The Knowledge Machine: How Irrationality Created Modern Science

by Michael Strevens

Among the ancients there was no lack of desire to understand the workings of the world. Around 580 BCE, the Greek philosopher Thales gazed out from the port city of Miletus into the Aegean blue, into the summer haze where sea merges imperceptibly with sky, and proposed that everything is ultimately made of water. His student Anaximenes disagreed: the fundamental stuff, he said, is air. Heraclitus, who lived in Sicily a few decades later, suggested fire. Back in Miletus, Anaximander—another student of Thales about whom we know equally little—had meanwhile hypothesized that all things are composed of invisible stuff of unlimited potential that he called apeiron, or “the boundless.” Though these thinkers, their contemporaries, and their successors—Chinese scholars, Islamic doctors, medieval European monks—argued ingeniously for their points of view, no one of their ideas could gain a foothold over the others. Searching for the deep structure of nature, they contributed immeasurably to humanity’s stock of brilliant and original hypotheses, but to its stock of knowledge, scarcely at all. The reason is straightforward. Although premodern inquirers into nature sometimes hit on the right idea, they had little ability to distinguish it from its rivals.

That great leap forward was made in the exhilarating period between the years 1600 and 1700, during which empirical inquiry evolved from the freewheeling, speculative frenzy of old into something with powers of discovery on a wholly new level—the knowledge machine. Driving this machine was a regimented process that subjected theories to a pitiless interrogation by observable evidence, raising up some and tearing down others, occasionally changing course or traveling in reverse but making in the long term unmistakable progress.

The natural philosophy that came before the Scientific Revolution was not less creative than modern science, and as practiced by thinkers such as Aristotle was no less methodical and no less concerned with the evidence of the senses. Yet something, it seems, was missing. For that extraordinary something, why the excruciating wait? Why, after philosophy and democracy and mathematics tumbled through the doors of the ancient thinkers’ consciousness in quick succession, did science dawdle on the threshold?

It seems, to all the world, that there is something about the nature of science itself that the human race finds hard to take on board. That, I believe, is the answer: science is an alien thought form. To understand its late arrival on the human scene, we need to appreciate the inherent strangeness of the scientific method.

understand why it has been so difficult to chase down. Those who have searched for a scientific method—the methodists—have been looking for a logical and behavioral directive that expunges human whim from scientific thought, replacing it with a standardized rule or procedure for judging theories in the light of evidence that explains science’s stupendous knowledge-producing capacity. The rule that governs science and explains its success is far weaker, however, than the methodists have supposed: it tells you what counts as evidence but offers no system for interpreting that evidence. Indeed, it says nothing about the significance of evidence at all. Further, the rule does not reside where the methodists have expected to find it, in scientists’ heads. It does not tell scientists what to think privately; it merely regulates how they argue publicly. It is not a method of reasoning but a kind of speech code, a set of ground rules for debate, compelling scientists to conduct all disputes with reference to empirical evidence alone.

How can a rule so scant in content and so limited in scope account for science’s powers of discovery? It may dictate what gets called evidence, but it makes no attempt to forge agreement among scientists as to what the evidence says. It simply lays down the rule that all arguments must be carried out with reference to empirical evidence and then steps back, relinquishing control. Scientists are free to think almost anything they like about the connection between evidence and theory. But if they are to participate in the scientific enterprise, they must uncover or generate new evidence to argue with. And so they do, with unfettered enthusiasm. The resulting productivity is what makes all the difference: science is a machine for motivating disputatious humans to carry out tedious measurements and perform costly and time-consuming experiments that they would otherwise not care to undertake. It is these empirical minutiae, so painful to collect, that single out the truth among the plausible falsehoods. Eventually, enough such evidence accumulates that just about every scientist, whatever their quirks, biases, and prejudices, agrees on its significance: one theory stands well above the rest as the best explainer and predictor of it all.

I won’t explain science’s late arrival by composing a history of the origins of the Scientific Revolution. My interest is in all the apparently propitious places and times that science failed to appear. That nonappearance is to be explained by something timeless: that the iron rule, the key to science’s success, is unreasonably closed-minded. It works superbly well, but from the outside, it looks to be, quite simply, an irrational way to inquire into the underlying structure of things. The ancient Greeks had poetry, music, drama, philosophy, democracy, mathematics—each an expression and an elevation of human nature. Science, by contrast, requires of its practitioners the strategic suppression of human nature, indeed, the suppression of the highest element of human nature, the rational mind. What Greek philosopher could have supposed that this was the route to unbounded knowledge of the world? The mystery is not that science arrived so late, but that as a technique for discovery it was ever hit upon at all.

