with what I read of science as a child. When I expressed my misgivings, my church told me that God was a God of Truth, and the teachings of the Church could not possibly contradict the Truth, once it was properly understood. So I withheld judgement until I could learn more. I held both the religious and the scientific worldview in my mind at once, in the hope that they could eventually be unified. I was compartmentalizing, but I was conscious that I was doing so. I could speculate and philosophize in either religious or scientific modes, and I knew which was

1gilch6y

Due to indexical uncertainty, we can always be surprised by low probability events. I don't see these as evidence of God though. Around in circles again, but is there a difference this time? Do we agree "fake alien God hypothesis" dominates "infinite God hypothesis"? When using induction? You don't seem to be disputing it. But is "approximate God" simpler than "fake alien God"? That depends! How good is your approximation of "infinite"? How complex are your aliens? But if you want to argue for a non-infinite God, that's OK with me, but even if you convince me, it won't be the infinite God you have convinced me of, but the finite approximation: Something more powerful than mankind, but not infinitely powerful. Something more knowledgeable than mankind, but not infinitely knowing... this sounds like you're describing advanced aliens. They're the same thing. I would then argue that the aliens are the reality and the "infinite God" is the approximation of them made by ignorant humans. Even I would be willing to call such aliens "gods" given certain conditions, but we're using your definition of "God". Can you convince me of approximately-God aliens? Maybe. My prior is not zero, but like the pet purple dragon from Mars, it would take a lot of evidence to convince me.

1gilch6y

It feels like we are going around in circles at this point. I'm not sure where the disconnect is. The set of all natural numbers is infinite, yet can be enumerated by a finite computer program (when run on an infinite computer, AKA, a Turing machine). There are many many other examples of infinite patterns enumerable by finite programs. And some of them, like "compute the digits of pi" seem pretty chaotic, yet their Kolmogorov complexity is small. One wrinkle, which you might be alluding to, is that no program with infinite output ever halts. This is true, but there are halting programs that can compute any finite prefix of pi. And like I said before, at no point is your observation infinite. It's always finite so far. The infinity is never completed. So the hypothesis "these are the digits of pi" is considered by Solomonoff induction, but maybe it looks like a weighted sum of a class of programs that say "compute pi up to the nth digit" for some n. These still compress quite well, (especially for compressible n's) so their Kolmogorov complexity is small. I don't think this is an obstacle for Solomonoff induction. Has Solomonoff induction got it wrong? Close but not quite? I would argue no. I don't believe uncomputable sets can physically exist. There are no perfect circles. The abstraction called pi is the approximation, for whatever algorithm physics is actually running, which Solomonoff induction would eventually find.

1gilch6y

The posterior becomes the next prior when updating again, so we still call it a "prior" even though this is not the same prior as before. Sorry for the confusion. My current prior is my current level of belief/confidence. Higher, yes, but (say) ten times almost nothing is still almost nothing. And that's only if the likelihood ratio for the evidence favors the hypothesis by that much, which it doesn't. That's right. No finite amount of evidence can overcome an infinitesimal prior. Your example "miracles" are evidence in favor of miracles existing (because we can hardly expect reports of miracles to be less common if miracles exist) but the likelihood ratio is very close to 1 because false positives (accidents, hallucinations, and hoaxes) are so common. On priors, these explanations are far more likely. That means your "miracle" reports are extremely weak evidence. I cannot lower my epistemic standards on this, or I would invite in flat-Earthers, UFO-ologists and various other conspiracy theorists, not to mention all the other religions who have similarly dubious paranormal claims. Why should I favor your paranormal claims over theirs? It's special pleading.

1valentinslepukhin6y

" but (say) ten times almost nothing is still almost nothing" Ok, cool. So if your prior will be one millionnth I will need just six miracles :)

1gilch6y

Strong enough evidence can overcome a very low prior, yes. And this doesn't have to take very many observations. But more instances do not necessarily stack like that. That can only happen to the degree they are independent sources. For example, suppose you write a dubious claim in a book, then you make nine more copies of the book. Does that make the claim ten times more likely to be true? What if it's a hundred thousand copies? Did that help? Of course it doesn't! You're re-counting the same evidence. The contribution of the nine books is completely screened off by the first; the new books have no new information. I think the cases of miracle reports like weeping icons are similarly not independent enough. A thousand weeping icons is barely more evidence than one. It just means that the hoaxers copied each other's scam. Furthermore, we already know that some similar instances of miracles were hoaxes. Shouldn't every new hoax report lower my prior that miracles are real?

1gilch6y

OK. What does "omniscience" mean? The root words translate to something like "all knowing". But what is "all", and what is "knowing"? What's the minimum qualification? Each successive option seems harder to prove: Option A: (sufficiently advanced aliens) God's knowledge isn't infinite or anything, just far beyond our current level. "Omniscience" is more metaphorical than literal. Option B: (semi-omniscient simulator) God can look up any past event in the world simulation, but isn't simultaneously conscious of all of them and cannot predict the future short of actually simulating it. He does not know all the logical implications of His knowledge and can be surprised by events. (Janet from The Good Place might be at this level.) Although perhaps he can rewind the simulation and try a different timeline, if He makes any changes, He can't always predict what would happen without actually trying it. He may also be ignorant of events in His native plane, outside of the world simulation. Option C: (halting oracle of the first degree) God is a halting oracle machine able to solve the halting problem for any Turing machine, but is unable to solve the halting problem for halting oracle machines like Himself. Option D: (higher-order halting oracle) God is a halting oracle machine able to solve the halting problem for any Turing machine, and halting oracle machines of some finite degree less than His own, but is unable to solve the halting problem for higher-order halting oracle machines like Himself, or those of any higher degree. There may possibly be beings of greater degree that know things God doesn't. Options A, and maybe B seem at least possible, but very very far from proven. Option C seems unprovable using any finite amount of evidence, but probably has a logically coherent definition. Option D seems unprovable even with infinite evidence, but again seems coherent. Or did you have some other option in mind? I don't know how to get past Option D without self-refer

