Archive for the 'Karl Popper' Category

Jack Schwartz on the Weaknesses of the Mathematical Mind

I was recently rereading an essay by Karl Popper, “A Realistic View of Logic, Physics, and History” published in his collection of essays, Objective Knowledge: An Evolutionary Approach, because it discusses the role of reductivism in science and philosophy, a topic about which I’ve written a number of previous posts discussing the microfoundations of macroeconomics.

Here is an important passage from Popper’s essay:

What I should wish to assert is (1) that criticism is a most important methodological device: and (2) that if you answer criticism by saying, “I do not like your logic: your logic may be all right for you, but I prefer a different logic, and according to my logic this criticism is not valid”, then you may undermine the method of critical discussion.

Now I should distinguish between two main uses of logic, namely (1) its use in the demonstrative sciences – that is to say, the mathematical sciences – and (2) its use in the empirical sciences.

In the demonstrative sciences logic is used in the main for proofs – for the transmission of truth – while in the empirical sciences it is almost exclusively used critically – for the retransmission of falsity. Of course, applied mathematics comes in too, which implicitly makes use of the proofs of pure mathematics, but the role of mathematics in the empirical sciences is somewhat dubious in several respects. (There exists a wonderful article by Schwartz to this effect.)

The article to which Popper refers appears by Jack Schwartz in a volume edited by Ernst Nagel, Patrick Suppes, and Alfred Tarski, Logic, Methodology and Philosophy of Science. The title of the essay, “The Pernicious Influence of Mathematics on Science” caught my eye, so I tried to track it down. Unavailable on the internet except behind a paywall, I bought a used copy for $6 including postage. The essay was well worth the $6 I paid to read it.

Before quoting from the essay, I would just note that Jacob T. (Jack) Schwartz was far from being innocent of mathematical and scientific knowledge. Here’s a snippet from the Wikipedia entry on Schwartz.

His research interests included the theory of linear operatorsvon Neumann algebrasquantum field theorytime-sharingparallel computingprogramming language design and implementation, robotics, set-theoretic approaches in computational logicproof and program verification systems; multimedia authoring tools; experimental studies of visual perception; multimedia and other high-level software techniques for analysis and visualization of bioinformatic data.

He authored 18 books and more than 100 papers and technical reports.

He was also the inventor of the Artspeak programming language that historically ran on mainframes and produced graphical output using a single-color graphical plotter.[3]

He served as Chairman of the Computer Science Department (which he founded) at the Courant Institute of Mathematical SciencesNew York University, from 1969 to 1977. He also served as Chairman of the Computer Science Board of the National Research Council and was the former Chairman of the National Science Foundation Advisory Committee for Information, Robotics and Intelligent Systems. From 1986 to 1989, he was the Director of DARPA‘s Information Science and Technology Office (DARPA/ISTO) in Arlington, Virginia.

Here is a link to his obituary.

Though not trained as an economist, Schwartz, an autodidact, wrote two books on economic theory.

With that introduction, I quote from, and comment on, Schwartz’s essay.

Our announced subject today is the role of mathematics in the formulation of physical theories. I wish, however, to make use of the license permitted at philosophical congresses, in two regards: in the first place, to confine myself to the negative aspects of this role, leaving it to others to dwell on the amazing triumphs of the mathematical method; in the second place, to comment not only on physical science but also on social science, in which the characteristic inadequacies which I wish to discuss are more readily apparent.

Computer programmers often make a certain remark about computing machines, which may perhaps be taken as a complaint: that computing machines, with a perfect lack of discrimination, will do any foolish thing they are told to do. The reason for this lies of course in the narrow fixation of the computing machines “intelligence” upon the basely typographical details of its own perceptions – its inability to be guided by any large context. In a psychological description of the computer intelligence, three related adjectives push themselves forward: single-mindedness, literal-mindedness, simple-mindedness. Recognizing this, we should at the same time recognize that this single-mindedness, literal-mindedness, simple-mindedness also characterizes theoretical mathematics, though to a lesser extent.

It is a continual result of the fact that science tries to deal with reality that even the most precise sciences normally work with more or less ill-understood approximations toward which the scientist must maintain an appropriate skepticism. Thus, for instance, it may come as a shock to the mathematician to learn that the Schrodinger equation for the hydrogen atom, which he is able to solve only after a considerable effort of functional analysis and special function theory, is not a literally correct description of this atom, but only an approximation to a somewhat more correct equation taking account of spin, magnetic dipole, and relativistic effects; that this corrected equation is itself only an ill-understood approximation to an infinite set of quantum field-theoretic equations; and finally that the quantum field theory, besides diverging, neglects a myriad of strange-particle interactions whose strength and form are largely unknown. The physicist looking at the original Schrodinger equation, learns to sense in it the presence of many invisible terms, integral, intergrodifferential, perhaps even more complicated types of operators, in addition to the differential terms visible, and this sense inspires an entirely appropriate disregard for the purely technical features of the equation which he sees. This very healthy self-skepticism is foreign to the mathematical approach. . . .

Schwartz, in other words, is noting that the mathematical equations that physicists use in many contexts cannot be relied upon without qualification as accurate or exact representations of reality. The understanding that the mathematics that physicists and other physical scientists use to express their theories is often inexact or approximate inasmuch as reality is more complicated than our theories can capture mathematically. Part of what goes into the making of a good scientist is a kind of artistic feeling for how to adjust or interpret a mathematical model to take into account what the bare mathematics cannot describe in a manageable way.

The literal-mindedness of mathematics . . . makes it essential, if mathematics is to be appropriately used in science, that the assumptions upon which mathematics is to elaborate be correctly chosen from a larger point of view, invisible to mathematics itself. The single-mindedness of mathematics reinforces this conclusion. Mathematics is able to deal successfully only with the simplest of situations, more precisely, with a complex situation only to the extent that rare good fortune makes this complex situation hinge upon a few dominant simple factors. Beyond the well-traversed path, mathematics loses its bearing in a jungle of unnamed special functions and impenetrable combinatorial particularities. Thus, mathematical technique can only reach far if it starts from a point close to the simple essentials of a problem which has simple essentials. That form of wisdom which is the opposite of single-mindedness, the ability to keep many threads in hand, to draw for an argument from many disparate sources, is quite foreign to mathematics. The inability accounts for much of the difficulty which mathematics experiences in attempting to penetrate the social sciences. We may perhaps attempt a mathematical economics – but how difficult would be a mathematical history! Mathematics adjusts only with reluctance to the external, and vitally necessary, approximating of the scientists, and shudders each time a batch of small terms is cavalierly erased. Only with difficulty does it find its way to the scientist’s ready grasp of the relative importance of many factors. Quite typically, science leaps ahead and mathematics plods behind.

Schwartz having referenced mathematical economics, let me try to restate his point more concretely than he did by referring to the Walrasian theory of general equilibrium. “Mathematics,” Schwartz writes, “adjusts only with reluctance to the external, and vitally necessary, approximating of the scientists, and shudders each time a batch of small terms is cavalierly erased.” The Walrasian theory is at once too general and too special to be relied on as an applied theory. It is too general because the functional forms of most of its reliant equations can’t be specified or even meaningfully restricted on very special simplifying assumptions; it is too special, because the simplifying assumptions about the agents and the technologies and the constraints and the price-setting mechanism are at best only approximations and, at worst, are entirely divorced from reality.

Related to this deficiency of mathematics, and perhaps more productive of rueful consequence, is the simple-mindedness of mathematics – its willingness, like that of a computing machine, to elaborate upon any idea, however absurd; to dress scientific brilliancies and scientific absurdities alike in the impressive uniform of formulae and theorems. Unfortunately however, an absurdity in uniform is far more persuasive than an absurdity unclad. The very fact that a theory appears in mathematical form, that, for instance, a theory has provided the occasion for the application of a fixed-point theorem, or of a result about difference equations, somehow makes us more ready to take it seriously. And the mathematical-intellectual effort of applying the theorem fixes in us the particular point of view of the theory with which we deal, making us blind to whatever appears neither as a dependent nor as an independent parameter in its mathematical formulation. The result, perhaps most common in the social sciences, is bad theory with a mathematical passport. The present point is best established by reference to a few horrible examples. . . . I confine myself . . . to the citation of a delightful passage from Keynes’ General Theory, in which the issues before us are discussed with a characteristic wisdom and wit:

“It is the great fault of symbolic pseudomathematical methods of formalizing a system of economic analysis . . . that they expressly assume strict independence between the factors involved and lose all their cogency and authority if this hypothesis is disallowed; whereas, in ordinary discourse, where we are not blindly manipulating but know all the time what we are doing and what the words mean, we can keep ‘at the back of our heads’ the necessary reserves and qualifications and adjustments which we shall have to make later on, in a way in which we cannot keep complicated partial differentials ‘at the back’ of several pages of algebra which assume they all vanish. Too large a proportion of recent ‘mathematical’ economics are mere concoctions, as imprecise as the initial assumptions they reset on, which allow the author to lose sight of the complexities and interdependencies of the real world in a maze of pretentions and unhelpful symbols.”

Although it would have been helpful if Keynes had specifically identified the pseudomathematical methods that he had in mind, I am inclined to think that he was expressing his impatience with the Walrasian general-equilibrium approach that was characteristic of the Marshallian tradition that he carried forward even as he struggled to transcend it. Walrasian general equilibrium analysis, he seems to be suggesting, is too far removed from reality to provide any reliable guide to macroeconomic policy-making, because the necessary qualifications required to make general-equilibrium analysis practically relevant are simply unmanageable within the framework of general-equilibrium analysis. A different kind of analysis is required. As a Marshallian he was less skeptical of partial-equilibrium analysis than of general-equilibrium analysis. But he also recognized that partial-equilibrium analysis could not be usefully applied in situations, e.g., analysis of an overall “market” for labor, where the usual ceteris paribus assumptions underlying the use of stable demand and supply curves as analytical tools cannot be maintained. But for some reason that didn’t stop Keynes from trying to explain the nominal rate of interest by positing a demand curve to hold money and a fixed stock of money supplied by a central bank. But we all have our blind spots and miss obvious implications of familiar ideas that we have already encountered and, at least partially, understand.

Schwartz concludes his essay with an arresting thought that should give us pause about how we often uncritically accept probabilistic and statistical propositions as if we actually knew how they matched up with the stochastic phenomena that we are seeking to analyze. But although there is a lot to unpack in his conclusion, I am afraid someone more capable than I will have to do the unpacking.

[M]athematics, concentrating our attention, makes us blind to its own omissions – what I have already called the single-mindedness of mathematics. Typically, mathematics, knows better what to do than why to do it. Probability theory is a famous example. . . . Here also, the mathematical formalism may be hiding as much as it reveals.

Dr. Popper: Or How I Learned to Stop Worrying and Love Metaphysics

Introduction to Falsificationism

Although his reputation among philosophers was never quite as exalted as it was among non-philosophers, Karl Popper was a pre-eminent figure in 20th century philosophy. As a non-philosopher, I won’t attempt to adjudicate which take on Popper is the more astute, but I think I can at least sympathize, if not fully agree, with philosophers who believe that Popper is overrated by non-philosophers. In an excellent blog post, Phillipe Lemoine gives a good explanation of why philosophers look askance at falsificationism, Popper’s most important contribution to philosophy.

According to Popper, what distinguishes or demarcates a scientific statement from a non-scientific (metaphysical) statement is whether the statement can, or could be, disproved or refuted – falsified (in the sense of being shown to be false not in the sense of being forged, misrepresented or fraudulently changed) – by an actual or potential observation. Vulnerability to potentially contradictory empirical evidence, according to Popper, is what makes science special, allowing it to progress through a kind of dialectical process of conjecture (hypothesis) and refutation (empirical testing) leading to further conjecture and refutation and so on.

Theories purporting to explain anything and everything are thus non-scientific or metaphysical. Claiming to be able to explain too much is a vice, not a virtue, in science. Science advances by risk-taking, not by playing it safe. Trying to explain too much is actually playing it safe. If you’re not willing to take the chance of putting your theory at risk, by saying that this and not that will happen — rather than saying that this or that will happen — you’re playing it safe. This view of science, portrayed by Popper in modestly heroic terms, was not unappealing to scientists, and in part accounts for the positive reception of Popper’s work among scientists.

But this heroic view of science, as Lemoine nicely explains, was just a bit oversimplified. Theories never exist in a vacuum, there is always implicit or explicit background knowledge that informs and provides context for the application of any theory from which a prediction is deduced. To deduce a prediction from any theory, background knowledge, including complementary theories that are presumed to be valid for purposes of making a prediction, is necessary. Any prediction relies not just on a single theory but on a system of related theories and auxiliary assumptions.

So when a prediction is deduced from a theory, and the predicted event is not observed, it is never unambiguously clear which of the multiple assumptions underlying the prediction is responsible for the failure of the predicted event to be observed. The one-to-one logical dependence between a theory and a prediction upon which Popper’s heroic view of science depends doesn’t exist. Because the heroic view of science is too simplified, Lemoine considers it false, at least in the naïve and heroic form in which it is often portrayed by its proponents.

But, as Lemoine himself acknowledges, Popper was not unaware of these issues and actually dealt with some if not all of them. Popper therefore dismissed those criticisms pointing to his various acknowledgments and even anticipations of and responses to the criticisms. Nevertheless, his rhetorical style was generally not to qualify his position but to present it in stark terms, thereby reinforcing the view of his critics that he actually did espouse the naïve version of falsificationism that, only under duress, would be toned down to meet the objections raised to the usual unqualified version of his argument. Popper after all believed in making bold conjectures and framing a theory in the strongest possible terms and characteristically adopted an argumentative and polemical stance in staking out his positions.