Popper heard Einstein lecture on his new theory of relativity: “I remember only that I was dazed. This thing was quite beyond my understanding.” But he was struck by Einstein’s willingness to subject his theory to empirical tests that might disprove it: Thus I arrived, by the end of 1919, at the conclusion that the scientific attitude was the critical attitude, which did not look for verifications but for crucial tests; tests which could refute the theory tested, though they could never establish it. In that single italicized word germinated Popper’s greatest and most influential idea.

by eating fruit from that kind of tree; and so on. This sort of generalization from experience is called inductive reasoning, or, for short, induction. What, Hume asked, justifies these generalizations?

Why think that future behavior is in general like past behavior? There’s an obvious answer to that question, too. We think that behavior will be the same in the future as it was in the past because in our experience, it always has been the same. We justify our belief in uniformity, then, by saying that nature has always been uniform in the past, so we expect it to continue to be uniform in the future. But that, as Hume observed, is itself a kind of inductive thinking, generalizing as it does from past to future. We are using induction to justify induction.

This might sound like just the sort of insanity that Russell feared. But Popper was no poached egg. Science, he thought, had a powerful replacement for the inductive thinking undermined by Hume. There may be no such thing as evidence for a theory, but what there can be—and here Popper recalled his youthful bedazzlement by Einstein in 1919—is evidence against a theory. “If the redshift of spectral lines due to the gravitational potential should not exist,” Einstein wrote of a certain phenomenon predicted by his ideas, “then [my] general theory of relativity will be untenable.” As Einstein saw, we can know for sure that any theory that makes false predictions is false. To put it another way, a true theory will always make true predictions; false predictions can issue only from falsehood. No assumptions about the uniformity of nature are needed to grasp that.

Science gathers evidence not to validate theories but to refute them—to rule them out of the running. The job of scientists is to go through the list of all possible theories and to eliminate as many as possible, or, as Popper said, to “falsify” them. Suppose that you have accumulated much evidence and discarded many theories. Of the theories that remain on the list, it is impossible, according to Popper, to say that one is more likely to be true than any of the others: “Scientific theories, if they are not falsified, forever remain . . . conjectures.” No matter how many true predictions a theory has made, you have no more reason to believe it than to believe any of its unfalsified rivals. Let me repeat that. Popper is sometimes said (by the New Oxford American Dictionary, for example) to have claimed that no theory can be proved definitively to be true. But he held a far more radical view than this: he thought that of the theories that have not yet been positively disproved, we have absolutely no reason to believe one rather than another. It is not that even our best theory cannot be definitively proved; it is rather that there is no such thing as a “best theory,” only a “surviving theory,” and all surviving theories are equal.

Scientists should consequently devote themselves to reducing the size of the pool of surviving theories by refuting as many ideas as possible. Scientific inquiry is essentially a process of disproof, and scientists are the disprovers, the debunkers, the destroyers. Popper’s logic of inquiry requires of its scientific personnel a murderous resolve. Seeing a theory, their first thought must be to understand it and then to liquidate it. Only if scientists throw themselves single-mindedly into the slaughter of every speculation will science progress.

TO BE AN IMAGINATIVE EXPLORER of new theoretical possibilities and a ruthless critic, determined to uncover falsehood wherever it is found—that is the Popperian ideal. Scientists are both empirical warriors and intuitive artists, combining originality and openness to new ideas with an intellectual honesty that regards nothing as above suspicion.

Puzzling over Aristotle’s theory of physics, which “seemed to me full of egregious errors,” Kuhn looked out the window and had an epiphany: Suddenly the fragments in my head sorted themselves out in a new way, and fell into place together. My jaw dropped, for all at once Aristotle seemed a very good physicist indeed, but of a sort I’d never dreamed possible. Now I could understand why he had said what he’d said. Kuhn did not, of course, come to believe Aristotle’s physical theory, but he did come to see it as a system that, by its own lights, constituted a coherent and powerful explanatory framework. To appreciate its cogency, however, he had to set aside his habitual ways of thinking about the world, conditioned by twentieth-century physics, and to adopt temporarily a wholly new worldview. From this experience he learned that some revisions of scientific theory are so profound that they require a complete overturning of the cognitive order—a revolution.

