George H. Blackford, Ph.D.

 Economist at Large

 Email: george(at)


It ain't what you don't know that gets you into trouble.

It’s what you know for sure that just ain't so.
Attributed to Mark Twain (among others)


Economic Papers
Political Essays


On the Pseudo-Scientific Nature of Friedman’s as if Methodology*

George H. Blackford © (8/13/16 updated 1/11/17)

 Consider the problem of predicting the shots made by an expert billiard player. It seems not at all unreasonable that excellent predictions would be yielded by the hypothesis that the billiard player made his shots as if he knew the complicated mathematical formulas that would give the optimum directions of travel, could estimate accurately by eye the angles, etc., describing the location of the balls, could make lightning calculations from the formulas, and could then make the balls travel in the direction indicated by the formulas. Our confidence in this hypothesis is not based on the belief that billiard players, even expert ones, can or do go through the process described; it derives rather from the belief that, unless in some way or other they were capable of reaching essentially the same result, they would not in fact be expert billiard players.

Milton Friedman, Essays in Positive Economic, 1953

It was 1967 when I first read Friedman’s essay on “The Methodology of Positive Economics” in which the above billiard-player analogy can be found.  I was dumbfounded.  To say an expert billiard player plays “as if he knew . . . complicated mathematical formulas” may be an interesting analogy, but it tells us nothing about billiard players.  It was obvious to me at the time that Friedman’s argument to the contrary is circular: How do we know expert players play this way? If they didn’t play this way they would not be expert players. And I was not at all impressed by the fact that Friedman’s logic is firmly rooted in his “belief” that this makes sense. [1]


Friedman posed this analogy in the midst of a convoluted argument by which he attempts to show that a scientific theory (hypothesis or formula) cannot be tested by testing the realism of its assumptions.  All that matters is the accuracy of a theory’s predictions, not whether or not its assumptions are true.  He attempts to demonstrate this by examining “the law of falling bodies” where he tells us that it “is an accepted hypothesis that the acceleration of a body dropped in a vacuum is a constant—g, or approximately 32 feet per second per second on the earth . . . .” (p. 18) According to Friedman, it is meaningless to argue this law assumes a vacuum.  The only thing that matters is the accuracy of the predictions obtained if we assume bodies fall as if they are falling in a vacuum.  It is the role of the scientist to “to specify the circumstances under which the formula works or, more precisely, the general magnitude of the error in its predictions under various circumstances.”  Even though a more general theory exists that can give more accurate predictions “it does not always pay to use the more general theory because the extra accuracy it yields may not justify the extra cost.”[2]


Specifying "the circumstances under which the formula works or, more precisely, the general magnitude of the error in its predictions under various circumstances" makes perfect sense when probing the limits of quantum field theory and general relativity, but I seriously doubt that scientists in general view probing the limits of theories that have been replaced by more general theories that give more accurate predictions "because the extra accuracy it yields may not justify the extra cost" as the essence of science though I can imagine situations in which engineers might be motivated to so.  The essence of science, as I saw it then and still see it today, is to understand and explain the subject matter of a scientific discipline.  This cannot be done simply by cataloging when a theory works and the magnitude of errors when it does not.  An attempt has to be made to understand and explain why a theory does not work and to try to find theories that do work.  This, in my view, is the essence of science, not simply cataloging and measuring errors, and, yet, Friedman’s engineering view of science has stood at the very core of mainstream economics for well over sixty years.[3]


There are, of course, a number of economists who openly reject the engineering view of scientific inquire embodied in Friedman’s as if methodology that ignores the realism of assumption, but they appear to be relatively few and to have relatively little influence within the discipline. At the same time there are many mainstream economists who reject Friedman’s methodology on its face when confronted with it directly but are compelled, as a result of their training and the need to accumulate publications in mainstream economic journals, to abide by its rules which are imbedded in the culture of the discipline.  The result has proved to be disastrous. The fundamental paradigm of economics that emerged from this methodology not only failed to anticipative the Crash of 2008 and its devastating effects, it has proved incapable of producing a consensus within the discipline as to the nature and cause of the economic stagnation we find ourselves in the midst of today.


