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 -
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?
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.
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 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.
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.
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).
I've been very clear I am talking about only the planets in our solar system.
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.
Okay, I guess not, but again, I don't understand how this isn't different from arguing against empiricism in general?
By your logic why can't I say that you have no justified belief the moon isn't made of cheese, because it could be cheese in the infinitely many moments when your not looking at it?
I'm not asking anything about universal law or if it will flip heads. If I put a coin in front of you, is there anything you can do to come with some quantifiable belief about it?
To reiterate my point, on your initial post you went to great emphasis to single out belief in the universality of physical laws as uniquely flawed, yet if I understand your logic correctly it seems there is no belief about reality (universal or not) can be quantifiably justified, is that correct?
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.
Okay, but then I don't see how your whole argument isn't really just an argument against empiricism in general.
Is there any way we can establish anything?
Like if I put a coin in front of you do you believe is there anything we can do to come to any sort of quantifiable belief about it (with out miracles)?
You claim not to be arguing philosophical skepticism, but I don't see how not. What knowledge of the world can we have?
You singled out physical/universal laws as specifically needing miracles to have justified belief in, but unless I misunderstand you, your position is really that we need miracles to have justified belief about everything in the world, not just universal physical laws.
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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?
I can't think of a statistical rule that would justify it. Can you?
I agree there is no statistical rule, but why do we need one? Via math if a simple polygon is three sided, it has an internal angle of 180 degrees.
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've been very careful to not give them a name, for good reason. There may well be objects in the box that behave differently. I am not talking about those objects.
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?
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:
Because it allows to speak in universally. To go back to your newton's law example:
We can say this with confidence, because this law is a consequence of what mass is, mathematically. The law was determined empirically, and you are correct that if it was a purely empirical conclusion, we could never truly speak confidently about everything in the universe. But we've since discovered that this law is consequence of the mathematical definition of mass. If something has "mass" as defined by certain mathematics, then it must attract every object as you quote.
What would it mean for an object not too? Well I can imagine two possibilities.
or
This is simply not correct to say about the Law of Gravity. It is almost correct to say about the second law of motion:
F = MA
with one caveat. Newton implicitly assumes that each particle has a property, called its mass, which is constant over time. It turns out this not true: the mass of a particle can vary over time as a function of the object's velocity, according to the special theory of relativity. If you alter Newton's theory to make mass, force, and acceleration functions of time, then I think you are correct and the second law of motion is just the definition of mass. But then, by itself, it does not predict anything (since you could measure the mass of a particle, then perform an experiment, and anything could happen since the mass might have changed between weighing the particle and doing the experiment).
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