Toned-Down Falsificationism

In his tone-downed version of falsificationism, Popper acknowledged that one can never know if a prediction fails because the underlying theory is false or because one of the auxiliary assumptions required to make the prediction is false, or even because of an error in measurement. But that acknowledgment, Popper insisted, does not refute falsificationism, because falsificationism is not a scientific theory about how scientists do science; it is a normative theory about how scientists ought to do science. The normative implication of falsificationism is that scientists should not try to shield their theories by making just-so adjustments in their theories through ad hoc auxiliary assumptions, e.g., ceteris paribus assumptions, to shield their theories from empirical disproof. Rather they should accept the falsification of their theories when confronted by observations that conflict with the implications of their theories and then formulate new and better theories to replace the old ones.

But a strict methodological rule against adjusting auxiliary assumptions or making further assumptions of an ad hoc nature would have ruled out many fruitful theoretical developments resulting from attempts to account for failed predictions. For example, the planet Neptune was discovered in 1846 by scientists who posited (ad hoc) the existence of another planet to explain why the planet Uranus did not follow its predicted path. Rather than conclude that the Newtonian theory was falsified by the failure of Uranus to follow the orbital path predicted by Newtonian theory, the French astronomer Urbain Le Verrier posited the existence of another planet that would account for the path actually followed by Uranus. Now in this case, it was possible to observe the predicted position of the new planet, and its discovery in the predicted location turned out to be a sensational confirmation of Newtonian theory.

Popper therefore admitted that making an ad hoc assumption in order to save a theory from refutation was permissible under his version of normative faslisificationism, but only if the ad hoc assumption was independently testable. But suppose that, under the circumstances, it would have been impossible to observe the existence of the predicted planet, at least with the observational tools then available, making the ad hoc assumption testable only in principle, but not in practice. Strictly adhering to Popper’s methodological requirement of being able to test independently any ad hoc assumption would have meant accepting the refutation of the Newtonian theory rather than positing the untestable — but true — ad hoc other-planet hypothesis to account for the failed prediction of the orbital path of Uranus.

My point is not that ad hoc assumptions to save a theory from falsification are ok, but to point out that a strict methodological rules requiring rejection of any theory once it appears to be contradicted by empirical evidence and prohibiting the use of any ad hoc assumption to save the theory unless the ad hoc assumption is independently testable might well lead to the wrong conclusion given the nuances and special circumstances associated with every case in which a theory seems to be contradicted by observed evidence. Such contradictions are rarely so blatant that theory cannot be reconciled with the evidence. Indeed, as Popper himself recognized, all observations are themselves understood and interpreted in the light of theoretical presumptions. It is only in extreme cases that evidence cannot be interpreted in a way that more or less conforms to the theory under consideration. At first blush, the Copernican heliocentric view of the world seemed obviously contradicted by direct sensory observation that earth seems flat and the sun rise and sets. Empirical refutation could be avoided only by providing an alternative interpretation of the sensory data that could be reconciled with the apparent — and obvious — flatness and stationarity of the earth and the movement of the sun and moon in the heavens.

So the problem with falsificationism as a normative theory is that it’s not obvious why a moderately good, but less than perfect, theory should be abandoned simply because it’s not perfect and suffers from occasional predictive failures. To be sure, if a better theory than the one under consideration is available, predicting correctly whenever the one under consideration predicts correctly and predicting more accurately than the one under consideration when the latter fails to predict correctly, the alternative theory is surely preferable, but that simply underscores the point that evaluating any theory in isolation is not very important. After all, every theory, being a simplification, is an imperfect representation of reality. It is only when two or more theories are available that scientists must try to determine which of them is preferable.

Oakeshott and the Poverty of Falsificationism

These problems with falsificationism were brought into clearer focus by Michael Oakeshott in his famous essay “Rationalism in Politics,” which though not directed at Popper himself (whose colleague at the London School of Economics he was) can be read as a critique of Popper’s attempt to prescribe methodological rules for scientists to follow in carrying out their research. Methodological rules of the kind propounded by Popper are precisely the sort of supposedly rational rules of practice intended to ensure the successful outcome of an undertaking that Oakeshott believed to be ill-advised and hopelessly naïve. The rationalist conceit in Oakesott’s view is that there are demonstrably correct answers to practical questions and that practical activity is rational only when it is based on demonstrably true moral or causal rules.

The entry on Michael Oakeshott in the Stanford Encyclopedia of Philosophy summarizes Oakeshott’s position as follows:

The error of Rationalism is to think that making decisions simply requires skill in the technique of applying rules or calculating consequences. In an early essay on this theme, Oakeshott distinguishes between “technical” and “traditional” knowledge. Technical knowledge is of facts or rules that can be easily learned and applied, even by those who are without experience or lack the relevant skills. Traditional knowledge, in contrast, means “knowing how” rather than “knowing that” (Ryle 1949). It is acquired by engaging in an activity and involves judgment in handling facts or rules (RP 12–17). The point is not that rules cannot be “applied” but rather that using them skillfully or prudently means going beyond the instructions they provide.

The idea that a scientist’s decision about when to abandon one theory and replace it with another can be reduced to the application of a Popperian falsificationist maxim ignores all the special circumstances and all the accumulated theoretical and practical knowledge that a truly expert scientist will bring to bear in studying and addressing such a problem. Here is how Oakeshott addresses the problem in his famous essay.

These two sorts of knowledge, then, distinguishable but inseparable, are the twin components of the knowledge involved in every human activity. In a practical art such as cookery, nobody supposes that the knowledge that belongs to the good cook is confined to what is or what may be written down in the cookery book: technique and what I have called practical knowledge combine to make skill in cookery wherever it exists. And the same is true of the fine arts, of painting, of music, of poetry: a high degree of technical knowledge, even where it is both subtle and ready, is one thing; the ability to create a work of art, the ability to compose something with real musical qualities, the ability to write a great sonnet, is another, and requires in addition to technique, this other sort of knowledge. Again these two sorts of knowledge are involved in any genuinely scientific activity. The natural scientist will certainly make use of observation and verification that belong to his technique, but these rules remain only one of the components of his knowledge; advances in scientific knowledge were never achieved merely by following the rules. . . .

Technical knowledge . . . is susceptible of formulation in rules, principles, directions, maxims – comprehensively, in propositions. It is possible to write down technical knowledge in a book. Consequently, it does not surprise us that when an artist writes about his art, he writes only about the technique of his art. This is so, not because he is ignorant of what may be called asesthetic element, or thinks it unimportant, but because what he has to say about that he has said already (if he is a painter) in his pictures, and he knows no other way of saying it. . . . And it may be observed that this character of being susceptible of precise formulation gives to technical knowledge at least the appearance of certainty: it appears to be possible to be certain about a technique. On the other hand, it is characteristic of practical knowledge that it is not susceptible of formulation of that kind. Its normal expression is in a customary or traditional way of doing things, or, simply, in practice. And this gives it the appearance of imprecision and consequently of uncertainty, of being a matter of opinion, of probability rather than truth. It is indeed knowledge that is expressed in taste or connoisseurship, lacking rigidity and ready for the impress of the mind of the learner. . . .

Technical knowledge, in short, an be both taught and learned in the simplest meanings of these words. On the other hand, practical knowledge can neither be taught nor learned, but only imparted and acquired. It exists only in practice, and the only way to acquire it is by apprenticeship to a master – not because the master can teach it (he cannot), but because it can be acquired only by continuous contact with one who is perpetually practicing it. In the arts and in natural science what normally happens is that the pupil, in being taught and in learning the technique from his master, discovers himself to have acquired also another sort of knowledge than merely technical knowledge, without it ever having been precisely imparted and often without being able to say precisely what it is. Thus a pianist acquires artistry as well as technique, a chess-player style and insight into the game as well as knowledge of the moves, and a scientist acquires (among other things) the sort of judgement which tells him when his technique is leading him astray and the connoisseurship which enables him to distinguish the profitable from the unprofitable directions to explore.

Now, as I understand it, Rationalism is the assertion that what I have called practical knowledge is not knowledge at all, the assertion that, properly speaking, there is no knowledge which is not technical knowledge. The Rationalist holds that the only element of knowledge involved in any human activity is technical knowledge and that what I have called practical knowledge is really only a sort of nescience which would be negligible if it were not positively mischievous. (Rationalism in Politics and Other Essays, pp. 12-16)

Almost three years ago, I attended the History of Economics Society meeting at Duke University at which Jeff Biddle of Michigan State University delivered his Presidential Address, “Statistical Inference in Economics 1920-1965: Changes in Meaning and Practice, published in the June 2017 issue of the Journal of the History of Economic Thought. The paper is a remarkable survey of the differing attitudes towards using formal probability theory as the basis for making empirical inferences from the data. The underlying assumptions of probability theory about the nature of the data were widely viewed as being too extreme to make probability theory an acceptable basis for empirical inferences from the data. However, the early negative attitudes toward accepting probability theory as the basis for making statistical inferences from data were gradually overcome (or disregarded). But as late as the 1960s, even though econometric techniques were becoming more widely accepted, a great deal of empirical work, including by some of the leading empirical economists of the time, avoided using the techniques of statistical inference to assess empirical data using regression analysis. Only in the 1970s was there a rapid sea-change in professional opinion that made statistical inference based on explicit probabilisitic assumptions about underlying data distributions the requisite technique for drawing empirical inferences from the analysis of economic data. In the final section of his paper, Biddle offers an explanation for this rapid change in professional attitude toward the use of probabilistic assumptions about data distributions as the required method of the empirical assessment of economic data.

By the 1970s, there was a broad consensus in the profession that inferential methods justified by probability theory—methods of producing estimates, of assessing the reliability of those estimates, and of testing hypotheses—were not only applicable to economic data, but were a necessary part of almost any attempt to generalize on the basis of economic data. . . .

This paper has been concerned with beliefs and practices of economists who wanted to use samples of statistical data as a basis for drawing conclusions about what was true, or probably true, in the world beyond the sample. In this setting, “mechanical objectivity” means employing a set of explicit and detailed rules and procedures to produce conclusions that are objective in the sense that if many different people took the same statistical information, and followed the same rules, they would come to exactly the same conclusions. The trustworthiness of the conclusion depends on the quality of the method. The classical theory of inference is a prime example of this sort of mechanical objectivity.

Porter [Trust in Numbers: The Pursuit of Objectivity in Science and Public Life] contrasts mechanical objectivity with an objectivity based on the “expert judgment” of those who analyze data. Expertise is acquired through a sanctioned training process, enhanced by experience, and displayed through a record of work meeting the approval of other experts. One’s faith in the analyst’s conclusions depends on one’s assessment of the quality of his disciplinary expertise and his commitment to the ideal of scientific objectivity. Elmer Working’s method of determining whether measured correlations represented true cause-and-effect relationships involved a good amount of expert judgment. So, too, did Gregg Lewis’s adjustments of the various estimates of the union/non-union wage gap, in light of problems with the data and peculiarities of the times and markets from which they came. Keynes and Persons pushed for a definition of statistical inference that incorporated space for the exercise of expert judgment; what Arthur Goldberger and Lawrence Klein referred to as ‘statistical inference’ had no explicit place for expert judgment.

Speaking in these terms, I would say that in the 1920s and 1930s, empirical economists explicitly acknowledged the need for expert judgment in making statistical inferences. At the same time, mechanical objectivity was valued—there are many examples of economists of that period employing rule-oriented, replicable procedures for drawing conclusions from economic data. The rejection of the classical theory of inference during this period was simply a rejection of one particular means for achieving mechanical objectivity. By the 1970s, however, this one type of mechanical objectivity had become an almost required part of the process of drawing conclusions from economic data, and was taught to every economics graduate student.

Porter emphasizes the tension between the desire for mechanically objective methods and the belief in the importance of expert judgment in interpreting statistical evidence. This tension can certainly be seen in economists’ writings on statistical inference throughout the twentieth century. However, it would be wrong to characterize what happened to statistical inference between the 1940s and the 1970s as a displace-ment of procedures requiring expert judgment by mechanically objective procedures. In the econometric textbooks published after 1960, explicit instruction on statistical inference was largely limited to instruction in the mechanically objective procedures of the classical theory of inference. It was understood, however, that expert judgment was still an important part of empirical economic analysis, particularly in the specification of the models to be estimated. But the disciplinary knowledge needed for this task was to be taught in other classes, using other textbooks.

And in practice, even after the statistical model had been chosen, the estimates and standard errors calculated, and the hypothesis tests conducted, there was still room to exercise a fair amount of judgment before drawing conclusions from the statistical results. Indeed, as Marcel Boumans (2015, pp. 84–85) emphasizes, no procedure for drawing conclusions from data, no matter how algorithmic or rule bound, can dispense entirely with the need for expert judgment. This fact, though largely unacknowledged in the post-1960s econometrics textbooks, would not be denied or decried by empirical economists of the 1970s or today.

This does not mean, however, that the widespread embrace of the classical theory of inference was simply a change in rhetoric. When application of classical inferential procedures became a necessary part of economists’ analyses of statistical data, the results of applying those procedures came to act as constraints on the set of claims that a researcher could credibly make to his peers on the basis of that data. For example, if a regression analysis of sample data yielded a large and positive partial correlation, but the correlation was not “statistically significant,” it would simply not be accepted as evidence that the “population” correlation was positive. If estimation of a statistical model produced a significant estimate of a relationship between two variables, but a statistical test led to rejection of an assumption required for the model to produce unbiased estimates, the evidence of a relationship would be heavily discounted.

So, as we consider the emergence of the post-1970s consensus on how to draw conclusions from samples of statistical data, there are arguably two things to be explained. First, how did it come about that using a mechanically objective procedure to generalize on the basis of statistical measures went from being a choice determined by the preferences of the analyst to a professional requirement, one that had real con-sequences for what economists would and would not assert on the basis of a body of statistical evidence? Second, why was it the classical theory of inference that became the required form of mechanical objectivity? . . .