1valentinslepukhin6y

Yes, I have option E: Everything. God just know everything, all the possible universes, - not calculating, just having them in His memory that is infinite. As I stated in the previous comment , there is no reason for the exact theory to be finite, while approximations can be finite (would you like me to copy it or you can find it?).

1gilch6y

That's your crux? Lesser interpretations than E won't do? I am not convinced that E is logically coherent. It's as meaningless as "married bachelor". * Suppose that God's memory is the set of "all facts" O. * The set of all subsets (or powerset) of O, we'll call p(O). Then, for any given fact f, there is a further fact f ' stating that it's either in or not in each subset of O in p(O). Thus, there must be at least as many facts as there are elements of p(O), which, being the powerset of O, by Cantor's Theorem must have a strictly greater cardinality than O. But we assumed that O contains all facts. Contradiction! And Cantor's Theorem holds even for infinite sets! Q.E.D. Did I just disprove God?

1quwgri6mo

Good evening. Sorry to bring up this old thread. Your discussion was very interesting. Specifically regarding this comment, one thing confuses me. Isn't "the memory of an omniscient God" in this thought experiment the same as "the set of all existing objects in all existing worlds"? If your reasoning about the set paradox proves that "the memory of an omniscient God" cannot exist, doesn't that prove that "an infinite universe" cannot exist either? Or is there a difference between the two? (Incidentally, I would like to point out that the universe and even the multiverse can be finite. Then an omniscient monotheistic God would not necessarily have infinite complexity. But for some reason many people forget this.)

3gilch5mo

The main idea here is that one can always derive a "greater" set (in terms of cardinality) from any given set, even if the given set is already infinite, because there are higher degrees of infinity. There is no greatest infinity, just like there is no largest number. So even if (hypothetically) a Being with infinite knowledge exists, there could be Beings with greater knowledge than that. No matter which god you choose, there could be one greater than that, meaning there are things the god you chose doesn't know (and hence He isn't "omniscient", and therefore isn't "God", because this was a required attribute.) I don't know how to interpret "all existing objects", because I don't know what counts as an "object" in your definition. Set theory doesn't require ur-objects (although those are known variations) and just starts with the empty set, meaning all "objects" are themselves sets. The powerset operation evaluates to the set of all subsets of a set. The powerset of a set always has greater cardinality than the set you started with. That is, for any given collection of "objects", the number of possible groupings of those objects is always a greater number than the number of objects, even if the collection of objects you started with had an infinite number to begin with. So no, this doesn't prove that an infinite universe cannot exist, just that there are degrees of infinities (and no "greatest" one). Naiive set theory leads to paradoxes when defining self-referential sets. The idea of "infinite" gods seem to have similar problems. There are various ways to resolve this. The typical one used in foundations of mathematics is the notion of a collection that is too large to be a set, a "proper class". ("Class" used to be synonymous with "set".) But later on in the discussion it was pointed out that this isn't the only possible resolution.

1quwgri5mo

"An infinite universe can exist." "A greatest infinity cannot exist." I think there is some kind of logical contradiction here. If the Universe exists and if it is infinite, then it must correspond to the concept of "the greatest infinity." True, Bertrand Russell once expressed doubt that one can correctly reason about the "Universe as a whole." I don't know. It seems strange to me. As if we recognize the existence of individual things, but not of all things as a whole. It seems like some kind of arbitrary crutch, a private "ad hoc" solution, conditioned by the weakness of our brain. As for God or Gods, then, hypothetically, in the case of the coincidence of their value systems and the mental interaction between them according to a common agreed protocol, these problems should not be very important.

2gilch5mo

I'm hearing intuitions, not arguments here. Do you understand Cantor's Diagonalization argument? This proves that the set of all integers is "smaller" (in a well-defined way) than the set of all real numbers, despite the set of all integers being already infinite in size. And it doesn't end there. There is no largest set. Russell's paradox arises when a set definition refers to itself. For example, in a certain town, the barber is the one who shaves all those (and only those) who do not shave themselves. This seems to make sense its face. But who shaves the barber? Contradiction! Not all set definitions are valid, and this includes the universal one, which can be proved to not exist in many ways, at least in the usual ZFC (and similar). There are two ways to construct a universal object. Either make it a non-set notion like a "proper class", which can't be an element of a set (and thus can't contain itself or any other proper class), or restrict the axiom of comprehension in a way which results in a non-well-founded set theory. Cantor's Theorem doesn't hold for all sets in NF. The diagonal set argument can't be constructed (in all cases) under its rules. NF has a universal set that contains itself, but it accomplishes this by restricting comprehension to stratified formulas. I'm not a set theorist, so I'm still not sure I understand this properly, but it looks like an infinite hierarchy of set types, each with its own universal set. Again, no end to the hierarchy, but in practice all the copies behave the same way. So instead of strictly two types of classes, the proper class and the small class, you have some kind of hyperset that can contain sets, but not other hypersets, and hyper-hypersets that can contain both, but not other hyper-hypersets, and so forth, ad infinitum. Personally, I'm rather sympathetic to the ultrafinitists, and might be a finitist myself. I can accept the slope of a vertical line being "infinite" in the limit. That's just an artifact of ho

