samedi 24 septembre 2016

Against abduction

Abduction (or "inference to the best explanation") is the cornerstone of scientific realism. There are always many different theories, or hypothesis that could account for some given phenomena, but scientists make their choice on the basis of non-empirical criteria, such as simplicity: they choose the best explanation. According to a realist, this means one likely to be true. This, in essence, is abductive reasoning: an inference from non-empirical, explanatory virtues to truth, or to likelihood. Furthermore, the realist claims that her position, that our best scientific theories are approximately true, is itself the best explanation to their predictive success. That's what we could call a meta-abduction: a justification of abduction (best explanations are true) by means of abduction (that best explains their success, so it's true). So it's clear that abduction is essential to realism, perhaps its definite characteristic. But is abduction a valid form of inference?

Abduction or induction?

View of Ueno-Nakasendo railway from Ueno station2

Say my train stops right in the middle of a forest. There is a lot of wind. The best explanation is this: a tree fell on the way, because of the wind. Certainly, this is a good explanation. But is it the right one? I don't know. Why is it plausible? Because I know that trees often fall when there is wind, especially in forests where there are lots of trees, and I know that things falling on the way sometimes make trains stop. Ok. But this is induction, no? What makes this explanation plausible is that, given that there is wind and that we are in a forest, there is a not-too-low probability that a tree fell on the way, and given that the train stopped, there is a not-too-low probability that it was because of a tree fall. If you put them together, the joint probability that this is the right explanation is quite high, as compared to other explanations. But still, I'd like to see some new evidence for this, just to be sure. Perhaps there was a problem in the engine, or perhaps an animal on the way. I merely gave credence to a certain hypothesis, on the basis of my past experience and current evidence, but this looks very much like a form of probabilistic inference.

Now you'll say that in practice, I cannot evaluate the exact probability that a tree stopped the train. I cannot even imagine all possible alternative explanations. Fair enough. But that only means that I'm using a liberal, informal form of induction. I'm not giving more credence to this hypothesis in virtue of some putative characteristics, such as simplicity, that would make this explanation a good one, the best one, independently of the evidence. Nor am I dismissing other possible explanations because they're only the second or third best ones. My explanation is as much likely as what current evidence and past experience of train breakdowns and storms allow me to infer. As van Fraassen shows, were this likelihood to depart from this inductive evaluation, I would fall prey to a Dutch book argument: someone could bet against me, and win. Van Fraassen's argument rests on the assumption that probabilities can be evaluated, and we've just said it's not the case here, but the fact that I cannot evaluate precisely the likelihood of my explanation does not entitle me to give warrant to non empirical criteria that I would consider irrelevant if I had more information, or if the range of possible explanations were more limited. The fact that there are more possible explanations that I can imagine, if anything, should make my hypothesis less likely, not more.

Abduction as strategy

First steam train leaving Yokohama2

To be precise, there are two issues to consider: one is the means by which I come to formulate and consider an hypothesis and the second is to what extent this hypothesis is justified. Perhaps I came to the hypothesis that a tree fell because it's simple. This is the first hypothesis that came to my mind. Now arguably, I should consider simple hypothesis first: they are more easily confronted to evidence (or, as Popper would have it, they are more refutable). We'll see if a tree fell or not. If I was postulating that invisible aliens stopped my train, I would have a hard time to check if it's true or not. That could be a rule of thumb in any enquiry: let us start with the simplest hypothesis (with a minimum plausibility): we'll see if it works or not, quite straightforwardly, and then (if it doesn't) we can consider more complex hypothesis. That's strategic reasoning, and of course, simplicity doesn't have to be the sole criteria (for example, conservatism with regards to well entrenched theories could play a role too: why re-invent the wheel?).

Does it mean that my hypothesis is more probably true just because it is simple (or conservative)? Certainly not. It only means that the best way to enquire into why the train stopped is to test this hypothesis first, and then go along with more complex or less tractable hypotheses, that will take more time to check. Abduction is valid as a way to select hypotheses to test, not as a substitution to empirical tests. That's what Peirce had in mind when he introduced the term "abduction": to him, abduction is about discovery, or selection of hypotheses during enquiry, and only deduction and induction are involved in justifying hypotheses.