Perhaps searching for an explanation that focuses on the classical theory of inference as a means of achieving mechanical objectivity emphasizes the wrong characteristic of that theory. In contrast to earlier forms of mechanical objectivity used by economists, such as standardized methods of time series decomposition employed since the 1920s, the classical theory of inference is derived from, and justified by, a body of formal mathematics with impeccable credentials: modern probability theory. During a period when the value placed on mathematical expression in economics was increasing, it may have been this feature of the classical theory of inference that increased its perceived value enough to overwhelm long-standing concerns that it was not applicable to economic data. In other words, maybe the chief causes of the profession’s embrace of the classical theory of inference are those that drove the broader mathematization of economics, and one should simply look to the literature that explores possible explanations for that phenomenon rather than seeking a special explanation of the embrace of the classical theory of inference.

I would suggest one more factor that might have made the classical theory of inference more attractive to economists in the 1950s and 1960s: the changing needs of pedagogy in graduate economics programs. As I have just argued, since the 1920s, economists have employed both judgment based on expertise and mechanically objective data-processing procedures when generalizing from economic data. One important difference between these two modes of analysis is how they are taught and learned. The classical theory of inference as used by economists can be taught to many students simultaneously as a set of rules and procedures, recorded in a textbook and applicable to “data” in general. This is in contrast to the judgment-based reasoning that combines knowledge of statistical methods with knowledge of the circumstances under which the particular data being analyzed were generated. This form of reasoning is harder to teach in a classroom or codify in a textbook, and is probably best taught using an apprenticeship model, such as that which ideally exists when an aspiring economist writes a thesis under the supervision of an experienced empirical researcher.

During the 1950s and 1960s, the ratio of PhD candidates to senior faculty in PhD-granting programs was increasing rapidly. One consequence of this, I suspect, was that experienced empirical economists had less time to devote to providing each interested student with individualized feedback on his attempts to analyze data, so that relatively more of a student’s training in empirical economics came in an econometrics classroom, using a book that taught statistical inference as the application of classical inference procedures. As training in empirical economics came more and more to be classroom training, competence in empirical economics came more and more to mean mastery of the mechanically objective techniques taught in the econometrics classroom, a competence displayed to others by application of those techniques. Less time in the training process being spent on judgment-based procedures for interpreting statistical results meant fewer researchers using such procedures, or looking for them when evaluating the work of others.

This process, if indeed it happened, would not explain why the classical theory of inference was the particular mechanically objective method that came to dominate classroom training in econometrics; for that, I would again point to the classical theory’s link to a general and mathematically formalistic theory. But it does help to explain why the application of mechanically objective procedures came to be regarded as a necessary means of determining the reliability of a set of statistical measures and the extent to which they provided evidence for assertions about reality. This conjecture fits in with a larger possibility that I believe is worth further exploration: that is, that the changing nature of graduate education in economics might sometimes be a cause as well as a consequence of changing research practices in economics. (pp. 167-70)

The correspondence between Biddle’s discussion of the change in the attitude of the economics profession about how inferences should be drawn from data about empirical relationships is strikingly similar to Oakeshott’s discussion and depressing in its implications for the decline of expert judgment by economics, expert judgment having been replaced by mechanical and technical knowledge that can be objectively summarized in the form of rules or tests for statistical significance, itself an entirely arbitrary convention lacking any logical, or self-evident, justification.

But my point is not to condemn using rules derived from classical probability theory to assess the significance of relationships statistically estimated from historical data, but to challenge the methodological prohibition against the kinds of expert judgments that many statistically knowledgeable economists like Nobel Prize winners such as Simon Kuznets, Milton Friedman, Theodore Schultz and Gary Becker routinely used to make in their empirical studies. As Biddle notes:

In 1957, Milton Friedman published his theory of the consumption function. Friedman certainly understood statistical theory and probability theory as well as anyone in the profession in the 1950s, and he used statistical theory to derive testable hypotheses from his economic model: hypotheses about the relationships between estimates of the marginal propensity to consume for different groups and from different types of data. But one will search his book almost in vain for applications of the classical methods of inference. Six years later, Friedman and Anna Schwartz published their Monetary History of the United States, a work packed with graphs and tables of statistical data, as well as numerous generalizations based on that data. But the book contains no classical hypothesis tests, no confidence intervals, no reports of statistical significance or insignificance, and only a handful of regressions. (p. 164)

Friedman’s work on the Monetary History is still regarded as authoritative. My own view is that much of the Monetary History was either wrong or misleading. But my quarrel with the Monetary History mainly pertains to the era in which the US was on the gold standard, inasmuch as Friedman simply did not understand how the gold standard worked, either in theory or in practice, as McCloskey and Zecher showed in two important papers (here and here). Also see my posts about the empirical mistakes in the Monetary History (here and here). But Friedman’s problem was bad monetary theory, not bad empirical technique.

Friedman’s theoretical misunderstandings have no relationship to the misguided prohibition against doing quantitative empirical research without obeying the arbitrary methodological requirement that statistical be derived in a way that measures the statistical significance of the estimated relationships. These methodological requirements have been adopted to support a self-defeating pretense to scientific rigor, necessitating the use of relatively advanced mathematical techniques to perform quantitative empirical research. The methodological requirements for measuring statistical relationships were never actually shown to be generate more accurate or reliable statistical results than those derived from the less technically advanced, but in some respects more economically sophisticated, techniques that have almost totally been displaced. One more example of the fallacy that there is but one technique of research that ensures the discovery of truth, a mistake even Popper was never guilty of.

Methodological Prescriptions Go from Bad to Worse

The methodological requirement for the use of formal tests of statistical significance before any quantitative statistical estimate could be credited was a prelude, though it would be a stretch to link them causally, to another and more insidious form of methodological tyrannizing: the insistence that any macroeconomic model be derived from explicit micro-foundations based on the solution of an intertemporal-optimization exercise. Of course, the idea that such a model was in any way micro-founded was a pretense, the solution being derived only through the fiction of a single representative agent, rendering the entire optimization exercise fundamentally illegitimate and the exact opposite of micro-founded model. Having already explained in previous posts why transforming microfoundations from a legitimate theoretical goal into methodological necessity has taken a generation of macroeconomists down a blind alley (here, here, here, and here) I will only make the further comment that this is yet another example of the danger of elevating technique over practice and substance.

Popper’s More Important Contribution

This post has largely concurred with the negative assessment of Popper’s work registered by Lemoine. But I wish to end on a positive note, because I have learned a great deal from Popper, and even if he is overrated as a philosopher of science, he undoubtedly deserves great credit for suggesting falsifiability as the criterion by which to distinguish between science and metaphysics. Even if that criterion does not hold up, or holds up only when qualified to a greater extent than Popper admitted, Popper made a hugely important contribution by demolishing the startling claim of the Logical Positivists who in the 1920s and 1930s argued that only statements that can be empirically verified through direct or indirect observation have meaning, all other statements being meaningless or nonsensical. That position itself now seems to verge on the nonsensical. But at the time many of the world’s leading philosophers, including Ludwig Wittgenstein, no less, seemed to accept that remarkable view.

Thus, Popper’s demarcation between science and metaphysics had a two-fold significance. First, that it is not verifiability, but falsifiability, that distinguishes science from metaphysics. That’s the contribution for which Popper is usually remembered now. But it was really the other aspect of his contribution that was more significant: that even metaphysical, non-scientific, statements can be meaningful. According to the Logical Positivists, unless you are talking about something that can be empirically verified, you are talking nonsense. In other words they were deliberately hoisting themselves on their petard, because their discussions about what is and what is not meaningful, being discussions about concepts, not empirically verifiable objects, were themselves – on the Positivists’ own criterion of meaning — meaningless and nonsensical.

Popper made the world safe for metaphysics, and the world is a better place as a result. Science is a wonderful enterprise, rewarding for its own sake and because it contributes to the well-being of many millions of human beings, though like many other human endeavors, it can also have unintended and unfortunate consequences. But metaphysics, because it was used as a term of abuse by the Positivists, is still, too often, used as an epithet. It shouldn’t be.

Certainly economists should aspire to tease out whatever empirical implications they can from their theories. But that doesn’t mean that an economic theory with no falsifiable implications is useless, a judgment whereby Mark Blaug declared general equilibrium theory to be unscientific and useless, a judgment that I don’t think has stood the test of time. And even if general equilibrium theory is simply metaphysical, my response would be: so what? It could still serve as a source of inspiration and insight to us in framing other theories that may have falsifiable implications. And even if, in its current form, a theory has no empirical content, there is always the possibility that, through further discussion, critical analysis and creative thought, empirically falsifiable implications may yet become apparent.

Falsifiability is certainly a good quality for a theory to have, but even an unfalsifiable theory may be worth paying attention to and worth thinking about.

Hayek, Deflation and Nihilism: A Popperian Postscript

In my previous post about Hayek’s support for deflationary monetary policy in the early 1930s, I wrote that Hayek’s support for deflation in the hope that it would break rigidities (he thought) were blocking the relative-price adjustments whereby self-correcting market forces would induce a spontaneous recovery from the Great Depression reminded me of the epigram attributed to Lenin: “you can’t make an omelet without breaking eggs.” I actually believed that that was a line that I had seen Karl Popper use somewhere. But in searching unsuccessfully for that quotation in Popper, I did find the following passage in Popper’s autobiography (Unended Quest), which seems to me to be worth reproducing. Popper describes the circumstances that led him while still a teenager to renounce his youthful Marxism.

The incident that turned me against communism, and that soon led me away from Marxism altogether, was one of the most important incidents in my life. It happened shortly before my seventeenth birthday. In Vienna, shooting broke out during a demonstration by unarmed young socialists who, instigated by the communists, tried to help some communists to escape who were under arrest in the central police station in Vienna. Several young socialist and communist workers were killed. I was horrified and shocked by the brutality of the police, but also by myself. For I felt that as a Marxist I bore part of the responsibility for the tragedy – at least in principle. Marxist theory demands that the class struggle be intensified, in order to speed up the coming of socialism. Its thesis is that although the revolution may claim some victims, capitalism is claiming more victims than the whole socialist revolution.

That was the Marxist theory – part of so-called “scientific socialism”. I now asked myself whether such a calculation could ever be supported by “science”. The whole experience, and especially this question, produced in me a life-long revulsion of feeling.

Communism is a creed which promises to bring about a better world. It claims to be based on knowledge: knowledge of the laws of historical development. I still hoped for a better world, a less violent and more just world, but I questioned whether I really knew – whether what I thought was knowledge was perhaps not more than mere pretence. I had, of course, read some Marx and Engels – but had I really understood it? Had I examined it critically, as anybody should do before he accepts a creed which justifies its means by a somewhat distant end?

I was shocked to have to admit to myself that not only had I accepted a complex theory somewhat uncritically, but that I had also actually noticed quite a bit of what was wrong, in the theory as well as in the practice of communism. But I had repressed this – partly out of loyalty to my friends, partly out of loyalty to “the cause”, and partly because there is a mechanism of getting oneself more and more deeply involved: once one has sacrificed one’s intellectual conscience over a minor point one does not wish to give in too easily; one wishes to justify the self-sacrifice by convincing oneself of the fundamental goodness of the cause, which is seen to outweigh any little moral or intellectual compromise that may be required. With every such moral or intellectual sacrifice one gets more deeply involved. One becomes ready to back one’s moral or intellectual investments in the cause with further investments. It is like being eager to throw good money after bad.

I saw how this mechanism had been working in my case, and I was horrified. I also saw it at work in others, especially my communist friends. And the experience enabled me to understand later many things which otherwise I would not have understood.

I had accepted a dangerous creed uncritically, dogmatically. The reaction made me first a sceptic; then it led me, though only for a very short time, to react against all rationalism. (As I found later, this is a typical reaction of a disappointed Marxist.)

By the time I was seventeen I had become an anti-Marxist. I realized the dogmatic character of the creed, and its incredible intellectual arrogance. It was a terrible thing to arrogate to oneself a kind of knowledge which made it a duty to risk  the lives of other people for an uncritically accepted dogma or for a dream which might turn out not to be realizable. (pp. 32-34)

Popper’s description of the process whereby emotional investment in a futile, but seemingly noble, cause leads to moral self-corruption is both chilling and frighteningly familiar to anyone paying attention to the news.

What’s so Great about Science? or, How I Learned to Stop Worrying and Love Metaphysics

A couple of weeks ago, a lot people in a lot of places marched for science. What struck me about those marches is that there is almost nobody out there that is openly and explicitly campaigning against science. There are, of course, a few flat-earthers who, if one looks for them very diligently, can be found. But does anyone — including the flat-earthers themselves – think that they are serious? There are also Creationists who believe that the earth was created and designed by a Supreme Being – usually along the lines of the Biblical account in the Book of Genesis. But Creationists don’t reject science in general, they reject a particular scientific theory, because they believe it to be untrue, and try to defend their beliefs with a variety of arguments couched in scientific terms. I don’t defend Creationist arguments, but just because someone makes a bad scientific argument, it doesn’t mean that the person making the argument is an opponent of science. To be sure, the reason that Creationists make bad arguments is that they hold a set of beliefs about how the world came to exist that aren’t based on science but on some religious or ideological belief system. But people come up with arguments all the time to justify beliefs for which they have no evidentiary or “scientific” basis.

I mean one of the two greatest scientists that ever lived criticized quantum mechanics, because he couldn’t accept that the world was not fully determined by the laws of nature, or, as he put it so pithily: “God does not play dice with the universe.” I understand that Einstein was not religious, and wasn’t making a religious argument, but he was basing his scientific view of what an acceptable theory should be on certain metaphysical predispositions that he held, and he was expressing his disinclination to accept a theory inconsistent with those predispositions. A scientific argument is judged on its merits, not on the motivations for advancing the argument. And I won’t even discuss the voluminous writings of the other one of the two greatest scientists who ever lived on alchemy and other occult topics.

