The use of mathematics in economics has been widely discussed. The philosophical discussion on what mathematics is remains unsettled on why it can be applied to the study of the real world. We propose to get back to some philosophical conceptions that lead to a language-like role for the mathematical analysis of economic phenomena and present some problems of interest that can be better examined in this light. Category theory provides the appropriate tools for these analytical approach.

Carl Menger's methodology describes reality as neatly organized, being constructed additively from strictly regular simple elements called pure types. Such a conception of the world's structure seems to invite mathematical treatment. Yet, his economics is not a mathematical one, and he even explicitly rejected mathematical approach to economics. This apparent puzzle is explained by Menger's failure to deliver in his methodological writings a realistic portrayal of what he was actually doing in his economics. His implicit ambition to (...) retain the full meaning of the natural language concepts while using them simultaneously as theoretical concepts makes his economics dependent on the general human knowledge. Because the latter is mostly non-mathematical, so has to remain the former. This makes his economics both richer as well as fuzzier as compared with mathematical economics. This seems to be the result of a deliberate decision to keep his economic theory more realistic. (shrink)

Economic methodology has been dominated by developments in the philosophy of science. This book's central thesis is that a great deal can be gained by refocusing attention on developments in the philosophy of mathematics, in particular those that took place over the course of the twentieth century. In this book the authors argue that a close examination of the major developments in the philosophy of mathematics both deepens and enriches our understanding of the formalisation of economics, while also offering (...) novel methods of critically evaluating the strengths and limitations of formalism in economics. This book represents an innovative attempt to more fully understand the complexity of the interaction between developments in the philosophy of mathematics and the process of formalisation in economics. (shrink)

Even the briefest and most superficial perusal of leading mainstream economics journals will attest to the degree that mathematical formalism has captured the economics profession. Whereas up to the early 20th century virtually all of the output of the dismal scientists was in the literary format, by the early 21st century this is not at all any longer the case. Mathematical formalism is supposed to serve economics, and yet now true economic insight has been crowded out by (...) the math. If mainstream neoclassical economics is to come back to its proper path, a far less central role for mathematical economics, statistics and econometrics will have to be fashioned. (shrink)

Making sense of economists and their world in a persuasive and entertaining style, Arjo Klamer, the author of a number of influential books including _Conversation with Economists_ and _The Consequences of Economic Rhetoric_, shows that economics is as much about how people interact as it is about the models, the mathematics, the econometrics, the theories and the ideas that come from the enormous aggregate of economics literature. Knowing and understanding economics requires both bookwork and mingling with other (...) economists. Viewing the subject as a collection of conversations, Klamer examines fundamental disagreements over the nature and purpose of the discipline, addressing how it is that a discipline that so permeates daily life is at once ‘soft’ and scientific, powerful and ignored, noble and disdained and in a reader-friendly style – without eschewing academic methodology demonstrates economics to be a living, breathing discipline rooted in the real world. Whether you are a student, academician, journalist, practising economist or interested outsider, _Speaking of Economics_ will get you interested in a conversation about economics. (shrink)

The "mathematization" of knowledge is a historically inevitable process governed by two circumstances. In the first place there is the need for the further extension of knowledge in all areas of human activity, whether it be the study of natural phenomena or the theory of taking decisions in the economic or social sphere. Marx pointed out long ago that a science reaches its highest levels only when it succeeds in making use of mathematics. The second circumstance rendering the process (...) of deepening and broadening the mathematization of knowledge not only necessary but possible lies in the constant development both of mathematics itself and of the technical means broadening the sphere of its application. (shrink)

The field of economics proves to be a matter of metaphor and storytelling - its mathematics is metaphoric and its policy-making is narrative. Economists have begun to realize this and to rethink how they speak. This volume is the result of a conference held at Wellesley College, involving both theoretical and applied economists, that explored the consequences of the rhetoric and the conversation of the field of economics.

