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
1mo ago
To me, what justifies the claim that failing to find a counter example makes the hypothesis more likely is statistics.
If you point me to a statistical method that can give objective evidence for nonzero confidence in a universal generalization (such as Newton's Law of Gravity), you will have taught me the most interesting thing I have learned in a month.
Success rates matter.
The success rate of science in enabling improvements to our material lives is pretty good. The success rate of science in yielding justifiable nonzero confidence in universal natural laws may be zero. Can you defend the proposition that it is not? It would be a compelling refutation of my argument if someone were to give a single universal natural law of the physical world -- take your pick -- and give an objective argument why we should have greater than zero confidence in its literal truth. Now that I think about it, that is the straightforward path to refuting my argument, and it is notable that one has attempted to take it.
A word of advice if you proceed: don't waste your time trying to use Bayesian reasoning; you will not get a nonzero posterior unless you have a nonzero prior, and that would be begging the question. And don't bother trying to use parametric statistics, because no finite number of observations will get you there.
But is says nothing whatever about future performance, or about the "reliability" of a theory.
I think I see now why I, like many people, misread Popper. Frankly, I think the position he expresses here is so egg-headed that I did not anticipate it. He implicitly conditions future performance (aka reliability) on justified confidence in general, literal truth, and so winds up concluding that theories of physical world have only two levels of reliability: known false, and other. This position hamstrings his theory of corroboration with respect to establishing a rational basis for action -- and that moves him to the bottom of my reading list for philosophy of science. It's not that his work has no intellectual merit (it's all very interesting); it's just that I have better things to do, because I am interested science as a rational basis for discriminating between alternative courses of action, and in philosophy of science as an articulated theory of the rules of evidence for doing so.
It appears that Popper (1) accepts the essence of my argument in the original post, but (2) doesn't believe in miracles -- which commits him to his position on reliability and future-performance, and also makes his theory of corroboration impotent a basis for rational action. I share his view of (1) but not (2).
For clarity, do you agree with the Popper on this (that corroboration says nothing whatever about the future performance of a theory)?
NelsonRushton
1mo ago
I’m failing to understand why this is a bar any epistemology needs to clear... science as a method verifiably works at improving our material lives because it produces sufficiently accurate information. The utility is the payoff, but the correlation to reality is what enables it.
I did not say that any epistemology needed to clear that bar. If your position is that science a collection of useful fictions, and that discerning the (literally true) laws of nature falls outside the scope of its business, then your position is immune to my argument. For myself, I am a little more romantic about the goals of science.
Those who think rationality can lead to justified beliefs think that justification and evidence can make it so that we objectively rationally ought to believe a justified theory
There is a nuance to my position that this glosses over. In my view, scientific epistemology is not just matter of ought vs ought not; it is a matter of rationally obligatory degrees of preference for better tested theories, on a continuum. However, when one theory is better tested than another on this continuum, and on some occasion we have to choose between the two, then we rationally ought to trust the better tested theory on that occasion.
This is subjective in the sense that our preference for a theory is our decision, but it's not like a preference for an ice cream flavor
If I understand your position correctly, it is an awful lot like the preference among ice cream flavors. Let's say you have to choose from chocolate, vanilla, and strawberry -- but you know the strawberry is poisoned. So strawberry is a not a viable choice, but the choice between vanilla and strawberry remains wholly subjective. Similarly, (in your view as I understand it) when choosing among alternative theories to act on, the choice among those theories that have not been disconfirmed is a subjective preference as much as chocolate vs. vanilla.
For example, suppose a person has a choice between action A and action B, and that their goal in making that choice is to maximize the likelihood that they will continue living. Action A maximizes their chance of surviving if a certain viable (tested, not disconfirmed) theory is true, and B maximizes their chance of surviving if a certain other viable theory, in another domain, is true. They know one of those theories is substantially better confirmed than the other by every relevant criterion (say, the law of gravity vs. the most recent discovery in quantum computing). I say there is only one rational action in that scenario (trust the better tested theory). Do you say the same or different?
NelsonRushton
1mo ago
How about the finding that nothing with mass can exceed the speed of light? This is something backed by math and logic, as well as experimentation. If it were otherwise physics would break, is my layman’s understanding anyway... Is that sufficiently “universal”?
It sure is. Thanks for taking me up on the offer.
I am looking for objective evidence of the theory, Nullius in verba [Latin: No one's words (will be trusted)]. If you claim something is a theorem, show me the proof. If you claim something is experimentally verified, describe the experimental design and its results. What we have here is an appeal to authority claiming that the theory is "backed by math and logic" or that "physics would break" if it were untrue, omnes in verbo [all on the word (of authority)].
I would not be so demanding that I ask anyone to perform experiments, or even look up experimental data in literature, for the purpose of making a "Motte" post. A plausible (but concrete) story of what such evidence would look like -- in evidence of any theory of your choice -- would be enough to rebut my argument.
