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Karl R. Popper
It’s a pity for many reasons that Karl Popper didn’t live longer, but in particular what would he have thought of what happened to astrophysics not quite twenty years ago?
For those unfamiliar: Popper is best known for his concept of demarcation: that there is a divide between intellectual effort that qualifies as science and every other sort. Popper’s demarcation is testability, or falsifiability—in distinction from the practice of collecting data in justification of a theory. He remarks that you can find this latter sort of corroboration for just about any nonsense, including astrology. But a scientific theory must be able to withstand tests, which means it must have a predictive element. Disprove the prediction and you’ve falsified the theory. The poster child is General Relativity, which predicted that light would bend as it passed a gravity well. It wasn’t a minor point, apparently, but essential to the theory. If light were observed not to bend, General Relativity would be in trouble. An eclipse early in the last century provided an opportunity to test this proposition, and the prediction was borne out. (Now the Hubble telescope picks up evidence of the phenomenon on a cosmic scale, and high school students can marvel if they wish at the beauty of gravitational lensing.) That didn’t mean, by Popper’s standard, that General Relativity had been proven correct. It meant that it had withstood substantial challenge. The more a theory can survive repeated, ingenious challenges, the more respect it earns. It’s that kind of corroboration that Popper found valuable.
But there is a tentativeness in all this. The best we can say, by Popper’s reckoning, is that this is how things appear to be at this time. Tomorrow may bring new information that undoes our most strongly held conviction. And it is the negative discovery—the one that negates prior understanding—that advances our knowledge. Popper died in 1994, at age 92. If he had held on a few years longer, he would have seen a dramatic negation in astrophysics. It is as close as you come to settled science that systems lose energy. Therefore it was believed that the universe itself must be losing energy and that its rate of expansion had to be slowing. How could it be otherwise? In the late 1990s, Adam Riess at Johns Hopkins was among the astrophysicists who tested red shift in far-off supernovae and came up with evidence that no, despite everything the discipline believed, the expansion was accelerating. The impact of this evidence is hard to overstate. It turned on its head much of what scientists thought they knew about the mechanics of the universe.
The Space Telescope Science Institute at Hopkins holds regular lectures as part of its public outreach program. It was poignant to hear this program’s host lament one evening that he had gotten his Ph.D. under “the old model.” He went on to say that the discipline used to believe it understood ninety-five percent of how the universe operates. Now it might understand five percent. Trying to cope, astronomers have devised space-fillers like “dark energy” to supply what’s missing in the equations.
I imagine Popper would have loved this upheaval. Right in front of us, a theory built logically on centuries of accumulated knowledge was demolished. It was falsification on a grand scale. It posed new questions, rather than supplying answers, and sent research off in new directions.
Popper titled his memoir Unended Quest. The book describes his search as a young man in Vienna for a demarcation to separate science from pseudo-science. Before he was done, he had consigned much of the soft sciences to the latter category. That wasn’t a declaration that their insights were useless. It was only a recognition that their claims weren’t susceptible to testing; they had to remain matters of anecdote, and assertions that they identified regularities in human affairs deserved skepticism. Popper noticed among other weaknesses a willingness of adherents to make ad hoc adjustments in theories in order to accommodate what critical observers might have taken as counter-examples. Soon after obtaining his doctorate, while working at a school, he described the symptoms of a troubled youth to one of Freud’s disciples, Alfred Adler. Adler based much of his work on a theory of inferiority complexes. Popper told the doctor he wasn’t certain how the young student’s symptoms fitted Adler’s theory. Oh, cried Adler, this fits my theory perfectly! How can you be certain, Popper inquired, when you haven’t examined the patient? I’m certain, Adler replied, because of the thousand previous examples I’ve seen. Popper replied, I assume with scorn: And now you have a thousand one. In Popper’s estimation, a theory that could accommodate every possible set of observations, including one not observed, wasn’t much of a theory.
It’s interesting to read books of clinical observations. The observations are hardly worthless. But are they science? Are they, in short, more than assemblages of anecdotes that lay, depending on the vanity of the author, varied degrees of false claim to scientific authority? The same question can be posed for narratives of history and other social sciences. Popper tried to answer this question with his demarcation theory. And his answer was: Sorry. No.
His attack on the validity of scientific induction was broad and deep, and so are its implications for all claims of knowledge—and with that, for all claims of authority derived from knowledge. This shaped Popper’s politics.