In attempting to understand why this is so it is instructive to examine the nature of Friedman’s arguments within the context in which he formulated them, especially his argument that the truth of a theory’s assumptions is irrelevant so long as the inaccuracy of a theory’s predictions are cataloged and we argue as if those assumptions are true. The place to begin is with the history of the law of falling bodies that Friedman alludes to, and then ignores.  


The Law of Falling Bodies

Our understanding of this ‘law’ did not just suddenly appear out of nowhere.  It grew out of the work of Galileo in attempting to explain the anomalies in Aristotle’s theory of motion.  According to Aristotle, a constant force applied to an object will cause it to move at a constant velocity, the greater the force the greater the velocity.  He also assumed that heavier bodies fall with a greater velocity than lighter bodies.[4] This seemed to make perfect sense as an explanation of the way in which a feather falls compared to a stone, but Galileo observed that heavier stones do not fall at greater velocities than lighter stones and that the longer a stone falls the greater its velocity becomes (up to a point) even though the force of gravity acting on it (apparently) does not change.  


As a result of his incredibly complex and thorough analysis of falling bodies Galileo concluded that the differences in the behaviors he observed could be understood and explained if he rejected Aristotle’s assumptions and, instead, assumed: 1) the existence of momentum (i.e., that a body at rest tends to remain at rest and a body in motion tends to remain in motion) and 2) that when a constant force is applied to an object it causes that object to accelerate at a constant rate rather than to move at a constant velocity.  He also concluded, guided by observations, measurements, logic, and reason that in the absence of external resistance caused by the medium through which an object fell—that is, in a vacuum—all falling bodies would accelerate at the same constant rate irrespective of their shape, density, weight, or the distance through which they fell.[5] 


While these assumptions were enough to arrive at Galileo’s understanding of the law of falling bodies it was not until Newton had integrated the observations of Copernicus, Kepler, and Galileo to arrive at Newton’s three laws of motion and theory of universal gravitation that the Newtonian understanding of this law emerged.  This understanding differed from Galileo’s in that Galileo had assumed the rate of acceleration of a falling body in a vacuum would be constant throughout its fall.  This assumption is logically inconsistent with Newton’s second law of motion and theory of universal gravitation. 


Newton’s second law assumes that force is equal to mass times acceleration. His theory of gravity assumes that there is an inverse-square relationship between the force of gravity and the distance between the centers of gravity of the earth and a falling body.  These two assumptions, taken together, imply that the rate of acceleration must increase as a falling body and earth approach each other since the force of gravity must increase as the falling body approaches the earth.[6]  Thus to make Galileo’s law of falling bodies logically consistent with Newton’s integration, not only must the validity of this law assume a vacuum, it must also assume that the rate of acceleration increases as the falling body and earth approach each other in accordance with Newton’s theory of gravity and second law of motion.


At this point it should at least be apparent that Friedman’s assertion that the law of falling bodies “is accepted because it works” is not nearly as clear cut as Friedman tries to make it seem.  Friedman, himself, expounded on but a few of the innumerable situations in which this law, as he states it, does not work, and, in fact, there are relatively few practical applications for Friedman’s statement of this law other than as a basis on which high-school physics students can construct lab experiments.  The fact is that Galileo accepted his understanding of this law, not simply because it works, but because his understanding of this law is implied by the assumptions embodied in the cosmology within which Galileo attempted to understand and explain the physical universe.  Similarly, Newton accepted his version of Galileo’s law, not simply because it works, but because his understanding of this law is implied by the assumptions embodied in the cosmology within which Newton attempted to understand and explain the physical universe. 


Newton’s cosmology made it possible to understand and explain astronomical observations with a degree of accuracy that was heretofore impossible.  As a result, after Newton, any other interpretation of Galileo’s law would be viewed as pure nonsense by any educated person other than those who wished to cling desperately to the cosmology implicit in the Ptolemaic view of the universe and who were unwilling or unable, for whatever reason, to accept a heliocentric view of reality. 