NelsonRushton
1mo ago
Looking at blades of grass won't help you because you have prior knowledge that blades of grass aren't crows, and actually looking at them provides you with no additional evidence that is not subsumed by your existing knowledge. If you started picking random things in the universe without prior knowledge of whether they are crows, and then it turned out that they were all non-black non-crows, that would be evidence.
Thanks for the statistically literate post. So please tell me,
If you started picking random things in the universe without prior knowledge of whether they are crows, and then it turned out that they were all non-black non-crows, that would be evidence.
by what rule of inference? If you say Bayes, it would be nice if you sketch your priors and your sampling method, to lend some plausibility to the answer.
After I swore it off, you made this place worth lurking in again.
I'm flattered!
I browsed your bio, and am paranoid enough in consideration of this [https://www.newswire.com/news/elemental-cognition-sets-new-standard-for-generative-ai-achieves-100-22248725] press release's claims to wonder at the ulterior motives for this post. and whether a human is the (primary) author:
If I were a bot, and my goal were to mine data to train an LLM, and I were smart enough to fool you into thinking I'm something else, would I say that I work for an AI research startup?
Laugh at me if you wish, in a thread investigating the very foundations of what we colloquially call "truth" I don't see why I shouldn't indulge my most schizophrenic tendencies.
Then again, maybe my plan is to make little mistakes like that throw you off the trail. Buahahhahahaha!
I do not think my position is fairly characterized as denying that there are shades of grey, or that science has been building knowledge bit by bit, or that I am calling for "perfection" as the only alternative to "fiction". If someone gave objective evidence that would justify, say, 1% confidence in some particular universal physical law (of gravity, or electromagnetism, or whatever), that would be a shade of grey (1% is pretty small; 10% would be better; 78% would be nice); it would be only one fact in a growing field (building knowledge bit by bit); it would be decidedly imperfect in the sense of low certainty. Yet my claim is that we cannot accomplish even that, based on objective evidence, even if we take for granted that the universe is persistently governed by fixed laws.
So I am not challenging anyone to deliver certainty, perfection, or complete knowledge. I am challenging them to deliver objective evidence for nonzero confidence in a universal physical law. As far as degrees of certainty go, the alternative to nonzero is zero -- and I do not think it is unfair to call a proposition a fiction if we have zero confidence in its truth. Even if it is a useful fiction.
I am also not saying that I do not have (positive) confidence in some of the known laws of nature -- though, somewhat to my surprise, several posters have indicated that they take that position. I am saying that to be in that position requires faith in something that is so unlikely a priori -- not to mention strange and wonderful -- that it could be fairly characterized as a miracle.
NelsonRushton
1mo ago
Well I’m a layman at physics, so I’d suggest finding someone who can lay out the math, theory, and experimentation that shows it is impossible for any object with mass to travel faster than the speed of light.
Great idea! Bring it on -- but I get to cross examine.
To recollect (since the conversation is pretty deeply threaded now), this was the original challenge:
It would be a compelling refutation of my argument if someone were to give a single universal natural law of the physical world -- take your pick -- and give an objective argument why we should have greater than zero confidence in its literal truth.
and the response:
How about the finding that nothing with mass can exceed the speed of light? This is something backed by math and logic, as well as experimentation. If it were otherwise physics would break, is my layman’s understanding anyway... Is that sufficiently “universal”?
It may help to step back and consider the role of appeals to authority in general, in terms of when they are conventionally accepted and when they are not. When experts communicate with other experts in post-enlightenment scholarly discourse, appeals to authority are verboten. The sacred rule of scientific dialectic is Nullius in verba [nothing on the word (of authority)]. I did not get that out a fortune cookie; it is the motto of the Royal Society of London (British equivalent of our Academy of Science), established in 1660, and now the oldest scientific academy in the world. As Turing Award Laureate Judea Pearl put it, the scientific revolution began when Galileo said, "I don't care about Aristotle and his fancy books; I want to see these two rocks dropped from the tower of Pisa, and I want to see them with my own two eyes." The hair stands up on the back of my neck every time I re-read Pearl's words, because, whether it began with Galileo or not, science in the strict sense emerged when appeals to authority were banished from scholarly discourse -- so that ideas came to be considered on their intrinsic merits rather than the merits of their inventor or advocate. It did not happen that long ago, it has not yet happened everywhere, and we are very fortunate to have that ethos as part of our heritage.
On the other hand, in a classroom or a court of law, it is conventional (and reasonable per common sense) for lay people to accept expert testimony on the merits of the speaker, if, or to the extent that they assess the speaker to be an expert on the topic in question. In these cases, the burden of rationality for the listener shifts -- from weighing the evidence that the speaker's claims stand on their merits, to rationally weighing the evidence of his merits as a trustworthy source on the topic. For example, if a professor of ornithology from Stanford tells me he is confident that we are looking at a red-bellied wood thrush (or whatever), and that is not disputed by another expert of comparable or greater standing, I would tend to believe him. If he got his bachelor's from the University of Alabama, on the other hand, I would be less inclined. (I'm just kidding; I would grudgingly believe the Alabama grad -- but War Eagle!)