Kuhn’s famous book The Structure of Scientific Revolutions was published in 1962, 15 years after his epiphany and just 3 years after Popper’s own great work on the scientific method first appeared in English. Nothing before or since has had a comparable impact on the philosophy of science; nothing has so altered the course of the Great Method Debate. A book on revolutions that took the ’60s by storm? You might suppose that Kuhn’s picture of science was a model of intellectual ferment, radical thinking, inspired resistance to the choke hold of tradition. Not so. Science is capable of world-altering progress only because, according to Kuhn, scientists are quite incapable of questioning intellectual authority.

Any branch of science—microeconomics, nuclear physics, genetics—has at all times, says Kuhn, a single dominant ideological mind-set, something he calls a paradigm. The paradigm is built around a high-level theory about the way the world works, such as Newton’s theory of gravitation or Mendel’s laws of genetics, but it contains much more as well: it identifies, in the light of the theory, what problems are important, which methods are valid ways...

For Popper, what matters above all else to the successful operation of the knowledge machine is scientists’ acute faculty for critical thought. They can survey the theoretical possibilities, and they see clearly how each theory might, in the face of the evidence, collapse. For Kuhn, such a survey, the essential precondition for criticism, is psychologically impossible.

(A lowercase scientific revolution should not be confused with the uppercase Scientific Revolution, of which there has been only one. In a lowercase scientific revolution, one way of doing science is replaced by another. In the uppercase Scientific Revolution, something that was not science—natural philosophy, I have called it—was replaced by a far more effective form of empirical inquiry, modern science itself.)

It was not easy for human minds to let go of the centrality of the earth, the perfection of the heavens, and the palpability of speed. This intellectual stasis Kuhn put down to the paradigm’s stifling embrace. Copernicus triumphed all the same.

Kuhn scandalized the world of science with this picture of revolutionary scientific change. Previous historians and philosophers had seen scientific change as a largely rational process: the ideas of Copernicus, of Kepler, of Galileo, of Newton, however radical, were accepted because they were so clearly superior to the old ideas, both in their predictive successes and in their explanatory beauty. If Kuhn is right, then this older, more dignified conception of scientific progress must be wrong, for in Kuhn’s view, it is impossible to compare paradigms: “When paradigms enter, as they must, into a debate about paradigm choice, their role is necessarily circular.” Perhaps if you had two brains as you have two hands, you could weigh one paradigm against another. But you have only a single brain, and a single brain is capable of grasping only a single paradigm. You cannot simultaneously appreciate the merits of the Aristotelian and the Newtonian worldviews any more than you can simultaneously be a fervent Muslim and a devoted Roman Catholic. At the height of his rhetoric, Kuhn wrote that the Aristotelian and the Newtonian live in different worlds; you can live in one world or the other, but you cannot be in two different places at the same time. A rational comparison of competing paradigms is therefore humanly impossible. In the place of logical evaluation, Kuhn posits a leap of faith: a giddy jump through ideologically empty space from the traditional view of things to the rev...

That science’s success is explained by a kind of intellectual confinement—that is the single most astonishing thesis in Kuhn’s celebrated book. It is easy to see how the characteristic intellectual demeanor of the Popperian scientist—unbounded imaginer, unrelenting refuter—might sustain the extraordinary productivity of the knowledge machine. But Kuhn’s scientists? How could their inability to contemplate or even comprehend new ideas possibly drive discovery? Science is boring. Science is frustrating. Or at least, that is true 99 percent of the time. Readers of popular science see the 1 percent: the intriguing phenomena, the provocative theories, the dramatic experimental refutations or verifications. Behind these achievements, however—as every working scientist knows—are long hours, days, months of tedious laboratory labor. The single greatest obstacle to successful science is the difficulty of persuading brilliant minds to give up the intellectual pleasures of continual speculation and debate, theorizing and arguing, and to turn instead to a life consisting almost entirely of the production of experimental data.

