Unmoored theory

I’ve written before about the dichotomy of descriptive vs theoretical sciences, but I’ve recently noticed another apparent dichotomy within theoretical sciences—expansionary vs focusing sciences. Expansionary sciences are those whose domain tends to expand—(neo)classical economics seems to claim all human interaction in its domain; formal semantics now covers pragmatics, hand gestures, and monkey communication—while focusing sciences tend to rather constant domain or even a shrinking one—chemistry today is about pretty much the same things as it was in the 17th century; generative syntactic theory is still about the language faculty. Assuming this is true,[1]It’s pretty much a tautology that a science’s domain will either grow, stay constant, or shrink over time the question is, whether it reflects some underlying difference between these sciences. I’d like to argue that the distinction follows from how firm its foundations are, and in particular what I’ll call its empirical conjecture.

Every scientific theory, I think, basically takes the form of a conjoined sentence “There are these things/phenomena in the world and they act like this.” The second conjunct is the formal system that give a theory its deductive power. The first conjunct is the empirical conjecture, and it turns the deductions of the formal system into predictions. While every science that progresses does so by positing new sorts of invisible entities, categories, etc., they all start with more or less familiar entities, categories, etc.—planets, metals, persons, etc. This link to the familiar, is the empirical foundation of a science. Sciences with a firm foundation are those whose empirical conjecture can be uncontroversially explained to a lay person or even an expert critic operating in good faith.

Contemporaries of, say, Robert Boyle might have thought the notion of corpuscles insanity, but they wouldn’t disagree that matter exists, exists in different forms, and that some of those forms interact in regular ways. Even the fiercest critic of UG, provided they are acting in good faith, would acknowledge that humans have a capacity for language and that that capacity probably has to do with our brains.

The same, I think, cannot be said about (neo)classical economics or formal semantics.[2]Now obviously, there’s a big difference between the two fields—neoclassical economics is extremely useful to the rich and powerful since it let’s them justify just about any … Continue reading Classical economics starts with the conjecture that there are these members of the species homo economicus—the perfectly rational, self-interested, utility maximizing agent—and derives theorems from there. This is obviously a bad characterization of humans. It is simultaneously too dim of a view of humans—we behave altruistically and non-individualistically all the time—and one that gives us far too much credit—we are far from perfectly rational. Formal semantics, on the other hand, starts with the conjecture that meaning is reference—that words have meaning only insofar as they refer to things in the world. While not as obviously false as the homo economicus conjecture, the referentialist conjecture is still false—most words, upon close inspection, do not refer[3]I could point you to my own writing on this, the works of Jerrold Katz, and arguments from Noam Chomsky on referentialsm, or I could point out that one of the godfathers of referentialism, Ludwig … Continue reading, and there is a whole universe of meaning that has little to do with reference.

Most economists and semanticists would no doubt object to what the previous paragraph says about their discipline, and the objections would take one of two forms. Either they would defend homo economicus/referentialism, or they would downplay the importance of the conjecture in question—“Homo economicus is just a useful teaching tool for undergrads. No one takes it seriously anymore!”[4]Though, as the late David Graeber pointed out, economists never object when homo economicus is discussed in a positive light. “Semanticists don’t mean reference literally, we use model theory!”—and it’s this sort of response that I think can explain the expansionary behaviour of these disciplines. Suppose we take these objections to be honest expressions of what people in the field believe—that economics isn’t about homo economicus and formal semantics isn’t about reference. Well then, what are they about? The rise of behavioural economics suggests that economists are still looking for a replacement model of human agency, and model theory is basically just reference delayed.

The theories, then, seem to be about nothing at all—or at least nothing that exists in the real world—and as a result, they can be about anything at all—they are unmoored.

Furthermore, there’s an incentive to expand your domain when possible. A theory of nothing obviously can’t be justified by giving any sort of deep explanation of any one aspect of nature, so it has to be justified by appearing to offer explanations to a breadth of topics. Neoclassical economics can’t seem to predict when a bubble will burst, or what will cause inflation, but it can give what looks like insight into family structures. Formal semantics can’t explain why “That pixel is red and green.” is contradictory, but it provides a formal language to translate pragmatics into.

There’s a link here to my past post about falsification, because just as a theory about nothing can be a theory about anything, a theory about nothing cannot be false. So, watch out—if your empirical domain seems to be expanding, you might not be doing science any more.

References

References
1 It’s pretty much a tautology that a science’s domain will either grow, stay constant, or shrink over time
2 Now obviously, there’s a big difference between the two fields—neoclassical economics is extremely useful to the rich and powerful since it let’s them justify just about any horrendous crimes they would want to commit in the name of expanding their wealth and power, while formal semantics is a subdiscipline of a minor oddball discipline on the boundaries of humanities, social science, and cognitive science. But I’m a linguist, and I think mostly linguists read this.
3 I could point you to my own writing on this, the works of Jerrold Katz, and arguments from Noam Chomsky on referentialsm, or I could point out that one of the godfathers of referentialism, Ludwig Wittgenstein, seems to have repudiated it in his later work.
4 Though, as the late David Graeber pointed out, economists never object when homo economicus is discussed in a positive light.

What does falsification look like anyway?

