NelsonRushton
Doctorate in mathematics, specializing in probability theory, from the University of Georgia. Masters in AI from the University of Georgia. 15 years as a computer science professor at Texas Tech. Now I work as a logician for an AI startup. Married with one son. He's an awesome little dude.
I identify as an Evangelical Christian, but many Evangelicals would say that I am a deist mystic, and that I am going to Hell. Spiritually, the difference between me and Jordan Peterson is that I believe in miracles. The difference between me and Thomas Paine (an actual deist mystic) is that I believe the Bible is a message to us from the Holy Spirit, and the difference between me and Billy Graham is that I think there is noise in the signal.
User ID: 2940
NelsonRushton
6mo ago
Your statements of "duty" were very declarative,
I cannot tell which "statements of 'duty'" this refers to.
NelsonRushton
6mo ago
People also tend to upvote a nice, spicy polemic
Incidentally, I don't care for the term "spicy" as a euphemism for things that are uncomfortable, or potentially expensive, or potentially dangerous to say. If someone declines to make an objectively reasonable post because it is spicy", then maybe they just don't like spicy stuff; different strokes! On the other hand, if someone declines to make a post because it is uncomfortable (or expensive or dangerous), they are keeping their head down, or perhaps cowering, instead of speaking the truth. There are times to keep your head down, but there is never a time to deceive yourself about the fact that you are keeping your head down.
NelsonRushton
6mo ago
the net upvotes tell the story of which way TheMotte leans ideologically.
It is a little sad, for The Motte, that it can be assumed people upvote arguments whose conclusions they agree with (as opposed to meritorious arguments on all sides).
Not to derail, and it's possible that you're still right, since I don't know what exactly constitutes hatred for you, but I do think the scriptures are pretty clear that homosexual sex is bad.
Important enough question for a derail, IMO. What constitutes hatred, for me, is taking carnal delight in the pain and loss (or prospective pain and loss) of another person. This is as opposed to indignation, by which I mean making a judgment that someone's conduct is immoral and, if it rises to a certain level, calls for punishment. In that light, my case is twofold. First (as I think @Felagund anticipated),
For I was an hungred, and ye gave me no meat: I was thirsty, and ye gave me no drink: I was a stranger, and ye took me not in: naked, and ye clothed me not: sick, and in prison, and ye visited me not. Then shall they also answer him, saying, Lord, when saw we thee an hungred, or athirst, or a stranger, or naked, or sick, or in prison, and did not minister unto thee? Then shall he answer them, saying, Verily I say unto you, Inasmuch as ye did it not to one of the least of these, ye did it not to me. [Matthew 25: 42-45 KJV]
Jesus doesn't say "I was in prison for something I did not do and ye visited me not", or "I was in prison for a minor offense, and you visited me not". The people who count as the least of our brothers include people who have actually committed a major offense. So I think it is consistent, and indeed only right, to judge an action as a sin without hating the person who committed it. If my brother drove home drunk from a night on the town, or even murdered someone, I could acknowledge that as wrong, or gravely wrong in the latter case, without hating him.
Second, the Bible does condemn homosexual sodomy. Just as strongly, it condemns witchcraft, idol worship, working on Saturday, cursing your parents, eating meat of an animal that been strangled, consuming animal blood (e.g., blood sausage), premarital sex, and many other things which call for the death penalty under Mosaic law. Some of these prohibitions, including idol worship, consuming animal blood, and eating the meat of a strangled animal, carry over explicitly into New Testament law [cf. Acts 15]. Bible believing Christians, as a rule, do not take all of those seriously as sins, let alone call for death by stoning for all of them -- so they have to square with that one way or another.
But of all ways to square with it, to arbitrarily pick one of those alleged sins and lift it up as an abomination on Biblical grounds, while discounting or ignoring the rest, and then to use that capricious choice to justify hating another person, is not only hypocritical but blasphemous -- insofar as it also recklessly puts your bigoted words in God's mouth. Yet, as a group characteristic, that is what Evangelicals [my people] have historically done, and to some degree continue to do, in large numbers by comparison with the general population. I'm not saying we all do it or ever did; I am saying that (1) we did/do it significantly more than our outgroups in the Western world (e.g., white collar Democrats), (2) those of us who do not vocally acknowledge that are part of the problem.
This is kind of the opposite of my statement.
These are the statements I am comparing:
- @AhhhTheFrench: So you really must "call out" every moment of evil you see in the world or you're guilty too?