Economics today cannot predict the likely outcome of specific events any better than it could in the time of Adam Smith. This is Alexander Rosenberg's controversial challenge to the scientific status of economics. Rosenberg explains that the defining characteristic of any science is predictive improvability--the capacity to create more precise forecasts by evaluating the success of earlier predictions--and he forcefully argues that because economics has not been able to increase its predictive power for over two centuries, it (...) is not a science. (shrink)

This research aims at establishing the impact of information and communication technologies (ICT) on e-commerce development of industrial enterprises by means of economic and mathematical modelling. The goal was achieved using the following methods: theoretical generalization, analysis and synthesis (to critically analyse the scientific approaches of scientists regarding the expediency of using mathematical models in the context of enterprises’ e-commerce development), target, comparison and grouping (to reveal innovative methodological approach to assessing ICT impact on e-commerce development of industrial enterprises), tabular, (...) analytical and integral method (for summarizing the analysis results of enterprises readiness to implement ICT, ICT use in the activities of industrial enterprises of Ukraine and the analysis of e-commerce development), mathematical modelling (to build a regression model determining impact of changes in ICT use on the market share occupied by industrial enterprises), generalization (to determine promising directions of e-commerce developing of industrial enterprises). The implementation of a comprehensive approach to understanding the importance of ICT influence on e-commerce development of industrial enterprises will ensure acceleration of the digitalization of business processes, will contribute to the speed increase of enterprises response to customer requests, and increase the market share occupied by enterprises. A new vision of directions for developing e-commerce of industrial enterprises is suggested, which are determined by the need for enterprise rebranding, the development of e-commerce tools and technologies, the importance of outsourcing service automation and promotion of subscription trade. ICT is considered as integration factor that determines prospects for e-commerce development of industrial enterprises and contributes to increasing efficiency of online business management. Research results demonstrate that the use of economic and mathematical modelling is an important tool for assessing ICT impact, and its absence can negatively affect the accuracy and validity of online business management. (shrink)

Contemporary mainstream economics cannot be seen as disconnected from philosophical concerns. On the contrary, it should be understood as a defence for a specific philosophy, namely, crude quantitative hedonism where money would measure pleasure and pain. Disguised among a great mathematical apparatus involving utility functions, supply, and demand, lies a specific hedonist philosophy that every year is lectured to thousands of economic and business students around the world. This hedonist philosophy is much less sophisticated than that in ancient hedonist (...) philosophers as Epicurus or Lucretius. Furthermore, it does not solve any of the systematic difficulties regularly faced by hedonist philosophy. However, the argument that economics is detached from philosophy works as a rhetorical artifice to protect its dominant underlying philosophy: Philosophical disputes would have to be addressed within the biased mathematical apparatus of quantitative hedonism. Economists and business students must learn to identify the underlying philosophy in mainstream economics and alternative philosophical systems. (shrink)

Economics is a culturally and politically powerful and contested discipline, and it has been that way as long as it has existed. For some commentators, economics is the "queen of the social sciences", while others view it as a "dismal science" (and both of these epithets allow for diverse interpretations; see Mäki 2002). Economics is also a discipline that deals with a dynamically complex subject matter and has a tradition of reducing this complexity by using systematic procedures (...) of simplification. Nowadays, these procedures involve for the most part building and using mathematical models (for an overview of the philosophical issues, see Morgan and Knuuttila 2011). In the dominant circles of the discipline, one is not regarded as a serious economist having a professional expert view on any given economic or social issue without having a model about it. Much of the power of the discipline and its characteristic contestations therefore involve models and modelling: the successes and failures of the dismal queen are those of modeling. The issues involved in conomic modeling have been made particularly acute once again by the financial crisis of 2008-2009 and its aftermath: the discipline of economics is among the candidates for the major blame for failure. I will first outline some thoughts about the characteristics disciplinary conventions that guide and constrain modeling in economics. I will then summarize my account of the very ideas of models and modeling. Finally, within the framework of that account, I will highlight some major issues of contestation and sketch the respective notions of potential success and failure in economic modeling with illustrations. These notions are motivated by my subscription to a (flexible and discipline-sensitive) realist philosophy of science (e.g. Mäki 2005). (shrink)

Francis Ysidro Edgeworth’s unduly neglected monograph New and Old Methods of Ethics (1877) advances a highly sophisticated and mathematized account of social well-being in the utilitarian tradition of his 19th-century contemporaries. This article illustrates how his usage of the ‘calculus of variations’ was combined with findings from empirical psychology and economic theory to construct a consequentialist axiological framework. A conclusion is drawn that Edgeworth is a methodological predecessor to several important methods, ideas, and issues that continue to be discussed in (...) contemporary social well-being studies. (shrink)