But first things first. The core assumption in induction is that the next example will be much like the previous ones—enough alike, in any event, to provide a basis for identifying some regularity. This isn’t a foolish assumption. It underlies every heuristic, and knowledge derived from prior examples can save us from repeated costly errors. But Popper’s argument is that there is no logical necessity underlying this assumption, in the way there is a necessity in deductive statements. If A supposes B and B supposes C, then necessarily A supposes C. But induction doesn’t have a comparable logical formula: it might be a bad idea to ignore prior observations, but they don’t logically require that the next example will be of the same sort. The hackneyed illustration of this point is the million white swans you see leading to a seemingly reasonable conviction that all swans are white. Or, in Nassim Taleb’s parable, the thousand days in the life of a Thanksgiving turkey leading it inductively to believe it is worshipped as a god: fed, cosseted, medicated, right up until the thousand first day, just before Thanksgiving.
Even the argument based on induction that “this is probably true” lacks a sound footing, by Popper’s reckoning. To speak of probabilities you have to know the number of examples from which you’re taking a sample, and know in advance the range of possibilities. A casino owner knows those things. The rest of us don’t know the extent of our environment or its variation. Those are what we want to learn, and sampling is an unreliable method; statistical sampling is a pretense at science unless you know the approximate size of the group from which you’re drawing samples.
This seems enormously frustrating, and the frustration may explain some of the neglect of Popper. If you’re a researcher, it must be hard to fall in love with someone who says your search for evidence in support or justification of a theory is misguided and, at its heart, false. It must be even worse if he says it’s the destruction of a theory—the observation of facts that are inconsistent with the theory’s claim of identifying a regularity of nature—that best advances our knowledge, pointing us away from error in a direction that may be less wrong. As the host at the Space Telescope said, he’d gotten his degree under the old way of looking at things. But there is no reason for us to believe that reality should be kind to our conjectures, or to careers built on them.
“It is part of my thesis,” Popper says in the preface to the second edition of Conjectures and Refutations, “that all our knowledge grows only through the correcting of our mistakes.” In short, the thousand confirmatory examples are of limited value, but the single non-confirmation, or refutation, is potentially (if it holds up) definitive. You would think that science would love such a powerful tool for refuting error.
There's an anecdote that tells of evolutionist J.B.S. Haldane being challenged at a lecture. A questioner asked, approximately, "What, sir, would falsify your Darwinian doctrine?" Haldane supposedly replied, "Rabbit bones in the Precambrian would be a problem." Darwinian theory precluded rabbits having lived a half-billion years ago. In that sense the theory was predictive—it predicted that no such observations would be made—and it was falsifiable: it included enough specific information that the contradiction of that information would potentially prove the theory wrong.
The more predictions a theory offers, the more information it contains, it follows the more valuable it is, because it explains potentially a great deal about the world. But also the less probable it is. “. . . [T]he probability of a statement (or set of statements) is always the greater the less the statement says; it is inverse to the content or the deductive power of the statement, and thus to its explanatory power,” Popper argued in a 1953 lecture. “Accordingly every interesting and powerful statement must have a low probability; and vice versa: a statement with a high probability will be scientifically uninteresting because it says little and has no explanatory power.” Thus science seeks “powerful and improbable theories.” That passage is easily misunderstood. “Improbable” isn’t an approximation of “absurd”; Popper is speaking of a theory that says a great deal that is specific, the multiple specifics increasing its explanatory power while reducing statistically its probability. And, as noted, the more specifics, the more potential for critics to find error.
“. . . [T]he method of science is criticism,” Popper wrote. And this may explain in part why you can ask contemporary science students about this father of the philosophy of science and receive in response a blank stare. Isn’t it more useful, they might say, to think about how to write grant proposals? Or to seek guidance in p-hacking? The structure of research is hardly given to destroying theories, least of all one’s own lab’s. Grants are given to prove, to affirm, not to undermine. The absolute disaster in replicability across a number of scientific fields is one possible consequence of this lack of a critical approach.
Marx and Freud suffer badly at Popper’s hands on the same, anti-inductivist ground. Popper’s 1936 paper, later published as The Poverty of Historicism, was a demolition of Marxism and other historicist doctrines. A key argument was stated concisely later by Amos Tversky, who observed that historians have displayed zero predictive skill. Yet the data available may be the very sets on which elaborate explanatory narratives are built after the fact. What does this say of the historicists' claims to have understood events, or of the explanatory value of their theories?
