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Instrumentalism and shades of grey (36 Views of Mount CritRat)

An instrumental theory is one that makes accurate predictions but doesn’t explain the link between cause and effect. Many philosophers and some scientists dislike instrumental theories.

I’ll give four examples of instrumental theories and conclude that lack of causal explanations isn’t a good reason to discard a theory. I’ll suggest a better criterion. (Plot twist: Lakatos was right!)

About this series

A bad instrumental theory

I start with observations of events in the physical world:

Abraham Lincoln and John Kennedy were two Presidents of the United States.
They were both assassinated.
Lincoln had a secretary named Kennedy, and Kennedy had a secretary named Lincoln. Valerie Klein, “The Odd Parallels Between Kennedy and Lincoln,” 2002.

Now, I’m not willing to say Kennedy’s later decision affected the long-dead Lincoln’s fate – let’s leave reverse causality via black holes out of it – but what about the other way ‘round?

Let’s suppose I check the history and discover that the assassinated President James Garfield had a secretary named Washington. Also, of all the Presidents who were not assassinated, none of them had secretaries that matched an earlier President’s name. Don’t quote me on this paragraph. I didn’t actually check.

So I have a hypothesis:

Any US President who has a secretary sharing a family name with any past president will be assassinated during his or her term of office.

That’s testable. We can persuade the current President to pick an appropriately-named secretary. Or we can wait for a “natural experiment” where a President – ignorant of the risk – chooses someone with the right (wrong?) name.

In either case, let’s suppose the hypothesis is falsified. President Memphis hires a secretary named Taft, but is not assassinated.

So I scour the records and discover that both Kennedy and Lincoln had Vice Presidents named Johnson. That one’s true. That suggests a new hypothesis:

Any US President who has a secretary sharing a family name with any past president AND a Vice President named Johnson will be assassinated during his or her term of office. The secretary’s name still matters because Martin Van Buren survived having Richard Mentor Johnson as his VP.

Let’s suppose a series of Presidential terms allow us to test this hypothesis, and it remains unrefuted. Question: how should we feel about this? It follows the critical rationalist methodology to the letter, after all.

But still. This sure doesn’t seem scientific, not until someone shows a causal path from the choice of coworkers to the assassin’s bullet. It’s not enough that Lincoln/Kennedy/Johnson Theory (L/K/J Theory) works; that is, makes good predictions. We want to know why it works before we accept it. (Especially because we don’t believe there is a causal mechanism – it’s got to be coincidence, right?)

A great instrumental theory

People don’t mention it, but Newton’s masterwork – his law of gravitation – is instrumental. He did not propose a causal mechanism in his Principia. Instead, his theory relied on action at a distance, even though Newton believed that invalid: Sir Isaac Newton (Third letter to Bentley, 25 Feb 1693). Quoted in The Works of Richard Bentley, D. D. (1838), Vol. 3, 212-3.

“That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance, through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking, can ever fall into it.”

In later years, Newton attempted an explanation in which masses, through some form of direct contact, moved each other. For example: This proposal and the following are from the Wikipedia article “Mechanical explanations of gravitation.”

“[Gravity is the result of] a condensation causing a flow of aether with a corresponding thinning of the aether density associated with the increased velocity of flow.”

Bernhard Riemann had a related theory that “the gravitational aether is an incompressible fluid and normal matter represents sinks in this aether.” Ivan Osipovich Yarkovsky had yet another related theory.

Newton later proposed that the aether thinned out proportionally to the inverse square law, which is why gravitation obeys the same law. Leonhard Euler proposed a variant of that.

Robert Hooke thought gravity had something to do with masses emitting waves. James Challis had a similar theory.

Carl Anton Bjerknes knew that if two spheres in a fluid pulsate in phase, they will draw together. He proposed that all bodies pulsate in the aether, and that’s what gravity is. Lord Kelvin joined him in that proposal.

All of these theories had problems. But by the time of Bjerknes and Kelvin, it was getting close to 1916, when Einstein solved the action-at-a-distance problem with his general theory of relativity.

What’s interesting to me is that, from 1687 to 1916, the majority of scientists worked happily, though instrumentally, with Newtonian mechanics and gravitation, doing things like devising an equation for the motion of the simple pendulum, then moving on to pendulums of arbitrary shape, upside-down pendulums, spherical pendulums, and so on.

Obviously Newtonian mechanics and gravitation is a better scientific theory than my own L/K/J Theory, but why?

An even greater instrumental theory

The current versions of quantum theory (quantum field theory and the Standard Model) have fewer anomalies than Newtonian gravitation (which didn’t work when relatively small masses like Mercury are quite near large masses like the Sun). Physicist David Tong says:

“The Standard Model is, by any measure, the most successful scientific theory of all time. The culmination of 350 years of scientific enquiry, it correctly explains every experiment that we’ve ever done (at least if you’re willing to turn a blind eye to gravity for now).”

But the philosopher of science Tim Maudlin doesn’t call quantum field theory and the Standard Model “theories.” Rather: Tim Maudlin, Philosophy of Physics: Quantum Theory, 2018, ch 1, epub location 9.7, 9.10. His emphasis.