It is essential to understand, however, that the Newtonian understanding of this law was not simply accepted because it worked in the way Friedman describes Galileo’s law as working.  The Newtonian understanding of this law was accepted because neither the law itself, nor any of the assumptions embodied in Newton’s cosmology that were needed to derive the Newtonian understanding of this law were demonstrably false in the sense of being contradicted by empirical observations.  If it could have been shown that any of the assumptions on which the derivation of the Newtonian understanding of this law depend were demonstrably false, the Newtonian understanding of this law would most certainly not have been accepted, at least not by physicists.  That this is so is made clear by the rejection of the Newtonian understanding of this law by physicists after it was discovered that Newton’s assumption of the independence of space and time was contradicted by empirical observations and replaced by Einstein’s assumption of a space-time continuum as embodied in Einstein’s theory of relativity.  Einstein’s theory of relativity led to an entirely different understanding of Galileo’s law.[7] 


Thus, when we examine the history of the law of falling bodies that Friedman alludes to and then ignores we find that all of the major advances in the physics that have come about since the time of Galileo were accomplished as a result of 1) Galileo rejecting the unrealistic assumptions of Aristotle, 2) Newton rejecting the unrealistic assumptions of Galileo, and 3) Einstein rejecting the unrealistic assumptions of Newton, and, yet, Friedman argues:

In so far as a theory can be said to have "assumptions" at all, and in so far as their "realism" can be judged independently of the validity of predictions, the relation between the significance of a theory and the "realism" of its "assumptions" is almost the opposite of that suggested by the view under criticism. Truly important and significant hypotheses will be found to have "assumptions" that are wildly inaccurate descriptive representations of reality, and, in general, the more significant the theory, the more unrealistic the assumptions (in this sense). (p. 14)

The Irrelevance of Logic in Friedman's Methodology

The degree to which Friedman’s arguments are totally oblivious to the central role played by assumptions in scientific inquiry is indicated by his delineation of this role as he sees it:

So far as I can see, the "assumptions of a theory" play three different, though related, positive roles: (a) they are often an economical mode of describing or presenting a theory; (b) they sometimes facilitate an indirect test of the hypothesis by its implications; and (c) . . . they are sometimes a convenient means of specifying the conditions under which the theory is expected to be valid.  (p. 23)

There is not even a hint of acknowledgement in this passage of the fact that a scientific theory is, in fact, the embodiment of its assumptions. There can be no theory without assumptions since it is the assumptions embodied in a theory that provide, by way of reason and logic, the implications by which the subject matter of a scientific discipline can be understood and explained.  These same assumptions provide, again, by way of reason and logic, the predictions that can be compared with empirical evidence to test the validity of a theory.  It is a theory’s assumptions that are the premises in the logical arguments that give a theory’s explanations meaning, and to the extent those assumptions are false, the explanations the theory provides are meaningless no matter how logically powerful or mathematically sophisticated those explanations based on false assumptions may seem to be.


It is the form of a logical argument that makes it valid, irrespective of the truth of its premises.[8]   The argument a) all men with blue eyes are infallible, b) I have blue eyes, therefore, c) I am infallible is logically valid even though, in light of reason, this is not the kind of argument my wife finds convincing.  And even if I were infallible this argument would have no substantive meaning, in spite of its logical validity and my blue eyes, because it is based on the demonstrably false premise that all men with blue eyes are infallible.  It is intuitively obvious that a logical argument only has substantive meaning if its premises are true even to those who lack a formal understanding of logic.  As a result, few scientists would be willing to follow Friedman’s methodology and attempt to catalog when the blue-eyed theory of infallibility ‘works’ and when it doesn’t.  And, yet, this is the kind of reasoning in which mainstream economist indulge when they ignore the realism of their assumptions.  


In spite of the simple fact that scientific understandings and explanations arise through logic and reason from the implications of the assumptions (i.e., premises) on which scientific arguments are based, and that a logical argument only has substantive meaning to the extent the premises on which it is based are true, Friedman argues that the relevance of a theory cannot be judged by the realism of its assumptions so long as it is also argued that it is as if its assumptions were true.  Aside from the fact that this argument makes absolutely no sense at all as a foundation for scientific inquiry, it begs the question: Why should mainstream economists be taken seriously if their theories and, hence, their arguments are based on false assumptions?  This question is particularly relevant with regard to the policy recommendations of mainstream economist when the realism of the assumptions on which the arguments that justify their recommendations are blithely ignored.


