Blog-Reference and Blog-Reference
Barkley Rosser summarizes: “Regarding the Horgan piece on pluralistic math, he is not up on the deeper aspects of this, which have been around for a long time, ….” and “This actually has spilled over into economics with the group calling themselves ‘computable economists’ …, whose leader has long been Kumaraswamy Vela Velupillai. He and his followers think basic economics theorems should be proven using constructicist methods, …” and “This is certainly very esoteric theoretical stuff without obvious direct implications for current policy disputes. It is also true that even within the world of pure economic theory, it may well be that this constructivist computable program may simply lead to the theory being harder to do or prove.”
The simple fact of the matter is that science is about true/false but about 99 percent of any population are not scientists but live in the swamp between true/false where “nothing is clear and everything is possible.” (Keynes) This applies, in particular, to economists. The major approaches ― Walrasianism, Keynesianism, Marxianism, Austrianism, MMT ― are mutually contradictory, axiomatically false, materially/formally inconsistent, and ALL got the foundational concept of the subject matter ― profit ― wrong. What we actually have is the pluralism of provably false theories.
This, of course, is absolutely at odds with the very essence of science: “In order to tell the politicians and practitioners something about causes and best means, the economist needs the true theory or else he has not much more to offer than educated common sense or his personal opinion.” (Stigum)
Economists do not have the true theory to this day. Because of this, the “Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel” is plain fraud.
Economists, of course, do not admit that they are stupid or corrupt or both but simply try to redefine science: “The first distinction you draw is that the old paradigm (OPE) is anti-pluralist (as in classical physics), while the new paradigm (NPE) is pluralist (as in modern physics).” (Fullbrook)#1, #2, #3
In order to cover their scientific failure and to justify swampiness, economists love to cite stuff they do not understand like Heisenberg’s Uncertainty Principle, Gödel’s Incompleteness Theorems or the alleged pluralism of mathematics.#4
The point to grasp is that pluralism is a political principle that can be traced back to the Peace of Westphalia which ended the European wars of religion in 1648. The guiding idea is since then the peaceful coexistence of incompatible religious beliefs and the end of attempts to prove hallucinatory religious truths by victory in battle.
This laudable political principle, though, does not carry over to science where truth comes in the singular and NOT as pluralism of provably false theories. The very characteristic of science is to replace the pluralism of opinions with certain knowledge.#6 Scientific truth is well-defined: “Research is, in fact, a continuous discussion of the consistency of theories: formal consistency insofar as the discussion relates to the logical cohesion of what is asserted in joint theories; material consistency insofar as the agreement of observations with theories is concerned.” (Klant)
According to this criterion, economics is a failed science. Economists, of course, try to evade this conclusion. Since Adam Smith/Karl Marx they insist on doing science. What they have been doing, though, is political agenda-pushing in the cloak of science.
The dismal scientific fact of the “dismal science” is that economists are too stupid for the elementary algebra that underlies macroeconomics. Logical consistency, as it is embodied in the corpus of mathematics, has always been the weak point of economics.
This weakness did not escape mathematicians: “Walras approached Poincaré for his approval. ... But Poincaré was devoutly committed to applied mathematics and did not fail to notice that utility is a nonmeasurable magnitude. ... He also wondered about the premises of Walras’s mathematics: It might be reasonable, as a first approximation, to regard men as completely self-interested, but the assumption of perfect foreknowledge ‘perhaps requires a certain reserve’.” (Porter)
Later on, von Neumann started in earnest to rectify the formalism of Walrasian economics: “You know, Oskar, if those books are unearthed sometime a few hundred years hence, people will not believe they were written in our time. Rather, they will think that they are about contemporary with Newton, so primitive is their mathematics. Economics is simply still a million miles away from the state in which an advanced science is, such as physics.” (quoted in Ingrao et al.) The final result of von Neumann’s intervention was General Equilibrium Theory. Von Neumann and others rectified the mathematical formalism, however, they retained the Walrasian axioms (methodological individualism, constrained optimization, equilibrium, etcetera).#6
Moreover, GE has been established by an existence proof. The fixpoint theorem, though, does not tell the coordinates of equilibrium nor whether and how it can be reached. This is where the critique of Kumaraswamy Velupillai and the concept of computable economics kicks in. However, as the ToC of Computable Economics shows (e.g. Computable Rationality, Adaptive Behavior, Learning in a Computable Setting, etcetera), Velupillai sticks to the old Walrasian behavioral concepts. What Velupillai does NOT realize is that economics cannot be based on behavioral microfoundations.
