The so-called "scientific method" is, I think, rather poorly understood. For example, let us consider one of the best-known laws of nature, often simply referred to as the Law of Gravity:
Newton's Law of Universal Gravitation: Every object in the universe attracts every other object toward it with a force proportional to the product of their masses, divided by the square of the distance between their centers of mass.
Now here is a series of questions for you, which I often ask audiences when I give lectures on the philosophy of science:
- Do you believe Newton's Law of Universal Gravitation is true?
- If so, how sure are you that it is true?
- Why do you believe it, with that degree of certainty?
The most common answers to these questions are "yes", "very sure", and "because it has been extensively experimentally verified." Those answers sound reasonable to any child of the Enlightenment -- but I submit, on the contrary, that this set of answers has no objective basis whatsoever. To begin with, let us ask, how many confirming experiments do you think would have been done, to qualify as "extensive experimental verification." I would ask that you, the reader, actually pick a number as a rough, round guess.
Whatever number N you picked, I now challenge you state the rule of inference that allows you to conclude, from N uniform observations, that a given effect is always about from a given alleged cause. If you dust off your stats book and thumb through it, you will find no such rule of inference rule there. What you will find are principles that allow you to conclude from a certain number N of observations that with confidence c, the proportion of positive cases is z, where c < 1 and z < 1. But there is no finite number of observations that would justify, with any nonzero confidence, that any law held universally, without exception (that is, z can never be 1 for any finite number of observations, no matter how small the desired confidence c is, unless c = 0). . And isn't that exactly what laws of nature are supposed to do? For Pete's sake it is called the law of universal gravitation, and it begins with the universal quantifier every (both of which may have seemed pretty innocuous up until now).
Let me repeat myself for clarity: I am not saying that there is no statistical law that would allow you to conclude the law with absolute certainty; absolute certainty is not even on the table. I am saying that there is no statistical law that would justify belief in the law of universal gravitation with even one tenth of one percent of one percent confidence, based on any finite number of observations. My point is that the laws of the physical sciences -- laws like the Ideal gas laws, the laws of gravity, Ohm's law, etc. -- are not based on statistical reasoning and could never be based on statistical reasoning, if they are supposed, with any confidence whatsoever, to hold universally.
So, if the scientific method is not based on the laws of statistics, what is it based on? In fact it is based on the
Principle of Abductive Inference: Given general principle as a hypothesis, if we have tried to experimentally disprove the hypothesis, with no disconfirming experiments, then we may infer that it is likely to be true -- with confidence justified by the ingenuity and diligence that has been exercised in attempting to disprove it.
In layman's terms, if we have tried to find and/or manufacture counterexamples to a hypothesis, extensively and cleverly, and found none, then we should be surprised if we then find a counterexample by accident. That is the essence of the scientific method that underpins most of the corpus of the physical sciences. Note that it is not statistical in nature. The methods of statistics are very different, in that they rest on theorems that justify confidence in those methods, under assumptions corresponding to the premises of the theorems. There is no such theorem for the Principle of Abductive Inference -- nor will there ever be, because, in fact, for reasons I will explain below, it is a miracle that the scientific method works (if it works).
Why would it take a miracle for the scientific method to work? Remember that the confidence with which we are entitled to infer a natural law is a function of the capability and diligence we have exercised in trying to disprove it. Thus, to conclude a general law with some moderate degree of confidence (say, 75%), we must have done due diligence in trying to disprove it, to the degree necessary to justify that level confidence, given the complexity of the system under study. But what in the world entitles us to think that the source code of the universe is so neat and simple, and its human denizens so smart, that we are capable of the diligence that is due?
For an illuminating analogy, consider that software testing is a process of experimentation that is closely analogous to scientific experimentation. In the case of software testing, the hypothesis being tested -- the general law that we are attempting to disconfirm -- is that a given program satisfies its specification for all inputs. Now do you suppose that we could effectively debug Microsoft Office, or gain justified confidence in its correctness with respect to on item of its specification, by letting a weasel crawl around on the keyboard while the software is running, and observing the results? Of course not: the program is far too complex, its behavior too nuanced, and the weasel too dimwitted (no offense to weasels) for that. Now, do you expect the source code of the Universe itself to be simpler and friendlier to the human brain than the source code of MS Office is to the brain of a weasel? That would be a miraculous thing to expect, for the following reason: a priori, if the complexity of that source code could be arbitrarily large. It could be a googleplex lines of spaghetti code -- and that would be a infinitesimally small level of complexity, given the realm of possible complexities -- namely the right-hand side of the number line.