Today we find ourselves in the midst of a world-wide economic, political, and social catastrophe that has followed in the wake of the worst financial crisis since the 1930s. This crisis, in turn, was the direct result of the financial deregulation policies implemented over the past forty years at the behest of mainstream economists—policies that mainstream economists justified on the basis of an economic theory that assumes speculative bubbles cannot exist in spite of the innumerable economic, political, and social catastrophes that have followed in the wake of speculative bubbles throughout the course of history.[9] And yet, mainstream economists are at a loss in trying to come to a consensus as to what went wrong. Such is the power of Friedman's as if methodology within the discipline of economics.


The Ideological Nature of Friedman's Logic

Even more problematic is Friedman’s attempt to give substance to his engineering view of science by arguing that after all of the situations in which hypotheses work and do not work have been cataloged within a discipline, and after all of the evidence with regard to the lack of realism of the assumptions embodied in these hypotheses has been ignored, the scientist should look to “the tradition and folklore of a science revealed in the tenacity with which hypotheses are held” to find the truth.  He then argues that since the “capacity to judge . . . is something that cannot be taught [and] can be learned . . . only by experience and exposure in the ‘right’ scientific atmosphere” we must look to the wise men and women of the discipline who have been exposed to “the ‘right’ scientific atmosphere” to find where “the thin line is drawn which distinguishes the ‘crackpot’ from the scientist.” [10]


This may seem to make sense to an engineer who wishes to learn the current state of the art of bridge building, or to an ideologue who wishes to provide a logical foundation for his or her most cherished delusions irrespective of the circular reasoning and false assumptions upon which that logic is based, but this is not science!  If physical scientists had taken this approach to science throughout the course of history—relying on “folklore” and “the tenacity with which hypotheses are held” and on those who have been exposed to “the ‘right’ scientific atmosphere” as they ignored the realism of assumptions—we would still be living in a Ptolemaic universe cataloging the situations in which Aristotle’s assumptions do and do not work. 


Friedman is quite wrong in his assertion that there is a “thin line . . . which distinguishes the ‘crackpot’ from the scientist.”  That line is not thin.  It is the clear, bright line that exists between those who accept arguments based on circular reasoning and false assumptions as meaningful and those who do not. This should be obvious, yet there are economists who hold tenured positions at prestigious universities and responsible positions in government agencies and international institutions who accept Friedman’s nonsense as gospel. They delude themselves into believing that on the basis of their faith in this gospel they are among the privileged few capable of drawing the line that “distinguishes the ‘crackpot’ from the scientist.”  They are also without a clue as to the fact that they are not on the side of that line they believe themselves to be.  To make matters worse, the vast majority of economists seem to assume that since so many others accept this kind of nonsense it must, somehow, make sense, and relatively few speak out against it.  Nor do they seem to realize the extent to which this kind of pseudo-scientific reasoning permeates the discipline of economics or to understand the harm that it does. [Blackford (2016a; 2016b)]


What Friedman's Methodology has Wrought

As a result of the centrality of Friedman’s understanding of science within the discipline of economics, the discipline has become dominated by a nineteenth century, Walrasian free-market ideological view of reality that, at its core, consists of a logically consistent and mathematically elegant paradigm of market behavior that describes how an ideal system of human interaction in a hypothetical free-market society is supposed to work, as well as the prerequisites for such a system to actually work, that is totally out of touch with reality.  A paradigm in which the assumptions on which its logical consistency depends—the most important being that no economic actor has the power to directly influence market prices, all market participants have perfect information as to the determination of market prices, that there are no external costs or benefits associated with the production or consumption of goods, and that people behave rationally as the term “rationally” is defined by economists—are not simply unrealistic and contradicted by empirical evidence but are, in fact, impossible to achieve in the real world. [Blackford (2013)]  


Is it any wonder that this paradigm ignores the relevance of the essential role of cooperative action through democratic government to “establish Justice, insure domestic Tranquility, provide for the common defence, promote the general Welfare, and secure the Blessings of Liberty to ourselves and our Posterity” in spite of the fact that the nature of economic behavior is critically dependent on the government’s ability to perform these vital functions, and to the extent the government fails to perform these functions an efficiently functioning economic system is not only impossible, but the entire concept of economic efficiency [Heyne] that economist hold dear is meaningless? [11]   


Is it any wonder that the assumptions on which this paradigm is based has provided the foundation for mainstream economist to delude themselves into believing in a world in which markets are efficient; expectations are rational; there is no need to regulate international capital flows; speculative bubbles are a figment of the imagination; the economic system automatically adjusts to achieve full employment; fraud is not a problem given the efficacy of market discipline; factors of production receive the value of their marginal products; monopolies, monopsonies, and oligopolies are irrelevant as is an increasing concentration of income and a rising debt relative to income; increasing the propensity to save increases economic growth to the benefit of all; trade deficits are inconsequential; and in which financial institutions are fully capable of regulating themselves for the good of all humanity due to the enlightened self interest of bankers? [Blackford (2014, Ch. 1; 2016a; 2016b)]


Is it any wonder that the economic models created by mainstream economists in the wake of Friedman’s billiard-player analogy have ignored the long-run relationship between consumption and effective demand, output, and employment examined by Keynes in The General Theory of Employment, Interest, and Money to the effect that the logical implications of mainstream economic models have been used to justify deregulating the domestic and international financial systems, cutting taxes on the wealthy and increasing taxes on the not so wealthy, eliminating usury laws, promoting the adoption of private retirement accounts, destroying labor unions, converting Social Security from a pay-as-you-go into a partial-prepayment system, opposing increases in the minimum wage and many other policies that only make sense within a paradigm that not only ignores the essential role of government in providing for the common good but also ignores the long-run relationship between consumption and effective demand as well and simply assumes that increasing saving enhances economic growth in spite of the utter absurdity of this assumption? [12]  


The end result of these policies has been a dramatic increase in our current account deficit along with an equally dramatic increase in the concentration of income at the top of the income distribution. This, in turn, has led to a situation in which saving in the foreign sector has increased dramatically (by way of our increased current account deficit) and at the top of the income distribution in the private sector (by way of the higher propensity to save at the top of the income distribution than at the bottom). This increase in saving in the foreign sector and at the top of the income distribution in the private sector has been partially offset by dissaving in the public sector and at the bottom of the income distribution in the private sector.  It has also been accompanied by dramatic increases in investment as a result of speculative bubbles in the commercial real estate market in the 1980s, in the markets for tech stocks in the 1990s, and in the housing market in the 2000s. [Blackford (2014, Ch. 1 and Ch. 3)]


To the casual observer it would appear that as a result of the policies supported by mainstream economists over the past fifty years our economic system has been transformed in such a way that, given the resulting current account deficits and concentration of income at the top, the mass markets for consumption goods in the United States have been undermined to the point that the economic system can no longer achieve potential output and employment with the given state of mass-production technology in the absence of a continual increase in debt relative to income.  It would also appear that it is the unsustainability of a continual increase in private-sector debt relative to income that eventually led to the Crash of 2008.  And it would appear that, given the distribution of income and the state of mass-production technology, it is the inability to either a) continually reduce the trade deficit, b) continually increase debt relative to income through dissaving at the bottom of the income distribution, c) continually increase debt relative to income in the public sector, or d) continually create speculative bubbles that has led to the diminished long-term expectation with regard to consumption that is the primal cause of the economic stagnation we have experienced since 2007. [Blackford (2014, Ch. 1, Ch. 3, Ch. 12; 2016a; 2016b)]


And, yet, in spite of the mighty accomplishments in economic theory that have been achieved since the publication of Friedman’s essay on “The Methodology of Positive Economics” that so many economists hold dear, the fundamental paradigm of economics that has emerged from these accomplishments is incapable of providing a consensus within the discipline of economics as to the nature and cause of the economic stagnation we find ourselves in the midst of today.  To make matters worse, the kind of explanation of this stagnation given above cannot even be examined within the context of this fundamental paradigm let alone understood within this context since the effects of accumulating debt or of changes in the distribution of income are assumed to be irrelevant within this paradigm. [13]


It’s as if mainstream economists are so enthralled with Friedman’s billiard-player analogy that it is virtually impossible for them to even imagine the possibility that the acceptance of a lack of realism in their assumptions, fostered by a free-market, ideological bias, is the reason for their inability to come to a consensus with regard to the nature and cause of the economic catastrophe we are in the midst of today.  Such is the legacy of Friedman’s pseudo-scientific as if methodology.