Standard economics is false because it is based on false microeconomic axioms. Keynesian economics is false because it is based on false macroeconomic axioms. Velupillai’s shift from set theory to recursion theory is pointless because he makes the same mistake as von Neumann, i.e. he does not realize that economics is axiomatically defective. A computable equilibrium is pointless, to begin with because equilibrium is a petitio principii since Jevons/Walras/Menger.
What is straightforwardly computable in economics is, for example, profit. Curiously, the promoter of computable economics has never computed the key variable macroeconomic profit. Worse, he has not even realized that Keynesian macroeconomics is utter algebraic garbage.
Proof: “Income = value of output = consumption + investment. Saving = income − consumption. Therefore saving = investment.” (Keynes, GT, p. 63) is false. Instead of I=S, Q≡I−S holds in the most elementary case with Q as macroeconomic profit.#7, #8
The balance of the business sector, i.e. macroeconomic profit, is computable, however, the champion of computable economics failed to this day to compute the pivotal variable of all of economics. The mathematical incompetence of economists is the ultimate reason why economics is nothing more than the forever unacceptable pluralism of false theories. This, in turn, means that economic policy guidance NEVER had sound scientific foundations.#9 Computable economics has NOT rectified this lethal defect and, given scientifically incompetent promoters like Kumaraswamy Velupillai, never will.
#1 How Heterodoxy became the venue for science’s scum
#2 Failed economics: The losers’ long list of lame excuses
#3 A political stench is in the air
#4 Scientific American, Is Mathematics, like Science, Pluralistic? Mathematicians disagree over whether their fundamental assumptions, or axioms, are true
#5 “There are always many different opinions and conventions concerning any one problem or subject-matter... This shows that they are not all true. For if they conflict, then at best only one of them can be true. Thus it appears that Parmenides ... was the first to distinguish clearly between truth or reality on the one hand, and convention or conventional opinion (hearsay, plausible myth) on the other ...” (Popper)
#6 “But this [establishing the analytic mother-structure] required one very crucial maneuver that was nowhere stated explicitly: namely, that the model of Walrasian general equilibrium was the root structure from which all further work in economics would eventuate.” (Weintraub)
#7 How Keynes got macro wrong and Allais got it right
#8 Knowledge is attainable ― even in economics
#9 For details see cross-references Methodology
Related 'How economists shoot themselves non-stop in the methodological foot'
Since Sonnenschein/Mantel/Debreu it is generally known that General Equilibrium Theory = mainstream economics is a failed approach. This means (i) that economic policy guidance has NO valid scientific foundations, (ii) that economics needs a Paradigm Shift: “There is another alternative: to formulate a completely new research program and conceptual approach. As we have seen, this is often spoken of, but there is still no indication of what it might mean.” (Ingrao et al., 1990)
Obviously, there is to this very day ‘no indication of what it might mean’ to perform the indispensable Paradigm Shift.
In his formal rectification of Walrasian economics, von Neumann applied set theory. This was state-of-art with regard to mathematics but was not such a good idea with regard to economics: “Thus not all axiomatic theories need to be phrased in terms of set theory but much more conveniently and intelligibly rather in terms of some advanced mathematical structures.” (Schmiechen)
Therefore, Velupillai’s shift from set theory to recursion theory is certainly a promising move to get out of von Neumann’s set-theoretical dead end. The irony is that economists fail to this day already at the simple algebra of macroeconomic accounting.#1
The remark: “At the end of his life von Neumann eseentially sided with Velupillai in pointing to greater use of computers, …” shows that you are still deep in the woods. Computable economics is a methodological issue for economists, the greater use of computers is a practical issue for all walks of life.
Right policy depends on true theory. Because economic theory is axiomatically false, economic policy can only make matters worse.
#1 For details of the big picture see cross-references Accounting
Brouwer, Gödel, et al., and all the questions about the foundations of mathematics are irrelevant for economics. Economics needs only elementary algebra for a start. And neither Brouwer nor Gödel contested the validity of algebra. The fact of the matter is that the representative economist is too stupid for algebra.
Von Neumann’s lethal blunder was to adopt the concept of utility/preferences from Neoclassics (see The Notion of Utility, ToG, p. 15ff). For deeper methodological reasons, which have been given elsewhere, economics cannot be built upon the behavioral assumption of (cardinal/ordinal) utility maximization.
Von Neumann axiomatized game theory which is absolutely irrelevant for economics. Game theory deals with zero-sum games and “payouts” and it should be obvious to every economist that the economy is NOT a zero-sum game and that profit is NOT a “payout”. Macroeconomic profit is for 200+ years now greater than zero which tells one that von Neumann had NO idea what profit ― the foundational magnitude of economics ― is.