Economists have long grappled with the problem of how economic theories relate to empirical evidence: how can abstract mathematized theories be used to produce empirical claims? How are such theories applied to economic phenomena? What does it mean to "test" economic theories? This book introduces, explains, and develops a structural philosophy of economics which addresses these questions and provides a unifying philosophical/logical basis for a general methodology of economics. The book begins by introducing a rigorous view of the (...) logical foundations and structure of scientific theories based upon the work of Alfred Tarski, Patrick Suppes, Karl Marx, and others. Using and combining their methods, the book then goes on to reconstruct important economic theories - including utility theory, game theory, Marxian economics, Sraffian economic theory, and econometrics - proving all the main theorems and discussing the key claims and the empirical applicability of each theory. Through these discussions, this book presents, in a systematic fashion, a general philosophy of economics grounded in the structural view. Offering rigorous formulations of important economic theories, A Structuralist Theory of Economics will be invaluable to all readers interested in the logic, philosophy, and methodology of economics. It will also appeal particularly to those interested in economic theory. (shrink)

Unification of natural science and social science is a centuries-old, unmitigated debate. Natural science has a chronological advantage over social science because the latter took time to include many social phenomena in its fold. History of science witnessed quite a number of efforts by social scientists to fit this discipline in a rational if not mathematical framework. On the other hand a tendency among some physicists has been observed especially since the last century to recast a number of social phenomena (...) in the mould of events taking place in physical world and governed by well-known systems and equations of physics. It necessitated the introduction of social physics as a new inter-disciplinary subject. Obviously this attempt is aimed at explaining hitherto unsolved or highly debated issues of social science. Physicists are showing special interest on problems on economics, ranging from some topics of normative economics to the movement of prices of derivatives. Statistics has been widely used in these attempts and at least two sub-disciplines of the subject, namely, stochastic process and time series analysis deserve special mention. All these research activities gave birth to another inter-disciplinary subject named as econophysics. Interestingly, global financial crisis of 2007–08 has revived the need of determination of prices of derivatives in a more accurate manner. This article adumbrates a sketch of the theoretical synthesis between physics and economics and the role played by statistics in this process. (shrink)

The concept of sustainable development considers environmental, social and economic issues in general. And the goals of resource conservation and socio-economic development do not contradict each other, but contribute to mutual reinforcement. The purpose of this study is to build and test an economic and mathematical model for the formation of strategies for the behavior of an economic entity with an increase in the impact of negative environmental factors. The proposed strategies and their models are based on the income-expenditure balance (...) equation, which takes into account both quantitative and qualitative characteristics. The constructed models are considered in the state space. The research methodology is based on building models in the form of linear combinations of functions of a homogeneous external impact and various spatial combinations of economic sources (sinks). The study makes it possible to assess the dependence of the amount of resources used for life support on the chosen adaptive strategy. Within the framework of the proposed model, it was found that the criterion for the effectiveness of the applied strategy can be an indicator of satisfaction with the state, the preservation of which, simultaneously with the preservation of the size of resources used, corresponds to the direction of optimization. This approach is consistent with the concept of sustainable development. (shrink)

The paper contends that neoclassical ideology stems, to a great extent, from mathematical analysis. It is suggested that mainstream economic thought can be comprehensively revisited if both histories of mathematical and economic thought are to be taken collaboratively into account. Ideology is understood as a 'social construction of reality' that prevents us from evaluating our own standpoint, and impedes us from realising our value judgments as well as our theories of society and nature. However, the mid-19th century's intellectual controversies about (...) the validity of mathematical thought, truth and knowledge can procure new interesting insights concerning the ideological stance of the first marginalists. In this respect, the methodological categories of analysis and synthesis serve as the basis for the crucial distinction between old geometry and mathematical analysis, indicating that the discipline of mathematics has its own history of fundamentally unresolved disputes. Lastly, this may also shed some light on Alfred Marshall's peculiarly reluctant attitude towards the use of mathematical analysis in his work. (shrink)

Harold Hotelling’s articles in mathematical economics from the 1930s are classics. Some are keystones of entire sub-disciplines of economic theory such as location economics [Hotelling...