1quwgri5mo

We can leave theology. It is not so important. I am more concerned with the questions of finitism and infinitism in relation to paradox of sets. Finitism is logically consistent. However, it seems to me that it suffers from the same problem as the ontological proof of the existence of God. It is an attempt to make a global prediction about the nature of the Universe based on a small thought experiment. Predictions like "Time cannot be infinite", "Space cannot be infinite" follow directly from finitism. It turns out that we make these predictions based on our mathematical problems with the paradox of sets. At the same time, the paradox of sets itself resembles the paradox "I'm telling a lie now". and, it seems, should look for a solution somewhere in the same area. If we think off the cuff, it seems to me naively that the very concept of "ordinary set" is composed in such a way as to lead to paradoxes. This is the problem of the concept of "ordinary set". This is not the problem of the existence/non-existence of physical infinity. Oh, okay. I don't really understand this topic. But as far as I know, not all mathematicians are finitists. So it seems that the proofs of finitism are not flawless. On the other hand, how is the problem of the set paradox solved in cosmological infinitism? Something like "The Infinite Universe may exist, but it is forbidden to talk about it as an object"? Because any attempt to do so will bring you back to the set paradox, if you take it seriously. "Talk about any particular part of the Universe as much as you like, but don't even think about the Universe as a whole"? This risks forming a somewhat patchwork model of the worldview. "It may exist, but you cannot think about it intelligently and rationally." One is reminded of Zeno's attempts to prove that one cannot think about motion without contradictions.

2gilch5mo

Finitism doesn't reject the existence of any given natural number (although ultrafinitism might), nor the validity of the successor function (counting), nor even the notion of a "potential" infinity (like time), just the idea of a completed one being an object in its own right (which can be put into a set). The Axiom of Infinity doesn't let you escape the notion of classes which can't themselves be an element of a set. Set theory runs into paradoxes if we allow it. Is it such an invalid move to disallow the class of Naturals as an element of a set, when even ZFC must disallow the Surreals for similar reasons? Before Cantor, all mathematicians were finitists. It's not a weird position historically. We do model physics with "real" numbers, but that doesn't mean the underlying reality is infinite or even infinitely divisible. My finitism is motivated by my understanding of physics and cosmology, not the other way around. Nature seems to cut us off from any access to any completed infinity, and it's not clear that even potential infinities are allowed (hence my sympathy with ultrafinitism). I have no need of that axiom. Quantum Field Theory, though traditionally modeled using continuous mathematics, implies the Bekenstein bound: a finite region of space contains a finite amount of information. There are no "infinite bits" available to build the real numbers with. However densely you store information, eventually, at some point, your media collapses into a black hole, and packing in more must take up more space. Physical space can't be a continuum like the "reals". It's not infinitely divisible. Measuring distance with increasing precision requires higher frequency waves, and thus higher energies, which eventually has enough effective mass to gravitationally distort the very space you are measuring, eventually collapsing into a black hole. Below a certain limit, distance isn't physically meaningful. If you assume an electron is a point particle with "infinitesimal"

1quwgri5mo

I don't quite understand how actual infinity differs from potential infinity in this context. Time in ToR is considered one of the dimensions of space. How can space be considered "potential infinity"? It subjectively looks like that to a forward-traveling observer. But usually we use the paradigm of objective reality, where everything is assumed to exist equally. Together with the past and the future, if we recall ToR again. Are we supposed to have a special case here, where we need to switch to the paradigm of subjective reality? I am familiar with the idea that "the information that enables us to act best is true", but it seems to me to be just a beautiful phrase, because in most cases, in order to develop a model that enables us to act best, we still have to be guided by "truth" in the old, ordinary sense. That is, we obtain some initial "atoms of truth" through experience, but later we have to take care of their logical consistency. And we are not quite right to call some high-level construction "truth", even if it works well, if it does not logically agree with the "atoms" we used to create it. This case is free from this problem, since practical verification in this area is impossible. But still, the feeling of some hypocrisy in front of oneself does not disappear. To admit at least in the edge of consciousness the possibility that "the Universe is not X" and at the same time use only "the Universe is X" in calculations - there is some kind of contradiction in this. This is either an act of doublethink (for an agnostic) or an act of politeness (for an ultrafinitist). The difference between repeating patterns could manifest itself if there were interactions between them. But here reality rather speaks in favor of ultrafinitism. If the hierarchy of complication of structures with interactions could continue to infinity (even at the cost of slowing down the interactions), then theoretically we could find ourselves at any level of the hierarchy. Then we most l

1valentinslepukhin6y

Well, your argument should be able to kill the concept of Tegmark mathematical multiverse then, so you can guess it is not a "silver bullet" :) Two possible answers: 1. You can not just change the word "mathematical universe" to the word "fact" in my definition E. "Mathematical universe stating that..." makes no sense for me. 2. Cantor's theorem is based on particular set axiomatic. However, there are different set theory axiomatics. Some of them allow universal sets https://en.wikipedia.org/wiki/Universal_set

1gilch6y

OK, that's a good point. I had not heard of the universal sets that contain themselves, which I thought would lead to contradictions. I'm really not persuaded by the MUH, but at least it's based on reasoned a priori arguments. Do you have similar a priori arguments for God? There's no way for evidence to ever be enough establish omniscience by itself.