- The serpent: Did God actually say, You shall not eat of any tree in the garden’?
They are both phrased as questions; notably both use some version of "actually"/"really", and both suggest a narrative that, in order to do right, you have to go to onerous extremes -- which makes a great excuse to do as you please. Generally, I think it is a common pattern when someone is confronted with a duty, that they respond by saying, "What am I supposed to do, Give away all of my stuff? go around jumping in every time someone is getting bullied? Starve myself so kids in Uganda can eat? Never have any fun? Fall on my sword over every little thing? etc. etc. etc.
So you really must "call out" every moment of evil you see in the world or you're guilty too?
Of course not. This all-or-nothing, fall-on-your-sword straw man was first thing the Devil ever said: "Did God actually say, You shall not eat of any tree in the garden’?”"
Most people are just humans trying to get by, and that is alright.
It might be "alright", whatever that means, but it makes them lesser men. We (Americans) live in a relatively free, safe, and prosperous society because the founding fathers and continental soldiers answered the call of duty to a higher purpose than minding their own business. We owe them a monumental debt that we can never pay back. We can only pay it forward by living up to their legacy of duty and sacrifice.
"We do not say that a man who takes no interest in politics is a man who minds his own business; we say that he has no business here at all." [Pericles]
The easy solution is to simply reject the idea of "our community".
This may be an ideal solution, but I do not believe it is an easy solution. A community collectively and instinctively puts people in categories, assigns default characteristics to people in these categories, views the categories as part of the identity of its members, and views the categories as competing factions. If you think you can easily (or totally) escape buying into that factionalism, I think you are under an illusion. The trick is not to eliminate identity groups as functional units of society, but to make the competition between them honest, healthy, and based on furthering interests that are shared among the identity groups.
I feel the OP's pain. But the closer you are to God, the less it will matter to you whether you are a member of a group that happens to suffer from an epidemic of foolishness (whether it is biological or cultural). Moreover, if your people are acting like fools, you dissociate yourself from the foolishness precisely to the extent that you call it out. For example, as a white Christian Republican, my people have a history of irrational and immoral hatred for gays. As a Southerner from Alabama, my people have a history of hypocritically identifying as Christian while also having racist contempt for blacks. If I call those sins out, I am not stained by them. I can actually feel my conscience being freed when I acknowledge them. But, to the extent that I remain silent about those corporate sins of my own people, and at the same time identify as members of those groups, I am truly guilty by association (whether I am individually an offender or not).
The same thing goes for other groups. If you are a Muslim and that is part of your identity, that does not make you part of the problems of Islamic fascism, genocidal antisemitism, and terrorism -- but, if you aren't talking about those problems in the Muslim world and calling them out, then you are part of the problems -- even if you don't advocate for Sharia law, or hate jews, or fly airplanes into buildings. Similarly, if you are black, and you aren't talking about the problems of black supremacy, anti-intellectualism, deadbeat dads, serially pregnant welfare moms, gang violence, or whatever you honestly see as the problems in your community, then you are part of those problems. On the other hand, if you are vocally calling them out and trying to address those issues, then you are not part of the problem -- and also, you are fundamentally part of a bigger identity group called "Honest, caring people".
NelsonRushton
7mo ago
Do you honestly believe that we can't say, by study of the motion of say, the planets of our solar system, be justified in believing a theory about the motion of the planets (and only the planets).I am not talking about everything in the universe.
Yes, that is what I believe. I invite you to make the opposite case by sharing with me whatever rule of evidence you think can establish otherwise.
NelsonRushton
7mo ago
If you are an EA buff, I'd be happy if you'd share with me the case for one of their better, or best projects.
NelsonRushton
7mo ago
Republicans should not concede illegal results If this is uniquely democracy-destroying, and unacceptable, then: Republicans need to cheat harder. Since in many ways (2) is worse than (1), I'm skeptical of any argument that supposes that conceding a rigged election is the healthy and adult decision.
The nuance here is that (1) we don't know if the election was rigged, and (2) that, by itself, is the problem. Every week I hear people say there is no evidence that the election was rigged. That is the wrong place to put the burden of proof. There is no evidence that the 1946 Russian elections were rigged either, but as Stalin said, "It's not who votes that matters, but who counts." The question is not whether there is evidence the election was rigged, but whether the election was conducted in such a way that there would be evidence if the election were rigged. I think the answer to that question is no -- because if it were yes, Democrats would say that and back it up instead of gaming the burden of proof a la Stalin.
