Ready for some Logic 101? Something real easy, I promise. We’ll use it in service to show why falsificationism is not that interesting, or useful, and we’ll need it in judging how good models, theories and the like are.
If you have a valid sound argument that proves a certain proposition is false, then your riches have doubled, for you also have in hand an argument that proves that the contrary of that proposition is true. Prove one, get one free!
By contrary I of course mean the logical contrary.
For instance, P = “It is raining”. And your argument is, “I’m looking out the window, and it’s not raining (and, implicitly, my observation is sound, and, implicitly, the meanings of all the words, grammar, and punctuation I’m using)”, then P is false. Which makes P’ true (as it is sometimes written), i.e. the logical contrary of P is true. In this case, that contrary is easy to speak: “It is not raining.” (Sometimes people write not P’ but Pc or other similar things.)
Easy promised, easy delivered.
Want even better news? This simple bit o’ logic applies to all scientific hypotheses, models, theories, laws and whatnot.
Now I claim, and with the blessing will prove to you, that all these labels speak of the same thing. Logically, there is no difference between a hypothesis, model, theory, or law. There may be, and are, many practical separations which are used as bookkeeping, tools to divide labor, and trust given to different labels, as it were. But logically speaking, there is no difference between any of them.
All of them take the form of a list of propositions speaking about some conclusion, just like the argument about the rain. That list of propositions, explicit and implicit, is the argument. In science, the conclusion, itself too a proposition, says something about Reality.
We did the “law” of gravity before. Quoting the argument portion:
“F = GMm/r^2,
where F is the force, G is a constant, M and m the masses of two bodies, and r the distance between them.”
As an argument, this is incomplete, as the linked article proves. It speaks of a part of Reality (the masses, for instance), but it doesn’t say how to apply it to real objects. For instance, the earth is here and the moon there, so what happens to both at some future point? We can’t tell just from this. That only means we take all those extra propositions as implicit when we speak of “laws” like this. They are there, but not written down. Just as the meanings of the symbols are there, even though not written down.
A hypothesis is the same thing. If all theses things hold, the hypothesis says, the “all these things” forming an argument, then this-and-such will happen in Reality, plus or minus. That “plus or minus” is optional. Think statistical or quantum mechanical hypotheses.
Again, the same is true for theories and models.
Of course, we speak of different parts of the arguments, those propositions in the middle, as it were, in all sorts of ways, giving them individual names, like with mathematical theorems that are components of most scientific theories. Or like how we speak of the force part of the “law” of gravity, as if it exists by itself (it does not). Yet the only way the “law” itself is accorded any weight is because of the tacit premises that made predictions possible.
With all that, here is what all theories, models, hypotheses, propositions, laws look like:
Premises -> Bit of Reality.
Which is to say, an argument. The Bit of Reality may be certain, or only probable, or even false. Some or all of the premises may be mere assumptions. Whatever.
Like with unconditional probability, which is impossible to write down, I invite skeptical readers to show how any of these, models etc., do not fit into the scheme I outline. Can’t be done.
For ease, I’ll call all entities models. They are all models because they are not Reality, but abstractions of it. See the original gravity post for details about the differences between “laws” (i.e. models) and causal powers.
Expanding the prior formula, all models are arguments of the form:
M = P_1 & P_2 & … & P_m -> Bit of Reality,
where each of these individual propositions P_i are often themselves compound propositions, containing logical ors, ands, ifs, and so forth, including observations. The tacit and implicit premises are all there, which again they are usually not written. Here they are all there. Which means even the simplest model is huge, rich in premises (word definitions are there!).
That makes the little “m” quite large, at least for any model of non-trivial importance. Because if there’s any math in the model, we have all the propositions supporting that math in the list, too. And so on.
Here’s the falsification part.
Suppose a model said Y was impossible. Y could not happen. It’s not conceivable that Y could occur, according to our model. M says, “Y is out of the question. So there.”
Yet, one day, Lo!, Y is observed!
This is just like the rain argument. We have proved our model is false. Which—we are now back at the beginning—means we have also proved its contrary is true! M’ is true, given the observation Y is observed. (That is a separate argument!) That contrary of M is this:
M’ = (P_1 & P_2 & … & P_m)’.
That only means that at least one of these propositions inside M is false; not that all are (though that could be true). And since each P_i may itself be compound, if P_i is the one false proposition, it could only be some element of P_i that is the offending part.
Now M itself has been (in our example) falsified. It must therefore be abandoned. Tossed out. Thrown away. Spoken of with disdain. And, worst of all, unfunded.
But that’s not what happens. When a model is falsified, especially a beloved or well funded model, it is tweaked. Some minor change in one of the P_i, is made, or more usually some new P_(m+1) is added. The result is not M, but something else which is called M. Since so much of the original M remains intact, it’s natural to call the new model M, too. Even though M has been falsified.
In practice, it’s not only small tweaks, but large ones, too. Surgery to the original M can be gruesome, like some aging celebrity whose face is pulled into the shape of a demonic cat. But still the new thing will be called M. Because there is something in that original M that retains a powerful grasp on the minds of those who love it.
Technically—by which I mean logically—any change in M probative about Reality results in a new model. Even each new (probative) data point added results in a new model, logically speaking, though most people will go on using the same old name. That’s to make bookkeeping easier, and because the alternative is not known.
I keep saying “probative” because we could add any number of propositions in M that have nothing to do with the Reality spoken of, even necessary truths (which is like multiplying a simple equation by 1). But none of these change what M says about Reality.
Which means that to judge M we can only look at those propositions which have something to say about Reality.
That is enough for now. We’ve done a lot but haven’t yet put our finger on the real problem. Which is how some people judge the model’s goodness in reference to itself, and not in its performance. That will have to wait.
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