In this paper we explore the hypothesis that constrained uses of imagination are crucial to economic modeling. We propose a theoretical framework to develop this thesis through a number of specific hypotheses that we test and refine through six new, representative case studies. Our ultimate goal is to develop a philosophical account that is practice oriented and informed by empirical evidence. To do this, we deploy an abductive reasoning strategy. We start from a robust set of hypotheses and leave space (...) for the generation of further hypotheses and theoretical claims based on the qualitative analysis of new empirical data. (shrink)

This dissertation attempts to settle some challenging historiographic issues concerning the origin and development of the concept of economic equilibrium. Specifically, our research goal is to identify the philosophical and historical drivers of the mathematization of economic theory. To this end, we attempt to answer three fundamental research questions. First, why (and not how) has economics become a mathematical science? Second, what are the major methodological blunders that lie at the foundations of Modern General Equilibrium Theory? Third, is (...) the contemporary criticism of Modern General Equilibrium Theory meaningful and well-founded? In order, chapters 1-3 address the first question, chapters 4 and 5 address the second, whereas chapter 6 addresses the third question. Regarding the first question, we investigate the methodological relationships between Modern Physics, Modern Philosophy, and Walras’s Theory of General Equilibrium. Interestingly, our findings reveal that while the study of motion in Modern Physics relies upon a clear distinction between static and dynamic equilibrium, early mathematical economics borrows its methodology from Modern Physics but relies upon an Aristotelian conception of equilibrium. Furthermore, we identify exciting analogies between Kant’s philosophy and Walras’s Elements. Finally, we show that the so-called Walras Paradox also features another unexplored dimension. Namely, Walras’s work overall relies upon a bottom-up approach to mathematics. Yet Walras’s work includes problems that require a top-down approach to mathematics to be solved. Regarding the second question, we delve into the tight relationship between the History of Mathematics in the 19th Century, the Philosophy of Mathematics in the 20th Century, and the development of Modern General Equilibrium Theory in the 20th Century. Notably, we find that the top-down approach to mathematics provides economists with a reliable methodology to resolve the problems in Walras’s original work. Hence, the mathematization of General Equilibrium Theory in the 20th Century is a child of its time that carries the inapplicability of pure mathematics to real-world problems along with itself. Therefore, although the mathematization of General Equilibrium Theory is an unprecedented milestone in economic theory, the foundations of Modern General Equilibrium Theory inherit the methodological shortcomings of Contemporary Mathematics. That is why the Sonnenschein-Mantel-Debreu does not overtake the Aristotelian conception of equilibrium. Accordingly, we rebut the claim that Debreu and colleagues' mathematization of General Equilibrium Theory resolves the fundamental methodological shortcomings of Walras’s original work. Eventually, we use our answers to our first and second research questions to address the contemporary criticism of General Equilibrium Theory. On the one hand, we show that the latter criticism does not account for the fact that General Equilibrium Theory inherits the scientific realism and determinism of Modern Physics. In other words, we argue that the inability of General Equilibrium models to manage uncertainty effectively has nothing to do with its mathematization in the 20th Century. Instead, it results from the unexplored dimension of the Walras Paradox, which we uncover. On the other hand, we show that common accusations of inconsistency, incompleteness, and undecidability in General Equilibrium Theory are ill-founded. That is because other rigorous alternatives to axiomatization in economics are not paradox-free. On these grounds, we conclude that a much better option is to employ a topic-neutral language to provide rigorous presentations of contested concepts in economics. Particularly, we show that formal mereology offers a convenient methodological framework to resolve the disagreement between the Neoclassical and Institutionalist economists’ respective definitions of the concept of the market. In this way, we show that the latter concept is definable as a process. But, more importantly, we note that formal mereology also offers a convenient framework to reformulate other economic concepts concisely and rigorously. In this regard, we observe that formal mereology might provide a resolution for Hayek’s Problem because it would enable economists to define general equilibrium as a perduring socioeconomic process. -/- In case you want a copy of my dissertation, please email me. (shrink)

When President Reagan and Prime Minister Thatcher adopted the neoliberal doctrine as the paradigm of economics, there was no evidence that the move would have been successful, but thirty years on, the recurrent crises that culminated in 2008 suggest a serious mis-match between expectations and outcomes: a re-examination of the paradigm is in order. This book focuses on Milton Friedman's formulation of the neoliberal doctrine, and analyses two aspects that were essential to turning it into a fully-fledged paradigm: the (...) attribution of scientific status to positive economics, which led to informing public policies on the requirements of the market; and the characterisation of economic freedom as capable of promoting political freedom, which led to identifying free market with democracy. The book exposes Friedman's methodological argument for attributing positive economics scientific status as a failure, and his characterisation of economic freedom as a delusion; it identifies in the emergence as the mainstream in economics of the neoclassical synthesis, which borrowed from Walras' the mathematical treatment of equilibrium but not the ethical and social framework in which it was inscribed, a development that facilitated the transition from the Keynesian to the neoliberal paradigm. Dr. Mosini shows that the gigantic bail-outs carried out courtesy of the public purse, which institutionalised the practice of collectivising losses while keeping profits private, were no accident, but the consequence of the rethinking of the function of lender of last resort according to Friedman's conception of rationality in relation to risk, combined with his interpretation of the 1930s recession. The book concludes that the neoliberal paradigm has served the interests of the economically powerful social strata it was designed to benefit extremely well, but that the deep, and deepening, injustice it has brought about calls for a complete rethinking of the paradigm of economics according to ethical principles respectful of human values. This book should be of interest to students and researchers of Political Economy, Economic Methodology, History of Economic Thought and Philosophy. (shrink)