NelsonRushton
7mo ago
To be a really fine point on this, what happens in the real world when there is an armed resistance against a government that lacks maximal willingness and ability to kill 'em all and let God (or Allah, as it were) sort 'em out? The most salient example in a first-world nation seems like the Irish Republican Army and their experience is not at all consistent with the idea that armed resistance doesn't do anything
Amen.
Also, I would look at the low (single digit percent) compliance rate with the "assault weapons" bans in Connecticut and New York. They knew (from sales records) who had the guns, so why didn't they go door to door and confiscate them? Because their owners had already demonstrated that they were willing to become felons on a matter of principle, so some of them just might be willing to shoot it out with the cops. And if even one, let alone three or five, of those incidents happened, where the gun owner was killed by the police in the raid along with possibly one or more cops, it would spark a backlash that would be very bad for the politicians who ordered the raid. Hence, those laws are not being enforced.
Also, if you are from NY or CT and are one of the patriots who didn't register your "assault weapon", then you are a friend of mine -- and if we ever meet dinner is on me.
If you're not playing some kind of game that amounts to wanting people to stop snorting when someone brings up god in an intellectual context?
I'm glad you mentioned that. I am actually not interested in the reactions of people who scoff (or "snort") when someone brings up God in an intellectual context. The readers that interests me for this argument are people like political scientist Charles Murray and historian Tom Holland, who do not scoff, and who are even sympathetic to the idea, but who are not believers because they cannot find reasons to believe.
just parsing the differences between degrees of philosophical certainty that no one out in the world ever thinks about when making decisions?
My argument isn't about parsing degrees of certainty
Then I'll leave you to your hobby and continue to be puzzled as to the appeal. Back in the world where people make decisions, the fact that science does in fact produce functional results obliterates every other consideration anyway.
Look, I'll be honest:...
I'm glad you are being honest. In that same spirit, I think it is Philistine to separate the effort to reveal the true laws of nature from "the world where people make decisions". Science, conceived as the effort to reveal the laws of nature, involves making many of decisions; I believe it is what many scientists perceive themselves as doing, and I believe it is a worthwhile pursuit for its own sake -- independently from its applications to such things as bread and circuses.
Besides, the best, most accurate superforecasters and people like quants absolutely pull it out and do explicit work. In their case, the effort really is worth it. You can't beat them without doing the same.
I know quants do this, but I think it is a special case. Show me a hundred randomly selected people who are making predictions they suffer consequences for getting wrong, and are succeeding, I will show you maybe 10 (and I think that's generous) that are writing down priors and using Bayes rule. Medical research, for example, uses parametric stats overwhelmingly more than Bayes (remember all those p-values you were tripping over?), as do the physical sciences.
If the effective altruism (EA) crowd are in the habit of regularly writing down priors (not just "there exist cases"), then I must be mistaken in the spirit of my descriptive claim that nobody writes them down. On the other hand, I would not count EA as people who pay consequences of being wrong, or that is doing a demonstrably good job of anything. If they aren't doing controlled experiments (which would absolutely be possible in the domain of altruism), they are just navel gazing -- and making it look like something else by throwing numbers around. I have a low opinion of EA in the first place; in fact, in the few cases where I looked at the details of the quantitative reasoning on sites like LessWrong, it was so amateurish that I wasn't sure whether to laugh or cry. So an appeal to the authority if LessWrong doesn't cut much ice with me.
I should give an example of this. Here is an EA article on the benefits of mosquito nets from Givewell.org. It is one of their leading projects. (https://www.givewell.org/international/technical/programs/insecticide-treated-nets#How_cost-effective_is_it). At a glance, to an untrained eye, it looks like an impressive, rigorous study. To a trained eye the first thing that jumps out is that it is highly misleading. The talk about "averting deaths" would make an untrained reader think that they are counting the number of "lives saved". But this is not how experts think about "saving lives" and there is a good reason for it. Let's suppose that we take a certain child, that at 9 AM our project saves him from a fatal incident; at 10 Am another, at 11 AM another, but at noon he dies from exactly the peril our program is designed to prevent. Yay, we just averted 3 deaths! That is the stat that Givewell is showing you. Did we save three lives? no, we saved three hours of life.
