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)

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)

The present yearbook (which is the fourth in the series) is subtitled Trends & Cycles. It is devoted to cyclical and trend dynamics in society and nature; special attention is paid to economic and demographic aspects, in particular to the mathematical modeling of the Malthusian and post-Malthusian traps' dynamics. An increasingly important role is played by new directions in historical research that study long-term dynamic processes and quantitative changes. This kind of history can hardly develop without the application (...) of mathematical methods. There is a tendency to study history as a system of various processes, within which one can detect waves and cycles of different lengths – from a few years to several centuries, or even millennia. The contributions to this yearbook present a qualitative and quantitative analysis of global historical, political, economic and demographic processes, as well as their mathematical models. This issue of the yearbook consists of three main sections: (I) Long-Term Trends in Nature and Society; (II) Cyclical Processes in Pre-industrial Societies; (III) Contemporary History and Processes. We hope that this issue of the yearbook will be interesting and useful both for historians and mathematicians, as well as for all those dealing with various social and natural sciences. (shrink)

A more and more important role is played by new directions in historical research that study long-term dynamic processes and quantitative changes. This kind of history can hardly develop without the application of mathematical methods. The history is studied more and more as a system of various processes, within which one can detect waves and cycles of different lengths – from a few years to several centuries, or even millennia. This issue is the third collective monograph in (...) the series of History & Mathematics almanacs and it is subtitled Processes and Models of Global Dynamics. The contributions to the almanac present a qualitative and quantitative analysis of global historical, political, economic and demographic processes, as well as their mathematical models. This issue of the almanac consists of two main sections: (I) Analyses of the World Systems and Global Processes, and (II) Models of Economic and Demographic Processes. We hope that this issue of the almanac will be interesting and useful both for historians and mathematicians, as well as for all those dealing with various social and natural sciences. (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)

Scientists and engineers seek to understand how real-world systems work and could work better. Any modeling method devised for such purposes must simplify reality. Ideally, however, the modeling method should be flexible as well as logically rigorous; it should permit model simplifications to be appropriately tailored for the specific purpose at hand. Flexibility and logical rigor have been the two key goals motivating the development of Agent-based Computational Economics (ACE), a completely agent-based modeling method characterized by seven specific modeling principles. (...) This perspective provides an overview of ACE, a brief history of its development, and its role within a broader spectrum of experiment-based modeling methods. (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)

In recent academic and to some extent public debates, mainstream economics has been accused of excessive mathematization. The rejection of mathematical and other formal methods is often cited as a crucial trait of Austrian economics. Based on a systematic discussion of potential benefits and potential drawbacks of formalization in economics, the paper concludes that - contrary to the received view - the most prominent representatives of Austrian economists including Carl Menger, Ludwig Mises, and Friedrich August Hayek neither provide a (...) justification for a rejection of formalization tout court nor actually reject it. Those Neo- Austrians who do, seem to rely on an unconvincing Sprachgeist argument traceable to Friedrich Wieser. (shrink)

Economics is a science - at least positive economics must be. And science is in part applied mathematics, in part empirical observations and tests. Looking at the history of economics, one cannot find much testing done before the twentieth century, and even the collection of data, even in the manner Marx engaged in, was not common in his day. It is true that economic policy is an older field, and in that field much information is deployed for the purpose (...) of prescribing a course of action. But this is not to say that the information procured for that purpose is either based on observation or has been tested. In the seventeenth century some alchemists and economists hoped to boost the economy by manufacturing gold, others feared inflation; and the British Parliament legislated against manufacturing gold. David Hume proved in the eighteenth century - quite a priori - that doubling the quantity of gold will only double the price of each commodity and he thus set things at rest for a while. Later the question was opened again when Marx, for example, showed historically how the gold robbed from the Americas started Europe's boom. Yet the theory - the quantity theory of money, as it is called - which Hume proved a priori, is still contested and still hardly tested to economists' satisfaction: is the price level fixed mainly by the amount of available money? Some economists answer yes, others no. (shrink)