The widespread and long-lived failings of academic economics are due to an over-reliance on largely inappropriate mathematical methods of analysis. This is an assessment I have long maintained. Many heterodox economists, however, appear to hold instead that the central problem is a form of political-economic ideology. Specifically, it is widely contended in heterodox circles that the discipline goes astray just because so many economists are committed to a portrayal of the market economy as a smoothly or efficiently functioning system (...) or some such, a portrayal that, whether sincerely held or otherwise, is inconsistent with the workings of social reality. Here I critically examine the contention that a form of political-economic ideology of this sort is the primary problem and assess its explanatory power. I conclude that the contention does not fare very well. I do not, though, deny that ideology of some sort has a major impact on the output of the modern economics academy. However it is of a different nature to the form typically discussed, and works in somewhat indirect and complex ways. Having raised the question of the impact of ideology I take the opportunity to explore its play in the economics academy more generally. (shrink)

Kevin Hoover explores retroduction as a means of theorizing in macro-economics, rather than exclusive reliance on deductivism or inductivism. Retroduction is discussed as involving conceptualization with respect to empirical evidence as a means of identifying causal mechanisms as the basis for theory in the form of mathematical models. It is put forward as a preferred alternative to more fundamental reform of macro-economics, whose justification Hoover dismisses as being ‘ideological’. Yet ideology refers to a position on metaphysics such as (...) Hoover himself sets out in terms of open systems, which would significantly extend the scope for retroduction. (shrink)

The “embeddedness” of economic life in social relations has become a productive analytical principle and the basis of a penetrating critique of economic orthodoxy. But this critique raises another important, social and historical question, of how the economy became “disembedded” in the first place – how the multitude of transactions designated (somewhat arbitrarily) as economic were abstracted from the rest of social life and reconstituted as an object, the economy, which behaves according to its own logic. This article investigates the (...) social sources of some innovations in economic thought that contributed to the emergence of the economy, particularly statistical indicators and mechanical models. By examining the redefinitions of the object of economic research developed by Irving Fisher and Wesley Mitchell in the 1890s and the first decades of the twentieth century, I argue that the abstraction of the economy from the remainder of social life was a strategy linked to the position of these innovators within the field of economics, conceived as a social structure. Possessing a specialized scientific cultural capital, but lacking upper class background, contacts, and dispositions that characterized the founders of academic economics, Fisher and Mitchell elaborated new definitions of their discipline's object of study, and a new type of economic expertise. (shrink)

When reassessing the role of Debreu’s axiomatic method ineconomics, one has to explain both its success and unpopularity; onehas to explain the “bright shadow” Debreu cast on the discipline:sheltering, threatening, and difficult to pin down. Debreu himself didnot expect to have such an influence. Before he received the Bank ofSweden Prize in 1983 he had never openly engaged with themethodology or politics of mathematical economics. When in severalspeeches he later rigorously distinguished mathematical form fromeconomic content and claimed this as (...) the virtue of mathematicaleconomics, he did both: he defended mathematical reasoning againstthe theoretical innovations since the 1970s and expressed remorse forhaving promised too much because it cannot support claims abouteconomic content. The analysis of this twofold role of Debreu’saxiomatic method raises issues of the social and political responsibilityof economists over and above standard epistemic issues. (shrink)

This article attempts to account for professional historians’ relative neglect of the history of economic life over the past thirty years, looking mainly at the American case. This neglect seems paradoxical, considering the remarkable transformations that have taken place in world capitalism during this same period. I trace the neglect to the capture of the once interdisciplinary field of economic history by mathematically inclined economists and to the roughly simultaneous turn of historians from social to cultural history. I conclude by (...) suggesting some topics in the history of economic life that seem both timely and exciting. I also suggest some intellectual resources that other disciplines, particularly economic sociology and economic history, could offer should historians decide to tackle the history of economic life once again. (shrink)