This is the way anyone with a smidgeon of actuarial expertise thinks about "saving lives" -- in terms of saving days of life, not "averting deaths", and the Givewell and Lesswrong people either know that or ought to know it. If they don't know it, they are incompetent; and if they know it, then talking about "averting deaths" in their public facing literature is deliberately deceptive because it strongly suggests "saving lives", meaning whole lives, in the mind of the average reader. To be fair to givewell, their method of analyzing deaths averted apply to saving someone from malaria for a full year (not just an hour), but (1) that would not be apparent to a typical donor who is not versed in actuarial science, and (2) the fact remains that you could "avert the death" of the same person nine times while they still died of malaria (the peril the program is supposed to prevent) at the age of 10. The analysis and language around it is either incompetent or deceptive -- contrary to either one word or the other in the name of the endeavor, effective altruism.
That's not a cherry picked example; it was the first thing I saw in my first five minutes of investigating "effective altruism". It soured me and I didn't look much further, but maybe I'm mistaken. Maybe you can point me to some EA projects that are truly well reasoned, that are also on the top of the heap for the EA community.
NelsonRushton
7mo ago
While Predictive Processing theory, which posits that human cognition is inherently Bayesian,
I'm skeptical of this. I think predictive processing theory posits a model with certain qualitative features that Bayesian updating would also have, but there are scads of non-Bayesian approaches that would also have those qualitative properties. They would only look Bayesian from the point of view of someone who doesn't know any other theories of belief updating. Does PPT posit a model that have the quantitative properties of Bayesian updating in particular, and experimentally validate those? That would be a very interesting find. If you know of a source I'd be curious to look at it.
NelsonRushton
7mo ago
(4) For OP: you suggest downthread that we should be inclined to trust models like Newtonian or Einsteinian physics. Why should we trust them (if we cannot infer universal physical laws with nonzero confidence) and how much should we trust them?
We should trust them for two reasons. First, we do not need nonzero confidence in full generality to trust them for practical purposes. Being 99% sure the technology works 99% of the time is good enough -- or something like that, depending on the application. Second, I didn't say we cannot infer universal physical laws with nonzero confidence, just that we can't do it without believing in one more miracle, viz. that we are blessed with just enough intelligence, and a simple enough universe, that abductive reasoning is reliable (on top of the miracle that certain equations are physically instantiated in the form of a physical systems and consciousness, that this system continues persistently to be governed by those laws, that the parameters of those laws fall into the narrow range required for stars to form, etc.).
and how much should we trust them?
That depends on how many miracles you believe.
And if you start with 100% credence or 0% levels of disbelief, nothing anyone can do to you short of invasive neurosurgery (or maybe a shit ton of LSD) can change it.... What are the practical ramifications? Well, here, what Nelson is trying to argue is a waste of time. If you demand 100% confidence that the laws of physics are "universal" and timeless, you're SOL unless you assume the conclusion in advance. But we can approach arbitrarily close
This is mistaken. There are two quantifiers in an assertions about laws of nature: one might be called generality, which refers to the uniformity with which the law is believed to hold, and the other might be called confidence, which refers to the degree of belief that the law holds with the given generality. For example, if I say I firmly believe that at least 1% of crows are black, this statement would have high confidence and low generality -- whereas if I said, It is plausible that at least 99% of crows are black, that statement would have lower confidence and higher generality. Nothing in any of my posts mentioned 100% confidence; my thesis is about nonzero confidence in 100% generality.
Skip Popper. Get on the Bayes Boat, baby, it's all you need.
Funny thing: everybody loves Bayes rule; but they never state their priors. To that extent they never consciously use it. Nor is there any evidence that it models the unconscious process of real life rational cognition. The evidence to support that would need to be quantitative; not just "Hey I believed something, then I saw something, and I altered my degree of belief. Must have been using Bayes!"
Why don't you hold your self to the same standard you hold others? You demand they prove their math, but we are supposed to believe you because you "looked diligently"?
I think I am holding everyone to the same standard, but not everyone chooses to take the path through the constraints of that standard. As I said in the original post, the principle of abductive inference, which is considered good evidence by research in the physical sciences, says that diligently efforts to disconfirm a theory, which come up empty, are evidence for that theory. I used that rule and you are welcome to use the rule as well. I also argued that the use of that rule rests on a subjective faith in a certain miracle, which I do embrace. For a rough analogy, if I said that only people who believe in the Axiom of Choice can rationally assert the existence of non-measurable sets, I am holding everyone to the same standard -- even though some people will embrace the axiom and the theorem and some will embrace neither.