That is the Kuhnian answer to the motivation problem: mold scientists’ minds so that they fail to see that their research might be based on an error, on a false presupposition. If the validity of the paradigm is accepted without question, then the value of long and arduous empirical toil is also beyond question. The purpose of narrowing scientists’ horizons is to encourage them to work harder, to dig deeper, to go further than they would go if they could see their destination in perspective, if they had an accurate sense of their project’s proportion. Ultimately, it is only because scientists’ faith in the paradigm guarantees the importance of their research that they feel secure enough to work the paradigm to death—to experiment in such detail, with such precision, as to expose the paradigm’s shortcomings, to drive science to a crisis, and so to establish the preconditions for revolution. This is Kuhn’s marvelous paradox: A paradigm can change only because the scientists working within it cannot imagine it changing. It is their certainty of its success that secures its destruction.

Second, Popper and Kuhn were right in thinking that in order to explain science’s critical power, proprietary forms of motivation are at least as important as proprietary logical tools. The tools tell you what to do with the evidence, but that is of no use unless you have the right kind of data, and plenty of it. The production of such data requires, in most cases, an intense and prolonged focus on details of little intrinsic interest. Scientific inquiry needs something, then, to induce thinkers to devote their lives to an enterprise that is in its daily routine mundane and largely negative—while discouraging them from the glamorous alternative, the philosophical strategy of inventing new ideas and new styles of thought at every turn.

Does contemporary science display the paradigmatic structure described by Kuhn, in which a single ideology and methodology guides all scientists working in any given domain? Ask the sociologists. Was there a sudden and unprecedented onset of paradigm-governed groupthink in the Scientific Revolution? Ask the historians. Do scientists fight to preserve the status quo, as Kuhn’s theory would tend to suggest, or to overthrow it, as Popper would have it? For contemporary scientists, ask the sociologists; for the scientists of yore, the historians. Over the past few decades, the answers have come in. They are almost entirely negative. There is little evidence, as you will see, for a dispassionate Popperian critical spirit, but also little evidence for universal subservience to a paradigm. Indeed, in their thinking about the connection between theory and data, scientists seem scarcely to follow any rules at all.

The criminal justice system strives to uncover the truth. Even when it operates as it should, however, its interpretation of the evidence may depend on whether a witness is reliable or a theory—such as the arson investigators’ assumptions about the effect of accelerants—is correct. At the moment when it matters most, there may be no objective basis for answering such questions. Information is limited, yet a determination must be made. The deliberators have no choice but to fall back on what seems most plausible to them. Much later, it may become clear that a witness was untrustworthy or that a theory was flawed. Lacking a crystal ball, the jury must do its best with what it has at the time. It is the same in science. Sometimes it is a measurement instrument—a witness, if you will—on which the issue hinges. Sometimes, it is a theory. Scientists seeking to make sense of the evidence cannot be neutral. They must take a stand on whether the instrument is relaying the truth, on whether the theoretical assumptions hold. Having nothing further to guide them, they must go with whatever seems right. They must resort to educated guesswork, and that makes scientific reasoning irreducibly, unavoidably, essentially subjective.

The earth is actually over 4.5 billion years old, and it has harbored life for at least 3.5 billion of those years. How did Kelvin get it so badly wrong? Like Todd Willingham’s jurors, who were presented with an inadequate theory of the way in which house fires develop and burn, he was relying on assumptions that were mistaken in several respects. First, though he had no way of knowing it, the heat of the rock making up the continents is considerably increased by the decay of radioactive elements. Second, heat is transported from the earth’s core not by conduction through solid rock, as Kelvin had supposed, but by convection, in which rock in the earth’s mantle flows from the core to the crust carrying heat with it, warming the crust far more efficiently than conduction could. As a consequence, an old earth can have, as ours does, a surprisingly warm crust. In effect, Kelvin sipped the top layer of a cup of coffee and, finding it to be piping hot, concluded that it had been freshly poured. In fact it had been there for ages, but sitting on a warmer and continually stirred. Huxley was right. Kelvin had poured chaff into his finely calibrated mathematical mill and produced indigestible grit. Were Kelvin, Tait, and other advocates of a “youngish earth” being unscientific? Not at all; there were good reasons and great uncertainty on both sides. The physicists saw their assumptions about the geological structure of the earth as natural and reasonable compared with the largely s...

When making theoretical assumptions, he said, be bold. Choose hypotheses that, by making strong claims, expose themselves forthrightly to falsification. Kelvin and Darwin certainly did that. But they had no way, in their lifetimes, of testing their claims.