a Mathematicians, like Proust and everyone else, are at their best when writing about their first lovea (TM) a ] They are among the very best we have; and their best is very good indeed. a ] One approaches this book with high hopes. Happily, one is not disappointed. a ]In paperback it might well have become a best seller. a ]read it. From The Mathematical Intelligencer Mathematics is shaped by the consistent concerns and styles of powerful minds a (...) three of which are represented here. Kaca (TM)s work is marked by deep commitment and breadth of inquiry. Rota is the easiest of these authors to reada ]a delight: witty and urbane, with a clear and interesting agenda and an astonishing intellectual range. To read him is to be a part of a pleasant and rewarding conversation. Jacob T. Schwartz attacks problems ina ]computer science, mathematical economics, computer and instructional a ] No matter how slippery the problem, Schwartz manages to capture a substantial chunk of it in his mathematical net. a Mathematics Magazine This is a volume of essays and reviews that delightfully explore mathematics in all its moods a from the light and the witty, and humorous to serious, rational, and cerebral. Topics include: logic, combinatorics, statistics, economics, artificial intelligence, computer science, and applications of mathematics broadly. You will also find history and philosophy covered, including discussion of the work of Ulam, Kant, Heidegger among others. (shrink)

Mathematics is everywhere and yet its objects are nowhere. There may be five apples on the table but the number five itself is not to be found in, on, beside or anywhere near the apples. So if not in space and time, where are numbers and other mathematical objects such as perfect circles and functions? And how do we humans discover facts about them, be it Pythagoras’ Theorem or Fermat’s Last Theorem? The metaphysical question of what numbers are and (...) the epistemological question of how we know about them are central to the philosophy of mathematics. These and related philosophical questions are of particular interest because of mathematics’ unusual status. Mathematics is exceptional in that, on the one hand, it appears unhesitatingly true—no one doubts that 2 + 3 = 5—but on the other, as just noted, it is not about the physical world. This ambivalent status is what gives the philosophy of mathematics its special interest. The philosophy of mathematics is also one of the oldest academic fields, more or less coeval with philosophy itself. But contemporary philosophy of mathematics is rather different from its pre-twentieth-century antecedents, largely for three reasons. The first is that since the seventeenth century, mathematics has become integral to science. Science has over the past few centuries become increasingly mathematical, and indeed the fundamental science of nature, physics, is today recognised as a branch of applied mathematics. The second is that mathematics underwent a transformation in the course of nineteenth century: having started the century as a rather traditional-looking science of quantity it emerged a hundred years later a radically transformed abstract theory of structure. The final factor in the transformation of the philosophy of mathematics is the rise of modern logic. Developed by Frege, Cantor and others in the late nineteenth century, modern logic pervades contemporary mathematics, philosophy and computer science, and has had an immeasurable effect on the philosophy of mathematics. These volumes will collect the major works in this major field, with a focus on the last few decades. The anthology will include technical work, which interprets philosophically significant mathematical results or subfields of mathematics, as well as purely philosophical writing, aimed at those without advanced mathematics. The collection should be of interest to both philosophers and mathematicians, as well as to anyone who is susceptible to wondering what the main intellectual tool used in science, economics and finance, and indeed everyday life is ultimately about. (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)

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)

The economics of search is a prominent component of economic theory, and it has a richness and elegance that underpins a host of practical applications. In this book Brian and John McCall present a comprehensive overview of the economic theory of search, from the classical model of job search formulated 40 years ago to the recent developments in equilibrium models of search. The book gives decision-theoretic foundations to seemingly slippery issues in labour market theory, estimation theory and economic dynamics in (...) general, and surveys the entire field of the economics of search, including its history, theory, and econometric applications. Theoretical models of the economics of search are covered as well as estimation methods used in search theory and topics covered include job search, turnover, unemployment, liquidity, house selling, real options and auctions. The mathematical methods used in search theory such as dynamic programming are reviewed as well as structural estimation methods and econometric methods for duration models. The authors also explore the classic sequential search model and its extensions in addition to recent advances in equilibrium search theory. (shrink)