Why don't you prove that z can never be 1 for any finite number of observations, no matter how small the desired confidence c is, unless c = 0
As far as confidence intervals go, this actually is a theorem, and does not rest on abductive reasoning. For a pretty accessible special case you can read this article: https://en.wikipedia.org/wiki/Rule_of_three_(statistics). I know statistics pretty well and I do not know of any method that gets around this limitation. This includes Bayes rule (see below). You can soundly refute my claim by showing us a statistical inference that does.
I will point out this is another claim you've provided no proof for: It will be mathematically impossible for you to produce a nonzero posterior probability if you do not have a nonzero prior
I assumed this would be obvious to anyone who was familiar Bayes rule in the first place, and that people who are not familiar with Bayes rule are probably not familiar with probability theory, and would not be interested in reading mathematical proofs about it -- but since you asked, here is the proof: Bayes law says that P(A | B) = P(B | A)*P(A)/P(B). Suppose the prior, P(A), is zero; then the righthand side is zero, and so the left hand side, which is the posterior is also zero. This shows that if the prior is then the posterior is zero. Thus, if the posterior is nonzero, then the prior must be nonzero as well.
I mean, we know they are not always true, but you can certainly measure how far a planet's position deviates from that as predicted by Kepler's laws after some time.
You can measure that, and then measure it again and again and again. That comes to four measurements. But the law says that everything orbiting everything in the universe follows the same rule, and those four measurements don't support that conclusion. They don't even support the conclusion that the law continued to hold at each of the infinitely many times between when you took your measurements.
can you come up with an objective, quantifiable number of confidence for whether a coin will flip heads?
No, but I do not claim to believe that the coin will flip heads, much less that it is a universal law that it will flip heads every time. Some people do believe such things, though, about the some of the laws of physics (viz., that they work every time).
NelsonRushton
7mo ago
Okay well in that case it's also hypocritical to criticize Cthulhu and Star Wars lore for not being literally true. Hooray, solipsism. This entire line of argument advances absolutely nothing.
If someone just jumped into this thread without reading the history, they might gather that I (or someone else) had criticized Cthulhu on the grounds of not being literally true. So for anyone who is jumping in in the middle, nothing of the sort happened.
Moreover, I would never detract from the merit of Shakespeare or Homer on the grounds that there is no evidence for the literal truth of their writings. Nor would I detract from the merit of a physics text on the grounds that there is no objective evidence that its contents are literally true. I do not think I am asking for special status for anything. I am arguing against a special status for the physical sciences, that I believe is widely attributed to them.
It essentially amounts to a theist's special request for their beliefs to be treated as intellectually serious even though they can't point to any justification... request denied until one of these arguments successfully and meaningfully distinguishes Christianity, theism, whatever, from an infinite number of bullshit things I could make up on the spot.
I agree that you should deny that request if somebody made it -- but I don't think I did (unless "whatever" casts a very wide net).
My thesis is that (1) if you hold nonzero confidence in the literal truth of a universal physical law, then you should be able to give reasons for your belief, and (2) the only rule of evidence I know of that would justify such a conclusion (abductive inference) -- and the one that is actually used in the physical sciences to establish credibility of physical theories -- rests on premises that are infinitesimally unlikely to hold in the absence of a miracle.
NelsonRushton
7mo ago
It is an interesting thought experiment to pull things at random from an infinite box, but I think to draw conclusions about it, it needs to be described a little more concretely. If you keep a list of patterns that you have consistently seen as you drew out objects (e.g., every object that was yellow had an even number on it), then it will certainly be true that every object you draw out, that follows the rules on your list, will follow the rules on your list. But that isn't saying much, and there may more objects in the box that don't follow those rules. All in all, I don't really see what you are driving at with this:
But of those in the box which follow the same rules as the one's we've pulled out of the box, can we say they also have an internal angle of 180 degrees?
I agree with most of the substance of this, but have a couple of quibbles.
#1
so Occam's razor would suggest that our laws of physics roughly apply in the observable
I think this is an oversimplification. It could be interpreted to mean something true, but it could just as easily be interpreted to mean something false, and the burden of clarity is on the author. As you probably know, relatively is not even approximately true in the small, and quantum mechanics is not even approximately true in the large. So it is more precise to say that our known laws are approximately true when applied within the scope of their well tested and intended use -- which is also true of classical mechanics, Hooke's law of springs, the ideal gas laws, etc. But the scope of well tested and intended use is a loop we have to be in to make it work. The laws themselves are not as intrinsically accurate as your statement would suggest to an average reader.