Similarly, there are climate-change deniers who question the scientific basis for asserting that temperatures have been rising around the world, and that the increase in temperatures results from human activity that discharges greenhouse gasses into the atmosphere. Deniers of global warming may be biased and may be making bad scientific arguments, but the mere fact – and for purposes of this discussion I don’t dispute that it is a fact – that global warming is real and caused by human activity does not mean that to dispute those facts unmasks that person as an opponent of science. R. A. Fisher, the greatest mathematical statistician of the first half of the twentieth century, who developed most of the statistical techniques now used in experimental research, severely damaged his reputation by rejecting or dismissing evidence that smoking tobacco is a primary cause of cancer. Some critics accused Fisher of having been compromised by financial inducements from the tobacco industry, while others attribute his positions to his own smoking habits or anti-puritanical tendencies. In any event, Fisher’s arguments against a causal link between smoking tobacco and lung cancer are now viewed as an embarrassing stain on an otherwise illustrious career. But Fisher’s lapse of judgment, and perhaps of ethics, don’t justify accusing him of opposition to science. Climate-change deniers don’t reject science; they reject or disagree with the conclusions of most climate scientists. They may have lousy reasons for their views – either that the climate is not changing or that whatever change has occurred is unrelated to the human production of greenhouse gasses – but holding wrong or biased views doesn’t make someone an opponent of science.

I don’t say that there are no people who dislike science – I mean don’t like it because of what it stands for, not because they find it difficult or boring. Such people may be opposed to teaching science and to funding scientific research and don’t want scientific knowledge to influence public policy or the way people live. But, as far as I can tell, they have little influence. There is just no one out there that wants to outlaw scientific research, or trying to criminalize the teaching of science. They may not want to fund science, but they aren’t trying to ban it. In fact, I doubt that the prestige and authority of science has ever been higher than it is now. Certainly religion, especially organized religion, to which science was once subordinate if not subservient, no longer exercises anything near the authority that science now does.

The reason for this extended introduction into the topic that I really want to discuss is to provide some context for my belief that economists worry too much about whether economics is really a science. It was such a validation for economists when the Swedish Central Bank piggy-backed on the storied Nobel Prize to create its ersatz “Nobel Memorial Prize” for economic science. (I note with regret the recent passing of William Baumol, whose failure to receive the Nobel Prize in economics, like that of Armen Alchian, was in fact a deplorable failure of good judgment on the part of the Nobel Committee.) And the self-consciousness of economists about the possibly dubious status of economics as a science is a reflection of the exalted status of science in society. So naturally, if one is seeking to increase the prestige of his own occupation and of the intellectual discipline in which one does research, it helps enormously to be able to say: “oh, yes, I am an economist, and economics is a science, which means that I really am a scientist, just like those guys that win Nobel Prizes.” It also helps to be able to show that your scientific research involves a lot of mathematics, because scientists use math in their theories, sometimes a lot of math, which makes it hard for non-scientists to understand what scientists are doing. We economists also use math in our theories, sometimes a lot math, and that’s why it’s just as hard for non-economists to understand what we economists are doing as it is to understand what real scientists are doing. So we really are scientists, aren’t we?”

Where did this obsession with science come from? I think it’s fairly recent, but my sketchy knowledge of the history of science prevents me from getting too deeply into that discussion. But until relatively modern times, science was subsumed under the heading of philosophy — Greek for the love of wisdom. But philosophy is a very broad subject, so eventually that part of philosophy that was concerned with the world as it actually exists was called natural philosophy as opposed to say, ethical and moral philosophy. After the stunning achievements of Newton and his successors, and after Francis Bacon outlined an inductive method for achieving knowledge of the world, the disjunction between mere speculative thought and empirically based research, which was what science supposedly exemplifies, became increasingly sharp. And the inductive method seemed to be the right way to do science.

David Hume and Immanuel Kant struggled with limited success to make sense of induction, because a general proposition cannot be logically deduced from a set of observations, however numerous. Despite the logical problem of induction, early in the early twentieth century a philosophical movement based in Vienna called logical positivism arrived at the conclusion that not only is all scientific knowledge acquired inductively through sensory experience and observation, but no meaning can be attached to any statement unless the statement makes reference to something about which we have or could have sensory experience; to be meaningful a statement must be verified or at least verifiable, so that its truth could be either verified or refuted. Any reference to concepts that have no basis in sensory experience is simply meaningless, i.e., a form of nonsense. Thus, science became not just the epitome of valid, certain, reliable, verified knowledge, which is what people were led to believe by the stunning success of Newton’s theory, it became the exemplar of meaningful discourse. Unless our statements refer to some observable, verifiable object, we are talking nonsense. And in the first half of the twentieth century, logical positivism dominated academic philosophy, at least in the English speaking world, thereby exercising great influence over how economists thought about their own discipline and its scientific status.

Logical positivism was subjected to rigorous criticism by Karl Popper in his early work Logik der Forschung (English translation The Logic of Scientific Discovery). His central point was that scientific theories are less about what is or has been observed, but about what cannot be observed. The empirical content of a scientific proposition consists in the range of observations that the theory says are not possible. The more observations excluded by the theory the greater its empirical content. A theory that is consistent with any observation, has no empirical content. Thus, paradoxically, scientific theories, under the logical positivist doctrine, would have to be considered nonsensical, because they tell us what can’t be observed. And because it is always possible that an excluded observation – the black swan – which our scientific theory tells us can’t be observed, will be observed, scientific theories can never be definitively verified. If a scientific theory can’t verified, then according to the positivists’ own criterion, the theory is nonsense. Of course, this just shows that the positivist criterion of meaning was nonsensical, because obviously scientific theories are completely meaningful despite being unverifiable.

Popper therefore concluded that verification or verifiability can’t be a criterion of meaning. In its place he proposed the criterion of falsification (i.e., refutation, not misrepresentation), but falsification became a criterion not for distinguishing between what is meaningful and what is meaningless, but between science and metaphysics. There is no reason why metaphysical statements (statements lacking empirical content) cannot be perfectly meaningful; they just aren’t scientific. Popper was misinterpreted by many to have simply substituted falsifiability for verifiability as a criterion of meaning; that was a mistaken interpretation, which Popper explicitly rejected.

So, in using the term “meaningful theorems” to refer to potentially refutable propositions that can be derived from economic theory using the method of comparative statics, Paul Samuelson in his Foundations of Economic Analysis adopted the interpretation of Popper’s demarcation criterion between science and metaphysics as if it were a demarcation criterion between meaning and nonsense. I conjecture that Samuelson’s unfortunate lapse into the discredited verbal usage of logical positivism may have reinforced the unhealthy inclination of economists to feel the need to prove their scientific credentials in order to even engage in meaningful discourse.

While Popper certainly performed a valuable service in clearing up the positivist confusion about meaning, he adopted a very prescriptive methodology aimed at making scientific practice more scientific in the sense of exposing theories to, rather than immunizing them against, attempts at refutation, because, according to Popper, it is only if after our theories survive powerful attempts to show that they are false that we can have confidence that those theories may be truthful or at least come close to being truthful. In principle, Popper was not wrong in encouraging scientists to formulate theories that are empirically testable by specifying what kinds of observations would be inconsistent with their theories. But in practice, that advice has been difficult to follow, and not only because researchers try to avoid subjecting their pet theories to tests that might prove them wrong.

Although Popper often cited historical examples to support his view that science progresses through an ongoing process of theoretical conjecture and empirical refutation, historians of science have had no trouble finding instances in which scientists did not follow Popper’s methodological rules and continued to maintain theories even after they had been refuted by evidence or after other theories had been shown to generate more accurate predictions than their own theories. Popper parried this objection by saying that his methodological rules were not positive (i.e., descriptive of science), but normative (i.e., prescriptive of how to do good science). In other words, Popper’s scientific methodology was itself not empirically refutable and scientific, but empirically irrefutable and metaphysical. I point out the unscientific character of Popper’s methodology of science, not to criticize Popper, but to point out that Popper himself did not believe that science is itself the final authority and ultimate arbiter of scientific practice.

But the more important lesson from the critical discussions of Popper’s methodological rules seems to me to be that they are too rigid to accommodate all the considerations that are relevant to assessing scientific theories and deciding whether those theories should be discarded or, at least tentatively, maintained. And Popper’s methodological rules are especially ill-suited for economics and other disciplines in which the empirical implications of theories depend on a large number of jointly-maintained hypotheses, so that it is hard to identify which of several maintained hypotheses is responsible for the failure of a predicted outcome to match the observed outcome. That of course is the well-known ceteris paribus problem, and it requires a very capable practitioner to know when to apply the ceteris paribus condition and which variables to hold constants and which to allow to vary. Popper’s methodological rules tell us to reject a theory when its predictions are mistaken, and Popper regarded the ceteris paribus quite skeptically as an illegitimate immunizing stratagem. That describes a profound dilemma for economics. On the one hand, it is hard to imagine how economic theory could be applied without using the ceteris paribus qualification, on the other hand, the qualification diminishes empirical content of economic theory.

Empirical problems are amplified by the infirmities of the data that economists typically use to derive quantitative predictions from their models. The accuracy of the data is often questionable, and the relationships between the data and the theoretical concepts they are supposed to measure are often dubious. Moreover, the assumptions about the data-generating process (e.g., independent and identically distributed random variables, randomly selected observations, omitted explanatory variables are uncorrelated with the dependent variable) necessary for the classical statistical techniques to generate unbiased estimates of the theoretical coefficients are almost impossibly stringent. Econometricians are certainly well aware of these issues, and they have discovered methods of mitigating them, but the problems with the data routinely used by economists and the complicated issues involved in developing and applying techniques to cope with those problems make it very difficult to use statistical techniques to reach definitive conclusions about empirical questions.

Jeff Biddle, one of the leading contemporary historians of economics, has a wonderful paper (“Statistical Inference in Economics 1920-1965: Changes in Meaning and Practice”)– his 2016 presidential address to the History of Economics Society – discussing how the modern statistical techniques based on concepts and methods derived from probability theory gradually became the standard empirical and statistical techniques used by economists, even though many distinguished earlier researchers who were neither unaware of, nor unschooled in, the newer techniques believed them to be inappropriate for analyzing economic data. Here is the abstract of Biddle’s paper.

This paper reviews changes over time in the meaning that economists in the US attributed to the phrase “statistical inference”, as well as changes in how inference was conducted. Prior to WWII, leading statistical economists rejected probability theory as a source of measures and procedures to be used in statistical inference. Haavelmo and the econometricians associated with the early Cowles Commission developed an approach to statistical inference based on concepts and measures derived from probability theory, but the arguments they offered in defense of this approach were not always responsive to the concerns of earlier empirical economists that the data available to economists did not satisfy the assumptions required for such an approach. Despite this, after a period of about 25 years, a consensus developed that methods of inference derived from probability theory were an almost essential part of empirical research in economics. I close the paper with some speculation on possible reasons for this transformation in thinking about statistical inference.

I quote one passage from Biddle’s paper:

As I have noted, the leading statistical economists of the 1920s and 1930s were also unwilling to assume that any sample they might have was representative of the universe they cared about. This was particularly true of time series, and Haavelmo’s proposal to think of time series as a random selection of the output of a stable mechanism did not really address one of their concerns – that the structure of the “mechanism” could not be expected to remain stable for long periods of time. As Schultz pithily put it, “‘the universe’ of our time series does not ‘stay put’” (Schultz 1938, p. 215). Working commented that there was nothing in the theory of sampling that warranted our saying that “the conditions of covariance obtaining in the sample (would) hold true at any time in the future” (Advisory Committee 1928, p. 275). As I have already noted, Persons went further, arguing that treating a time series as a sample from which a future observation would be a random draw was not only inaccurate but ignored useful information about unusual circumstances surrounding various observations in the series, and the unusual circumstances likely to surround the future observations about which one wished to draw conclusions (Persons 1924, p. 7). And, the belief that samples were unlikely to be representative of the universe in which the economists had an interest applied to cross section data as well. The Cowles econometricians offered to little assuage these concerns except the hope that it would be possible to specify the equations describing the systematic part of the mechanism of interest in a way that captured the impact of factors that made for structural change in the case of time series, or factors that led cross section samples to be systematically different from the universe of interest.

It is not my purpose to argue that the economists who rejected the classical theory of inference had better arguments than the Cowles econometricians, or had a better approach to analyzing economic data given the nature of those data, the analytical tools available, and the potential for further development of those tools. I only wish to offer this account of the differences between the Cowles econometricians and the previously dominant professional opinion on appropriate methods of statistical inference as an example of a phenomenon that is not uncommon in the history of economics. Revolutions in economics, or “turns”, to use a currently more popular term, typically involve new concepts and analytical methods. But they also often involve a willingness to employ assumptions considered by most economists at the time to be too unrealistic, a willingness that arises because the assumptions allow progress to be made with the new concepts and methods. Obviously, in the decades after Haavelmo’s essay on the probability approach, there was a significant change in the list of assumptions about economic data that empirical economists were routinely willing to make in order to facilitate empirical research.

Let me now quote from a recent book (To Explain the World) by Steven Weinberg, perhaps – even though a movie about his life has not (yet) been made — the greatest living physicist:

Newton’s theory of gravitation made successful predictions for simple phenomena like planetary motion, but it could not give a quantitative account of more complicated phenomena, like the tides. We are in a similar position today with regard to the strong forces that hold quarks together inside the protons and neutrons inside the atomic nucleus, a theory known as quantum chromodynamics. This theory has been successful in accounting for certain processes at high energy, such as the production of various strongly interacting particles in the annihilation of energetic electrons and their antiparticles, and its successes convince us that the theory is correct. We cannot use the theory to calculate precise values for other things that we would like to explain, like the masses of the proton and neutron, because the calculations is too complicated. Here, as for Newton’s theory of the tides, the proper attitude is patience. Physical theories are validated when they give us the ability to calculate enough things that are sufficiently simple to allow reliable calculations, even if we can’t calculate everything that we might want to calculate.