One can find this problem across disciplines. It isn’t just the wobbly-eyed stock market chart-reader who gets it right in retrospect time after time, but cannot forecast the market with any greater accuracy than chance would deliver. Or the mogul whose formula for fortune-building denies randomness as a factor in his success. The Ph.D.s staffing the Federal Reserve have a proven inability to model the future, though it’s an article of faith in their historicist discipline—their inductive discipline—that events of the past establish patterns of regularities enabling economists to predict future economic activity with enough accuracy to guide policy that affects every citizen. This makes the false claims of a biolab p-hacker seem inconsequential by comparison.
Popper has been adopted by some on the political left. He was, in fact, a European Liberal, and his thinking meshed comfortably enough with that of Friedrich A. Hayek, another Liberal who challenged collectivism’s “scientism” and “pretense of knowledge,” that Popper’s essay collection Conjectures and Refutations bears a dedication to Hayek. The core idea they explored through their lives was the difficulty of knowledge, and the unspeakable damage done in the name of claims to knowledge that can never be proven. Popper inscribed The Poverty of Historicism as follows: “In memory of the countless men and women of all creeds or nations or races who fell victims to the fascist and communist belief in Inexorable Laws of Historical Destiny.” There were no such laws, only pretenses of knowledge cloaked in the guise of science but lacking the rigor of science; propagated by adherents whose many questionable motives included an eagerness to believe doctrines that could explain so much, if only they weren’t examined critically.
“What we should do, I suggest,” Popper said in a 1960 lecture before the British Academy, “is to give up the idea of ultimate sources of knowledge, and admit that all knowledge is human; that it is mixed with our errors, our prejudices, our dreams, and our hopes; that all we can do is to grope for truth even though it be beyond our reach. We may admit that our groping is often inspired, but we must be on our guard against the belief, however deeply felt, that our inspiration carries any authority, divine or otherwise. If we thus admit that there is no authority beyond the reach of criticism to be found within the whole province of our knowledge, however far it may have penetrated into the unknown, then we can retain, without danger, the idea that truth is beyond human authority. And we must retain it. For without this idea there can be no objective standards of inquiry; no criticisms of our conjectures; no groping for the unknown; no quest for knowledge.”
July 29 2017
For those unfamiliar: Popper is best known for his concept of demarcation: that there is a divide between intellectual effort that qualifies as science and every other sort. Popper’s demarcation is testability, or falsifiability—in distinction from the practice of collecting data in justification of a theory. He remarks that you can find this latter sort of corroboration for just about any nonsense, including astrology. But a scientific theory must be able to withstand tests, which means it must have a predictive element. Disprove the prediction and you’ve falsified the theory. The poster child is General Relativity, which predicted that light would bend as it passed a gravity well. It wasn’t a minor point, apparently, but essential to the theory. If light were observed not to bend, General Relativity would be in trouble. An eclipse early in the last century provided an opportunity to test this proposition, and the prediction was borne out. (Now the Hubble telescope picks up evidence of the phenomenon on a cosmic scale, and high school students can marvel if they wish at the beauty of gravitational lensing.) That didn’t mean, by Popper’s standard, that General Relativity had been proven correct. It meant that it had withstood substantial challenge. The more a theory can survive repeated, ingenious challenges, the more respect it earns. It’s that kind of corroboration that Popper found valuable.
But there is a tentativeness in all this. The best we can say, by Popper’s reckoning, is that this is how things appear to be at this time. Tomorrow may bring new information that undoes our most strongly held conviction. And it is the negative discovery—the one that negates prior understanding—that advances our knowledge. Popper died in 1994, at age 92. If he had held on a few years longer, he would have seen a dramatic negation in astrophysics. It is as close as you come to settled science that systems lose energy. Therefore it was believed that the universe itself must be losing energy and that its rate of expansion had to be slowing. How could it be otherwise? In the late 1990s, Adam Riess at Johns Hopkins was among the astrophysicists who tested red shift in far-off supernovae and came up with evidence that no, despite everything the discipline believed, the expansion was accelerating. The impact of this evidence is hard to overstate. It turned on its head much of what scientists thought they knew about the mechanics of the universe.