To the topic at hand, I am not assuming the role of a layman in this discussion. I consider myself an expert in logic and probabilistic reasoning, but you can be the judge of whether you agree. I have a doctorate in that subject from the University of Georgia and 11 published scholarly papers in the field (as well as 22 in other fields of mathematics and computer science). During my career as a professor at Texas Tech University, I was lead investigator in over one million dollars in research contracts sponsored by NASA and DARPA. I served as chief scientist of Texas Multicore Technologies from 2011 to 2017. My most cited paper on probabilistic reasoning [Baral, Gelfond, and Rushton (2009): "Probabilistic Reasoning with Answer Sets] (https://arxiv.org/pdf/0812.0659.pdf) has 293 citations per Google Scholar, about one third of which occurred within the past two years -- which puts it in approximately the top 1% of academic papers by number of citations, as well as indicating interest in my research that is growing over time.
I am not asking you to assume the role of a layman either, and I do not expect to be taken one bit more seriously than my arguments merit on their substance. But, given an unsupported assertion that "If it were otherwise physics would break, is my layman’s understanding", I am not willing to assent to it, let alone consider it objectively established, without seeing direct evidence (Nullius in verba) -- either from you or from the alleged expert source -- in order to examine, not content of the physics theory, but the probabilistic and/or logical rules of inference that are used to support that theory. As (Pearl imagined) Galileo said, I want to see that it is true with my own eyes.
If you don't believe we can go from experimental evidence to justified belief in theory, then we have bigger problems.
I do not believe we can, without a prodigious leap of faith in the power of the human mind relative to the complexity of Nature, unjustified by any articulable, objective reason. If you disagree, then I ask you which rules of inductive inference you would use to draw those conclusions from that evidence. So, do we have "bigger problems"?
NelsonRushton
1mo ago
I won't relitigate the influence of Christianity on the Enlightenment since that veers off topic,
IMO it is pretty adjacent to the topic of the original post.
As for your the law of gravity vs. the most recent discovery in quantum computing example, it's slightly confusing to me. Does option B that uses quantum computing go against the law of gravity? If so, I would reject it, since I believe the law of gravity to be true (tentatively, without justification). Or does option B use both the law of gravity and quantum computing? In that case I'm not really choosing between gravity and quantum computing, but whether to additionally also use quantum computing in my plan, in which case how well-tested quantum computing is compared with gravity is not really relevant, since I'm using gravity as well.
I meant something like this: the safety of A rests on the law of gravity but not the law of quantum computing; the safety of B rests on the law of quantum computing but not the law of gravity. To make the example a little more concrete (but science-fiction requiring some suspension of disbelief), your choices are to take (1) a self-flying plane that is programmed with a model using the Law of Gravity, but no laws of quantum computing, and has been operating safely for thirty years, or (2) the new teleporter -- whose safety has been tested but not disconfirmed, and has been proven safe contingent on the latest law of quantum computing, but not the law of gravity. Your goal in the selection is to maximize the probability of your survival.
NelsonRushton
1mo ago
I'd definitely be interested in testing the teleporter, but I wouldn't risk my safety in a first test of something, so I'd choose the plane, which I believe is safe (tentatively, as my best guess upon rational deliberation that produces no justification but may eliminate errors). Like I said, choices and beliefs can only be rational in the sense of using deliberation and reason to make our best guess, and are never rational in the sense of being justified, warranted, reliable, established, or anything of that sort, as this is not possible.
Well I'd definitely be interested in testing the teleporter, but I wouldn't risk my safety in a first test of something, so I'd choose the plane,
Remember, I stipulated in the hypothetical that the goal of the reasoner in the story is to maximize their probability of survival. The intent is not to ask what you would do; if curiosity trumps safety for you as an ultimate value, so be it. The question is, given that the reasoner's goal is to maximize his or her safety, would it be rational for them to take the teleporter?
NelsonRushton
1mo 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?
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.
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?
NelsonRushton
1mo 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?
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
1mo 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?
NelsonRushton
1mo 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.
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).
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!"
NelsonRushton
1mo 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.
Well, that is the trillion-dollar question. The fact is that is an inference rule often used in the physical sciences -- and it is the only inference rule that can give us any nonzero confidence in a universal generalization (such as a universal natural law, such the laws of thermodynamics or electromagnetism). Statistical methods cannot give objective evidence for such laws.
So either (1) abductive inference is only good for generating useful fictions (with zero reason to ever believe they are anything but fictions), or (2) it can sometimes be used to yield nonzero confidence in certain universal natural laws. If you choose door number 1, so be it. If you choose door number 2, and you ask me where the logic is, I will tell you that there isn't any unless we are blessed with minds so powerful, and a universe so simple, that if counterexamples to the law existed, we would be tolerably likely to find them. So, unless the corpus of physics is a useful fiction, with no reason to believe anything in it is anything but a fiction, you tell me: where's the logic?
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