Blog-Reference and Blog-Reference on Apr 8 adapted to context
The inevitable failure of economics started with Jevons/Walras/Menger but Arrow gave the final push with this fundamental methodological specification: “It is a touchstone of accepted economics that all explanations must run in terms of the actions and reactions of individuals. Our behavior in judging economic research, in peer review of papers and research, and in promotions, includes the criterion that in principle the behavior we explain and the policies we propose are explicable in terms of individuals, not of other social categories.” (Arrow, 1994)
The definition of the subject matter translates into the following hardcore propositions, a.k.a. axioms: “HC1 economic agents have preferences over outcomes; HC2 agents individually optimize subject to constraints; HC3 agent choice is manifest in interrelated markets; HC4 agents have full relevant knowledge; HC5 observable outcomes are coordinated, and must be discussed with reference to equilibrium states.” (Weintraub, 1985)
Obviously, this axiom set contains THREE NONENTITIES: (i) constrained optimization (HC2), (ii) rational expectations (HC4), (iii) equilibrium (HC5). Every theory/model that contains a nonentity is A PRIORI false. By consequence, General Equilibrium Theory of the Arrow-Debreu type and its offspring until DSGE/RBC/New Keynesianism is scientifically worthless.
Related 'Where economics went wrong' and 'Economics is NOT a misunderstanding but cargo cultic crap' and 'Modern macro moronism' and 'There is no scientific elite in economics' and 'Note on Lars Syll on Axiomatization' and 'Economists ― medics or barber-surgeons?' and cross-references Axiomatization and cross-references Paradigm shift
You say: “You appear to be unaware of the great John Stuart Mill’s wisdom about the nature of axioms.”
What John Stuart Mill said about methodology is this: “In the definition which we have attempted to frame of the science of Political Economy, we have characterized it as essentially an abstract science, and its method as the method à priori.”
The foundational question for the application of what today is called the axiomatic-deductive method is what the axioms are: “What are the propositions which may reasonably be received without proof? That there must be some such propositions all are agreed, since there cannot be an infinite series of proof, a chain suspended from nothing. But to determine what these propositions are, is the opus magnum of the more recondite mental philosophy.” (Mill)
It was pretty obvious to Mill that the axiomatic-deductive method is NOT a formal exercise that is detached from reality, just the contrary: “The ground of confidence in any concrete deductive science is not the à priori reasoning itself, but the accordance between its results and those of observation à posteriori.”
Mill’s understanding of methodology is IDENTICAL with that of modern physics: “He [Dirac] identified three revolutions in modern physics ― relativity, quantum mechanics, and cosmology ― and hinted that he expected them one day to be understood within a unified framework. Although he did not mention John Stuart Mill, Dirac was seeking to answer the same question posed in A System of Logic: ‘What are the fewest general propositions from which all the uniformities existing in nature could be deduced?’” (Farmelo)
The inexcusable scientific blunder of Arrow consists in messing up the axiomatic foundations of economics. More precisely, methodological individualism and the neo-Walrasian axiom set HC1/HC5 (above) are one of the greatest embarrassments in the history of the sciences.#1
Only scientific imbeciles like the representative economist accept green cheese behavioral assumptions like constrained optimization, rational expectations, and equilibrium as axiomatic foundations of economics.#2 General Equilibrium Theory is what Feynman called cargo cult science and Arrow was a fake scientist. All this follows from the methodological wisdom of the great John Stuart Mill.
#1 For details see ‘Economics is NOT a misunderstanding but cargo cultic crap’ and ‘Where economics went wrong’
#2 See ‘If it isn’t macro-axiomatized, it isn’t economics’
To put equilibrium (HC5) into the premises/axioms is a methodological blunder that is known since antiquity as petitio principii.#1
Your argument: “Zero-sum is … one of the truest axioms in nature. Thus economics must be zero-sum.” is beside the point because zero-sum and equilibrium are two entirely different things.#2
To be axiomatically false is the death sentence for a paradigm. Therefore it holds: (i) because of material/formal inconsistency General Equilibrium Theory can never be admitted to the corpus of science; GET is cargo cult science, (ii) Arrow can never be admitted to the scientific community, (iii) because the representative economist does not understand what science is all about he has not realized (i)/(ii) until this very day.
GET and its acceptance by economists is one of the greatest embarrassments in the history of science.
#1 For details see here.
#2 The zero-sum law says Qm+Sm=0, see here.