Open Access Journal Article

The gap between formalism and empirical science: the example of the non-dictatorship condition

by W. Robert J. Alexander a,* orcid
a
School of Business and Creative Industries, University of the Sunshine Coast, Sippy Downs, Australia
*
Author to whom correspondence should be addressed.
EAL  2023, 39; 2(4), 39; https://doi.org/10.58567/eal02040005
Received: 12 June 2023 / Accepted: 18 July 2023 / Published Online: 7 August 2023
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Abstract

Since the establishment of neoclassical economics in the nineteenth century, there has been a debate in the economics profession over the role played by mathematics. Mathematics can add precision to discussion of real-world empirical problems in economics, but care needs to be taken when formalizing a problem to ensure that errors of translation are not made. Formalism allows one to be sure that a chain of reasoning is correct but applying conclusions back to an empirical science problem is fraught if an error of translation has been made. We illustrate such a difficulty in the context of Arrow’s impossibility theorem, specifically the mistranslation of the non-dictatorship condition. The notion of dictatorship entails causality, but causality does not correspond to the usage of the implication sign in mathematics or logic. We use the rules of logic to illustrate that the way that dictatorship is rendered mathematically in the impossibility theorem makes the existence of a dictator (or dictators) not only reasonable but likely.

Keywords: Formalist theory; empirical science; mathematization of economics; impossibility theorem; social welfare function;
Copyright: © 2023 by J. Alexander. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) (Creative Commons Attribution 4.0 International License). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

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ACS Style
J. Alexander, W. R. The gap between formalism and empirical science: the example of the non-dictatorship condition. Economic Analysis Letters, 2023, 2, 39. https://doi.org/10.58567/eal02040005
AMA Style
J. Alexander W R. The gap between formalism and empirical science: the example of the non-dictatorship condition. Economic Analysis Letters; 2023, 2(4):39. https://doi.org/10.58567/eal02040005
Chicago/Turabian Style
J. Alexander, W. R. 2023. "The gap between formalism and empirical science: the example of the non-dictatorship condition" Economic Analysis Letters 2, no.4:39. https://doi.org/10.58567/eal02040005
APA style
J. Alexander, W. R. (2023). The gap between formalism and empirical science: the example of the non-dictatorship condition. Economic Analysis Letters, 2(4), 39. https://doi.org/10.58567/eal02040005

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