This is the classic work upon which modern-day game theory is based. What began as a modest proposal that a mathematician and an economist write a short paper together blossomed, when Princeton University Press published Theory of Games and Economic Behavior. In it, John von Neumann and Oskar Morgenstern conceived a groundbreaking mathematical theory of economic and social organization, based on a theory of games of strategy. Not only would this revolutionize economics, but the entirely new field of scientific (...) inquiry it yielded--game theory--has since been widely used to analyze a host of real-world phenomena from arms races to optimal policy choices of presidential candidates, from vaccination policy to major league baseball salary negotiations. And it is today established throughout both the social sciences and a wide range of other sciences. (shrink)

The goal of the article is to substantiate that despite the criticism the paradigm in economics will not change because of the axiomatic assumptions of value-free economics. How these assumptions work is demonstrated on the example of Gary Becker’s economic approach which is analyzed from the perspective of scientific research programme. The author indicates hard core of economic approach and the protective belt which makes hard core immune from any criticism. This immunity leads economists to believe that they (...) are objective scientists and, consequently, it results in epistemological hubris. Due to its tautological nature, economic approach is considered to be a degenerative programme. This conclusion is extended on value-free economics. In spite of these problems, many economists still believe in positive economics and they dismiss normative approaches. It has a negative influence on people. The conclusion of the article is that thanks to axiomatic assumptions economists do not have objective and ironclad methodology and they should accept normative values in their research. (shrink)

This paper supports the literature which argues that derivational robustness can have epistemic import in highly idealized economic models. The defense is based on a particular example from mathematical economic theory, the dynamic Walrasian general equilibrium model. It is argued that derivational robustness first increased and later decreased the credibility of the Walrasian model. The example demonstrates that derivational robustness correctly describes the practices of a particular group of influential economic theorists and provides support for the arguments of philosophers who (...) have offered a general epistemic justification of such practices. (shrink)

Achille Nicolas Isnard an engineer with a keen interest in political economy, is best known for demonstrating the concept of market equilibrium using a system of simultaneous equations. The breadth and depth of his work undoubtedly established him as one of the forerunners of modern mathematical economics, yet his seminal contributions to the study of economics remained largely unrecognized until the latter half of the twentieth century. This pioneering new book, the first in English, examines Isnard’s life and (...) illuminates his major contributions to political economy. It contains substantial extracts from a number of his publications presented both in English translation and in the original French so Isnard can now finally achieve his place at the heart of discussion on the origins of mathematical economics. The diverse issues covered here will ensure that this book appeals not only to economists with an interest in the history of mathematical economics, but to anyone interested in the emergence of political economy and in wider social thought during the Enlightenment. (shrink)

In the spirit of Von Neumann and Morgenstern (Theory of games and economic behavior, Princeton University Press, Princeton, 1944), we introduce a notion of network stability. We study the structure of stable economic networks and their associated stable payoff allocations by analyzing the conditions under which complete networks and star networks (both with desirable property of inclusiveness) are stable. We also address conditions for existence and uniqueness of stable set of networks.

ABSTRACTThis paper offers a re-interpretation of the development of practical mathematics in Elizabethan England, placing artisanal know-how and the materials of the discipline at the heart of analysis, and bringing attention to Tudor economic policy by way of historical context. A major new source for the early instrument trade is presented: a manuscript volume of Chancery Court documents c.1565–c.1603, containing details of a patent granting a monopoly on making and selling mathematical instruments, circa 1575, to an unnamed individual, identified here (...) as the instrument maker Humphrey Cole. Drawing on economic and legal history, the paper argues that practical mathematics needs to be understood as one ‘project’ among many, at a time when monopoly patents were used to advance industry, lower unemployment, secure the realm and reward invention. Drawing on the history and sociology of technology, it argues that the management and control of materials – mathematical instruments themselves, and the local socio-legal context within which they could be made – needs to be understood as prior to and separate from the rhetoric of mathematical authors, which is of interest in its own right but which may not have a direct relationship to mathematical practice. (shrink)