Summary In terms of control of composition, the fabrication of money was arguably the most demanding of all pre-Industrial Revolution metallurgical practices. The calculations involved in such control needed arithmetical computations involving repeated multiplications and divisions, not only of integers but also of mixed numbers. Such computations were possible using Roman numerals, but with some difficulties. The advantages gained by employing arithmetic using Indo-arabic numerals for alloying calculations would have been the same as for other types of commercial calculations. A (...) method of calculating the proportions of two coinage alloys of different compositions that were needed to produce a third alloy of specified intermediate composition, eventually known as the rule of alternate alligation, was however a specific requirement in the minting of money. This requirement made a particular demand on medieval mathematics, as a solution was not possible using arithmetic alone. Furthermore, the problem became indeterminate when more than two components were available for mixing. All the necessary methods of calculation were described by Fibonacci in his Liber abbaci. These methods are to be found in a sequence of practical arithmetics that stretch through the trattati d'abbaco of the Italian city states during the fourteenth and fifteenth centuries, to the first printed books of Continental authors such as Pacioli. Of the earliest sixteenth-century printed English books on practical arithmetic, The Grounde of Artes by Robert Recorde contained the first advance in the methodology of alternate alligation since Fibonacci. In the seventeenth century, formal proof of the rule of alternate alligation was given by Kersey in his practical arithmetics and in his treatise on algebra. The topic was also addressed by several authors of academic algebras. It was in this century that the problem of indeterminacy in the solution of alternate alligation involving the mixture of more than two components, was finally resolved. English mint accounts provide little direct information on the alloying calculation carried out, and nothing on the methods used. However, the continued description of such calculations in other mint documents, merchants notebooks, and in goldsmiths' handbooks spanning four centuries imply that the calculations described in practical arithmetics were used in practice. Monetary matters had high economic and political profiles during the whole of the time span covered in this study. The influence of such considerations pervades the history of the technology of minting and the mathematics on which it called, and is discussed in context. (shrink)

Economics has developed into one of the most specialised social sciences. Yet at the same time, it shares its subject matter with other social sciences and humanities and its method of analysis has developed in close correspondence with the natural and life sciences. This book offers an up to date assessment of economics in relation to other disciplines. -/- This edited collection explores fields as diverse as mathematics, physics, biology, medicine, sociology, architecture, and literature, drawing from selected contributions to the (...) 2005 Annual Conference of the European Society for the History of Economic Thought (ESHET). There is currently much discussion at the leading edges of modern economics about openness to other disciplines, such as psychology and sociology. But what we see here is that economics has drawn on (as well as contributed to) other disciplines throughout its history. In this sense, in spite of the increasing specialisation within all disciplines, economics has always been an open discipline and the chapters in this volume provide a vivid illustration for this. -/- Open Economics is a testament to the intellectual vibrancy of historical research in economics. It presents the reader with a historical introduction to the disciplinary context of economics that is the first of its kind, and will appeal to practising economists and students of the discipline alike, as well as to anybody interested in economics and its position in the scientific and social scientific landscape. -/- Table of Contents -/- Introduction: Economics in relation to other disciplines Richard Arena, Sheila Dow and Matthias Klaes Part I. Economics in relation to the humanities and social sciences 1. The social science of economics Brian J. Loasby 2. Economics and literature Bruna Ingrao 3. Happiness: what Kahneman could have learnt from Pietro Verri Pier Luigi Porta Part II. Economics in relation to the life and natural sciences 4. Newtonian physics, experimental moral philosophy and the shaping of political economy Sergio Cremaschi 5. Evolutionary biology and economic behaviour: re-visiting Veblen's instinct of workmanship Mark Harrison 6. Medicine and economics in pre-classical economics Alain Clément and Ludovic Desmedt Part III. