You summarize how ergodicity came to economics: “Samuelson said that we should accept the ergodic hypothesis because if a system is not ergodic you cannot treat it scientifically.” (See intro)
This is pretty much the same way how most other core concepts and foundational propositions came to economics as Mirowski has shown (1995).
And this eventually resulted in the neo-Walrasian axiom set with these core propositions: “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. By definition, the hard-core propositions are taken to be true and irrefutable by those who adhere to the program.” (Weintraub, 1985, p. 147)
Now it is obviously a methodological mistake to take equilibrium into the premises and then to establish and discuss the properties of general equilibrium. The same holds for ergodicity and most other foundational propositions. This mistake — known since antiquity as petitio principii* — is an age-old characteristic of incompetent scientists or savants: “These savants, as Galileo put it, first decided how the world should function in accordance with their preconceived principles. ... He openly criticized scientists and philosophers who accepted laws which conformed to their preconceived ideas as to how nature must behave. Nature did not first make men’s brains, he said, and then arrange the world so that it would be acceptable to human intellects.” (Kline, 1982, p. 48)
Now we can argue whether equilibrium, constrained optimization, rational expectations, ergodicity, well-behaved production functions, or any other nonentity is the worst petitio principii. But this itself is a methodological mistake: ‘someone has to say “stop, that’s enough”’ (See intro).
Any discussion about nonentities falls into the how-many-angels-can-dance-on-a-pinpoint category and is merely a pastime of savants and other scientific dilettantes.
The right thing to do is to throw the neo-Walrasian axiom set and all its nonentities and all textbooks from Samuelson to Rodrik without further ado out of the window and to move from microfoundations to macrofoundations. As Joan Robinson put it: “Scrap the lot and start again.”
Kline, M. (1982). Mathematics. The Loss of Certainty. Oxford, New York, NY: Oxford University Press.
Mirowski, P. (1995). More Heat than Light. Cambridge: Cambridge University Press.
Weintraub, E. R. (1985). Joan Robinson’s Critique of Equilibrium: An Appraisal. American Economic Review, Papers and Proceedings, 75(2): 146–149. URL
* Wikipedia "To beg a question means to assume the conclusion of an argument — a type of circular reasoning. This is an informal fallacy, in which an arguer includes the conclusion to be proven within a premise of the argument, often in an indirect way such that its presence within the premise is hidden or at least not easily apparent. The term "begging the question", as this is usually phrased, originated in the 16th century as a mistranslation of the Latin petitio principii, which actually translates as 'assuming the initial point'."