1valentinslepukhin6y

" OK, that's a good point. I had not heard of the universal sets than contain themselves, which I thought would lead to contradictions. " Great, the update of belief :)

1gilch6y

Yeah, given New Foundations, I'm no longer confident that "omniscience" is a logical contradiction, but neither am I confident that it isn't. And I still think it would take an infinite amount of evidence to prove inductively, so you would need some kind of a priori argument for it instead (or why believe it at all?). That's one obstacle down, but still a long way to go.

1gilch6y

It took a great deal of evidence to nail down both the existence of new particles and their properties to that degree of precision. It's already strong enough to overcome a low prior, but due to mathematical symmetries in nature, some particles were even predicted in advance of experimental discovery. In other words, they had a high prior given what was known, which is why scientists were willing to go to the great expense of looking for them. We do not have any strong evidence for God, and assuming omniscience alone gives Him an infinitesimal prior, which means no amount of evidence could ever be enough.

1gilch6y

No. That is not fundamental at all. Bell's Theorem only rules out local hidden variables. The Many-Worlds Interpretation and De Broglie–Bohm interpretation are deterministic.

1valentinslepukhin6y

Yes it is for the observer. You can not deduce Born's rule from the ^HΨ=iℏ∂Ψ∂t. No interpretation of quantum mechanics can help you with it. " Bell's Theorem only rules out local hidden variables. " - ok. Do you prefer non-local theory then?

1gilch6y

Yes, MWI still has indexical uncertainty. This is a property of the observer, not the universe, which remains deterministic. But you can still simulate the wavefunction on a Turing machine and use it to make predictions, which was my point. It's in the space of hypotheses of Solomonoff induction. I don't really prefer non-local theory, but the laws of nature are what they are and don't care what I want.

1valentinslepukhin6y

Of course, the Universe as a whole is deterministic since it obeys Schreodinger equation. However, the only thing we have access to is observation, and the observation is probabilistic. You can not predict with the deterministic Turing machine, what is the outcome of the observation, only the probabilities for this outcome. Well, the laws of nature of course what they are. However, you can interpret it in different ways. You can say that there is fundamental probability, wavefunction, and all this stuff, as the most scientist do when they perform calculations. Or you can start introducing hidden non-local variables, that does not improve your predictions but just make theory more complicated. There was an April, 1st paper introducing particles as sentient beings communicating with each other superluminously to deceive experimentalists. It is your choice which representation you prefer, but I thought you wanted the simplest one.

1gilch6y

I think you completely missed my point about the toast. I was trying to be humorous by referencing an actual case, but one that I found especially silly. It's just pareidolia. It's the same as seeing animals in clouds. But which animal you see depends on which animals you're familiar with. Toast patterns are noisy, so are clouds. The human perceptual system is constantly trying to recognize what it knows in what it sees, and seems particularly good at finding faces. And we have a pretty good idea how this works. See DeepDream. Yes, I can see that the pattern resembles a human face, and a feminine one. But I personally think that the toast looks more like Abby Sciuto from NCIS than most Virgin Mary paintings.

2valentinslepukhin6y

Oh yeah I heard about this stuff too. No I do not consider pareidolia as miracle. Basically, I listed above (replying to what would disprove me) what I assume to be miracles. In short - stuff that not only one old lady claim to be miracle, not only few local priests and bishop, but special committee from the Church (after a certain investigation), and, a result, whole Church.

1TAG6y

If you apply that consistently, you get instrumentalism. Most people here aren't instrumentalists, and do care about theories that dont constrain experience., such as [MWI], MUH and the simulation hypothesis. If you are going to reject metaphysics, you should reject all of it.

1gilch6y

Sorry, what's a MEU?

1TAG6y

Typo for MWI

1gilch6y

OK, so when things behave as normally expected, that's just laws of nature, but whenever you're surprised we can blame it on the witch? This point is very important: The theory must make predictions to be knowledge--if your theory is equally good at explaining anything (like the witch), then you have zero knowledge, because it fails to constrain anticipation. The sword of prediction cuts both ways: In other words, how strong a piece of evidence should appear to you, depends on your priors; strength is not a property of the evidence alone. If you are claiming that your God hypothesis is not equally good at explaining anything (like the witch), and if you are (rationally) very confident that God exists, then you must have a weak expectation of seeing strong evidence the other way. That's a crux, right? What would be a big surprise to your theory? A corollary to conservation of evidence: Absence of evidence is evidence of absence, when the observation would be expected.

1TAG6y

"Laws of nature do not hold 100%" is a prediction. That's why atheists feel it necessary to argue against miracles.

1valentinslepukhin6y

Well, my expectations would decrease if some of the miracles I believe would be proven to be fakes or natural events. The miracles that I believe are not those that people believe locally, but those that the Church recognizes globally - usually they send a special commission to check if it is indeed miracle or just natural event (or fake). I would say, I put high probability that the miracles that was approved by this commission are indeed miracles, and if you demonstrate me that they are not it would decrease my probability. The miracles I can name: -different myrrh-streaming icons, as long as it passed the check by church officials not only on the local level -witnesses that are collecting for the canonization of saints. Each time when new person is canonized one of the main criteria is whether there are miracles by prayers to him. So it is quite large data of different witnesses. Most of them can be explained by coincidence or natural effects, however, there are more difficult witnesses such as very fast curing from disease that by doctor prognosis should have taken few orders of magnitude longer time (or should not have happen at all). -relics of saints. In some cases (quite often actually) when after long time the body of the dead person who is considered to be saint is taken back from the ground, it discovered to be not decomposed. It is not necessary condition - there are many saints who does not have it. However, it is interesting question, whether this effect is more often among saints that among usual people (taking into account only the cases when relics were taken from the ground after canonization, to exclude the bias). If it is indeed significantly more often, what can be the reason? Why would the situation be opposite on mount Athos, where non-decomposition of the body is considered to be a bad thing?