The Space Telescope Science Institute at Hopkins holds regular lectures as part of its public outreach program. It was poignant to hear this program’s host lament one evening that he had gotten his Ph.D. under “the old model.” He went on to say that the discipline used to believe it understood ninety-five percent of how the universe operates. Now it might understand five percent. Trying to cope, astronomers have devised space-fillers like “dark energy” to supply what’s missing in the equations.
I imagine Popper would have loved this upheaval. Right in front of us, a theory built logically on centuries of accumulated knowledge was demolished. It was falsification on a grand scale. It posed new questions, rather than supplying answers, and sent research off in new directions.
Popper titled his memoir Unended Quest. The book describes his search as a young man in Vienna for a demarcation to separate science from pseudo-science. Before he was done, he had consigned much of the soft sciences to the latter category. That wasn’t a declaration that their insights were useless. It was only a recognition that their claims weren’t susceptible to testing; they had to remain matters of anecdote, and assertions that they identified regularities in human affairs deserved skepticism. Popper noticed among other weaknesses a willingness of adherents to make ad hoc adjustments in theories in order to accommodate what critical observers might have taken as counter-examples. Soon after obtaining his doctorate, while working at a school, he described the symptoms of a troubled youth to one of Freud’s disciples, Alfred Adler. Adler based much of his work on a theory of inferiority complexes. Popper told the doctor he wasn’t certain how the young student’s symptoms fitted Adler’s theory. Oh, cried Adler, this fits my theory perfectly! How can you be certain, Popper inquired, when you haven’t examined the patient? I’m certain, Adler replied, because of the thousand previous examples I’ve seen. Popper replied, I assume with scorn: And now you have a thousand one. In Popper’s estimation, a theory that could accommodate every possible set of observations, including one not observed, wasn’t much of a theory.
It’s interesting to read books of clinical observations. The observations are hardly worthless. But are they science? Are they, in short, more than assemblages of anecdotes that lay, depending on the vanity of the author, varied degrees of false claim to scientific authority? The same question can be posed for narratives of history and other social sciences. Popper tried to answer this question with his demarcation theory. And his answer was: Sorry. No.
His attack on the validity of scientific induction was broad and deep, and so are its implications for all claims of knowledge—and with that, for all claims of authority derived from knowledge. This shaped Popper’s politics.
But first things first. The core assumption in induction is that the next example will be much like the previous ones—enough alike, in any event, to provide a basis for identifying some regularity. This isn’t a foolish assumption. It underlies every heuristic, and knowledge derived from prior examples can save us from repeated costly errors. But Popper’s argument is that there is no logical necessity underlying this assumption, in the way there is a necessity in deductive statements. If A supposes B and B supposes C, then necessarily A supposes C. But induction doesn’t have a comparable logical formula: it might be a bad idea to ignore prior observations, but they don’t logically require that the next example will be of the same sort. The hackneyed illustration of this point is the million white swans you see leading to a seemingly reasonable conviction that all swans are white. Or, in Nassim Taleb’s parable, the thousand days in the life of a Thanksgiving turkey leading it inductively to believe it is worshipped as a god: fed, cosseted, medicated, right up until the thousand first day, just before Thanksgiving.
Even the argument based on induction that “this is probably true” lacks a sound footing, by Popper’s reckoning. To speak of probabilities you have to know the number of examples from which you’re taking a sample, and know in advance the range of possibilities. A casino owner knows those things. The rest of us don’t know the extent of our environment or its variation. Those are what we want to learn, and sampling is an unreliable method; statistical sampling is a pretense at science unless you know the approximate size of the group from which you’re drawing samples.
This seems enormously frustrating, and the frustration may explain some of the neglect of Popper. If you’re a researcher, it must be hard to fall in love with someone who says your search for evidence in support or justification of a theory is misguided and, at its heart, false. It must be even worse if he says it’s the destruction of a theory—the observation of facts that are inconsistent with the theory’s claim of identifying a regularity of nature—that best advances our knowledge, pointing us away from error in a direction that may be less wrong. As the host at the Space Telescope said, he’d gotten his degree under the old way of looking at things. But there is no reason for us to believe that reality should be kind to our conjectures, or to careers built on them.
“It is part of my thesis,” Popper says in the preface to the second edition of Conjectures and Refutations, “that all our knowledge grows only through the correcting of our mistakes.” In short, the thousand confirmatory examples are of limited value, but the single non-confirmation, or refutation, is potentially (if it holds up) definitive. You would think that science would love such a powerful tool for refuting error.