So Weinberg is very much aware of the limits that even physics faces in making accurate predictions. Only a small subset (relative to the universe of physical phenomena) of simple effects can be calculated, but the capacity of physics to make very accurate predictions of simple phenomena gives us a measure of confidence that the theory would be reliable in making more complicated predictions if only we had the computing capacity to make those more complicated predictions. But in economics the set of simple predictions that can be accurately made is almost nil, because economics is inherently a theory a complex social phenomena, and simplifying the real world problems to which we apply the theory to allow testable predictions to be made is extremely difficult and hardly ever possible. Experimental economists try to create conditions in which this can be done in controlled settings, but whether these experimental results have much relevance for real-world applications is open to question.

The problematic relationship between economic theory and empirical evidence is deeply rooted in the nature of economic theory and the very complex nature of the phenomena that economic theory seek to explain. It is very difficult to isolate simple real-world events in which economic theories can be put to decisive empirical tests that allow us to put competing theories to decisive tests based on unambiguous observations that are either consistent with or contrary to the predictions generated by those theories. Under those circumstances, if we apply the Popperian criterion for demarcation between science and metaphysics to economics, it is not at all clear to me whether economics is more on the science side of the line than on the metaphysics side.

Certainly, there are refutable implications of economic theory that can be deduced, but these implications are often subject to qualification, so the refutable implications are often refutable only n principle, but not in practice. Many fastidious economic methodologists, notably Mark Blaug, voiced unhappiness about this state of affairs and blamed economists for not being more ruthless in applying Popperian test of empirical refutation to their theories. Surely Blaug had a point, but the infrequency of empirical refutation of theories in economics is, I think, less attributable to bad methodological practice on the part of economists than to the nature of the theories that economists work with and the inherent ambiguities of the empirical evidence with which those theories can be tested. We might as well just face up to the fact that, to a large extent, empirical evidence is simply not clear cut enough to force us to discard well-entrenched economic theories, because well-entrenched economic theories can be adjusted and reformulated in response to apparently contrary evidence in ways that allow those theories to live on to fight another day, theories typically having enough moving parts to allow them to be adjusted as needed to accommodate anomalous or inconvenient empirical evidence.

Popper’s somewhat disloyal disciple, Imre Lakatos, talked about scientific theories in the context of scientific research programs, a research program being an amalgam of related theories which share a common inner core of theoretical principles or axioms which are not subject to refutation. Lakatos called these deep axiomatic core of principles the hard core of the research program. The hard core defines the program so it is fundamentally fixed and not open to refutation. The empirical content of the research program is provided by a protective belt of specific theories that are subject to refutation and, when refuted, can be replaced as needed with alternative theories that are consistent with both the theoretical hard core and the empirical evidence. What determines the success of a scientific research program is whether it is progressive or degenerating. A progressive research program accumulates an increasingly dense, but evolving, protective belt of theories in response to new theoretical and empirical problems or puzzles that are generated within the research program to keep researchers busy and to attract into the program new researchers seeking problems to solve. In contrast, a degenerating research program is unable to find enough interesting new problems or puzzles to keep researchers busy much less attract new ones.

Despite its Popperian origins, the largely sociological Lakatosian account of how science evolves and progresses was hardly congenial to Popper’s sensibilities, because the success of a research program is not strictly determined by the process of conjecture and refutation envisioned by Popper. But the important point for me is that a Lakatosian research program can be progressive even if it is metaphysical and not scientific. What matters is that it offer opportunities for researchers to find and to solve or even just to talk about solving new problems, thereby attracting new researchers into the program.

It does appear that economics has for at least two centuries been a progressive research program. But it is not clear that is a really scientific research program, because the nature of economic theory is so flexible that it can be adapted as needed to explain almost any set of observations. Almost any observation can be set up and solved in terms of some sort of constrained optimization problem. What the task requires is sufficient ingenuity on the part of the theorist to formulate the problem in such a way that the desired outcome can be derived as the solution of a constrained optimization problem. The hard core of the research program is therefore never at risk, and the protective belt can always be modified as needed to generate the sort of solution that is compatible with the theoretical hard core. The scope for true refutation has thus been effectively narrowed to eliminate any real scope for refutation, leaving us with a progressive metaphysical research program.

I am not denying that it would be preferable if economics could be a truly scientific research program, but it is not clear to me how much can be done about it. The complexity of the phenomena, the multiplicity of the hypotheses required to explain the data, and the ambiguous and not fully reliable nature of most of the data that economists have available devilishly conspire to render Popperian falsificationism an illusory ideal in economics. That is not an excuse for cynicism, just a warning against unrealistic expectations about what economics can accomplish. And the last thing that I am suggesting is that we stop paying attention to the data that we have or stop trying to improve the quality of the data that we have to work with.

The Neoclassical Synthesis and the Mind-Body Problem

The neoclassical synthesis that emerged in the early postwar period aimed at reconciling the macroeconomic (IS-LM) analysis derived from Keynes via Hicks and others with the neoclassical microeconomic analysis of general equilibrium derived from Walras. The macroeconomic analysis was focused on an equilibrium of income and expenditure flows while the Walrasian analysis was focused on the equilibrium between supply and demand in individual markets. The two types of analysis seemed to be incommensurate inasmuch as the conditions for equilibrium in the two analysis did not seem to match up against each other. How does an analysis focused on the equality of aggregate flows of income and expenditure get translated into an analysis focused on the equality of supply and demand in individual markets? The two languages seem to be different, so it is not obvious how a statement formulated in one language gets translated into the other. And even if a translation is possible, does the translation hold under all, or only under some, conditions? And if so, what are those conditions?

The original neoclassical synthesis did not aim to provide a definitive answer to those questions, but it was understood to assert that if the equality of income and expenditure was assured at a level consistent with full employment, one could safely assume that market forces would take care of the allocation of resources, so that markets would be cleared and the conditions of microeconomic general equilibrium satisfied, at least as a first approximation. This version of the neoclassical synthesis was obviously ad hoc and an unsatisfactory resolution of the incommensurability of the two levels of analysis. Don Patinkin sought to provide a rigorous reconciliation of the two levels of analysis in his treatise Money, Interest and Prices. But for all its virtues – and they are numerous – Patinkin’s treatise failed to bridge the gap between the two levels of analysis.

As I mentioned recently in a post on Romer and Lucas, Kenneth Arrow in a 1967 review of Samuelson’s Collected Works commented disparagingly on the neoclassical synthesis of which Samuelson was a leading proponent. The widely shared dissatisfaction expressed by Arrow motivated much of the work that soon followed on the microfoundations of macroeconomics exemplified in the famous 1970 Phelps volume. But the motivation for the search for microfoundations was then (before the rational expectations revolution) to specify the crucial deviations from the assumptions underlying the standard Walrasian general-equilibrium model that would generate actual or seeming price rigidities, which a straightforward – some might say superficial — understanding of neoclassical microeconomic theory suggested were necessary to explain why, after a macro-disturbance, equilibrium was not rapidly restored by price adjustments. Two sorts of explanations emerged from the early microfoundations literature: a) search and matching theories assuming that workers and employers must expend time and resources to find appropriate matches; b) institutional theories of efficiency wages or implicit contracts that explain why employers and workers prefer layoffs to wage cuts in response to negative demand shocks.

Forty years on, the search and matching theories do not seem capable of accounting for the magnitude of observed fluctuations in employment or the cyclical variation in layoffs, and the institutional theories are still difficult to reconcile with the standard neoclassical assumptions, remaining an ad hoc appendage to New Keynesian models that otherwise adhere to the neoclassical paradigm. Thus, although the original neoclassical synthesis in which the Keynesian income-expenditure model was seen as a pre-condition for the validity of the neoclassical model was rejected within a decade of Arrow’s dismissive comment about the neoclassical synthesis, Tom Sargent has observed in a recent review of Robert Lucas’s Collected Papers on Monetary Theory that Lucas has implicitly adopted a new version of the neoclassical synthesis dominated by an intertemporal neoclassical general-equilibrium model, but with the proviso that substantial shocks to aggregate demand and the price level are prevented by monetary policy, thereby making the neoclassical model a reasonable approximation to reality.

Ok, so you are probably asking what does all this have to do with the mind-body problem? A lot, I think in that both the neoclassical synthesis and the mind-body problem involve a disconnect between two kinds – two levels – of explanation. The neoclassical synthesis asserts some sort of connection – but a problematic one — between the explanatory apparatus – macroeconomics — used to understand the cyclical fluctuations of what we are used to think of as the aggregate economy and the explanatory apparatus – microeconomics — used to understand the constituent elements of the aggregate economy — households and firms — and how those elements are related to, and interact with, each other.

The mind-body problem concerns the relationship between the mental – our direct experience of a conscious inner life of thoughts, emotions, memories, decisions, hopes and regrets — and the physical – matter, atoms, neurons. A basic postulate of science is that all phenomena have material causes. So the existence of conscious states that seem to us, by way of our direct experience, to be independent of material causes is also highly problematic. There are a few strategies for handling the problem. One is to assert that the mind truly is independent of the body, which is to say that consciousness is not the result of physical causes. A second is to say that mind is not independent of the body; we just don’t understand the nature of the relationship. There are two possible versions of this strategy: a) that although the nature of the relationship is unknown to us now, advances in neuroscience could reveal to us the way in which consciousness is caused by the operation of the brain; b) although our minds are somehow related to the operation of our brains, the nature of this relationship is beyond the capacity of our minds or brains to comprehend owing to considerations analogous to Godel’s incompleteness theorem (a view espoused by the philosopher Colin McGinn among others); in other words, the mind-body problem is inherently beyond human understanding. And the third strategy is to deny the existence of consciousness, because a conscious state is identical with the physical state of a brain, so that consciousness is just an epiphenomenon of a brain state; we in our naivete may think that our conscious states have a separate existence, but those states are strictly identical with corresponding brain states, so that whatever conscious state that we think we are experiencing has been entirely produced by the physical forces that determine the behavior of our brains and the configuration of its physical constituents.

The first, and probably the last, thing that one needs to understand about the third strategy is that, as explained by Colin McGinn (see e.g., here), its validity has not been demonstrated by neuroscience or by any other branch of science; it is, no less than any of the other strategies, strictly a metaphysical position. The mind-body problem is a problem precisely because science has not even come close to demonstrating how mental states are caused by, let alone that they are identical to, brain states, despite some spurious misinterpretations of research that purport to show such an identity.

Analogous to the scientific principle that all phenomena have material or physical causes, there is in economics and social science a principle called methodological individualism, which roughly states that explanations of social outcomes should be derived from theories about the conduct of individuals, not from theories about abstract social entities that exist independently of their constituent elements. The underlying motivation for methodological individualism (as opposed to political individualism with which it is related but from which it is distinct) was to counter certain ideas popular in the nineteenth and twentieth centuries asserting the existence of metaphysical social entities like “history” that are somehow distinct from yet impinge upon individual human beings, and that there are laws of history or social development from which future states of the world can be predicted, as Hegel, Marx and others tried to do. This notion gave rise to a two famous books by Popper: The Open Society and its Enemies and The Poverty of Historicism. Methodological individualism as articulated by Popper was thus primarily an attack on the attribution of special powers to determine the course of future events to abstract metaphysical or mystical entities like history or society that are supposedly things or beings in themselves distinct from the individual human beings of which they are constituted. Methodological individualism does not deny the existence of collective entities like society; it simply denies that such collective entities exist as objective facts that can be observed as such. Our apprehension of these entities must be built up from more basic elements — individuals and their plans, beliefs and expectations — that we can apprehend directly.

However, methodological individualism is not the same as reductionism; methodological individualism teaches us to look for explanations of higher-level phenomena, e.g., a pattern of social relationships like the business cycle, in terms of the basic constituents forming the pattern: households, business firms, banks, central banks and governments. It does not assert identity between the pattern of relationships and the constituent elements; it says that the pattern can be understood in terms of interactions between the elements. Thus, a methodologically individualistic explanation of the business cycle in terms of the interactions between agents – households, businesses, etc. — would be analogous to an explanation of consciousness in terms of the brain if an explanation of consciousness existed. A methodologically individualistic explanation of the business cycle would not be analogous to an assertion that consciousness exists only as an epiphenomenon of brain states. The assertion that consciousness is nothing but the epiphenomenon of a corresponding brain state is reductionist; it asserts an identity between consciousness and brain states without explaining how consciousness is caused by brain states.

In business-cycle theory, the analogue of such a reductionist assertion of identity between higher-level and lower level phenomena is the assertion that the business cycle is not the product of the interaction of individual agents, but is simply the optimal plan of a representative agent. On this account, the business cycle becomes an epiphenomenon; apparent fluctuations being nothing more than the optimal choices of the representative agent. Of course, everyone knows that the representative agent is merely a convenient modeling device in terms of which a business-cycle theorist tries to account for the observed fluctuations. But that is precisely the point. The whole exercise is a sham; the representative agent is an as-if device that does not ground business-cycle fluctuations in the conduct of individual agents and their interactions, but simply asserts an identity between those interactions and the supposed decisions of the fictitious representative agent. The optimality conditions in terms of which the model is solved completely disregard the interactions between individuals that might cause an unintended pattern of relationships between those individuals. The distinctive feature of methodological individualism is precisely the idea that the interactions between individuals can lead to unintended consequences; it is by way of those unintended consequences that a higher-level pattern might emerge from interactions among individuals. And those individual interactions are exactly what is suppressed by representative-agent models.

So the notion that any analysis premised on a representative agent provides microfoundations for macroeconomic theory seems to be a travesty built on a total misunderstanding of the principle of methodological individualism that it purports to affirm.