Science is driven onward by arguments between people who have made up their minds and want to convert or at least to confute their rivals. Opinion that runs hot-blooded ahead of established fact is the life force of scientific inquiry. For these reasons, Popper is now thought by most philosophers of science to fall short of providing a rule for bringing evidence to bear on theories that is both fully objective and adequate to science’s needs. What kind of rule might do better? There is philosophical consensus on this matter, too—and the answer is none. An objective rule for weighing scientific evidence is logically impossible. The impossibility arises from the same fact that makes Popperian falsification often such a contentious matter: a scientific theory issues predictions only when it is combined with various assumptions to compose a theoretical cohort. The members of the cohort—what philosophers call “auxiliary assumptions”—are a diverse range of suppositions. Some are high-level theories themselves, such as Kelvin’s assumption about the solid structure of the earth’s interior. Some are assumptions about the functioning and calibration of measuring instruments, such as Eddington’s assumptions, positive and negative, about his various telescopes. The auxiliary assumptions are like links in a chain leading from the theory to the evidence. The chain is only as strong as its weakest link; thus, to assess the strength of the chain—to assess the strength of a piece of eviden...

The experimenters on both sides of the spontaneous generation debate at the time had no way of independently verifying their most important auxiliary assumption. There is no way to get started, in such a situation, without assigning some likelihoods from scratch—not arbitrarily, exactly, but without the constraints imposed by a preexisting scheme for interpreting evidence. Needless to say, different scientists will choose different starting places, heavily influenced by personal tastes or aspirations. From that point on their estimates of evidential weight are liable to head in disparate directions. That is the origin of the essential subjectivity of science.

We expect Elizabethan drama to end stirringly in true love or violence, and modern drama (perhaps) in misery or self-recognition. The drama of science, however, never need end at all. Montague and Capulet can continue their dialogue indefinitely without running out of lines. That is because there is always a purely scientific way to perpetuate a scientific argument: make more measurements or conduct new experiments. The unending script, the code of conduct for scientific argument according to which Montague and Capulet may continue their debate indefinitely, is provided by the methodological precept that I call the iron rule of explanation. What the rule says is simple enough: it directs scientists to resolve their differences of opinion by conducting empirical tests rather than by shouting or fighting or philosophizing or moralizing or marrying or calling on a higher power. That is all; it makes no attempt to interpret the evidence, to decide winners and losers. Indeed, its function is not so much to resolve the dispute as to prolong it. This perpetuation of the dramatic conflict for its own sake is the essence of the scientific method, and as the perpetuator-in-chief, the iron rule establishes itself as the heart, the soul, the life force of scientific inquiry.

Here, then, in short, is the iron rule: 1. Strive to settle all arguments by empirical testing. 2. To conduct an empirical test to decide between a pair of hypotheses, perform an experiment or measurement, one of whose possible outcomes can be explained by one hypothesis (and accompanying cohort) but not the other. There lies the nub of the scientific method and so, once its subtleties have been spelled out in the chapters to come, the denouement of the Great Method Debate.

The ideas in the last few pages are some of the most important that I have to share. Together they capture the way in which the procedural consensus orchestrated by the iron rule powers the scientific knowledge machine. I’ll state them one more time. First, the consensus ensures continuity. Provided that there are resources and the will to continue the investigation, there is no prospect that Montague and Capulet will arrive at a position where they can think of nothing to do or say that might bring them any closer together. There are no duels or divorces in science, no schisms to parallel the historical schisms in religion, politics, and philosophy, where opposing camps stop talking or worse. Always there is something that even the most bitter adversaries can agree to do next: another test. Second (and consequently), the iron rule channels hope, anger, envy, ambition, resentment—all the fires fuming in the human heart—to one end: the production of empirical evidence. Capulet and Montague’s complex feelings about one another must, as long as they follow a scientific script, work themselves out in the lab, the field, or the observatory. Third, the fundamental conventions of the game, the legitimate evidential moves, are fixed for all time. This gives the players, the scientists, a quiet but firm certainty in the foundation of their enterprise, a stable intellectual and moral platform on which to construct great experimental enterprises, with all their financial, emotional, ...

In these ways, a protocol as weak as the iron rule—an agreement to argue by empirical testing alone conjoined with a fixed standard to determine what counts as an empirical test—gives science something that no other form of inquiry before it has had, a pool of empirical observations that dwarfs in its size, scope, subtlety, and precision anything the ancient or medieval natural philosophers could bring themselves to produce.