2TAG6y

Is that an argument against the Mathematical Universe Hypothesis? Wouldn't the ultimate ensemble have to include a halting oracle? Well, the relationship between infinite extent and infinite complexity is tricky. Everyone in the rationalsphere knows that pi has an infinite decimal expansion, and also that the digits can be generated by a finite program. "Every mathematical entity exists, and only mathematical entities exist" is likewise a brief compression of the MUH.

1gilch6y

You can't prove a halting oracle exists inductively. How could you? Solomonoff induction is doing induction perfectly, and a halting oracle is not even in the hypothesis space, because the space contains only computable functions, and the halting problem is not decidable. And even if it were, what use would that hypothesis be to you? You can't get any predictions from running a program on a halting oracle machine when you don't even have one. From the Wikipedia article: So this is a point that Tegmark himself considers fair. The CUH would not have a halting oracle.

1TAG6y

How is that relevant? It is perfectly possible for a mathematical universe to be a form of Platonic realism. Which implies that the MUH might.

1gilch6y

I find the MUH philosophically dubious. I also disagree with Wikipedia's characterization of the CUH as adding an additional hypothesis on top of MUH (I'm not sure if that's how Tegmark sees it, or if that was just an interpolation by the editor). Instead, the CUH is throwing out the dubious axiom that allows things like uncomputable sets to exist, which means by Occam's razor, I think the CUH is the simpler hypothesis. I don't exactly buy the CUH either, but I don't have a better idea. I disagree with your interpretation of "perfectly possible", but even if I hypothetically grant you that a halting oracle exists, how can an agent ever be rationally justified in believing that it does? It's something that takes an infinite amount of evidence to prove. The method clearly can't be induction.

0TAG6y

I think you are missing some things that are quite basic: essentially no one believes in things like the Mathematical Universe on the basis of empiricism or induction. Instead, Occams razor is the major factor. Note that by things like MUH include MWI. It is straightforwardly impossible to prove MWI or any other interpretation on the basis of evidence, because they make the same predictions. So the argument given for MWI is in terms of simplicity and consilience. Not many people here reject all reasoning of that type. Many reject it selectively. The simplicity criterion means MUH is preferable to CUH, since CUH has an additional constraint.

1[comment deleted]6y

1valentinslepukhin6y

Thank you! I will read and try to understand it

2gilch6y

I do not believe that Christians are at all special here. There are many other contradictory religious traditions that make similar claims to miracles, if you can even call them that. No miracle claim I know of will stand up to reasonable scrutiny, and if you are willing to lower your standards to accept them, then to be fair you must also accept the similarly-attested miracle claims of the other religions, a completely untenable position for monotheists who don't even attempt syncretism and categorically reject other gods as false. Not to mention the UFO sightings and various conspiracy theories that have similar levels of support.

3valentinslepukhin6y

I am not familiar with the miracles of other religions. I would even say I do not have a solid opinion about them. My idea of God does not forbid miracles outside Christianity. (It is not syncretism - it is just that the same God for some reason may do miracles for people outside Christianity too). I would even agree that really a lot of things that are considered to be miracles are not such. However, I can name a couple things I believe to be actually miracles. This, for example https://www.orthodoxhawaii.org/icons

5gilch6y

It's not enough that evidence be consistent with your hypothesis. To count in favor, it must be more consistent with your hypothesis than its converse. One of the key insights rationalists derive from Bayes is that you cannot ignore the false positives. You use both sides to compute the likelihood ratio. (Also, if you think that gods may be willing to perform miracles for other religions, that makes it very difficult to use miracles as evidence for your God in particular, as opposed to some other power.)

4gilch6y

I don't think you quite appreciate just how low my prior for your God is. It would take a miracle on the level of instantly teleporting the entire Solar System to the Andromeda Galaxy to even approach the quality of evidence required to establish that only a literally omnipotent being could have been behind it. And that still doesn't completely rule out alien teenagers using sufficiently advanced technology based on unknown physics! And even then, that would (tentatively) establish only one of the critical conjunctive attributes you say your God must have. Should God open the heavens and reveal Himself in a sacred vision, saying unto me "The Eastern Orthodox Church is the one true religion", then I still would not believe. My prior is that low. I already know that "visions" (hallucinations) can happen, and they can just as easily reveal the "wrong" gods. I know this because adherents of basically all of the old religions do claim at least this level of evidence, not just in the ancient past, but in the present day, and they still contradict each other. And the best you can do is a sweating icon? I am sorry, but that is just not going to cut it. This is exactly the type of "miracle" that I would expect to be an accident or a hoax. I don't claim to know exactly how this particular trick works, but "it must have been God" is not even in the running. Liquid myrrh is sometimes added to the egg tempera in the painting of icons. "myrrh" can also refer to other oils, like the kind that might be in treated wood. Cold objects can also collect condensation in humid air, and wood can wick it up through capillary action. The human nose can detect even trace quantities of fragrant chemicals, even if it's mostly water. That the paint is sweating ingredients it's literally made of can hardly be called miraculous. And that's just a possible natural explanation for an accident. Do you honestly think a competent stage magician couldn't produce a deception of a similar quality on

