A post that seems to subsume (quite rightly) Léon Walras’ place at the head of the marginalist revolution, might usefully provide his take on your theme of mathematics’ disproportional influence on economic science:
“In any case, the establishment sooner or later of economics as an exact science is no longer in our hands and need not concern us. It is already perfectly clear that economics, like astronomy and mechanics, is both an empirical and rational science. As for those economists who do not know any mathematics, who do not even know what is meant by mathematics and yet have taken the stand that mathematics cannot possibly serve to elucidate economic principles, let them go their way repeating that ‘human liberty will never allow itself to be cast into equations’ or that ‘mathematics ignores frictions which are everything in social science’ and other equally forceful and flowery phrases. They can never prevent the theory of the determination of prices under free competition from becoming a mathematical theory. Hence they will always have to face the alternative of either steering clear of this discipline and consequently elaborating a theory of applied economics without recourse to a theory of pure economics or tackling the problems of pure economics without the necessary equipment, thus producing not only very bad pure economics but also very bad mathematics.”
Léon Walras: preface to his Elements, 1877.
[Emphases are in the original.]
That said, please permit me to take issue with your assertion that . . .
“The theorems which Sonnenschein/Mantel/Debreu (SMD) produced in the 1970s completely undermined Walrasian general equilibrium by demonstrating, on its own terms, it could not reliably explain how an economy reaches a stable equilibrium point.”
Hugo Sonnenschein is more generally quoted (always without attribution) as saying that ‘the Arrow Debreu model cannot demonstrate the equilibrium that would emerge when agents make rational make rational choices in some institutional setting that in some way describes the key features of actual markets.’ (See Christian Arnsperger and Yanis Varoufakis, post-autistic economics review; Issue no. 38, 1 July 2006; article 1: “What Is Neoclassical Economics?” http://www.paecon.net/PAEReview/issue38/ArnspergerVaroufakis38.htm.)
For Sonnenschein’s own recollection of what he said, as well as where and when he said it, see file:///C:/01%20SFEcon/SFEcon%20Site/1_Discussions/12_SFEcon/125_Heterodox/1221_Declarations/Sonnenschein.png
. . . Western science operates on the principle of contradiction: if you are saying something cannot be done, and somebody does, you change your mind.
The only possible reply to Sonnenschein/Mantel/Debreu is to create an objective demonstration of optimality arriving with equilibrium under the premises of neoclassical causation. If mathematics are forbidden in the creating of such demonstrata, then you are simply refusing to engage in a scientific discussion of how economic QUANTA come to be distributed among profit-seeking agents.
A post that seems to subsume (quite rightly) Léon Walras’ place at the head of the marginalist revolution, might usefully provide his take on your theme of mathematics’ disproportional influence on economic science:
“In any case, the establishment sooner or later of economics as an exact science is no longer in our hands and need not concern us. It is already perfectly clear that economics, like astronomy and mechanics, is both an empirical and rational science. As for those economists who do not know any mathematics, who do not even know what is meant by mathematics and yet have taken the stand that mathematics cannot possibly serve to elucidate economic principles, let them go their way repeating that ‘human liberty will never allow itself to be cast into equations’ or that ‘mathematics ignores frictions which are everything in social science’ and other equally forceful and flowery phrases. They can never prevent the theory of the determination of prices under free competition from becoming a mathematical theory. Hence they will always have to face the alternative of either steering clear of this discipline and consequently elaborating a theory of applied economics without recourse to a theory of pure economics or tackling the problems of pure economics without the necessary equipment, thus producing not only very bad pure economics but also very bad mathematics.”
Léon Walras: preface to his Elements, 1877.
[Emphases are in the original.]
That said, please permit me to take issue with your assertion that . . .
“The theorems which Sonnenschein/Mantel/Debreu (SMD) produced in the 1970s completely undermined Walrasian general equilibrium by demonstrating, on its own terms, it could not reliably explain how an economy reaches a stable equilibrium point.”
Hugo Sonnenschein is more generally quoted (always without attribution) as saying that ‘the Arrow Debreu model cannot demonstrate the equilibrium that would emerge when agents make rational make rational choices in some institutional setting that in some way describes the key features of actual markets.’ (See Christian Arnsperger and Yanis Varoufakis, post-autistic economics review; Issue no. 38, 1 July 2006; article 1: “What Is Neoclassical Economics?” http://www.paecon.net/PAEReview/issue38/ArnspergerVaroufakis38.htm.)
For Sonnenschein’s own recollection of what he said, as well as where and when he said it, see file:///C:/01%20SFEcon/SFEcon%20Site/1_Discussions/12_SFEcon/125_Heterodox/1221_Declarations/Sonnenschein.png
Now: how, pray tell, does one does one DEMONSTRATE that something cannot be done? As asserted in my reply to “Learning Economics: Immature Learners” . . . https://austrianeconomics.substack.com/p/learning-economics-immature-learners?sd=pf
. . . Western science operates on the principle of contradiction: if you are saying something cannot be done, and somebody does, you change your mind.
The only possible reply to Sonnenschein/Mantel/Debreu is to create an objective demonstration of optimality arriving with equilibrium under the premises of neoclassical causation. If mathematics are forbidden in the creating of such demonstrata, then you are simply refusing to engage in a scientific discussion of how economic QUANTA come to be distributed among profit-seeking agents.