Vulcan vs Neptune

There’s an argument that plays out every so often in linguistics the goes as follows:

Critic: This data falsifies theory T.
Proponent: Not necessarily, if you consider arguments X,Y, and Z.
Critic: Well, then theory T seems to be unfalsifiable!

This is obviously a specious argument on the part of the critic, since unfalsified does not entail unfalsifiable, but I think it stems from a very understandable frustration—theorists often have an uncanny ability to wriggle free of data that appears to falsify their theories, even though falsificationism is assumed by a large majority of linguists. The problem is that the logic falsificationism, while being quite sound, maybe unimpeachable, turns out to be fiendishly difficult to apply.

At its simplest, the logic of falsificationism says that a theory is scientific insofar as one can construct a basic statementi.e., a statement of fact—that would contradict the theory. This, of course, is an oversimplification of Karl Popper’s idea of Critical Rationalism in a number of ways. For one, falsifiability is not an absolute notion. Rather, we can compare the relative falsifiability of two theories by looking at what Popper calls their empirical content—the number of basic statements that would contradict them. So if a simple theoretical statement P has a particular empirical content, then the conjunction P & Q will have a greater empirical content, and the disjunction P v Q will have a lesser empirical content. This is a useful heuristic when constructing or criticizing a theory internally, and seems like a straightforward guide to testing theories empirically. Historically, though, this is not the case, largely because it is often difficult to recognize when we’ve arrived at and accurately formulated a falsifying fact. In fact, it is often, maybe always, the case that we don’t recognize a falsifying fact as such until after one theory has been superseded by another.

Take for instance the case of the respective orbits of Mercury and Uranus. By the 19th century, Newtonian mechanics had allowed astronomers to make very precise predictions about the rotations of the planets, and based on those predictions, there was a problem: two of the planets were misbehaving. First, it was discovered that Uranus—then the last known planet from the sun—wasn’t showing up where it should have been. Basically, Newton’s mechanics predicted that on such and so day and time Uranus would be in a particular spot in the sky, but the facts were otherwise. Rather than cry “falsification!”, though, the astronomers of the day hypothesized an object on the other side of Uranus that was affecting its orbit. One such astronomer, Urbain Le Verrier was even able to work backwards and predict where that object could be found. So in September of 1846, armed with Le Verrier’s calculations, Johann Gottfried Galle, was able to observe an eighth planet—Neptune. Thus, an apparent falsification became corroboration.

Urbain Le Verrier (1811-1877)
Johann Galle (1812-1910)

I’ve previously written about this story as a vindication of the theory first approach to science. What I didn’t write about, and what is almost never discussed in this context is Le Verrier’s work on the misbehaving orbit of Mercury. Again, armed with Newton’s precise mechanics, Le Verrier calculated the Newtonian prediction for Mercury’s orbit, and again[1]Technically though, Le Verrier’s work on Mercury predated his work on Uranus Mercury didn’t behave as expected. Again, rather than throw out Newtonian mechanics, Le Verrier hypothesized the planet Vulcan between Mercury and the sun, and set about trying to observe it. While many people claimed to observe Vulcan, none of these observations were reliably replicated. Le Verrier was undeterred, though, perhaps because observing a planet that close to the sun was quite tricky. Of course, it would be easy to paint Le Verrier as an eccentric—indeed, his Vulcan hypothesis is somewhat downplayed in his legacy—but he doesn’t seem to have been treated so by his contemporaries. The Vulcan hypothesis wasn’t universally believed, but neither does it seem to be the Flat-Earth theory of its day.

It was only when Einstein used his General Theory of Relativity to accurately calculate Mercury’s orbit, that the scientific community seems to have abandoned the search for Vulcan. Mercury’s orbit is now considered a classical successful test of General Relativity, but why don’t we consider it a refutation of Newtonian Mechanics? Strict falsificationism would seem to dictate that, but then a strict falsificationist would have thrown out Newtonian Mechanics as soon as we noticed Uranus misbehaving. So, falsificationism of this sort leads us to something of a paradox—if a single basic statement contradicts a theory, there’s no way of knowing if there is some second basic statement that, in conjunction with the first, could save the theory.

Still, it’s difficult to toss out falsification entirely, because a theory that doesn’t reflect reality, may be interesting but isn’t scientific.[2]Though sometimes, theories which seem to be empirically idle end up being scientifically important (cf. non-Euclidean geometry) Also, any reasonable person who has ever tried to give an explanation to any phenomenon, probably rejects most of their own ideas rather quickly on empirical bases. We should instead adopt falsificationism as a relative notion—use it when comparing multiple theories. So, Le Verrier was ultimately wrong, but acted reasonably—he had a pretty good theory of mechanics so he worked to reconcile it with some problematic data. Had someone developed General Relativity in Le Verrier’s time, then it would have been unreasonable to insist that a hypothesized planet was a better explanation than an improved theory.

Returning to the hypothetical debate between the Critic and the Proponent, then, I think a reasonable albeit slightly rude response for the proponent would be “Well, do you have a better theory?”

References

References
1 Technically though, Le Verrier’s work on Mercury predated his work on Uranus
2 Though sometimes, theories which seem to be empirically idle end up being scientifically important (cf. non-Euclidean geometry)