#2
I also agree that in commonsense terms, "the moon is made of rock" means the moon is made primarily out of rock, and not the moon is made entirely of rock -- and that on that commonsense interpretation we are entitled to justified confidence in it on the bases of much fewer miracles that in a bona fide universal generalization.
But when you say this:
All models are wrong, some models are useful.
I do not believe we need to be resigned to it. That must mean that I believe in one more miracle than you.
NelsonRushton
7mo ago
If you are thinking of it as a theorem in geometry, there are these things called "axioms", which are needed to prove the theorem, as I mentioned above. To believe the theorem is true of every triangle in the infinite box, we would have to first know that the axioms were true of every triangle in the box. And what gives you that idea?
Can we make a "universal law" about the angles of all three sided polygons in the infinite box?
I can't think of a statistical rule that would justify it. Can you?
You say: z can never be 1 for any finite number of observations, no matter how small the desired confidence c is, unless c = 0 Well where is your proof for this?
That is my thesis (recall the context was statistical reasoning). My argument is that I do not know of an inference rule that would permit this without begging the question and I have looked diligently (abductive inference). You could disconfirm my thesis by pointing out such a rule. If you try to disconfirm it and fail (like I have), that would count as additional evidence for the thesis in my view -- because you are such a smart fellow.
Do you honestly believe that we can't say, by study of the motion of say, the planets of our solar system, be justified in believing a theory about the motion of the planets (and only the planets)?
My view is not that we cannot be justified, but that we cannot be objectively justified -- justified for an objective, articulable reason that does not rest on an article of faith as I described. The theory you are probably referring to is Kepler's law of orbital mechanics. What I believe about that is that we are objectively justified (statistically) in believing Kepler's equations are usually, approximately true. That is, they are at least a useful fiction. However, I do not see any objective reason (short of a miracle) to have nonzero confidence that Kepler's' equations are always exactly true, or even always approximately (to within specified tolerances).
Imagine, for example, that I am skeptical of whether Kepler's equations hold universally (as anyone, even Kepler, should be a priori); you claim to have a justified nonzero degree of belief that they do, and I ask you for evidence. What form of argument would you use to establish this?
Suppose you try to use Bayesian statistics. It will be mathematically impossible for you to produce a nonzero posterior probability if you do not have a nonzero prior, and a nonzero prior would beg the question, so that's out.
Suppose you try to use the standard go-to method of confidence intervals (as @self_made_human mentioned, p-values), to give a statistically significant confidence interval on the probability that Kepler's laws hold for a given occurrence. Now "the rule of 3" (https://en.wikipedia.org/wiki/Rule_of_three_(statistics)) says that as your number of observations approaches infinity, the lower bound on estimate of the success rate of Kepler's laws will approach 100%, but it will never be 1 with for finite number of observations. For example you can get a statistical result that Kepler's laws hold 99.9% of the time, but not 100% of the time -- that is, never any statistically significant evidence that they constitute a universal natural law of the physical world. So that's out. Moreover, it will not work to lower your confidence level to 90%, or 85%, or any other percentage other than zero. So that's out.
All other ideas I can come up with for an objective, quantifiable solution also fail. How about you? Note that I am not asking you to go out and gather the actual observations, or even to understand Kepler's equations; I am just asking for the statistical method that you would use to draw the onclusion from those observations.
Finally to address this:
Our observations inspire us to a mathematical proof that every three-sided polygon has an internal angle of 180 degrees. Would we be justified in believing that every three-sided polygon in the box, has an internal angle of 180 degrees
What we could prove, mathematically, is that in a space that satisfies the axioms of Euclidean geometry, the sum of the internal angles of every triangle is 180 degrees. However, that is not a theorem about the physical world, and it is not known whether or not the space we live in satisfies the axioms of Euclidean geometry. So we would have justified confidence in the theorem, insofar as some propositions logically entail others, but it is not a universal generalization about the physical world.
NelsonRushton
7mo ago
A prior is a function from subsets of a given sample space to [0,1]. A sampling method is a description of a procedure that gives enough detail that I should be able to repeat the procedure and expect to get results not statistically significantly different from yours. I don't see either of those things here. Did I miss something?
By "inflammatory" do you mean (a) inflammatory in the eyes of a reasonable person, or (b) something that will, if widely seen, get a lot of people riled up, reasonably or unreasonably?
More options
Context Copy link