It's unfortunate that this original sense got led astray into something so utterly illegitimate. Abduction is useful for finding good explanations to test, given our epistemic values, given our goals. But goals and values have nothing to do with truth, and the best explanation for our purposes does not have to be the right one. We do not decide what is true or not: nature decides.

That's why I don't understand the traditional justification of scientific realism. All remarks above apply in science as well: a theory being the "best" explanation, given some non-empirical criteria (simplicity or whatever) does not mean that it is likely to be true. That only means that we should test simple theories before to consider more complex ones, if the former don't work after all: non-empirical criteria are strategic criteria, not justifications. It's certainly true that abduction is important in science: as a way to construct hypothesis. Uranus' trajectories does not follow newtonian mechanics--unless there is a planet deviating Uranus. Let us call it Neptune. That's the best explanation, because it does not require throwing our well tested theory overboard. That does not mean that Neptune likely exists! Let us try to observe this planet: ok we found it. That's a great success for newtonian mechanics. Now we know that our explanation was true (by direct observation, not abduction). And we know that newtonian mechanics works well in different situations. But that's induction. Not abduction. And abduction is far from being systematically vindicated, as the case of Mercury and Vulcan shows.

How could we test realism anyway?

First steam train leaving Yokohama1

So abduction as a justification is not very convincing. What about meta-abduction? I think it's even worse.

The idea is this: successful predictions, in particular when theories are applied to new domains, could seem miraculous: it calls for an explanation. Realism, or the hypothesis that our theories are approximately true descriptions of the world (i.e. that first-level abduction, as performed by scientists, is a marker of truth) is such an explanation, and a good one (if not the only one): our theories are true, or approximately so, that's why they work! Since it's the best explanation, it must be the right one.

This line of reasoning is obviously circular: it merely justifies (scientific) abduction with (philosophical) abduction. It's not devoid of intuitive appeal, but it's not very clear how "good" this explanation is: what are the criteria involved? What kind of explanation is this? As Putnam puts it, scientific success would seem miraculous if our theories weren't true. Does it mean that the explanation is likely given the evidence, and not only good according to non-empirical criteria? A meta-induction rather than a meta-abduction?

The intuitive appeal of the argument seems to stem from this interpretation (realism seems very likely, not only a good explanation). But what could make us think that? Inferring the likelihood of realism from empirical adequacy through probabilistic inference would require being able to contemplate all possible theories, or at least having an idea of the ratio of true theories among the empirically successful ones, but that's not something we can ponder (it would be a base rate fallacy, as Magnus and Callender argued). In any case, the strategy is hazardous: after all, the best argument against scientific realism is based on a meta-induction on past theories: most successful ones are now considered false... So what else have we? Non-empirical criteria? Then the argument loses all its intuitive appeal: we are merely speculating.

As we can see, meta-abduction shares the problems of first level abduction: that realism is a "good" explanation to empirical success doesn't make it the right explanation. But things are worse: at least in the case of first-level abduction, non-empirical criteria could play a strategic role for selecting what hypothesis to test. However, in this case, meta-abduction cannot even be considered a good strategy: we cannot test realism any further once we've formulated the hypothesis.

Indeed, assume that realism is a good choice: it's the "best" explanation to empirical success. Ok. Let's test it empirically. Let's try to observe it, as we observed Neptune. But how could we do that? There is no further observations that could confirm that our theories are true: all that we confirm is that our theories fit the phenomena, again and again, which is only what needs to be explained. Realism is an explanation to this fit, but that doesn't make it a likely explanation, unless we test it independently: but it's not a testable hypothesis.

Structural realism faces the same problems. Assume that theories are approximately true about structure. If we ponder it a bit, it's not clear how, say, newtonian mechanics is approximately true about the "structure of the world", or how we could know that. That's still a hypothesis--and not a very clear one: what do we mean by "structure of the world"? What is clear, however, is that newtonian mechanics is approximately true about the structure of phenomena: it makes good predictions about observable regularities, mathematically expressed. It is empirically successful. And so are its successors. Of course, new theories share some common structure with newtonian mechanics: how could they be successful about the same phenomena if they didn't? But how does this imply that they are true beyond what they say about the observable, or the measurable? And if this hypothesis is "good", how could we test it further? I don't understand how structural realism, if sound, could be anything but structural empiricism.