Another Complaint about Modern Macroeconomics

In discussing modern macroeconomics, I’ve have often mentioned my discomfort with a narrow view of microfoundations, but I haven’t commented very much on another disturbing feature of modern macro: the requirement that theoretical models be spelled out fully in axiomatic form. The rhetoric of axiomatization has had sweeping success in economics, making axiomatization a pre-requisite for almost any theoretical paper to be taken seriously, and even considered for publication in a reputable economics journal.

The idea that a good scientific theory must be derived from a formal axiomatic system has little if any foundation in the methodology or history of science. Nevertheless, it has become almost an article of faith in modern economics. I am not aware, but would be interested to know, whether, and if so how widely, this misunderstanding has been propagated in other (purportedly) empirical disciplines. The requirement of the axiomatic method in economics betrays a kind of snobbishness and (I use this word advisedly, see below) pedantry, resulting, it seems, from a misunderstanding of good scientific practice.

Before discussing the situation in economics, I would note that axiomatization did not become a major issue for mathematicians until late in the nineteenth century (though demands – luckily ignored for the most part — for logical precision followed immediately upon the invention of the calculus by Newton and Leibniz) and led ultimately to the publication of the great work of Russell and Whitehead, Principia Mathematica whose goal was to show that all of mathematics could be derived from the axioms of pure logic. This is yet another example of an unsuccessful reductionist attempt, though it seemed for a while that the Principia paved the way for the desired reduction. But 20 years after the Principia was published, Kurt Godel proved his famous incompleteness theorem, showing that, as a matter of pure logic, not even all the valid propositions of arithmetic, much less all of mathematics, could be derived from any system of axioms. This doesn’t mean that trying to achieve a reduction of a higher-level discipline to another, deeper discipline is not a worthy objective, but it certainly does mean that one cannot just dismiss, out of hand, a discipline simply because all of its propositions are not deducible from some set of fundamental propositions. Insisting on reduction as a prerequisite for scientific legitimacy is not a scientific attitude; it is merely a form of obscurantism.

As far as I know, which admittedly is not all that far, the only empirical science which has been axiomatized to any significant extent is theoretical physics. In his famous list of 23 unsolved mathematical problems, the great mathematician David Hilbert included the following (number 6).

Mathematical Treatment of the Axioms of Physics. The investigations on the foundations of geometry suggest the problem: To treat in the same manner, by means of axioms, those physical sciences in which already today mathematics plays an important part, in the first rank are the theory of probabilities and mechanics.

As to the axioms of the theory of probabilities, it seems to me desirable that their logical investigation should be accompanied by a rigorous and satisfactory development of the method of mean values in mathematical physics, and in particular in the kinetic theory of gasses. . . . Boltzman’s work on the principles of mechanics suggests the problem of developing mathematically the limiting processes, there merely indicated, which lead from the atomistic view to the laws of motion of continua.

The point that I want to underscore here is that axiomatization was supposed to ensure that there was an adequate logical underpinning for theories (i.e., probability and the kinetic theory of gasses) that had already been largely worked out. Thus, Hilbert proposed axiomatization not as a method of scientific discovery, but as a method of checking for hidden errors and problems. Error checking is certainly important for science, but it is clearly subordinate to the creation and empirical testing of new and improved scientific theories.

The fetish for axiomitization in economics can largely be traced to Gerard Debreu’s great work, The Theory of Value: An Axiomatic Analysis of Economic Equilibrium, in which Debreu, building on his own work and that of Kenneth Arrow, presented a formal description of a decentralized competitive economy with both households and business firms, and proved that, under the standard assumptions of neoclassical theory (notably diminishing marginal rates of substitution in consumption and production and perfect competition) such an economy would have at least one, and possibly more than one, equilibrium.

A lot of effort subsequently went into gaining a better understanding of the necessary and sufficient conditions under which an equilibrium exists, and when that equilibrium would be unique and Pareto optimal. The subsequent work was then brilliantly summarized and extended in another great work, General Competitive Analysis by Arrow and Frank Hahn. Unfortunately, those two books, paragons of the axiomatic method, set a bad example for the future development of economic theory, which embarked on a needless and counterproductive quest for increasing logical rigor instead of empirical relevance.

A few months ago, I wrote a review of Kartik Athreya’s book Big Ideas in Macroeconomics. One of the arguments of Athreya’s book that I didn’t address was his defense of modern macroeconomics against the complaint that modern macroeconomics is too mathematical. Athreya is not responsible for the reductionist and axiomatic fetishes of modern macroeconomics, but he faithfully defends them against criticism. So I want to comment on a few paragraphs in which Athreya dismisses criticism of formalism and axiomatization.

Natural science has made significant progress by proceeding axiomatically and mathematically, and whether or not we [economists] will achieve this level of precision for any unit of observation in macroeconomics, it is likely to be the only rational alternative.

First, let me observe that axiomatization is not the same as using mathematics to solve problems. Many problems in economics cannot easily be solved without using mathematics, and sometimes it is useful to solve a problem in a few different ways, each way potentially providing some further insight into the problem not provided by the others. So I am not at all opposed to the use of mathematics in economics. However, the choice of tools to solve a problem should bear some reasonable relationship to the problem at hand. A good economist will understand what tools are appropriate to the solution of a particular problem. While mathematics has clearly been enormously useful to the natural sciences and to economics in solving problems, there are very few scientific advances that can be ascribed to axiomatization. Axiomatization was vital in proving the existence of equilibrium, but substantive refutable propositions about real economies, e.g., the Heckscher-Ohlin Theorem, or the Factor-Price Equalization Theorem, or the law of comparative advantage, were not discovered or empirically tested by way of axiomatization. Arthreya talks about economics achieving the “level of precision” achieved by natural science, but the concept of precision is itself hopelessly imprecise, and to set precision up as an independent goal makes no sense. Arthreya continues:

In addition to these benefits from the systematic [i.e. axiomatic] approach, there is the issue of clarity. Lowering mathematical content in economics represents a retreat from unambiguous language. Once mathematized, words in any given model cannot ever mean more than one thing. The unwillingness to couch things in such narrow terms (usually for fear of “losing something more intelligible”) has, in the past, led to a great deal of essentially useless discussion.

Arthreya writes as if the only source of ambiguity is imprecise language. That just isn’t so. Is unemployment voluntary or involuntary? Arthreya actually discusses the question intelligently on p. 283, in the context of search models of unemployment, but I don’t think that he could have provided any insight into that question with a purely formal, symbolic treatment. Again back to Arthreya:

The plaintive expressions of “fear of losing something intangible” are concessions to the forces of muddled thinking. The way modern economics gets done, you cannot possibly not know exactly what the author is assuming – and to boot, you’ll have a foolproof way of checking whether their claims of what follows from these premises is actually true or not.

So let me juxtapose this brief passage from Arthreya with a rather longer passage from Karl Popper in which he effectively punctures the fallacies underlying the specious claims made on behalf of formalism and against ordinary language. The extended quotations are from an addendum titled “Critical Remarks on Meaning Analysis” (pp. 261-77) to chapter IV of Realism and the Aim of Science (volume 1 of the Postscript to the Logic of Scientific Discovery). In this addendum, Popper begins by making the following three claims:

1 What-is? questions, such as What is Justice? . . . are always pointless – without philosophical or scientific interest; and so are all answers to what-is? questions, such as definitions. It must be admitted that some definitions may sometimes be of help in answering other questions: urgent questions which cannot be dismissed: genuine difficulties which may have arisen in science or in philosophy. But what-is? questions as such do not raise this kind of difficulty.

2 It makes no difference whether a what-is question is raised in order to inquire into the essence or into the nature of a thing, or whether it is raised in order to inquire into the essential meaning or into the proper use of an expression. These kinds of what-is questions are fundamentally the same. Again, it must be admitted that an answer to a what-is question – for example, an answer pointing out distinctions between two meanings of a word which have often been confused – may not be without point, provided the confusion led to serious difficulties. But in this case, it is not the what-is question which we are trying to solve; we hope rather to resolve certain contradictions that arise from our reliance upon somewhat naïve intuitive ideas. (The . . . example discussed below – that of the ideas of a derivative and of an integral – will furnish an illustration of this case.) The solution may well be the elimination (rather than the clarification) of the naïve idea. But an answer to . . . a what-is question is never fruitful. . . .

3 The problem, more especially, of replacing an “inexact” term by an “exact” one – for example, the problem of giving a definition in “exact” or “precise” terms – is a pseudo-problem. It depends essentially upon the inexact and imprecise terms “exact” and “precise.” These are most misleading, not only because they strongly suggest that there exists what does not exist – absolute exactness or precision – but also because they are emotionally highly charged: under the guise of scientific character and of scientific objectivity, they suggest that precision or exactness is something superior, a kind of ultimate value, and that it is wrong, or unscientific, or muddle-headed, to use inexact terms (as it is indeed wrong not to speak as lucidly and simply as possible). But there is no such thing as an “exact” term, or terms made “precise” by “precise definitions.” Also, a definition must always use undefined terms in its definiens (since otherwise we should get involved in an infinite regress or in a circle); and if we have to operate with a number of undefined terms, it hardly matters whether we use a few more. Of course, if a definition helps to solve a genuine problem, the situation is different; and some problems cannot be solved without an increase of precision. Indeed, this is the only way in which we can reasonably speak of precision: the demand for precision is empty, unless it is raised relative to some requirements that arise from our attempts to solve a definite problem. (pp. 261-63)

Later in his addendum Popper provides an enlightening discussion of the historical development of calculus despite its lack of solid logical axiomatic foundation. The meaning of an infinitesimal or a derivative was anything but precise. It was, to use Arthreya’s aptly chosen term, a muddle. Mathematicians even came up with a symbol for the derivative. But they literally had no precise idea of what they were talking about. When mathematicians eventually came up with a definition for the derivative, the definition did not clarify what they were talking about; it just provided a particular method of calculating what the derivative would be. However, the absence of a rigorous and precise definition of the derivative did not prevent mathematicians from solving some enormously important practical problems, thereby helping to change the world and our understanding of it.

The modern history of the problem of the foundations of mathematics is largely, it has been asserted, the history of the “clarification” of the fundamental ideas of the differential and integral calculus. The concept of a derivative (the slope of a curve of the rate of increase of a function) has been made “exact” or “precise” by defining it as the limit of the quotient of differences (given a differentiable function); and the concept of an integral (the area or “quadrature” of a region enclosed by a curve) has likewise been “exactly defined”. . . . Attempts to eliminate the contradictions in this field constitute not only one of the main motives of the development of mathematics during the last hundred or even two hundred years, but they have also motivated modern research into the “foundations” of the various sciences and, more particularly, the modern quest for precision or exactness. “Thus mathematicians,” Bertrand Russell says, writing about one of the most important phases of this development, “were only awakened from their “dogmatic slumbers” when Weierstrass and his followers showed that many of their most cherished propositions are in general false. Macaulay, contrasting the certainty of mathematics with the uncertainty of philosophy, asks who ever heard of a reaction against Taylor’s theorem. If he had lived now, he himself might have heard of such a reaction, for his is precisely one of the theorems which modern investigations have overthrown. Such rude shocks to mathematical faith have produced that love of formalism which appears, to those who are ignorant of its motive, to be mere outrageous pedantry.”

It would perhaps be too much to read into this passage of Russell’s his agreement with a view which I hold to be true: that without “such rude shocks” – that is to say, without the urgent need to remove contradictions – the love of formalism is indeed “mere outrageous pedantry.” But I think that Russell does convey his view that without an urgent need, an urgent problem to be solved, the mere demand for precision is indefensible.

But this is only a minor point. My main point is this. Most people, including mathematicians, look upon the definition of the derivative, in terms of limits of sequences, as if it were a definition in the sense that it analyses or makes precise, or “explicates,” the intuitive meaning of the definiendum – of the derivative. But this widespread belief is mistaken. . . .

Newton and Leibniz and their successors did not deny that a derivative, or an integral, could be calculated as a limit of certain sequences . . . . But they would not have regarded these limits as possible definitions, because they do not give the meaning, the idea, of a derivative or an integral.

For the derivative is a measure of a velocity, or a slope of a curve. Now the velocity of a body at a certain instant is something real – a concrete (relational) attribute of that body at that instant. By contrast the limit of a sequence of average velocities is something highly abstract – something that exists only in our thoughts. The average velocities themselves are unreal. Their unending sequence is even more so; and the limit of this unending sequence is a purely mathematical construction out of these unreal entities. Now it is intuitively quite obvious that this limit must numerically coincide with the velocity, and that, if the limit can be calculated, we can thereby calculate the velocity. But according to the views of Newton and his contemporaries, it would be putting the cart before the horse were we to define the velocity as being identical with this limit, rather than as a real state of the body at a certain instant, or at a certain point, of its track – to be calculated by any mathematical contrivance we may be able to think of.

The same holds of course for the slope of a curve in a given point. Its measure will be equal to the limit of a sequence of measures of certain other average slopes (rather than actual slopes) of this curve. But it is not, in its proper meaning or essence, a limit of a sequence: the slope is something we can sometimes actually draw on paper, and construct with a compasses and rulers, while a limit is in essence something abstract, rarely actually reached or realized, but only approached, nearer and nearer, by a sequence of numbers. . . .

Or as Berkeley put it “. . . however expedient such analogies or such expressions may be found for facilitating the modern quadratures, yet we shall not find any light given us thereby into the original real nature of fluxions considered in themselves.” Thus mere means for facilitating our calculations cannot be considered as explications or definitions.

This was the view of all mathematicians of the period, including Newton and Leibniz. If we now look at the modern point of view, then we see that we have completely given up the idea of definition in the sense in which it was understood by the founders of the calculus, as well as by Berkeley. We have given up the idea of a definition which explains the meaning (for example of the derivative). This fact is veiled by our retaining the old symbol of “definition” for some equivalences which we use, not to explain the idea or the essence of a derivative, but to eliminate it. And it is veiled by our retention of the name “differential quotient” or “derivative,” and the old symbol dy/dx which once denoted an idea which we have now discarded. For the name, and the symbol, now have no function other than to serve as labels for the defiens – the limit of a sequence.