In this light, if the human brain is better equipped to discover the laws of nature than a weasel is to confidently establish the correctness an item in the spec of MS Office, it would be a stunning coincidence. That is looking at it from the side of the a priori expected complexity of the problem, compared to any finite being's ability to solve it. But there is another side to look from, which is the side of the distribution of intelligence levels of the potential problem-solvers themselves. Obviously, a paramecium, for example, is not equipped to discover the laws of physics. Nor is an octopus, nor a turtle, nor a panther, nor an orangutan. In the spectrum of natural intelligences we know of, it just so happens that there is exactly one kind of creature that just barely has the capacity to uncover the laws of nature. It is as if some cosmic Dungeon Master was optimizing the problem from both sides, by making the source code of the universe just simple enough that the smartest beings within it (that we know of) were just barely capable of solving the puzzle. That is just the goldilocks situation that good DM's try to achieve with their puzzles: not so hard they can't be solved, not so easy that the players can't take pride in solving them
There is a salient counterargument I must respond to. It might be argued that, while it is a priori unlikely that any finite being would be capable of profitably employing the scientific method in a randomly constructed universe, it might be claimed that in hindsight of the scientific method having worked for us in this particular universe, we are now entitled, a posteriori, to embrace the Principle of Abductive Inference as a reliable method. My response is that we have no objective reason whatsoever to believe the scientific method has worked in hindsight -- at least not for the purpose of discovering universal laws of nature! I will grant that we have had pretty good luck with science-based engineering in the tiny little spec of the universe observable to us. I will even grant that this justifies the continued use of engineering for practical purposes with relative confidence -- under the laws of statistics, so long as, say, one anomaly per hundred thousand hours of use is an acceptable risk. But this gives no objective reason whatsoever (again under the laws of statistics) to believe that any of the alleged "laws of nature" we talk about is actually a universal law. That is to say, if you believe, with even one percent confidence, that we ever have, or ever will, uncover a single line of the source code of the universe -- a single law of Nature that holds without exception -- then you, my friend, believe in miracles. There is no reason to expect the scientific method to work, and good reason to expect it not to work -- unless human mind was designed to be able to uncover and understand the laws of nature, by Someone who knew exactly how complex they are.
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Notes -
Success rates matter.
If tarot reading worked as consistently physics or math then boy would that be something.
(Now social sciences, well…)
Science as a method frequently involves guessing and dumb luck and accidental discovery. But then the point is systematically testing findings and examining new evidence and ideas. Tarot reading doesn’t have iterative improvement going on.
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.
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.
Where does math fit here under “physical world”?
The thing you seem to be doing is putting forth a standard no epistemology can satisfy. It’s not like pure math and logic don’t have identified paradoxes and limitations. Just ask Bertrand Russell.
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”?
There are a lot of “universal” rules in physics, so long as you stay at the atomic level. (The quantum domain also has its rules, but they don’t break the atomic ones altogether.)
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.
An appeal to authority is warranted here, rebutting your argument doesn't actually hinge on the truth of the theory, it hinges on whether it is possible for experimental evidence to justify a belief in the correspondence of a theory and reality. If it does there are cases where the logic of the theory enforces universality.
To wit, taking Newton's law as an example (and supposing we only knew classical mechanics), would we be justified in saying that the masses we observe behave as per his theory?
I'm not saying universally, merely the things we've observed locally.
If so, it turns out there are other cases, where if we are justified in believing the theory, the theory says things about the universe as a whole.
If you don't believe we can go from experimental evidence to justified belief in theory, then we have bigger problems.
To recollect (since the conversation is pretty deeply threaded now), this was the original challenge:
and the response:
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.
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"?
Sorry, but no. We are on an internet forum. Asking:
It is absolutely ridiculous and comes across as raising your standards so as to avoid engaging with the argument, to ask people to describe the experimental design or the math of matters well settled in physics. That can be pages, and pages of work, it is ridiculous to ask for it, on an internet forum, especially, when if you honestly want it, a five second google search will suffice, You want to play this game? Two can do so.
You say:
Well where is your proof for this?
But no, rather then demanding proof for this, I accepted it.
Besides, what value is there in doing so for physics? We already know you do not believe the work the scientific community has done is sufficient to prove true, the laws in discussion, if you did, we would not be having that discussion, so what value is in there in reiterating it?
Really? You went to great effort to single out universal laws as specifically unbelievable, rather than coming down on empiricism in general. 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)? If not, is there an
Finally I've made an argument I am confident proves you incorrect, but to which you have not engaged.
Say we are pulling polygons out of an infinite box of simple polygons. We notice that every polygon with three sides, has an internal angle of 180 degrees. 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?
This is relevant because this is how we can truly justify belief in universal laws in physics, but I would like to know your opinion on the polygon idea before I do the further of work of going into the physics.
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.
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:
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.
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"?
Why don't you prove:
Then we can return to the discussion. Until then your whole argument rests on something you have no proof for.
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.
I will point out this is another claim you've provided no proof for.
Again, I am not seeing how this differs from skepticism in general. Like take your point about Bayesian statistics, forget universal physical laws, can you come up with an objective, quantifiable number of confidence for whether a coin will flip heads?
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I am not talking about our world, we have no box of infinite polygons in our world. This is a thought experiment. And yes, the polygons are Euclidean, as I said we are pulling simple polygons out of the box.
Can we make a "universal law" about the angles of all three sided polygons in the infinite box?
I agree no observational evidence could prove this (which I think is your point regarding physics), that is no, number of observations of three sided polygons with 180 degrees could justify our belief that all the three sided polygons in the box have an internal angle of 180 degrees. But surely the math can?
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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.
My layman’s understanding is that the fundamental properties of spacetime, mass, and energy as we understand them via Special Relativity make it impossible.
Here’s a bunch of physics nerds describing how it would violate causality:
https://physics.stackexchange.com/questions/671516/proof-for-impossibility-of-ftl-signals
Great idea! Bring it on -- but I get to cross examine.
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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.
You’re applying a rigid categorization of “fact or fiction” to an area where the practicality of “all models are wrong; some are useful” is the typical approach.
You’re calling for perfection or it’s fiction, when science has been building knowledge bit by bit. Things can have shades of gray.
Obviously, understanding the Ultimate Nature of Reality and Its Universal Laws is a fine goal, but the way to get there is almost certainly a pretty messy process.
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.
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