Neither has the applause-troll Barkley Rosser ― whose main business is the self-congratulation of failed economics, the erection of false-hero-memorials, the bestowal of fake Nobels, and the deception of the general public about the proto-scientific state of economics ― and the rest of scientifically incompetent economists. Fact is: the Profit Theory is false from Adam Smith to von Neumann to Barkley Rosser and this has NOTHING to do with constructive or intuitionist math.
Barkley Rosser claims “… but these days one cannot even get into a grad econ program without having a near perfect score on the quant GRE, at least in the US. Pretty much everybody going through econ grad school has a reasonably decent knowledge of algebra.”
EK-H claims: The representative economist is too stupid for the elementary algebra that underlies macroeconomics.
Proof: Keynes was a trained mathematician. He stated in his General Theory: “Income = value of output = consumption + investment. Saving = income − consumption. Therefore saving = investment.” (p. 63) This is provably false. The mathematically correct relationship reads Q≡I−S with Q as macroeconomic profit.
After-Keynesians who have allegedly “a reasonably decent knowledge of algebra” did NOT spot Keynes’ blunder to this day. For example, Paul Krugman still applies IS-LM.
Conclusion: Mathematically trained economists are too stupid for the elementary algebra that underlies macroeconomics. Their utter scientific incompetence notwithstanding, they are awarded “Nobels”.
Political implication: Economics is mathematically flawed to this day. Economic policy guidance NEVER had valid scientific foundations. Economists (left-center-right does NOT matter) are either stupid or corrupt or both and a hazard to their fellow citizens.
Barkley Rosser re-frames the point at issue: “Most of what he [Mark Thoma] links to are things with policy implications. But occasionally he posts oddball stuff that he thinks has some intellectual interest that is not directly policy related. This was one of those links, about ‘pluralistic math,’ something not many people know anything about.”
Nothing could be further from the truth. Mathematics, like economics long before, is now also politically weaponized. To recall, Walrasian General Equilibrium Theory claims that the market economy is a spontaneous self-optimizing stable system. Walras knew quite well that in the Age of Science he had to prove this claim. He failed, and the mathematicians von Neumann/Wald kicked off the formal rectification which ended with Arrow/Debreu/ McKenzie/Nash’s existence theorem. This theorem amounts politically to the scientific legitimization of Capitalism. Arrow/Debreu et al. were on the payroll of the Cowles Commission which is named after its founder and funder the “businessman and economist Alfred Cowles” (Wikipedia).
As it became increasingly clear that GET is proto-scientific garbage and the existence proof had been a contract job on behalf of the Oligarchy, Walrasian economics had to give up its claim to scientific truth. Strictly speaking, it had to bury itself at the Flat-Earth-Cemetery#1 but instead, it remained firmly in academic place and merely performed an orderly withdrawal. This move comes under the euphemism of Pluralism or Anything-Goes. People love Pluralism because it gives them the license to choose their subjective truth and to ignore the taxing demand for material/formal consistency that defines science for 2300+ years. Pluralism/Anything-Goes is anti-scientific but has some political merits. Economists busily produce many “truths” and the Oligarchy picks the one that fits the actual circumstances best. Thus, academic economists add some scientific legitimacy to economic policy. For their valuable propaganda services, economists are rewarded with the “Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel”. Pluralism is nothing but the methodological smoke screen of richly rewarded useful political idiots.
Remains one problem. Mathematics is binary true/false. Political creatures, though, thrive in the swampy zone of the excluded middle between true/false where “nothing is clear and everything is possible” (Keynes). Political agenda pushers try to keep everything open to interpretation and negotiation.#2 In the eyes of political agenda pushers, science/ mathematics with its insistence on consistency and proof is just a nuisance.
What Mark Thoma tells his fellow economists is NOT some oddball stuff about some remote “intellectual frisson” but that mathematics, too, is in the process of Pluralization. This is good news for all fake scientists and, contrary to the assertions of Barkley Rosser, it has enormous policy implications.
To replace the idea of scientific/mathematical truth with Pluralism is nothing else than the ultimate political corruption of science.
#1 “In economics we should strive to proceed, wherever we can, exactly according to the standards of the other, more advanced, sciences, where it is not possible, once an issue has been decided, to continue to write about it as if nothing had happened.” (Morgenstern)
#2 And the answer is NCND ― economics after 200+ years of Glomarization