The processes by which the paradigmatic revolutions took place in the physical sciences are examined in detail by Kuhn in terms of the empirical evidence against the assumptions embodied in an accepted paradigm growing until the paradigm collapses and is replaced by a new paradigm.  A similar revolution took place in economics following the 1930s collapse of the nineteenth century classical/neoclassical economic paradigm embedded in a free-market ideological view of reality.  That paradigm was replaced following World War II by what became known as the neoclassical-synthesis embedded in a Walrasian, mixed-economy ideological view of reality.  The collapse of the neoclassical-synthesis in the 1970s led to its integration with the old nineteenth century free-market paradigm into what is referred to by Goodfriend and King as the new-neoclassical synthesis. That synthesis, as with those that came before, proved to be little more than a house of cards resting on a foundation of sand.


It is not at all clear what kind of paradigm will emerge from the chaos within the discipline of economics that has resulted from the dramatic failure of the new-neoclassical synthesis to provide a context within which the Crash of 2008 and its aftermath can be understood or explained.  It is clear, however, or at least it should be clear, that continuing to adhere to Friedman’s as if methodology, guided by a Walrasian free-market ideology, and ignoring the unrealistic nature of the assumptions on which mainstream economic theories and arguments are based is not going to provide a useful guide to solving the economic, political, and social problems we face today.  Nor will it provide a useful guide to solving the economic, political, and social problems our children and grandchildren will be forced to endure in the future if mainstream economists continue to accept this absurd methodology. [Blackford (2013; 2014, Ch. 1, Ch. 3, Ch. 12; 2016a; 2016b)]



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Acemoglu, Daron and James Robinson, Why Nations Fail: The Origins of Power, Prosperity, and Poverty (2012) (Amazon)

Amy, Douglas J., Government is Good: An Unapologetic Defense of a Vital Institution (2010) (Amazon) (WEB)

Blackford, George H., “Ideology Versus Reality” (2013) (WEB)

———, Where Did All The Money Go? How Lower Taxes, Less Government, and Deregulation Redistribute Income and Create Economic Instability (2014; Ch. 1; Ch. 3; Ch. 12)  (Amazon)

———, “Liquidity-Preference/Loanable-Funds and The Long-Period Problem of Saving” (2016a) (WEB)

———, “A Note on Keynes’ General Theory of Employment, Interest, Money, and Prices” (2016b) (WEB)

Collin, Jason, "Please, Not Another Bias! The Problem with Behavioral Economics" (2016) (WEB)

Dal Bó, Ernesto, Pablo Hernandez-Lagos, Sebastián Mazzuca, “Failed states and the paradox of civilisation: New lessons from history” (2016) (WEB)

Einstein, Albert and H. Minkowski, Original Papers by A. Einstein and H. Minkowski (1920) (PDF)

Fox, Justin, The Myth of the Rational Market: A History of Risk, Reward, and Delusion on Wall Street (2009) (Amazon)

Friedman, Milton, Essays in Positive Economic (1953) (PDF)

Galilei, Galileo, Dialogues Concerning Two New Sciences (1632) Translated (1914) (PDF)

Goodfriend, Marvin, and Robert G. King, The New Neoclassical Synthesis and the Role of Monetary Policy” (1997) (PDF)

Heyne, Paul, “Efficiency” (2008) (WEB)

Kindleberger, Charles P. The World in Depression, 1929-1939: Revised and Enlarged Edition (History of the World Economy in the Twentieth Century) (1986) (Amazon)

Kuhn, Thomas, The Copernican Revolution: Planetary Astronomy in the Development of Western Thought (1957) (PDF)

———, The Structure of Scientific Revolutions (1962) (PDF)

Keynes, John M., The General Theory of Money, Interest, and Prices (1936) (PDF)

MacKay, Charles, Extraordinary Popular Delusions and the Madness of Crowds (1841) (Amazon)

Minsky, Hyman P., Stabilizing an Unstable Economy (1986/2008) (Amazon)

Newton, Isaac, The Principia (1686) Translated (1846) (PDF)

Polanyi, Karl, The Great Transformation (1944) (PDF) (Amazon)

Suppes, Patrick, Introduction to Logic (1957) (PDF)



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* I wish to gratefully acknowledge the editorial comments by G. William Domhoff, Gillian G. Garcia, Douglas J. Amy, Dolores M. Coulter, and David Harrison (along with an anonymous commenter, 'ohminus') on earlier drafts of this essay which significantly improved its clarity.  In no way, however, are they to be held responsible for the opinions expressed herein.

