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 -
See, the main crux of it is that if there's an objective reality out there (and there are a lot of very complex ideas hiding in those two simple words), we are simply powerless to directly perceive it.
In practice, I choose to act as if there is one. I have niggling doubts in my mind that the world as we see it could be fake, but I will throw up hands if asked how likely that is to be the case. Our decision theories really don't like infinities, and we need better ones if they're even possible.
So I certainly act as if my observations of reality or the advancements of science are evidence that my subjective reality aligns with (hypothetical) objective reality. Given that I don't have the mental bandwidth to hold that many layers of abstraction in my head at once all the time (and the expected return on doing so is minimal), I will happily say that Science provides "objective knowledge about the world" in the sense that it helps us establish or discover facts that are independent of observers (for all that I can't actually put myself in the shoes of another person and check).
You take it for granted that an objective reality exists. Which is fine, but I have more subtle theoretical concerns that prevent me from accepting that as axiomatic. I still think, as I've said, that this is potentially true and more importantly I can't show otherwise, so our behaviors do not diverge until the point the Creators/God show up or the butterfly stops dreaming of the human. I don't think those are likely to happen, so we act the same way and trust in empirical analysis in everything but metaphysical debate on a niche online underwater basket weaving forum.
But what this does mean is that I vigorously disagree that this is a failure of Bayesianism. We simply can't do better without taking as axiomatic that our observations are observations of an objective reality.* If you wish to do so, well you won't be harmed by it, but I act the same as you do without holding that belief.
I appreciate the nuanced debate, it's a shame it's buried so deep and we can't get more people into it, but feel free to ping anyone you think might have a useful opinion to offer.
*In the same vein that a theist might claim that Science is flawed because it cannot prove the existence of God, which becomes a pointless criticism for someone who finds the latter's existence dubious.
I'll do another reply since I think we're still talking past each other a bit.
And yeah, it's a shame our talk is buried so deep nobody is likely to read it :D Still, I found it really fun and useful!
First, let me say I don't take it for granted that objective reality exists - I believe it does, which is a conjecture like anything else, and open to criticism and revision. Objective truth, however, would exist even if there is no objective reality: in that case, the statement "there is no objective reality" would be objectively true, and this is what I would like to believe if it is true. Popperianism (or, as it's less cultishly called, critical rationalism) requires no assumptions that are not in principle open to critical discussion and rejection, which is in this view the main method of rational inquiry.
And, if I haven't made it clear enough, I'm actually a big fan of Bayesiansim. If I weren't a Popperian, I'd be a Bayesian! I'd even say it could add a lot to Popperiansim: although I think the basic Popperian picture of rational inquiry is correct, the formalization of the process of critical analysis that Bayesiansim could add to Popperiansim could definitely be useful (although I'm not smart enough and too confused by the many, many variants of Bayesiansim to attempt such a project myself). Overall though, some variants of Bayesianism, yours I believe included, are right about almost everything important to Popperians, especially the central point: accepting the skeptical and Humean objections to rational justification, while retaining the use of reason and evidence as the method of science. Popperians would add "and objective truth as the aim of science", on which I'm still not quite sure where you stand. The main disagreement, as I see it, is on the role of evidence, which is negative for Popper - evidence can only contradict theories - and positive for Bayesians - evidence can support theories, raising their subjective probabilty.
I think the discussion of whether objective reality exists and whether we can be certain of it is a bit of a sidetrack here - I completely agree with everything you said on it: we can never have direct access to objective reality (Popper would say that all our observations are "theory-laden"), and we cannot be sure that it exists, and I'm not saying I require you to demonstrate that it does to practice Bayesiansim. My main point is that Bayesian calculations are unmoored from objective reality (say nothing about it), unless you smuggle in additional induction-like assumptions that allow you to make inferences from Bayesian calculations to objective truth, in which case you run into Humean objections. And this is where I'm still uncertain of your position. You say:
But do you think your observations are evidence that your subjective reality aligns with objective reality? If yes, how does this relationship work, and how does it avoid Humean objections? If no, like I said, that'd be for me an unacceptable retreat from talking about what we are actually interested in, namely objective truth, not subjective probabilty. We can agree to disagree on that, that's not a problem, but I'm not totally clear what your position is on this, given that you have said things like the quote above, but also talked being able to convert subjective probabilty into truth. I'd like to understand how you think this works, from a logical standpoint. Or is it perhaps that your position is something analogous to Hume's solution to the problem of induction (which I also disagree with) - namely that we act as if induction is rational although we are irrational in doing so, for we have no other choice? This would be saying that while strictly speaking Bayesian calculations have no direct relationship to objective truth, we act as if it they do. This would be what I gather from the above quote, but you've also talked about probability-to-truth conversion, so I'm still unclear on that point.
Let me attempt an analogy using the map and territory metaphor to describe how I see our positions. It's a spur-of-the-moment thing, so I apologize in advance if it misses the mark, but in that case you explaining how it does so will likely be illuminating for me.
So we are blind men in a maze (the "territory"), and trying to map it out. We are blind because we can never directly see the maze, let alone get a bird's eye view of it. Now many people, the majority even, think that we are not blind and convince themselves that they can see the maze (that we can have justified true beliefs directly about objective reality). You and I agree that this is not possible, that our mapping of the maze is ultimately guesswork. We can't be sure there even is a maze! But we're trying to figure out how to act and what to believe. Now I think the best way to go about mapping the maze is to propose conjectures on the layout of various parts of the maze (i.e. scientific hypotheses), which will always be guesswork, and then test them out: if this map section I've proposed is correct, for instance, we should be able to walk 36 steps in this direction, and then turn left. If I attempt this and run into a wall, then my proposed map section guess isn't right - I gotta reject it (the hypothesis is falsified). Of course, I might have miscounted the steps, a wall may have collapsed, or any number of things might have messed up my experiment - like in the neutrino example, the experiment might be wrong, and falsification is guesswork too. But this is the role played by evidence: attempting to walk the maze, i.e. confronting our hypotheses with reality, and seeing where they clash, albeit blindly and without any justification. If my conjectural map seems to work out, if it passes the test, this says nothing additional about it corresponding to the maze. Evidence is used to contradict our guesses, not support them, in my view. And this is where we start to disagree. You think that every step you take that doesn't contradict your proposed map (all supporting evidence for the hypothesis) raises your subjective probabilty/expected utility/confidence in your proposed map of the labyrinth. To which I say ok, your confidence is increased by Bayesian calculation, but what does that tell us about the labyrinth? To me it seems you are calculating your confidence in the map, but it's the labyrinth we are interested in, and I'm not sure if and how you translate your confidence in the map into claims about the labyrinth. If you do translate your confidence in the map into claims about the labyrinth, I am not clear on how. I just directly make claims about the labyrinth, which are guesses, and my subjective confidence in them is irrelevant - the correspondece of my guesses to the labyrinth is what matters and what I'm trying to guess correctly. If you don't claim anything about the labyrinth at all and are only talking about your confidence in the map, then I think you're missing the mark - it's the labyrinth that we are interested in.
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