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.
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