Thus we have given up “explication” as a bad job. The intuitive idea, we found, led to contradictions. But we can solve our problems without it, retaining the bulk of the technique of calculation which originally was based upon the intuitive idea. Or more precisely we retain only this technique, as far as it was sound, and eliminate the idea its help. The derivative and the integral are both eliminated; they are replaced, in effect, by certain standard methods of calculating limits. (oo. 266-70)

Not only have the original ideas of the founders of calculus been eliminated, because they ultimately could not withstand logical scrutiny, but a premature insistence on logical precision would have had disastrous consequences for the ultimate development of calculus.

It is fascinating to consider that this whole admirable development might have been nipped in the bud (as in the days of Archimedes) had the mathematicians of the day been more sensitive to Berkeley’s demand – in itself quite reasonable – that we should strictly adhere to the rules of logic, and to the rule of always speaking sense.

We now know that Berkeley was right when, in The Analyst, he blamed Newton . . . for obtaining . . . mathematical results in the theory of fluxions or “in the calculus differentialis” by illegitimate reasoning. And he was completely right when he indicated that [his] symbols were without meaning. “Nothing is easier,” he wrote, “than to devise expressions and notations, for fluxions and infinitesimals of the first, second, third, fourth, and subsequent orders. . . . These expressions indeed are clear and distinct, and the mind finds no difficulty in conceiving them to be continued beyond any assignable bounds. But if . . . we look underneath, if, laying aside the expressions, we set ourselves attentively to consider the things themselves which are supposed to be expressed or marked thereby, we shall discover much emptiness, darkness, and confusion . . . , direct impossibilities, and contradictions.”

But the mathematicians of his day did not listen to Berkeley. They got their results, and they were not afraid of contradictions as long as they felt that they could dodge them with a little skill. For the attempt to “analyse the meaning” or to “explicate” their concepts would, as we know now, have led to nothing. Berkeley was right: all these concept were meaningless, in his sense and in the traditional sense of the word “meaning:” they were empty, for they denoted nothing, they stood for nothing. Had this fact been realized at the time, the development of the calculus might have been stopped again, as it had been stopped before. It was the neglect of precision, the almost instinctive neglect of all meaning analysis or explication, which made the wonderful development of the calculus possible.

The problem underlying the whole development was, of course, to retain the powerful instrument of the calculus without the contradictions which had been found in it. There is no doubt that our present methods are more exact than the earlier ones. But this is not due to the fact that they use “exactly defined” terms. Nor does it mean that they are exact: the main point of the definition by way of limits is always an existential assertion, and the meaning of the little phrase “there exists a number” has become the centre of disturbance in contemporary mathematics. . . . This illustrates my point that the attribute of exactness is not absolute, and that it is inexact and highly misleading to use the terms “exact” and “precise” as if they had any exact or precise meaning. (pp. 270-71)

Popper sums up his discussion as follows:

My examples [I quoted only the first of the four examples as it seemed most relevant to Arthreya’s discussion] may help to emphasize a lesson taught by the whole history of science: that absolute exactness does not exist, not even in logic and mathematics (as illustrated by the example of the still unfinished history of the calculus); that we should never try to be more exact than is necessary for the solution of the problem in hand; and that the demand for “something more exact” cannot in itself constitute a genuine problem (except, of course, when improved exactness may improve the testability of some theory). (p. 277)

I apologize for stringing together this long series of quotes from Popper, but I think that it is important to understand that there is simply no scientific justification for the highly formalistic manner in which much modern economics is now carried out. Of course, other far more authoritative critics than I, like Mark Blaug and Richard Lipsey (also here) have complained about the insistence of modern macroeconomics on microfounded, axiomatized models regardless of whether those models generate better predictions than competing models. Their complaints have regrettably been ignored for the most part. I simply want to point out that a recent, and in many ways admirable, introduction to modern macroeconomics failed to provide a coherent justification for insisting on axiomatized models. It really wasn’t the author’s fault; a coherent justification doesn’t exist.

Methodological Arrogance

A few weeks ago, I posted a somewhat critical review of Kartik Athreya’s new book Big Ideas in Macroeconomics. In quoting a passage from chapter 4 in which Kartik defended the rational-expectations axiom on the grounds that it protects the public from economists who, if left unconstrained by the discipline of rational expectations, could use expectational assumptions to generate whatever results they wanted, I suggested that this sort of reasoning in defense of the rational-expectations axiom betrayed what I called the “methodological arrogance” of modern macroeconomics which has, to a large extent, succeeded in imposing that axiom on all macroeconomic models. In his comment responding to my criticisms, Kartik made good-natured reference in passing to my charge of “methodological arrogance,” without substantively engaging with the charge. And in a post about the early reviews of Kartik’s book, Steve Williamson, while crediting me for at least reading the book before commenting on it, registered puzzlement at what I meant by “methodological arrogance.”

Actually, I realized when writing that post that I was not being entirely clear about what “methodological arrogance” meant, but I thought that my somewhat tongue-in-cheek reference to the duty of modern macroeconomists “to ban such models from polite discourse — certainly from the leading economics journals — lest the public be tainted by economists who might otherwise dare to abuse their models by making illicit assumptions about expectations formation and equilibrium concepts” was sufficiently suggestive not to require elaboration, especially after having devoted several earlier posts to criticisms of the methodology of modern macroeconomics (e.g., here, here, and here). That was a misjudgment.

So let me try to explain what I mean by methodological arrogance, which is not the quite the same as, but is closely related to, methodological authoritarianism. I will do so by referring to the long introductory essay (“A Realist View of Logic, Physics, and History”) that Karl Popper contributed to a book The Self and Its Brain co-authored with neuroscientist John Eccles. The chief aim of the essay was to argue that the universe is not fully determined, but evolves, producing new, emergent, phenomena not originally extant in the universe, such as the higher elements, life, consciousness, language, science and all other products of human creativity, which in turn interact with the universe, in fundamentally unpredictable ways. Popper regards consciousness as a real phenomenon that cannot be reduced to or explained by purely physical causes. Though he makes only brief passing reference to the social sciences, Popper’s criticisms of reductionism are directly applicable to the microfoundations program of modern macroeconomics, and so I think it will be useful to quote what he wrote at some length.

Against the acceptance of the view of emergent evolution there is a strong intuitive prejudice. It is the intuition that, if the universe consists of atoms or elementary particles, so that all things are structures of such particles, then every event in the universe ought to be explicable, and in principle predictable, in terms of particle structure and of particle interaction.

Notice how easy it would be rephrase this statement as a statement about microfoundations:

Against the acceptance of the view that there are macroeconomic phenomena, there is a strong intuitive prejudice. It is the intuition that, if the macroeconomy consists of independent agents, so that all macroeconomic phenomena are the result of decisions made by independent agents, then every macreconomic event ought to be explicable, and in principle predictable, in terms of the decisions of individual agents and their interactions.

Popper continues:

Thus we are led to what has been called the programme of reductionism [microfoundations]. In order to discuss it I shall make use of the following Table

(12) Level of ecosystems

(11) Level of populations of metazoan and plants

(10) Level of metezoa and multicellular plants

(9) Level of tissues and organs (and of sponges?)

(8) Level of populations of unicellular organisms

(7) Level of cells and of unicellular organisms

(6) Level of organelles (and perhaps of viruses)

(5) Liquids and solids (crystals)

(4) Molecules

(3) Atoms

(2) Elementary particles

(1) Sub-elementary particles

(0) Unknown sub-sub-elementary particles?

The reductionist idea behind this table is that the events or things on each level should be explained in terms of the lower levels. . . .

This reductionist idea is interesting and important; and whenever we can explain entities and events on a higher level by those of a lower level, we can speak of a great scientific success, and can say that we have added much to our understanding of the higher level. As a research programme, reductionism is not only important, but it is part of the programme of science whose aim is to explain and to understand.

So far so good. Reductionism certainly has its place. So do microfoundations. Whenever we can take an observation and explain it in terms of its constituent elements, we have accomplished something important. We have made scientific progress.

But Popper goes on to voice a cautionary note. There may be, and probably are, strict, perhaps insuperable, limits to how far higher-level phenomena can be reduced to (explained by) lower-level phenomena.

[E]ven the often referred to reduction of chemistry to physics, important as it is, is far from complete, and very possibly incompletable. . . . [W]e are far removed indeed from being able to claim that all, or most, properties of chemical compounds can be reduced to atomic theory. . . . In fact, the five lower levels of [our] Table . . . can be used to show that we have reason to regard this kind of intuitive reduction programme as clashing with some results of modern physics.

For what [our] Table suggests may be characterized as the principle of “upward causation.” This is the principle that causation can be traced in our Table . . . . from a lower level to a higher level, but not vice versa; that what happens on a higher level can be explained in terms of the next lower level, and ultimately in terms of elementary particles and the relevant physical laws. It appears at first that the higher levels cannot act on the lower ones.

But the idea of particle-to-particle or atom-to-atom interaction has been superseded by physics itself. A diffraction grating or a crystal (belonging to level (5) of our Table . . .) is a spatially very extended complex (and periodic) structure of billions of molecules; but it interacts as a whole extended periodic structure with the photons or the particles of a beam of photons or particles. Thus we have here an important example of “downward causation“. . . . That is to say, the whole, the macro structure, may, qua whole, act upon a photon or an elementary particle or an atom. . . .

Other physical examples of downward causation – of macroscopic structures on level (5) acting upon elementary particles or photons on level (1) – are lasers, masers, and holograms. And there are also many other macro structures which are examples of downward causation: every simple arrangement of negative feedback, such as a steam engine governor, is a macroscopic structure that regulates lower level events, such as the flow of the molecules that constitute the steam. Downward causation is of course important in all tools and machines which are designed for sompe purpose. When we use a wedge, for example, we do not arrange for the action of its elementary particles, but we use a structure, relying on it ot guide the actions of its constituent elementary particles to act, in concert, so as to achieve the desired result.

Stars are undersigned, but one may look at them as undersigned “machines” for putting the atoms and elementary particles in their central region under terrific gravitational pressure, with the (undersigned) result that some atomic nuclei fuse and form the nuclei of heavier elements; an excellent example of downward causation,of the action of the whole structure upon its constituent particles.

(Stars, incidentally, are good examples of the general rule that things are processes. Also, they illustrate the mistake of distinguishing between “wholes” – which are “more than the sums of their parts” – and “mere heaps”: a star is, in a sense, a “mere” accumulation, a “mere heap” of its constituent atoms. Yet it is a process – a dynamic structure. Its stability depends upon the dynamic equilibrium between its gravitational pressure, due to its sheer bulk, and the repulsive forces between its closely packed elementary particles. If the latter are excessive, the star explodes, If they are smaller than the gravitational pressure, it collapses into a “black hole.”

The most interesting examples of downward causation are to be found in organisms and in their ecological systems, and in societies of organisms [my emphasis]. A society may continue to function even though many of its members die; but a strike in an essential industry, such as the supply of electricity, may cause great suffering to many individual people. .. . I believe that these examples make the existence of downward causation obvious; and they make the complete success of any reductionist programme at least problematic.

I was very glad when I recently found this discussion of reductionism by Popper in a book that I had not opened for maybe 40 years, because it supports an argument that I have been making on this blog against the microfoundations program in macroeconomics: that as much as macroeconomics requires microfoundations, microeconomics also requires macrofoundations. Here is how I put a little over a year ago:

In fact, the standard comparative-statics propositions of microeconomics are also based on the assumption of the existence of a unique stable general equilibrium. Those comparative-statics propositions about the signs of the derivatives of various endogenous variables (price, quantity demanded, quantity supplied, etc.) with respect to various parameters of a microeconomic model involve comparisons between equilibrium values of the relevant variables before and after the posited parametric changes. All such comparative-statics results involve a ceteris-paribus assumption, conditional on the existence of a unique stable general equilibrium which serves as the starting and ending point (after adjustment to the parameter change) of the exercise, thereby isolating the purely hypothetical effect of a parameter change. Thus, as much as macroeconomics may require microfoundations, microeconomics is no less in need of macrofoundations, i.e., the existence of a unique stable general equilibrium, absent which a comparative-statics exercise would be meaningless, because the ceteris-paribus assumption could not otherwise be maintained. To assert that macroeconomics is impossible without microfoundations is therefore to reason in a circle, the empirically relevant propositions of microeconomics being predicated on the existence of a unique stable general equilibrium. But it is precisely the putative failure of a unique stable intertemporal general equilibrium to be attained, or to serve as a powerful attractor to economic variables, that provides the rationale for the existence of a field called macroeconomics.

And more recently, I put it this way:

The microeconomic theory of price adjustment is a theory of price adjustment in a single market. It is a theory in which, implicitly, all prices and quantities, but a single price-quantity pair are in equilibrium. Equilibrium in that single market is rapidly restored by price and quantity adjustment in that single market. That is why I have said that microeconomics rests on a macroeconomic foundation, and that is why it is illusory to imagine that macroeconomics can be logically derived from microfoundations. Microfoundations, insofar as they explain how prices adjust, are themselves founded on the existence of a macroeconomic equilibrium. Founding macroeconomics on microfoundations is just a form of bootstrapping.

So I think that my criticism of the microfoundations project exactly captures the gist of Popper’s criticism of reductionism. Popper extended his criticism of a certain form of reductionism, which he called “radical materialism or radical physicalism” in later passage in the same essay that is also worth quoting:

Radical materialism or radical physicalism is certainly a selfconsistent position. Fir it is a view of the universe which, as far as we know, was adequate once; that is, before the emergence of life and consciousness. . . .