The New Organon recommends this same technique to investigate every natural phenomenon, from lightning to laryngitis to life itself: gather the conditions under which the phenomenon occurs, the conditions under which it does not occur, its patterns of change, and find the hypothesis that explains the lot—the occurrences, the nonoccurrences, the variation. That hypothesis is the theory you’re looking for, the truth.

As evidence accumulates, plausibility rankings begin to converge. Differences in opinion become less extreme. Consensus emerges as to which are the leading theoretical contenders and which are the also-rans, then eventually on which is the best of them all. There is not complete agreement, but there is ever less disagreement. This is Baconian convergence.

That the secrets of the universe lie in minute structures, in nearly indiscernible details, in patterns that only the most sensitive, fragile, and expensive instruments can detect, is an insight so important that it deserves a name. I call it the Tychonic principle, after the sixteenth-century Danish astronomer Tycho Brahe, who, working just before the invention of the telescope, was the last and greatest “naked-eye” astronomer, using sextants and quadrants to pinpoint the positions of stars and the movements of planets to within 0.02 degrees. To achieve this level of accuracy, Tycho built an observatory called Stjerneborg (“castle of the stars”) entirely at basement level, seeking as Michelson and Morley later would to shelter from the inaccuracy inflicted by the bustle and noise of the world outside (Figure 5.2).

Bacon proposes that if we take explanatory power to be our guide, then empirical testing will ultimately single out the truth. The Tychonic principle says that much of that testing will be extraordinarily difficult to conduct. It is for this reason that the iron rule is essential to modern science’s success. The effort required to build a store of observable fact sufficient for Baconian convergence in a Tychonic world is so great that humans can be persuaded, induced, or impelled to take on the project only under exceptional circumstances. The iron rule engineers those circumstances and so “forces scientists to investigate some part of nature in a detail and depth that would otherwise be unimaginable.” Those are Thomas Kuhn’s words.

The Four Innovations That Made Modern Science 1. A notion of explanatory power on which all scientists agree 2. A distinction between public scientific argument and private scientific reasoning 3. A requirement of objectivity in scientific argument (as opposed to reasoning) 4. A requirement that scientific argument appeal only to the outcomes of empirical tests (and not to philosophical coherence, theoretical beauty, and so on)

In our Tychonic world, it is by accounting for the fraction of an inch, the sliver of a degree, that the truth will make itself known.

None of this, at first, made any sense to Kuhn; Aristotle’s claims seemed so obscure as to be unintelligible. Then he looked out the window and everything, as he said, “fell into place.” He achieved the ability to see the world as Aristotle did, to operate with Aristotelian principles for explaining the world—principles that were so strange as to be almost Atlantean. “Now I could understand why [Aristotle] had said what he’d said.” That experience inspired Kuhn’s conception of scientific progress as a series of leaps from framework to framework, with each such “paradigm shift” bringing a new explanatory system that mystifies scientists educated in an older way of looking at the world. A paradigm is more than an explanatory framework; it is a complete recipe for doing science, including goals and methods as well as modes of understanding.

Descartes dismisses Aristotle’s explanations as unintelligible; Aristotle would dismiss Descartes’s as hopeless. To each the other’s proprietary explanatory framework looks confused, empty, incomprehensible, absurd—as intellectually alien as the Atlantean rhyming scheme.

If Aristotle had surveyed the intellectual battlefields of the 1600s, he would surely have exclaimed, “Not again!” The atomists and other materialists, vanquished in fourth-century Athens, had returned and must be fought once more. It was just as Bacon said: the same arguments, going round in circles forever. And so it might have continued, had not something new appeared to break the cycle and to direct the investigation of nature onto a wholly new trajectory, along which profound disagreements about explanatory standards would become quite unknown.

Newton did not change his age’s conception of explanation but rather something deeper still—he changed its conception of empirical inquiry. To understand how, let us take a closer look at Newton’s own interpretation of his method, laid out in a postscript to the Principia’s second edition of 1713. There Newton summarizes the fundamental properties of gravitational attraction—that it increases “in proportion to the quantity of solid matter” and decreases in proportion to distance squared—and then continues: I have not as yet been able to deduce from phenomena the reason for these properties of gravity, and I do not feign hypotheses. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. . . . It is enough that gravity really exists and acts according to the laws that we have set forth and is sufficient to explain all the motions of the heavenly bodies and of our sea.

