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 -
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).
There is a very real sense is that this is determined by the mathematical structure of what mass is. I can make that argument, as I said,
If you would like me to, but I think its incidental to the real argument we are debating, which is, can we be justified in believing in universal laws?
My point is that while the laws of physics are discovered empirically, what lets us be justified in speaking universally of them, is math.
If all we had was empirical observations, I agree those empirical observations of "mass behaving in X way" would not allow us to conclude "everything with mass behaves in X way".
However, we can instead identify mass, as a certain mathematical structure, where the "must behave in X way" follows as a consequence of the math.
Then we can speak universally, because when we say "all things with mass behave in X way" we are saying "all things with this mathematical structure behave in X way".
If we can be confidant about what the math, of mass is, then we can be confidant about the behavior of mass universally, and unless you embrace philosophical skepticism, which you claim not too, I don't see why we can be confidant in the math.
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