What speaks in favour of radical materialism or radical physicalism is, of course, that it offers us a simple vision of a simple universe, and this looks attractive just because, in science, we search for simple theories. However, I think that it is important that we note that there are two different ways by which we can search for simplicity. They may be called, briefly, philosophical reduction and scientific reduction. The former is characterized by an attempt to provide bold and testable theories of high explanatory power. I believe that the latter is an extremely valuable and worthwhile method; while the former is of value only if we have good reasons to assume that it corresponds to the facts about the universe.

Indeed, the demand for simplicity in the sense of philosophical rather than scientific reduction may actually be damaging. For even in order to attempt scientific reduction, it is necessary for us to get a full grasp of the problem to be solved, and it is therefore vitally important that interesting problems are not “explained away” by philosophical analysis. If, say, more than one factor is responsible for some effect, it is important that we do not pre-empt the scientific judgment: there is always the danger that we might refuse to admit any ideas other than the ones we appear to have at hand: explaining away, or belittling the problem. The danger is increased if we try to settle the matter in advance by philosophical reduction. Philosophical reduction also makes us blind to the significance of scientific reduction.

Popper adds the following footnote about the difference between philosophic and scientific reduction.

Consider, for example, what a dogmatic philosophical reductionist of a mechanistic disposition (or even a quantum-mechanistic disposition) might have done in the face of the problem of the chemical bond. The actual reduction, so far as it goes, of the theory of the hydrogen bond to quantum mechanics is far more interesting than the philosophical assertion that such a reduction will one be achieved.

What modern macroeconomics now offers is largely an array of models simplified sufficiently so that they are solvable using the techniques of dynamic optimization. Dynamic optimization by individual agents — the microfoundations of modern macro — makes sense only in the context of an intertemporal equilibrium. But it is just the possibility that intertemporal equilibrium may not obtain that, to some of us at least, makes macroeconomics interesting and relevant. As the great Cambridge economist, Frederick Lavington, anticipating Popper in grasping the possibility of downward causation, put it so well, “the inactivity of all is the cause of the inactivity of each.”

So what do I mean by methodological arrogance? I mean an attitude that invokes microfoundations as a methodological principle — philosophical reductionism in Popper’s terminology — while dismissing non-microfounded macromodels as unscientific. To be sure, the progress of science may enable us to reformulate (and perhaps improve) explanations of certain higher-level phenomena by expressing those relationships in terms of lower-level concepts. That is what Popper calls scientific reduction. But scientific reduction is very different from rejecting, on methodological principle, any explanation not expressed in terms of more basic concepts.

And whenever macrotheory seems inconsistent with microtheory, the inconsistency poses a problem to be solved. Solving the problem will advance our understanding. But simply to reject the macrotheory on methodological principle without evidence that the microfounded theory gives a better explanation of the observed phenomena than the non-microfounded macrotheory (and especially when the evidence strongly indicates the opposite) is arrogant. Microfoundations for macroeconomics should result from progress in economic theory, not from a dubious methodological precept.

Let me quote Popper again (this time from his book Objective Knowledge) about the difference between scientific and philosophical reduction, addressing the denial by physicalists that that there is such a thing as consciousness, a denial based on their belief that all supposedly mental phenomena can and will ultimately be reduced to purely physical phenomena

[P]hilosophical speculations of a materialistic or physicalistic character are very interesting, and may even be able to point the way to a successful scientific reduction. But they should be frankly tentative theories. . . . Some physicalists do not, however, consider their theories as tentative, but as proposals to express everything in physicalist language; and they think these proposals have much in their favour because they are undoubtedly convenient: inconvenient problems such as the body-mind problem do indeed, most conveniently, disappear. So these physicalists think that there can be no doubt that these problems should be eliminated as pseudo-problems. (p. 293)

One could easily substitute “methodological speculations about macroeconomics” for “philosophical speculations of a materialistic or physicalistic character” in the first sentence. And in the third sentence one could substitute “advocates of microfounding all macroeconomic theories” for “physicalists,” “microeconomic” for “physicalist,” and “Phillips Curve” or “involuntary unemployment” for “body-mind problem.”

So, yes, I think it is arrogant to think that you can settle an argument by forcing the other side to use only those terms that you approve of.

Two Cheers (Well, Maybe Only One and a Half) for Falsificationism

Noah Smith recently wrote a defense (sort of) of falsificationism in response to Sean Carroll’s suggestion that the time has come for scientists to throw falisficationism overboard as a guide for scientific practice. While Noah isn’t ready to throw out falsification as a scientific ideal, he does acknowledge that not everything that scientists do is really falsifiable.

But, as Carroll himself seems to understand in arguing against falsificationism, even though a particular concept or entity may itself be unobservable (and thus unfalsifiable), the larger theory of which it is a part may still have implications that are falsifiable. This is the case in economics. A utility function or a preference ordering is not observable, but by imposing certain conditions on that utility function, one can derive some (weakly) testable implications. This is exactly what Karl Popper, who introduced and popularized the idea of falsificationism, meant when he said that the aim of science is to explain the known by the unknown. To posit an unobservable utility function or an unobservable string is not necessarily to engage in purely metaphysical speculation, but to do exactly what scientists have always done, to propose explanations that would somehow account for some problematic phenomenon that they had already observed. The explanations always (or at least frequently) involve positing something unobservable (e.g., gravitation) whose existence can only be indirectly perceived by comparing the implications (predictions) inferred from the existence of the unobservable entity with what we can actually observe. Here’s how Popper once put it:

Science is valued for its liberalizing influence as one of the greatest of the forces that make for human freedom.

According to the view of science which I am trying to defend here, this is due to the fact that scientists have dared (since Thales, Democritus, Plato’s Timaeus, and Aristarchus) to create myths, or conjectures, or theories, which are in striking contrast to the everyday world of common experience, yet able to explain some aspects of this world of common experience. Galileo pays homage to Aristarchus and Copernicus precisely because they dared to go beyond this known world of our senses: “I cannot,” he writes, “express strongly enough my unbounded admiration for the greatness of mind of these men who conceived [the heliocentric system] and held it to be true […], in violent opposition to the evidence of their own senses.” This is Galileo’s testimony to the liberalizing force of science. Such theories would be important even if they were no more than exercises for our imagination. But they are more than this, as can be seen from the fact that we submit them to severe tests by trying to deduce from them some of the regularities of the known world of common experience by trying to explain these regularities. And these attempts to explain the known by the unknown (as I have described them elsewhere) have immeasurably extended the realm of the known. They have added to the facts of our everyday world the invisible air, the antipodes, the circulation of the blood, the worlds of the telescope and the microscope, of electricity, and of tracer atoms showing us in detail the movements of matter within living bodies.  All these things are far from being mere instruments: they are witness to the intellectual conquest of our world by our minds.

So I think that Sean Carroll, rather than arguing against falisficationism, is really thinking of falsificationism in the broader terms that Popper himself laid out a long time ago. And I think that Noah’s shrug-ability suggestion is also, with appropriate adjustments for changes in expository style, entirely in the spirit of Popper’s view of falsificationism. But to make that point clear, one needs to understand what motivated Popper to propose falsifiability as a criterion for distinguishing between science and non-science. Popper’s aim was to overturn logical positivism, a philosophical doctrine associated with the group of eminent philosophers who made up what was known as the Vienna Circle in the 1920s and 1930s. Building on the British empiricist tradition in science and philosophy, the logical positivists argued that our knowledge of the external world is based on sensory experience, and that apart from the tautological truths of pure logic (of which mathematics is a part) there is no other knowledge. Furthermore, no meaning could be attached to any statement whose validity could not checked either by examining its logical validity as an inference from explicit premises or verified by sensory experience. According to this criterion, much of human discourse about ethics, morals, aesthetics, religion and much of philosophy was simply meaningless, aka metaphysics.

Popper, who grew up in Vienna and was on the periphery of the Vienna Circle, rejected the idea that logical tautologies and statements potentially verifiable by observation are the only conveyors of meaning between human beings. Metaphysical statements can be meaningful even if they can’t be confirmed by observation. Metaphysical statements are meaningful if they are coherent and are not nonsensical. If there is a problem with metaphysical statements, the problem is not necessarily because they have no meaning. In making this argument, Popper suggested an alternative criterion of demarcation to that between meaning and non-meaning: a criterion of demarcation between science and metaphysics. Science is indeed different from metaphysics, but the difference is not that science is meaningful and metaphysics is not. The difference is that scientific statements can be refuted (or falsified) by observations while metaphysical statements cannot be refuted by observations. As a matter of logic, the only way to refute a proposition by an observation is for the proposition to assert that the observation was not possible. Unless you can say what observation would refute what you are saying, you are engaging in metaphysical, not scientific, talk. This gave rise to Popper’s then very surprising result. If you positively assert the existence of something – an assertion potentially verifiable by observation, and hence for logical positivists the quintessential scientific statement — you are making a metaphysical, not a scientific, statement. The statement that something (e.g., God, a string, or a utility function) exists cannot be refuted by any observation. However the unobservable phenomenon may be part of a theory with implications that could be refuted by some observation. But in that case it would be the theory not the posited object that was refuted.

In fact, Popper thought that metaphysical statements not only could be meaningful, but could even be extremely useful, coining the term “metaphysical research programs,” because a metaphysical, unfalsifiable idea or theory could be the impetus for further research, possibly becoming scientifically fruitful in the way that evolutionary biology eventually sprang from the possibly unfalsifiable idea of survival of the fittest. That sounds to me pretty much like Noah’s idea of shrug-ability.

Popper was largely successful in overthrowing logical positivism, though whether it was entirely his doing (as he liked to claim) and whether it was fully overthrown are not so clear. One reason to think that it was not all his doing is that there is still a lot of confusion about what the falsification criterion actually means. Reading Noah Smith and Sean Carroll, I almost get the impression that they think the falsification criterion distinguishes not just between science and non-science but between meaning and non-meaning. Otherwise, why would anyone think that there is any problem with introducing an unfalsifiable concept into scientific discussion. When Popper argued that science should aim at proposing and testing falsifiable theories, he meant that one should not design a theory so that it can’t be tested, or adopt stratagems — ad hoc hypotheses — that serve only to account for otherwise falsifying observations. But if someone comes up with a creative new idea, and the idea can’t be tested, at least given the current observational technology, that is not a reason to reject the theory, especially if the new theory accounts for otherwise unexplained observations.

Another manifestation of Popper’s imperfect success in overthrowing logical positivism is that Paul Samuelson in his classic The Foundations of Economic Analysis chose to call the falsifiable implications of economic theory, meaningful theorems. By naming those implications “meaningful theorems,” Samuelson clearly was operating under the positivist presumption that only a proposition that could (at least in principle) be falsified by observation was meaningful. However, that formulation reflected an untenable compromise between Popper’s criterion for distinguishing science from metaphysics and the logical positivist criterion for distinguishing meaningful from meaningless statements. Instead of referring to meaningful theorems, Samuelson should have called them, more modestly, testable or scientific theorems.

So, at least as I read Popper, Noah Smith and Sean Carroll are only discovering what Popper already understood a long time ago.

At this point, some readers may be wondering why, having said all that, I seem to have trouble giving falisficationism (and Popper) even two cheers. So I am afraid that I will have to close this post on a somewhat critical note. The problem with Popper is that his rhetoric suggests that scientific methodology is a lot more important than it really is. Apart from some egregious examples like Marxism and Freudianism, which were deliberately formulated to exclude the possibility of refutation, there really aren’t that many theories entertained by scientists that can be ruled out of order on strictly methodological grounds. Popper can occasionally provide some methodological reminders to scientists to avoid relying on ad hoc theorizing — at least when a non-ad-hoc alternative is handy — but beyond that I don’t think methodology counts for very much in the day to day work of scientists. Many theories are difficult to falsify, but the difficulty is not necessarily the result of deliberate choices by the theorists, it is the result of the nature of the problem and the nature of the evidence that could potentially refute the theory. The evidence is what it is. It is nice to come up with a theory that predicts a novel fact that can be observed, but nature is not always so accommodating to our theories.

There is a kind of rationalistic (I am using “rationalistic” in the pejorative sense of Michael Oakeshott) faith that following the methodological rules that Popper worked so hard to formulate will guarantee scientific progress. Those rules tend to encourage an unrealistic focus on making theories testable (especially in economics) when by their nature the phenomena are too complex for theories to be formulated in ways that are susceptible to decisive testing. And although Popper recognized that empirical testing of a theory has very limited usefulness unless the theory is being compared to some alternative theory, too often discussions of theory testing are in the context of testing a single theory in isolation. Kuhn and others have pointed out that science is not routinely carried out in the way that Popper suggested it should be. To some extent, Popper acknowledged the truth of that observation, though he liked to cite examples from the history of science to illustrate his thesis, but argued that he was offering a normative, not a positive, theory of scientific discovery. But why should we assume that Popper had more insight into the process of discovery for particular sciences than the practitioners of those sciences actually doing the research? That is the nub of the criticism of Popper that I take away from Oakeshott’s work. Life and any form of endeavor involves the transmission of ways of doing things, traditions, that cannot be reduced to a set of rules, but require education, training, practice and experience. That’s what Kuhn called normal science. Normal science can go off the tracks too, but it is naïve to think that a list of methodological rules is what will keep science moving constantly in the right direction. Why should Popper’s rules necessarily trump the lessons that practitioners have absorbed from the scientific traditions in which they have been trained? I don’t believe that there is any surefire recipe for scientific progress.

Nevertheless, when I look at the way economics is now being practiced and taught, I can’t help but think that a dose of Popperianism might not be the worst thing that could be administered to modern economics. But that’s a discussion for another day.


About Me

David Glasner
Washington, DC

I am an economist in the Washington DC area. My research and writing has been mostly on monetary economics and policy and the history of economics. In my book Free Banking and Monetary Reform, I argued for a non-Monetarist non-Keynesian approach to monetary policy, based on a theory of a competitive supply of money. Over the years, I have become increasingly impressed by the similarities between my approach and that of R. G. Hawtrey and hope to bring Hawtrey's unduly neglected contributions to the attention of a wider audience.

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