1valentinslepukhin6y

Well, ok we discuss priors later, I need some time to learn it. * why I don't think it is natural effect - well, simply because of the amount and the longitude. Everything that could been inside should have gone away. * why I don't think it is hoax. Well, it is more complicated. I would say the probability of it to be hoax is very low, and since my priors are not that low as yours, it works for me. Now why I estimate the probability of the hoax to be low: * 1. If you read the story attentively, you see that there was an icon like that before (pretty recently actually, last quarter of XXth century), there also was a person who discovered it and was traveling with this icon everywhere (the same as current person travels now). The previous person was killed and tortured, the icon disappeared. The murderers were not found. It would be quite crazy idea, knowing this story, to make this mystification. To put your life under risk for what? For stupid hoax? You must be crazy to do it. And this person (current keeper) serves in police, so he must have some regular checks of his phychological state. Finally, simply anecdotical evidence - I saw him once, he seems to be normal guy (of course, I am not a specialist, it is just slight decreasing of probability him being a psycho) * 2. If I would need to do such a hoax, I would put some source of myrrh inside, and refill it periodically. It can be done of course. I could even believe that it can be done such that observer, taking the icon, would not notice any difference from the usual icon. But is it possible to avoid X-rays somehow? They travel by plane, I bet they do not put icon into luggage (it is too precious). So they must go with it as hand luggage. There the custom, using X-rays, observe small vessels inside the icons and asks what is it. And it is done, the hoax is over. I will disappear from here for few days - need to do my job, and also learn everything you send to me.

6kithpendragon6y

That this is not the first time an icon has produced myrrh is actually evidence in favor of a hoax or natural event. In either case, it's happened before so it must not be all that difficult for the conditions to be right or to set it up. As for the plane, at least several explanations are possible. 1. The event could actually be natural. Microscopic quantities of myrrh are quite detectible, and could be seeping from the paints for quite some time. * I can easily imagine the effect being encouraged by spraying a fine mist of oil, water, alcohol, or some other mild solvent over the icon. This could even be passed off as maintenance of some sort. "Just keeping it fresh. Travel is so hard on these paintings, you know." * The paint could be formulated with an unusually high myrrh content for some reason. This would go a long way to explain why not all myrrh-containing paints do this. * The guy who travels with it might not even know how it really works, but actually believe that it's a miracle. 2. Perhaps the myrrh could be applied directly to the icon in some way that doesn't really show up on an x-ray scanner. "Be careful please! Of course it smells like that. Don't you know what this is?" 3. The vessels containing the myrrh may be small enough that airport security doesn't care. A little goes a long way, and people travel with essential oils all the time. I can think of several ways to produce a myrrh distribution system by carving small channels in the frame. These would likely not even show up at airport security, and could contain enough myrrh to last for quite some time. 4. The supply of myrrh could be shipped by another means, or in checked luggage. 5. Charter planes don't have nearly the security considerations that public planes seem to require. 6. The myrrh supply doesn't necessarily have to travel at all. Myrrh is, in fact, reasonably easy to get in many places. I understand that christian book shops, for example, routinely sell the stuff

1gilch6y

I don't think that word means what you think it means. Did you mean "latitude"? Hawaii has a more tropical climate because it is near the equator, not because it's near the prime meridian. Or did you mean "longevity"? Either way, you can't expect all oils to evaporate quickly like water, even in a warm or arid climate. It's true that there are some oils used in paint that dry quickly, but there are other oils that do not dry out, even after a long time. Or greedy. How about for money? Fame? There are known examples of hoaxes with motives like these. A policeman might be even less afraid of criminals trying to kill him, because he already has to deal with them. If I needed to perform such a hoax, I wouldn't have to modify the icon at all. The Roman Catholics tend to use statues instead of icons, and they have examples of those weeping too. I heard of one case where someone was caught applying the "tears" with a squirt gun. You don't need to carve channels or secret compartments for a hoax. It's enough to have a spray bottle and vegetable oil, which are available for purchase pretty much anywhere. And if you use a non-drying oil, you don't even have to re-apply it! It will stay "wet" long after water would have dried out. I don't trust church officials any further than I can throw them. They have a fundamental conflict of interest. Their loyalty is to the Church, not the truth. The fact that someone is a priest makes me even less likely to trust them. The Roman Catholics have been rocked by child sexual abuse scandals which have been all over the news in this country, and worse, they attempted to cover them up to maintain the Church's reputation. A cursory web search reveals the Eastern Orthodox seem to have similar problems for similar reasons. The Churches cannot be trusted to be honest with us. These officials are clearly not rationalists (if they were, I would not expect them to be religious!) I don't expect most of them to even be scientists. But even if the

1gilch6y

I don't claim to understand how consciousness works. But if you do have good arguments about it, I am interested.

1gilch6y

The Gospels are wildly fictitious in content and structure, written decades after the supposed fact at a time and place where average human lifespan was much shorter than it is now. In other words, a full generation after the supposed facts. They contradict established history, and even to the extent they don't, that doesn't establish any credibility for the more miraculous parts we are interested in. It would be like finding a comic book and claiming that proves Spider-Man must have existed because New York City did. Furthermore, read with a critical eye and modern knowledge, Jesus seems very ignorant of science. This is more consistent with a legend than an actual God. The earlier epistles don't even claim that Jesus was anything more than an angel seen in visions (i.e. hallucinations). Note that contradictory religions also claim to have visions.