Shallow explanation does not require the explainer to grasp the implementation of the principles. More important still, it does not require the principles to pass any philosophical test or to conform to the explanatory prescriptions of a Kuhnian paradigm. Gravity might turn out to be transmitted by impact, but equally it might turn out to be authentic action at a distance. Either way, Newton maintains, we have a “sufficient explanation” for the purposes of empirical inquiry, or as Newton calls it, “experimental philosophy.” Newtonian explainers, like Popperian falsifiers, prove their worth by conforming closely not to intellectual precepts but to observed phenomena. The shallow conception of explanation thereby frees scientific theory builders to try just about anything, however ideologically abhorrent, in their attempts to explain the phenomena.

So the investigation of nature changed forever. No longer were deep philosophical insights of the sort that founded Descartes’s system considered to be the keys to the kingdom of knowledge. Put foundational matters aside, Newton’s example seemed to urge, and devote your days instead to the construction of causal principles that, in their forecasts, follow precisely the contours of the observable world. The thinkers around and after Newton got the message, one by one.

Matter, says quantum mechanics, occupies the state called superposition when it is not being observed. An electron in superposition occupies no particular point in space. It is typically, rather, in a kind of “mix” of being in many places at once. The mix is not perfectly balanced: some places are far more heavily represented than others. So a particular electron’s superposition might be almost all made up from positions near a certain atomic nucleus and just a little bit from positions elsewhere. That is the closest that quantum mechanics comes to saying that the electron is orbiting the nucleus.

As far as the iron rule is concerned, argument and reasoning are two quite separate things. Reasoning is what scientists do in their heads to get from the outcomes of tests to opinions, convictions, and plans of action. It is how they make up their minds whether some theory is surely false, likely true, or still up in the air. It is how they decide whether some research program is staid, foolish, or risky but bold. It is how they determine for themselves whether a therapy or experimental procedure is reliable, hopeless, or simply unproved. Vital to such thinking are plausibility rankings, which supply the auxiliary assumptions on which all scientific reasoning is based. It is because plausibility rankings are essentially subjective that scientific reasoning is essentially subjective. Scientific argument, by contrast, in the sense that matters to the iron rule, is what appears in science’s official channels for broadcasting research, namely, the scientific journals and conference presentations. It is only in such venues, on the printed page and the projected slide, that objectivity is required.

Every reader, then, pours their own plausibility rankings onto the desiccated framework of a scientific article, bringing it to life and drawing conclusions accordingly—conclusions that are saturated with subjectivity and that consequently differ from scientist to scientist. Each epoch, each research group, each individual scientist will interpret the scientific literature, and so the significance of the amassed scientific evidence, in their own way. Early on there will be doubt and disagreement, but as the evidence accumulates, it will emerge that whatever plausibility rankings you bring to the findings, one theory is far better than the rest at explaining all that has been observed. The meticulous preservation of data in its sterilized form smooths and speeds this process of Baconian convergence.

Compare Aristotle with Newton. Both were aiming for the same goal, a grand theory that explained the way things move and change. Their methods, however, were quite different. Aristotle but not Newton subjected his hypotheses to stringent philosophical tests. Newton but not Aristotle subjected his hypotheses to stringent quantitative tests, demanding they explain not only the qualities of motion—circular versus straight, up versus down—but also the finest details, such as the precise trajectories of the planets captured by Kepler’s laws. The quantitative tests, it turned out, were far more important. Although Aristotle carefully scrutinized all manner of natural phenomena and cared deeply about the power of his hypotheses to explain what he saw, he was typically content with accounting for broad patterns and not matters of particular detail. It is on those small facts, however, that much of science’s truth-finding power hinges. It is extraordinarily difficult, as Kuhn saw, for human beings to maintain any kind of prolonged interest in the all-important small facts. Minutiae are seldom intrinsically interesting; to transcribe them from nature is often tremendously hard work; and grand intellectual endeavors—conceptual, philosophical, systematizing—are always beckoning, luring the empirical investigator away from the lab bench or the observation post to the glittering land of ideas. Most scientific work is more like bookkeeping or long division than it is like poetic self-exp...