“What is presented in the average physics textbook, what students learn and researchers use, turns out not to be a precise physical theory at all. It is rather a very effective and accurate recipe for making certain sorts of predictions. […] [It] uses such terms as “observer” and “measurement” and “apparatus” that are not completely precise and clear.”

However: ibid. location 9.10. My emphasis.

“These imprecisions in the formulation of the quantum recipe do not have noticeable practical effects when it comes to making predictions. Physicists know well enough when a certain laboratory operation is to count as an observation, and what it is an observation of. Quantum theory predicts the outcomes of these experiments with stunning accuracy.”

Still, that’s insufficient: ibid., my emphasis.

“But if one’s main interest is in the nature of the physical world rather than the pragmatics of generating predictions, this ability is of no solace. For the recipe simply does not contain any univocal account of the world itself. To illustrate this, the standard recipe does use a mathematical operation that can be called “collapse of the wavefunction.” But if one asks whether that mathematical operation corresponds to a real physical change in the world itself, the recipe does not say.”

What Maudlin calls a “quantum recipe” is an instrumental theory par excellence.

Yes, and?

Although most theorists are working with the recipe, there are still quantum theorists trying to explain the nature of the physical world, working on questions like what an electron really is. My personal favorite is John Stuart Bell’s flash ontology, where matter (or “the localized material content of space-time”) is “not particles with continuous trajectories, nor continuously distributed fieldlike entities, nor vibrating strings, but rather point events.“ ibid., ch. 4, epub location 12.74. My understanding (and remember, I don’t have the math to really understand) is that, every so often (for an electron, about once every 10,000,000 years ibid., location 12.75.), what we call a particle will “flash” into existence in our space-time (at a location determined by its value in a much higher-dimensional “configuration space”). And these collections of flashes make up the macroscopic reality we see around us. Maudlin: ibid.

“What, then, would this “galaxy of flashes” look like? Leaving the protons and neutrons (and hence quarks) aside, there are about 10²⁸ electrons in a human body. That means, just from the electrons, about 10,000,000,000,000 flashes in a single second. The distribution of these flashes in space would trace out a quite detailed human form.”

You and I, per Bell, are a continual flicker of flashes dense enough to give not the appearance of solidity but solidity itself: macroscopic matter. What about entities between the quantum scale and the human scale? Cells, for example. “Only a few [flashes] occur per cell per second [but…] if we go about looking at a cell through even a regular optical microscope, the magnification process would entangle the wavefunction of the individual cell with macroscopic aspects of the equipment (or of the brain of the observer), and the ‘invisible’ parts of the cell would automatically become registered in the GRW flashes.” ibid, 12.76.

So the situation for quantum theory of the last 100 years has been the same as Newton’s theory endured for more than twice as long: the equations don’t map directly onto physical reality. Moreover, in both cases, some people extend those equations toward new problems, while others work on what causal operations on what entities justify (or generate) the instrumental equations.

And yet, as far as I know, nobody referred to Newton as the founder of “an anarchist cult of incomprehensible chaos" Criticism and the Growth of Knowledge, Lakatos & Musgrave (eds.) (1970) (full text) “The Methodology of Scientific Research Programmes,” p. 145. or “a danger to science.“ ibid., “Normal Science and its Dangers,” p. 53. Popper is talking about Kuhn’s “normal science,” but he explicitly calls out quantum mechanics as being “especially” (his word) exemplary of badness.

That’s puzzling.

Causality as a weapon

The science writer Tom Leveson has a new book, A Pox on Fools: The True Believers, Grifters, and Cynics Who Convinced Us to Reject Vaccines. I haven’t read it, but I listened to a podcast interview. In it, Leveson pointed out that, in the tobacco industry’s decades-long rearguard action against the reality that smoking causes cancer, causality was one of their weapons. They conceded there was statistical evidence but, they pointed out, no causal mechanism had been offered. In its absence, how can anyone be sure smoking causes cancer? Should society regulate smokers’ pleasure until we know what’s really going on?

⊕

These merchants of doubt cast – correctly, I think – “smoking causes cancer” as merely an instrumental theory – on par with the L/K/J theory of presidential assassination – and thus we should do nothing until the foundations of the theory are secure.

That was a ploy. “Well, are you sure? You need to do more to convince me” is a time-honored way to slow down change. Sometimes that’s prudent, but it sure seems it’s more often used disingenuously. “A disingenuous remark might contain some superficial truth, but it is delivered with the intent to deceive or to serve some hidden purpose.” – Merriam-Webster, my emphasis.

If I were a betting man…

We have four theories that provoke very different reactions. One (Newton) is accepted by everyone, and people don’t even notice it’s instrumental. One (quantum) is rejected by some people because it’s instrumental. See the previous post for more details. Another (cancer) is purportedly rejected because it’s instrumental, but actually because tobacco companies want to protect their profits. And another (L/K/J theory) is rejected because it’s obviously bogus.