1valentinslepukhin6y

Here I need more time.

1gilch6y

I also believe this, with some caveats. Note that pretty much all religions claim this, but make other claims that are contradictory, which means they can't all be correct. This technique, or variants will also work for other Gods, even pagan gods. Even My Little Ponies. These are examples of the watered-down Gods that I don't disagree exist. But I do disagree with other attributes ascribed to them.

3valentinslepukhin6y

Well ok I do not mean some kind of visions, voice etc. (I mean it can happen but I did not experience it). For me it is rather answers to my questions in form of quite unlikely coincidence. But this is for me, I would expect that it is individual.

2Slider6y

What would count as successful contact? Can an outside person verify that contact has happened? If someone would convince you that your contact was actually confirmation bias would you change your opinion or probablity in god existing?

1gilch6y

That sounds like simple confirmation bias. You notice the times you (coincidentally) get answers, and forget the many more times you don't. (And then wrongly credit God when He doesn't deserve it.) And of course seeking helps you find things, even when God is not involved.

3valentinslepukhin6y

I thought about it immediately after reading HPMOR :) . It is just seems to me still quite unlikely (if I would one time out of hundred correctly guess the natural number from the interval from 1 to 100 it would be absolutely a bias; but I feel that for me frequency is significantly higher than the probability).

8gilch6y

"I feel that for me" feels very wishy-washy for me. A feeling is not a statistic. It is very easy to misjudge frequencies and probabilities due to various well-known cognitive heuristics and biases. Credence calibration is a skill, and most people are bad at it. Are you writing these questions and answers down? Or are you relying on memory--the availability heuristic? Are you tracking the cases when the answers don't come to you? When the answer was wrong? If not, that sounds like confirmation bias. You need both sides to compute a likelihood ratio to evaluate evidence. If you keep seeking until you find the right answer, then obviously questions can only be "answered", or "not answered yet". That's just persistence, and I don't understand what you think God has to do with it. Do you track the time it takes to get answers? Have you seriously considered alternative hypotheses? I would expect that simply being mentally open to answers makes you more likely to notice them, even in unexpected places. Did you use experimental controls, like asking for God's guidance in some cases and not in others to see if it made any difference? How about asking pagan gods or deceased ancestors? How about asking your own subconscious mind to see if it's just openness? Did you look at base rates for other people? Did you ask for any kind of peer review of your methods? Are you keeping score with the kind of scientific rigor that could be peer-reviewed? You claim in your profile to have a scientific background. The scientific methods that I am describing should not be news to you. You know this stuff already, don't you? Science has developed these processes to avoid certain well-established epistemological failure modes. But religion tends to get mentally compartmentalized as a "separate magisterium". I'm suggesting that you also try to avoid these failure modes when thinking about God.

1gilch6y

Narrowing it down to a Christian God helps. (It does appear that we have a true disagreement.) But it does bring along a lot of historical and cultural baggage. In the interest of making it easier to find cruxes, I suspect that even if you discarded some of the burdensome conjunctive details, we may be left with a core set of attributes for a Being that we would both agree could be fairly called "God", such that if we removed any one of them, said being could not be called "God". In other words, there are probably many details such that if you discovered that you got them wrong (though some means you would consider authoritative), you would not abandon your faith. These details are not cruxes. Is "omnipotence" one of those necessary attributes such that if the Being in question did not have it, He could not be fairly called "God"? Or can that be discarded and replaced with a sufficient amount of "power"? Is "personality" one of those attributes? Must God have a mind to be "God"? Or can He be a Law of Cause-and-Effect with no will of His own? Can "God" be a rank or office that Beings may attain or abdicate? Is "omnibenevolence"? Or can God be morally neutral? Evil? Good to some degree, but imperfect? Are there others?

1valentinslepukhin6y

Omnipotence is necessary but only in a sense of programmer analogy. Personality is totally one of these attributes, otherwise it is just Laws of Nature Omnibenevolence - yes, but then we will need to define properly "what is love", "what is good" etc. We can do it if it is necessary.

2kithpendragon6y

I'm genuinely enjoying the idea of "limited omnipotence" right now. Not in a condescending way, but as an interesting paradox. Thanks for that! 🙂 Related thoughts: * Can God make a being greater than God? * Can God destroy God? * Can God take away God's powers? * Can we become or make beings at least as great as God? (In the Old Testament, God seems to worry about things like this on occasion. Else why strike folks down when they try?) I may as well also point out an old problem. Since we observe bad things in the world, God cannot logically be both omnipotent and omnibenevolent. Both are claimed by the church, though neither is demonstrated in the Christian Bible. That may well be one of my cruxes.