[1] An excellent example of the kind of fallacy involved in Friedman's argument to the effect that an expert billiard player plays "as if he knew . . . complicated mathematical formulas" because if he didn't play that way he wouldn't be an expert billiard player is to be found in Collin's discussion of the gaze heuristic.

[2] Friedman:

The history of [the law of falling bodies] . . . associated physical theory aside, is it meaningful to say that it assumes a vacuum? . . . The formula is accepted because it works, not because we live in an approximate vacuum—whatever that means.

The important problem in connection with the hypothesis is to specify the circumstances under which the formula works or, more precisely, the general magnitude of the error in its predictions under various circumstances. . . .

In the particular case of falling bodies a more general, though still incomplete, theory is available, largely as a result of attempts to explain the errors of the simple theory . . . . However, it does not always pay to use the more general theory because the extra accuracy it yields may not justify the extra cost of using it, so the question under what circumstances the simpler theory works "well enough" remains important. . . .  [T]he entirely valid use of "assumptions" in specifying the circumstances for which a theory holds is frequently, and erroneously, interpreted to mean that the assumptions can be used to determine the circumstances for which a theory holds, and has, in this way, been an important source of the belief that a theory can be tested by its assumptions. (pp. 18-9)

[3] While Friedman published his essay on methodology in 1953 it was circulated in the 1940s, and the acceptance of his engineering view of science by economists is implicit in the Keynesians’ rejection of Keynes’ Marshallian dynamic cause and effect methodology following World War II in favor of the Walrasian descriptive static equilibrium methodology. See Blackford (2016a; 2016b).

[4] Galileo:

. . . Aristotle . . . . supposes bodies of different weights to move in the same medium; then supposes, one and the same body to move in different media.  In the first case, he supposes bodies of different weight to move in one and the same medium with different speeds which stand to one another in the same ratio as the weights; so that, for example, a body which is ten times as heavy as another will move ten times as rapidly as the other.  In the second case he assumes that the speeds of one and the same body moving in different media are in inverse ratio to the densities of these media; thus, for instance, if the density of water were ten times that of air, the speed in air would be ten times greater than in water. (p. 61)

[5] Galileo:

I begin by saying that a heavy body has an inherent tendency to move with a constantly and uniformly accelerated motion toward the common center of gravity, that is, toward the center of our earth, so that during equal intervals of time it receives equal increments of momentum and velocity. This, you must understand, holds whenever all external and accidental hindrances have been removed; but of these there is one which we can never remove, namely, the medium which must be penetrated and thrust aside by the falling body. This quiet, yielding, fluid medium opposes motion through it with a resistance which is proportional to the rapidity with which the medium must give way to the passage of the body; which body, as I have said, is by nature continuously accelerated so that it meets with more and more resistance in the medium and hence a diminution in its rate of gain of speed until finally the speed reaches such a point and the resistance of the medium becomes so great that, balancing each other, they prevent any further acceleration and reduce the motion of the body to one which is uniform and which will thereafter maintain a constant value. There is, therefore, an increase in the resistance of the medium, not on account of any change in its essential properties, but on account of the change in rapidity with which it must yield and give way laterally to the passage of the falling body which is being constantly accelerated.

Now seeing how great is the resistance which the air offers to the slight momentum [momento] of the bladder and how small that which it offers to the large weight [peso] of the lead, I am convinced that, if the medium were entirely removed [i.e., in a vacuum], the advantage received by the bladder would be so great and that coming to the lead so small that their speeds would be equalized.  (pp. 118-9)

[6] Newton:


In two spheres mutually gravitating each towards the other, if the matter in places on all sides round about and equi-distant from the centres is similar, the weight of either sphere towards the other will be reciprocally as the square of the distance between their centres.  (p. 398)


The alteration of motion is ever proportional to the motive force impressed ; and is made in the direction of the right  line in which that force is impressed.  (p. 83)

[7] See Einstein’s “§21. Newton's theory as a first approximation” (Einstein and Minkowski, pp. 229-32) and also P. C. Mahalanobis:

From the conceptual stand-point there are several important consequences of the Generalized or Gravitational Theory of Relativity. Physical space-time is perceived to be intimately connected with the actual local distribution of matter. Euclid-Newtonian space-time is not the actual space-time of Physics, simply because the former completely neglects the actual presence of matter. Euclid-Newtonian continuum is merely an abstraction, while physical space-time is the actual framework which has some definite curvature due to the presence of Matter. Gravitational Theory of Relativity thus brings out clearly the fundamental distinction between actual physical space-time (which is non-isotropic and non-Euclid-Newtonian) on one hand and the abstract Euclid-Newtonian continuum (which is homogeneous, isotropic and a purely intellectual construction) on the other. (Einstein and Minkowski, pp. 30-1)

[8] See Suppes and cf. Galileo, Newton, Einstein, Keynes, and Blackford (2016a; 2016b).

[9] See Fox, Minsky, Polanyi, MacKay, Kindleberger, and Blackford (2014).

[10] Friedman:

An even more important body of evidence for the maximization-of-returns hypothesis is experience from countless applications of the hypothesis to specific problems and the repeated failure of its implications to be contradicted. This evidence is extremely hard to document; it is scattered in numerous memorandums, articles, and monographs concerned primarily with specific concrete problems rather than with submitting the hypothesis to test. Yet the continued use and acceptance of the hypothesis over a long period, and the failure of any coherent, self-consistent alternative to be developed and be widely accepted, is strong indirect testimony to its worth. The evidence for a hypothesis always consists of its repeated failure to be contradicted, continues to accumulate so long as the hypothesis is used, and by its very nature is difficult to document at all comprehensively. It tends to become part of the tradition and folklore of a science revealed in the tenacity with which hypotheses are held rather than in any textbook list of instances in which the hypothesis has failed to be contradicted. (pp. 22-3)


In seeking to make a science as "objective" as possible, our aim should be to formulate the rules explicitly in so far as possible and continually to widen the range of phenomena for which it is possible to do so. But, no matter how successful we may be in this attempt, there inevitably will remain room for judgment in applying the rules. Each occurrence has some features peculiarly its own, not covered by the explicit rules. The capacity to judge that these are or are not to be disregarded, that they should or should not affect what observable phenomena are to be identified with what entities in the model, is something that cannot be taught; it can be learned but only by experience and exposure in the "right" scientific atmosphere, not by rote. It is at this point that the "amateur" is separated from the "professional" in all sciences and that the thin line is drawn which distinguishes the "crackpot" from the scientist. (p. 25)

[11] See Amy, especially his website at, Dal Bó et. al., and Blackford ( 2013).

[12] See Keynes and Blackford (2014 Ch. 3; 2016a; 2016b).

[13] See Blackford (2014) with regard to debt in general, and specifically with regard to the distribution of income:

The idea that income must be redistributed to take advantage of an increase in productivity may seem to be unorthodox to some economists, but the need for redistribution is, in fact, implicit within the standard competitive model that lies at the core of neoclassical economics. The distribution of income is simply assumed to adjust automatically to accommodate increases in productivity in this model as the system is assumed to remain at full employment and long run economic profits are competed away. In the real world, of course, the economic system does not stay at full employment and economic profits do not necessarily get competed away. As a result, there is no reason to believe that a society that exists in the real world will be able to take full advantage of an increase in productivity irrespective of the distribution of income since the distribution of income does not necessarily adjust in the real world the way it is assumed to adjust in the competitive model.

It should, perhaps, also be noted that since this model is typically presented in terms of a system of equations derived from the optimizing behavior of a typical household and a typical firm, the distribution of income is not even considered in this model, except by way of the assumption that the amount of income the typical household receives is determined by the quantities of productive resources it owns and the prices these resources are able to command in the marketplace. As a result, the standard model gives only a partial explanation of the distribution of income.

Since income is determined by the ownership of productive resources in this model, it is implicitly assumed that the distribution of income is ultimately determined by the distribution of wealth among households. This means that to examine how the distribution of income affects the economic system we must go beyond the system of equations that are derived from the optimizing behavior of the typical household and firm and consider how the distribution of wealth can be expected to affect the preferences of the typical household and how these preferences can be expected to affect the typical firm.  (2014, fn4)


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