There's an anecdote that tells of evolutionist J.B.S. Haldane being challenged at a lecture. A questioner asked, approximately, "What, sir, would falsify your Darwinian doctrine?" Haldane supposedly replied, "Rabbit bones in the Precambrian would be a problem." Darwinian theory precluded rabbits having lived a half-billion years ago. In that sense the theory was predictive—it predicted that no such observations would be made—and it was falsifiable: it included enough specific information that the contradiction of that information would potentially prove the theory wrong.
The more predictions a theory offers, the more information it contains, it follows the more valuable it is, because it explains potentially a great deal about the world. But also the less probable it is. “. . . [T]he probability of a statement (or set of statements) is always the greater the less the statement says; it is inverse to the content or the deductive power of the statement, and thus to its explanatory power,” Popper argued in a 1953 lecture. “Accordingly every interesting and powerful statement must have a low probability; and vice versa: a statement with a high probability will be scientifically uninteresting because it says little and has no explanatory power.” Thus science seeks “powerful and improbable theories.” That passage is easily misunderstood. “Improbable” isn’t an approximation of “absurd”; Popper is speaking of a theory that says a great deal that is specific, the multiple specifics increasing its explanatory power while reducing statistically its probability. And, as noted, the more specifics, the more potential for critics to find error.
“. . . [T]he method of science is criticism,” Popper wrote. And this may explain in part why you can ask contemporary science students about this father of the philosophy of science and receive in response a blank stare. Isn’t it more useful, they might say, to think about how to write grant proposals? Or to seek guidance in p-hacking? The structure of research is hardly given to destroying theories, least of all one’s own lab’s. Grants are given to prove, to affirm, not to undermine. The absolute disaster in replicability across a number of scientific fields is one possible consequence of this lack of a critical approach.
Marx and Freud suffer badly at Popper’s hands on the same, anti-inductivist ground. Popper’s 1936 paper, later published as The Poverty of Historicism, was a demolition of Marxism and other historicist doctrines. A key argument was stated concisely later by Amos Tversky, who observed that historians have displayed zero predictive skill. Yet the data available may be the very sets on which elaborate explanatory narratives are built after the fact. What does this say of the historicists' claims to have understood events, or of the explanatory value of their theories?
One can find this problem across disciplines. It isn’t just the wobbly-eyed stock market chart-reader who gets it right in retrospect time after time, but cannot forecast the market with any greater accuracy than chance would deliver. Or the mogul whose formula for fortune-building denies randomness as a factor in his success. The Ph.D.s staffing the Federal Reserve have a proven inability to model the future, though it’s an article of faith in their historicist discipline—their inductive discipline—that events of the past establish patterns of regularities enabling economists to predict future economic activity with enough accuracy to guide policy that affects every citizen. This makes the false claims of a biolab p-hacker seem inconsequential by comparison.
Popper has been adopted by some on the political left. He was, in fact, a European Liberal, and his thinking meshed comfortably enough with that of Friedrich A. Hayek, another Liberal who challenged collectivism’s “scientism” and “pretense of knowledge,” that Popper’s essay collection Conjectures and Refutations bears a dedication to Hayek. The core idea they explored through their lives was the difficulty of knowledge, and the unspeakable damage done in the name of claims to knowledge that can never be proven. Popper inscribed The Poverty of Historicism as follows: “In memory of the countless men and women of all creeds or nations or races who fell victims to the fascist and communist belief in Inexorable Laws of Historical Destiny.” There were no such laws, only pretenses of knowledge cloaked in the guise of science but lacking the rigor of science; propagated by adherents whose many questionable motives included an eagerness to believe doctrines that could explain so much, if only they weren’t examined critically.
“What we should do, I suggest,” Popper said in a 1960 lecture before the British Academy, “is to give up the idea of ultimate sources of knowledge, and admit that all knowledge is human; that it is mixed with our errors, our prejudices, our dreams, and our hopes; that all we can do is to grope for truth even though it be beyond our reach. We may admit that our groping is often inspired, but we must be on our guard against the belief, however deeply felt, that our inspiration carries any authority, divine or otherwise. If we thus admit that there is no authority beyond the reach of criticism to be found within the whole province of our knowledge, however far it may have penetrated into the unknown, then we can retain, without danger, the idea that truth is beyond human authority. And we must retain it. For without this idea there can be no objective standards of inquiry; no criticisms of our conjectures; no groping for the unknown; no quest for knowledge.”
July 29 2017