1valentinslepukhin6y

1) No, it is logically impossible (I think so). 2) 3) I don't know. I would say "can but will not because of omnibenevolence". 4) The thing in the Old Testament I understand as sarcasm from God. I would say we can become "lower gods". This problem requires the definition "what is good" first basically. For example, is it better to give the gift immediately, or to give the person a difficult task first, knowing that he is capable to do it, and then to give this gift as an award? When the person would feel better? Also, when you are saying it is your crux, do you mean the statement "omnipotent omnibenevolent God is incompatible with observed Universe" is crux for "There is no omnipotent omnibenevolent God" ? So if this statement is false you would believe that there is a God? :)

5kithpendragon6y

What I'm saying is "omnipotent and omnibenevolent God is logically inconsistent", or maybe a better phrasing is "omnipotence and omnibenevolence are mutually exclusive descriptions of a single entity given the condition of the universe I find myself in". An omnipotent being would be able to prevent all, to borrow a religious term, "evil" from happening and an omnibenevolent being would be compelled to do so. Since we observe evil in the world, God cannot be both. Despite this, God is so described. This is a very old problem called theodicy that the christian church tends to call a "mystery of faith", which is nothing but a semantic stopsign. So if you can show that there is no logical inconsistency here, I will consider my prior for "there is God" to be substantially larger than I currently do. Then you have to overcome the whole existence-of-supernatural problem, and show overwhelming evidence that "there is specifically God and not Krishna or Allah or Jehovah or Elohim or Ganesh or Zeus or Odin or... ... ..." Even those names referring to the "God of Abraham" are presented within their respective faiths as belonging to very different deities. In the end, given the "perfectly good" (in the colloquial sense) physics explanations available for everything I have ever personally observed, when it comes to God, I have no need of that hypothesis. So you'd still have to demonstrate that need.

2gilch6y

I pretty much agree with all of this. I can't believe in a God that is simultaneously omnipotent and omnibenevolent without a solution to the Problem of Evil. It's a logical contradiction. But a solution to the Problem of Evil is not sufficient to make me believe God exists. So it's a co-crux for me.

4Raemon6y

FYI, while I still do not believe in God, I was... actually just pretty satisfied by Scott Alexander's Answer to Job? [edit: epistemic status: haven't actually thought seriously about it tho. Also, someone just gave a plausibly convincing counter argument]

1gilch6y

I am interested in that counterargument. Can you summarize or link?

2kithpendragon6y

God is such a complex claim that I would need this part solved before even allowing that God exists within the space of all logically consistent hypotheses to be considered. I suppose that's less of a crux and more part of a prerequisite definition, come to think of it.

1valentinslepukhin6y

So, regarding the omnibenevolence - again, we first need to clarify what means "good" and "evil". So, first we need to get, if we have the same understanding of this, otherwise it is the argument about definitions. I am not sure if it is possible to give a precise definition, but let me ask few question to see if we have the same answer to them or we understand it differently. 1) Is "good" only utilitarian (i.e. for some higher purpose - then which one?) or deontological (i.e., there are some good things that are good by default. It is good to bring some joy to the life of the old person even if he is totally useless and senile - like that). 2) Is good only result or there can be some goodness in the process? Is there any goodness in striving and gaining, playing hard game and winning - or only final result is important? Regarding no need of this hypothesis - somewhere below there is a thread where we argue about miracles.

1kithpendragon6y

What if we use a specific example of evil, in lieu of hashing out a complex definition that we can all accept. Let's use one provided by the church itself and still preached from thousands of pulpits today, which cannot reasonably be divorced from the question of God. Let's use Hell. Without getting too deeply into the weeds, Hell is at least one of: * What happens to evil people when they die * An evil (and, I might add, eternal) thing that happens to some people when they die * A... let's go with "place" here for simplicity's sake, where evil resides Either omnipotent God can stop this and yet allows it to continue, or omnibenevolent God is powerless to stop it.

1kithpendragon6y

I don't think we need a definition of evil at all. If we take omnipotence to be "able to do literally anything" and rephrase omnibenevolence to be "unable to abide evil" the meaning doesn't change but the paradox becomes evident. The two qualities are mutually exclusive regardless of your definition of "evil".

1gilch6y

So "omnipotence" is not absolute? There are certain laws of Nature or of Logic that even God is subject to? Or did God make Nature and Logic as well? (In which case the programmer analogy kind of breaks down and I still don't understand what "omnipotent" could mean.)

1Slider6y

Nature component doesn't really break the analogy and there are ways for which in can be made sense for part of the logic. If my program handles data a certain way as a programmer I would be free to alter that. I could for example go from using sets to using fuzzy sets. As I don't want to position myself as a crux party I will refrain from wanting what omnipotence should mean in this conversation.

1gilch6y

By "laws of nature that even God is subject to", I mean whatever laws of physics apply to the Programmer's world, even if they are different from ours. But notice that these are not entirely independent, as the Programmer's computer is built on the Programmer's physics, and the apparent universe is running on that computer. Even the Programmer is limited by his computer system. You are not totally free to handle data in any way you like. There are hardware constraints. Time in our universe would also take up time in the Programmer's universe, for example. The number of available bits in the Programmer's universe would be an upper bound on the number of available bits in ours.

5Slider6y

It could be entirely consistent that the programmer made nature_1 within the constraints of nature_2 and "laws of nature" referring to nature_2 laws is unstandard and surprising. it would be an assumption that nature_2 has time. Sure there are hardware constraints but their exact shape is hard to argue (I could come up with examples how simulated time takes simulator space and not time).

1gilch6y

Rotate 13 is a simple Caeser cipher: https://en.wikipedia.org/wiki/Rot13 A half-alphabet rotation of 13 is chosen for simplicity, because then the encryption function is the same as the decryption function. This is easy enough to do by hand, but there are numerous utilities and even JavaScript applications (like https://rot13.com/ ) that can do it quickly. The point is to prevent someone from reading something accidentally, like spoilers to movies or punchlines to jokes. Sometimes asking Google is faster than asking me.

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