This book provides a systematic exposition of mathematical economics, presenting and surveying existing theories and showing ways in which they can be extended. One of its strongest features is that it emphasises the unifying structure of economic theory in such a way as to provide the reader with the technical tools and methodological approaches necessary for undertaking original research. The author offers explanations and discussion at an accessible and intuitive level providing illustrative examples. He begins the work at an (...) elementary level and progessively takes the reader to the frontier of current research. This second edition brings the reader fully up to date with recent research in the field. (shrink)

Kumaraswamy Vela Velupillai [74] presents a constructivist perspective on the foundations of mathematical economics, praising the views of Feynman in developing path integrals and Dirac in developing the delta function. He sees their approach as consistent with the Bishop constructive mathematics and considers its view on the Bolzano-Weierstrass, Hahn-Banach, and intermediate value theorems, and then the implications of these arguments for such “crown jewels” of mathematical economics as the existence of general equilibrium and the second welfare theorem. He (...) also relates these ideas to the weakening of certain assumptions to allow for more general results as shown by Rosser [51] in his extension of Gödel’s incompleteness theorem in his opening section. This paper considers these arguments in reverse order, moving from the matters of economics applications to the broader issue of constructivist mathematics, concluding by considering the views of Rosser on these matters, drawing both on his writings and on personal conversations with him. (shrink)

E. Roy Weintraub’s How Economics Became a Mathematical Science (2002) presents a original, distinctive, and provocative perspective on the evolution of mathematical economics from the late nineteenth century to the late twentieth century. Its originality and distinctiveness and provocativeness extends as well to its view of the relationship between mathematics and economics. He reveals many little known facts and punctures many fallacious, if widespread ideas. At the same time, he ultimately leaves us hanging on certain crucial points (...) with an ambivalence that is never resolved. However, he is careful not to claim too much for his work: it is not the definitive history of mathematical economics nor does it claim to provide ultimate answers. (shrink)

A survey was carried out among two groups of undergraduate economics students and four groups of students in mathematics, law, philosophy and business administration. The main survey question involved a conflict between profit maximisation and the welfare of the workers who would be fired to achieve it. Significant differences were found between the choices of the groups. The results were reinforced by a survey conducted among readers of an Israeli business newspaper and PhD students of Harvard. It is argued (...) that the overly mathematical methods used to teach economics encourage students to lean towards profit maximisation. (shrink)

It can not be our purpose to give here a complete account of the phenomenological history of mathematical doctrine. It will be enough to refer to the battle of opinions in mathematical theory which was waged within the last eighty-five years, since Riemann's inaugural lecture on Non-Euclidean Geometry. Furthermore, the revolution which Einstein's theory of general relativity created is indicative of the complete absence of any general awareness that mathematics as a science has any relation to social reality. If we (...) are going to establish such relations, we are conscious of the fact that they would be hotly contended by many mathematicians. (shrink)

In economics there are several complex learning themes and tasks connected with them difficult for deeper understanding of the learning subject. These are the reasons originating serious learning problems for students in the form of Virtual Environment because deeper understanding requires high level mathematical skills. Actually the most important feature for discerning this part of economics is the set of qualitative shapes emerging in discrete dynamic systems when they are undergoing iterations and/or experimentation with parameters and initial coordinates (...) of variables. Among such shapes there are: - trajectories in evolving time; - trajectories in R2 of two variables; - cobweb portraits; - one control parameter bifurcation with first and/or with second variables; - two control parameters bifurcation in R2 ; - cycles; - basin of attraction of two variables; - one Lyapunov’s exponent against some of control parameters; - Lyapunov’s exponents with two control parameters in R2; - absorbing area with possibility to create critical curves and/or attractors. The hope is that products of computational intelligence may help them solve such problems. Naturally, the meant complex economic problems and tasks have discrete, qualitative and nonlinear nature resulting in increased level of difficulties. So with the term used in the head of this paper one has to understand narrowly: “qualitative nonlinear computational economics”. For better understanding the very nature of the problem we are using as appropriate example actual simulation of the model of new ICT products monopolies in virtual laboratory built in the routines setting dominantly in the software iDMC. (shrink)

The city of Kruja (Albania)contains three types of dwellings that date back to different periods of time: the historic ones, the socialist ones, the modern ones. This paper has to deal only with the historic building's typology. The questionnaire that is applied will be considered for the development of mathematical regression based on specific data for this category. Variation between the relevant variables of the questionnaire is fairly or inverse-linked with a certain percentage of influence. The aim of this study (...) is to have better insights into the important role of building occupancy, people's lifestyle, economic level, and the quality of life of the residents in the inner medieval citadel, the physics characteristics, and the energy efficiency of the historical dwellings. The variables such as the number of residents, quality of life, the surface of the dwellings, heating instruments and time spent in the dwelling, current living conditions, monthly bills, level of satisfaction, restoration, and building improvements, interact with each other with probabilities with different positive or negative percentages. (shrink)

