Our main goal is to learn if or how a theory can be falsified. Sound easy? It isn’t. In order to get there, we first need to grasp what is meant by prediction and explanation. And the reason we must start with these is that some say they are radically different, that falsification depends on one but not the other, or both but in different ways. None of this is so.
This may be somewhat confusing, so it is understandable if you only read the conclusion.
Let’s consider scientific theories. What are these? Well, a theory is that which makes predictions about observables. Take Newtonian physics for an example. That theory can predict what observable path a missile might fly.
Another way to define theories is that they “explain”. Explain what? Well, observations. Explanation is logically prior to prediction, you cannot predict without an explanation, but the two are not separable, because although it may not seem like it, you first need the predictions to make the explanations. Stated another way, prediction follows directly from explanation: you don’t have to make the prediction, but it’s there at all times because of the explanation.
You get both as a package; there is no peeling the two apart. If you can explain, you can predict. If you can predict, you must have begun with an explanation: you cannot make a prediction without an explanation.
Even a prediction of the form “just guessing” (about some observable thing) relies on an explanation, though a poor one. Explanations do not have to be true (though their truth is our goal) or accurate to make predictions. The explanation for “just guessing” is that the world is of the form of your guess, which is a sort of chaos. You also don’t have to believe your explanation, which nobody who is “just guessing” does. We are discussing matters of logic, of what follows from what, and not belief.
Here’s the key. There is nothing in “prediction” that says prediction must only be about the future. We say theories explain well because past observations exist which the theory could have predicted had these observations been in the future. The time the observations are made do not matter. That’s why the predictions are needed first, in a way, to help form the explanations.
All predictions are propositions like this: “Given X, Y will follow with such-and-such probability”. That probability may be any value between falsity and certainty. The “X” is the set of conditions which must exist for the prediction, and it here also contains the theory, which forms the explanation.
That’s how we know explanations make predictions not only of the future, but of the past. We simply look for instances at which X obtained, whenever these happened or will happen, and we check whether or not Y followed. The closer our predictions are to the observations, the better the explanation is.
We sometimes form, or reform, explanations by looking at the predictions. The process by which explanations are born or modified is iterative and involves all kind of other considerations. But those mechanics are not our interest here. We want to know when a theory, or equivalently an explanation, has been falsified, or its opposite, truthified (you heard me). For whenever you say a proposition is false, you have said its contradiction is true.
The only way to know or prove or give credence to the idea a theory has explained anything is to have observations in hand that have been predicted (in our sense of regardless when the measurements were taken) by the theory and are consistent with the theory.
With definitions out of the way, we come to what prediction and explanation mean to theories.
A theory can explain observables that no one has seen, or could see. Which is the same as making predictions that can never be verified. The example I have in mind, though some disagree, is the Many Worlds theory, which posits universes not “connected” to ours, and so that what happens in those universes can never be measured. We’ll come back to that disagreement another day.
We need not have such an esoteric example. For we can always tack onto any theory we like, and even stronger our best theories, an explanation of an observation that cannot be made. The rest of the theory is untouched, and remains as good as it always was, as long as the tacked-on explanation is not logically inconsistent with the base theory. The modified theory has an explanation that cannot be verified, even though the rest of the theory (we suppose) can be or has been.
For instance, we can tack onto the Standard Model something like super intelligent pink Leprechauns spontaneously popping into existence, but only inside black holes, for whatever explanatory reasons we can invent. This can never be checked (if black holes are real).
The point is that no theory gains, they do not become more likely to be true or even become more useful, because they contain extra explanations of unmeasureable observables. We can say the augmented theories have greater explanatory power, but since the claims can never be checked, it is always an idle boast. Besides, we can add to any theory as many extra unmeasureable explanations as we have the energy to invent. This does indeed give theories a boost in explanatory power, but of a completely sterile kind. (If our goal is to explain observables.)
Conclusion: while there is a difference between prediction and explanation, they are both implied by the other, they are inseparable. Therefore, if we’re searching for ways to falsify a theory, we must examine both.
Subscribe or donate to support this site and its wholly independent host using credit card click here. For Zelle, use my email: matt@wmbriggs.com, and please include yours so I know who to thank.
Well said, sir. Well said.
You have defined what you mean by the word “prediction”, but you have not defined what you mean by the word “explanation” (and no, it is absolutely NOT self-evident).
That makes it rather difficult to understand what you are trying to… well, explain.
Morten,
You caught me. I was hoping to leave that somewhat vague until I describe theories. For now, let’s say explanation is the theory or model of a thing.
Fair enough.
My own understanding of “explanation” would be something that makes an observation fit with whatever I happen to believe in advance. Fx. if I believe in evolution by sexual selection and I observe the tail of a peacock, the idea that an oversized useless tail proves superior fitness to potential mates would be an “explanation”. (I would need yet another “explanation” for sparrows, of course).)
