Gilboa, Postlewaite, Samuelson, Schmeidler ask: “What have these axiomatizations done for us lately?” Wrong question, of course. The right question economists have to ask themselves is: what have WE done for the proper axiomatization of economics lately.
Fact is, to begin with, that economic methodologists do not understand to this day what axiomatization is all about. Lars Syll even maintains that is a kind of mental body-building: “Studying mathematics and logic is interesting and fun. It sharpens the mind.”
It is not at all a surprise, therefore, that economics is a failed science. Walrasianism, Keynesianism, Marxianism, Austrianism is mutually contradictory, axiomatically false, and materially/formally inconsistent. As a result, economic policy guidance has NO sound scientific foundations since Adam Smith/Karl Marx.
This pluralism of provably false theories is pretty strange. How could it happen that economics is still at the proto-scientific level while science has made such incredible advances? The answer is that economics had been captured from the very beginning by political agenda pushers. Agenda-pushers, though, have no truck with science except for building Potemkin facades.
Science is binary true/false and NOTHING in between. Non-science is the swamp between true and false where “nothing is clear and everything is possible” (Keynes). Vagueness/ inconclusiveness is what Popper called an immunizing stratagem because: “Another thing I must point out is that you cannot prove a vague theory wrong.” (Feynman) While scientifically this is a bad thing, politically it is a good thing.
Because economists are not scientists but swamp creatures they see to it that no analysis and no debate ever leave the swamp. This is achieved by the tried and tested method of Glomarization.#1 For example, to the central question Does a General Economic Equilibrium exists? the answer is: “We can neither confirm nor deny the existence of a General Equilibrium.” And so on with NCND for any other question.#2, #3, #4
Accordingly, if a clear-cut refutation occasionally happens it is simply filibustered away: “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)
Glomarization is the communicative modus operandi in the political sphere. Science is the exact opposite of the political swamp. Science aims at a clear-cut true/false answer with truth well-defined as material and formal consistency. The methodological tool to achieve this is the axiomatic-deductive method. As Aristotle put it 2000+ years ago: “When the premises are certain, true, and primary, and the conclusion formally follows from them, this is demonstration, and produces scientific knowledge of a thing.” This is why axiomatization is of overriding importance.
Neither orthodox nor heterodox economists know how to apply the axiomatic-deductive method correctly.#5 This is why their economic policy proposals have no sound scientific foundation. To the question What have economists ever done for their fellow citizens? the clear-cut answer is nothing but vacuous political blather.
#1 Wikipedia, Glomar response
#2 How the representative economist gets it wrong big-time
#3 Economic recommendations out of the swamp between true and false
#4 Failed economics: The losers’ long list of lame excuses
#5 For details of the big picture see cross-references Axiomatization
Related 'Clueless about money and profit' and 'Keynesianism ― the economists’ senile dementia' and 'Buridan’s ass economics' and 'Knowledge is attainable ― even in economics' and 'Failed critique of failed economics' and 'Stop knowing nothing, start knowing something' and 'The scientific self-elimination of Heterodoxy' and 'Prophets of Preemptive Vanitizations' and 'Economics as fool’s paradise' and 'A heap of proto-scientific rubbish' and 'Truth by definition? The Profit Theory is axiomatically false for 200+ years' and 'Real-World Economics: The sanctuary of stupidity and corruption' and 'The inexorable paradigm shift in economics'.