Most papers in theoretical economics contain thought experiments. They take the form of more informal bits of reasoning that precede the presentation of the formal, mathematical models these papers are known for. These thought experiments differ from the formal models in various ways. In particular, they do not invoke the same idealized assumptions about the rationality, knowledge, and preferences of agents. The presence of thought experiments in papers that present formal models, and the fact that they differ from the (...) formal models in this way, is often ignored in debates on what, if anything, we can learn from formal models in theoretical economics. I show that paying due attention to thought experiments in theoretical economics has serious implications for this debate. Differences between thought experiments and formal models are especially problematic for Robert Sugden’s “credible worlds” account. (shrink)

The purpose of the study is to determine the concept of the axial line of the swarm of the global economy in the three-dimensional space of the economic indices EPI, BLI, CPI and to construct mathematical expressions that determine the shape of this line based on statistical data on the world economy. To construct the axial line the median points of the EPI-groups of the global economy were used. In the paper we discuss certain assumptions about the asymptotic behavior of (...) the axial line at small and large values of the CPI. Scientific novelty of research lies in the explicit construction of the axial line of the global economy. The existence and shape of this line reveal as a result some fundamental trend in the world economy, statistically linking at the level of EPI-groups the state of society, the measure of the state's social orientation and economic productivity. (shrink)

Thorstein Veblen once considered his work on instincts to be his only important contribution to economic theory. Instincts are the conditions and causes behind the formation of habits of thought, while the latter are the sine qua non elements of institutions. The article poses the question: If Veblenʼs relation instincts-habits of thought-institutions were to be thought of as a formal system, what role would they conceptually occupy? It interprets habits of thought as pure ideas in a Platonist fashion (eidos)—multiplicities thought (...) as Ideas—conceived by Georg Cantorʼs theory of manifolds and philosophically assessed by Alain Badiou positing that “mathematics is ontology.” The article aims: (1) to show how habits of thought, as institutions, abstracted from all content can be thought of as set-theoretic multiplicities; (2) to relate Veblenʼs prime instinct, the instinct of workmanship, in equivalence with set theory’s axiom of the empty set—pointing towards Veblenʼs materialist orientation. (shrink)

This textbook for postgraduate students learning mathematical methods in economics provides a comprehensive account of mathematics required to analyse and solve problems of choice encountered by economists. It looks at a wide variety of decision-making problems, both static and dynamic, in various contexts and provides mathematical foundations for the relevant economic theory.

Different applications of synthetic biology are alike in that their possible negative consequences are highly uncertain, potentially catastrophic, and perhaps irreversible; therefore, they are also alike in that public attitudes about them are fertile ground for behavioral economic phenomena. Findings from behavioral economics suggest that people may not respond to such applications according to the normal rules of economic evaluation, by which the value of an outcome is multiplied by the mathematical probability that the outcome will occur. Possibly, then, (...) synthetic biology applications challenge the normative postulates of the standard approach, too.I want to first consider how some of the phenomena described by behavioral economists—and behavioral scientists more broadly—might affect people's perceptions of the uncertainties associated with synthetic biology. My analysis will be far from complete, however, because behavioral economics is essentially the study of human behavior, and thus its reach is potentially vast and its development longstanding and ongoing. Nonetheless, I hope to give an indicative perspective on how some aspects of behavioral economics might affect the assessment and perceived acceptability of synthetic biology. I will then consider the issue of agency. Should policy‐makers respect people's reactions to synthetic biology when those reactions are known to be driven by behavioral economic phenomena rather than following the normative postulates of rational choice theory? Or should policy‐makers dismiss these reactions as inherently biased? I will argue that the normative force of these human reactions (probably) depends on phenomenon and context. (shrink)

Dramatic changes or revolutions in a field of science are often made by outsiders or 'trespassers,' who are not limited by the established, 'expert' approaches. Each essay in this diverse collection shows the fruits of intellectual trespassing and poaching among fields such as economics, Kantian ethics, Platonic philosophy, category theory, double-entry accounting, arbitrage, algebraic logic, series-parallel duality, and financial arithmetic.