But by this use of the word “explanation” most of your statements would be obviously false, so I assumed you must have some other understanding of the word.
All right, the day is ruined anyhow, so I might as well comment some more on the internet.
I have a quibble with your non-distinction between pre- and post-diction.
In practical terms it makes a huge difference. Given any set of numbers there is an uncountable infinity of functions reproducing it. Thus any given set of quantitative observations can be postdicted in infinitely many ways. But the propability that any given one of these functions will also by chance fit an observation made later is zero.
Thus prediction is the gold standard in science, while postdiction is at best silver – and more often just bullshit.
An example: CERN makes trillions of observations of particle collisions and since the processes are stochastic, by sheer chance there will be observed deviations from the predictions of the Standard Model. In a fit of statistical incompetence number grinders at CERN then calculate the propability of seeing the same deviation when the experiment is repeated and then claim that this low propability is also the propability that the deviation would occur in the dataset they began by analyzing. They then make a press announcement claiming, say, a “4 sigma event”, i.e. a “near discovery” of Beyond Standard Model physics. (In reality they should calculate the propability that any one of all possible 4 sigma events occur by chance, but that is of course impractical since the list of all such potential events is enormous.)
Subsequently thousands of articles are published by particle phenomenologists postdicting the observed deviations and predicting others (physicists call this “ambulance chasing”). Then the experiment is repeated at CERN and the original deviation just fades away. This has happened quite a number of times over the past many years, and it clearly shows the danger of putting pre- and post-dictions at the same level of significance.
Prediction is that ? (pi), e (Eulers), ? (phi) have no regular pattern and are “Irrational Transcendent”.
I have no spaceship for a trip to the moon; it’s most often a matter about feat and expense, and that expertocracy stops for asserting things instead of solving them.
Divide consecutive [cut the . out] digits of ? (pi), e (Eulers), ? (phi) by the nearest (yet <= ) power of 2 and see for yourself.
0 – I agree in principle, but not in detail.
1 – Twenty some years ago I took a major climate model apart: roughly 1% of the code reflected a 1960s box of fortran cards but another 20% or so came from patches introduced by decades of grad students trying to make it correctly predict the past – i.e. making it appear to fit; in one case by transforming some hard wired data to fit the output format. (Most of the rest was granulation and parallel processing related.)
So no – the apparent ability to predict backwards cannot be trusted.
2 – I can usually predict my wife’s reaction to some kinds of things (colors, people, foods) but have no explanation for any of it.
3 – predictions of the “fits this distribution” presume a probabilisic universe (nonsense even if spelt correctly) and fudge the issue. In physics I want predictions to be precise and singular: 1.72154GEV at .. etc Anything less is guesswork.
“The time the observations are made do not matter.”
Yes this is how they lie when they say their false theories predict anything. They are merely fudging the present to pretend had they predicted their false conclusion in the past it would have worked. Meanwhile conspiracy theory truly did predict the future and science predicted literally nothing.
Not everything is predictable but you can sometimes still explain it. Paul Murphy is correct, it’s easy to predict the behaviour of normies to pretty much any given stimulus but explaining why they would continue to repeat such madness is definitely beyond a rational man… the closest I can get is that P Zombies are in fact a thing rather than simply a though experiment but sometimes normies are too bizarre even for zombiedom.
Not every contradicted truth is false.
George Spencer-Brown gave the example of the perpetual liar, who states: “I always lie!” which implies he is not telling the truth in that statement, which makes the statement false, so he is telling the truth, which means he is a liar, …
He ended up with 3 categories: [T], [F] and [i], with ‘i’ being ‘imaginary’; or was it ‘self-referential’?
“Explanation is logically prior to prediction, you cannot predict without an explanation…”
I beg to differ. If you use an AI, for example, to predict a chess move, the weather, or any of a hundred other things, it may give you a prediction but most AIs will not give an explanation. They cannot, any more than a tennis player could write down the differential equations that explain why he hit the ball at a given moment and angle with a given power.
Arguably, explanations merely help human minds to “understand” – another intriguing undefined term – how things “work”. The Bohr model of the atom is an excellent example: maybe an atom is like a tiny Solar System. (Turns out it really isn’t).
Tom,
Yes, the “AI”, like any model, has an explanation. It doesn’t mean you know what it is, or can figure out what its parameters and their weights mean, but the model does. Indeed, the explanation is the model.
Your thinking is leading in just the right direction, however. Because there is ambiguity in “explanation”. What we all want to know is what is full cause of thing, i.e. cause in all its aspects. That’s the full and complete explanation, on one definition.