Meta-abduction and miracles

View of Ueno-Nakasendo railway from Ueno station1

These are some of the problems that I see with the meta-abduction involved in the justification of scientific realism, but there's a more pressing one: is there anything to be explained here? Is it really the case that empirical success could seem miraculous and calls for an explanation?

There are two levels where we could expect an explanation. The first is the theory level: why this particular theory is so succesful? A tentative explanation would be: because it is approximately true. However, given that our theory is probably one among many that would account for the same phenomena, this boils down to first-level abduction: this particular theory is true because it is the best one among its alternative (the most simple, ...). The second is at the level of science: the fact that scientific enquiry is so succesful in general calls for an explanation. The explanation, here, would be meta-abductive: science works so well because first-level abduction is an inference toward truth.

I explained in the last post why we should not think of empirical success as miraculous: the fact that novel predictions prove true is just the first step of an inductive reasoning--an induction on models of a theory, or on different types of situations. Given that a theory makes novel predictions, that it successfully applies to a new domain, we can be confident that it will continue do be efficient to predict various situations, that differ by their initial conditions, by what we measure, or by what type of system is involved. But that's not abduction! That's only induction on different possible configurations that could be exemplified in the world. It begins to be convincing after novel predictions prove successful, and it only concerns the theory that makes successful novel predictions: not all instances of abductive reasoning work. Meta-abduction makes no sense because there is nothing to be explained here: sometimes, abduction works, and sometimes it fails. Our best theories work because they are the result of a selective process: we only retained the ones that worked.

At the level of a particular theory, there's no miracle either: the assumption that a theory that proved succesful will continue to be succesful is the result of an induction, and that kind of induction does not require believing that the theory is true. We don't need realism to be confident that theories that make novel predictions will continue to be empirically adequate: at most, we need the kind of regularity assumption that supports inductive reasoning in general (this was explained in the last post), and once we've made this assumption, there's no miracle, and no need for further explanations.

In sum, the explanations we can give to the empirical success of scientific theories are these: at the level of theories, that the world is regular, including when it comes to trans-domain regularities (what I called structure in the last post), and, at the level of science, that through a selective process, after several failed trials, we eventually found a theory that matches these trans-domain observable regularities very well.

Some authors, such as Ladyman, argue that accounting for empirical adequacy as the result of a selective process is not the kind of explanation we need (as if we explained why birds fly with natural selection instead of physiological and physical mechanisms). What kind of explanation are they after? The first kind (birds fly because of natural selection) is analogous to science-level explanations. The second kind (birds fly because they have wings) is analogous to theory-level explanations. So if they're after the second kind of explanation, they want us to explain why particular theories are so succesful. Here it is: the natural world has observable regularities, and the predictions of our theories correspond to these regularities. How come so? Because they were selected for that. What more could be said? We could go into the philosophy of experimentation to explain the mechanisms by which theories make their predictions, and how they are confirmed or disconfirmed, but I'm not sure that it would be relevant. Or perhaps, more plausibly, the realist is after an explanation to observable regularities themselves. But that's precisely the point: we have no way to know, on the basis of these regularities alone, what the right explanation could be.

Shimbashi Station Hiroshige III


There is no reason to think that non-empirical criteria are indicators of truth: abduction, at best, is an informal form of probabilistic induction, but in general, it should better be thought of as a strategic process of hypothesis selection. Abduction, so conceived, has its full place in science, but extending it to philosophical reasoning is illegitimate: selecting hypothesis for test when we are unable to test any further makes no sense. There is no "success of abduction" to be explained at the level of science in general: sometimes it works, sometimes it doesn't, we select theories that work, and their continuing empirical success, at a theory level, is well accounted for by induction alone.

So, yes, abduction is central in science: as a good, strategic way to produce new hypothesis that we can test empirically, just as Peirce viewed it, certainly. But not as a justification for their truth. And it is certainly not a justification to indulge into crazy metaphysics and its loads of untestable hypotheses.

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