But is it? Remember, my story presumes that we get future confirmations of L/K/J theory and no refutations, which would increase its plausibility. Maybe it’s worth looking at some followup questions:

Does the rule apply to other nations with Presidential systems? (What’s Emmanuel Macron’s secretary’s name? He doesn’t have a Vice President, but maybe we can use the Prime Minister instead?)
What about other classes of rulers? Kings? Dictators? CEOs?
Is “Johnson” some kind of fundamental constant, like Planck’s Constant? Or can other names play its role? Perhaps other slang words for male bodily parts?

From such observations, perhaps we’d get a sharper, more precise description of entities in the instrumental theory, providing a clearer understanding of what a causal theory must explain – something a causal theorist can get a better grip on. The critical rationalists don’t talk about using a theory as a prompt for people to go out and do more observations. They don’t discuss observations except as the output of experiments that test theory-driven predictions. But I don’t think they disallow observations.

The reason I doubt that would happen, even in a future with more evidence for the theory, is: who will spend time on L/K/J theory? The subjective probability of discovering anything interesting would still be pretty low. Why risk your time with so little possibility for reward?

The critical rationalists have a single goal for science: producing universal statements that apply to an ever-expanding set of observable phenomena. (Alternately: that can make an ever-expanding range of predictions.) In addition to following the methodology, proper science looks for causal, not instrumental, theories.

I’d like to propose that the goal of science is to do more science. One measure of a theory is how well it provides ideas for new theories, experiments/applications, and observations. The pendulum is a good example:

Newton gave examples of using his recipe, focusing on freely-moving masses.
The simple pendulum involves two masses (the earth and a bob) where the latter is constrained by a (presumed massless) connection between the bob and a pivot point. The Newtonian recipe can be applied to this new situation.
Turn the bob and pendulum arm into a mass of arbitrary shape. This introduces a new (if imaginary) entity to the system: the center of oscillation. But the recipe still works.
Say, shouldn’t we include the effects of friction? Friction’s an F that ought to affect the a of the m, right?
⊕ Foucault's pendulum. Click to enlarge.
The pendulum always moves in the same plane. (There are no forces pushing it sideways.) What figure is traced out as the earth moves under it? Say, that would make a dandy museum exhibit.
What happens if you attach a second pendulum to the end of a first one? Call that a “double pendulum.” … Hmm. The recipe doesn’t do a good job of predicting the pendulum’s trajectory. And if you actually try it out, the behavior is bizarre. Hope someone figures it out someday.
We should send people up mountains and to distant lands to measure the local force of gravity, using… pendulums!
…

Not bad for one narrow application of an instrumental theory.

Quantum theory went through a similar process of adding complexity to situations and applying the recipe. With what results? Lasers! Electron microscopes! MRI machines! It’s a good thing physicists since ~1927 didn’t listen to the critics and methodologists. We’d be missing out on a lot if they’d taken to heart the claim that their quite handy recipe is Lakatos’s “incomprehensible chaos” and so left the field to a few people working on fundamentals.

I bet the discovery of a correlation between smoking and lung cancer also led to a lot of new research, as well as new opportunities to make a living bamboozling the public.

The L/K/J theory, alas, has much less potential for generating new science. Or, at least, much less obvious potential. But anything’s possible, I guess.

Lakatos was right

Both Popper and Lakatos allow theorists to keep working with a refuted theory. They differ in their level of enthusiasm. Popper allows it “until such time as [the theorist] has a better one to substitute for it.“ Conjectures and Refutations - but I lost the page number and don’t seem to have highlighted the paragraph. Lakatos, always more flamboyant, revels in it:“Theories grow in a sea of anomalies, and counterexamples are merrily ignored.“ For and Against Method: Including Lakatos’s Lectures on Scientific Method and the Lakatos-Feyerabend Correspondence, Motterlini (ed.), 1999, p. 99.

The biggest difference is that Lakatos allows backtracking. If a replacement theory is sufficiently different to constitute a new research programme – like starting to think about planetary motion using Newton’s laws of mechanics – then it is allowed to predict less than its competitor currently can. That is, if new-theory can explain a phenomenon that old-theory cannot, it can replace old-theory even if some phenomena that old-theory explains can’t be explained by new-theory. The reasoning: it’s early days; give the theorists some time to fill in those gaps.

Because of this, a scientist can rationally continue to work on a research programme so long as it’s progressive – keeps finding unexplained phenomena to successfully explain. (Put differently: it keeps making new predictions, at least some of which are not refuted.)

Such a methodologist, you would think, would be primed to accept quantum theory even though it’s merely instrumental. If you trust the theorists to someday resolve remaining experimental anomalies, why not trust them to someday figure out the causal underpinnings of their “recipe”? Especially since Lakatos thinks a good research program is one that generates new theories. “Mature science consists of research programmes in which not only novel facts but, in an important sense, also novel auxiliary theories, are anticipated.” Criticism, p. 175. Why can’t some of the novel theories be ones that work toward causal underpinnings? That go “downward,” as it were, rather than just “upward”? Especially since the recipe predicts experimental results with “stunning accuracy”?

But Lakatos doesn’t accept quantum theory. I don’t know why. People are weird, self-described rationalists perhaps more than most.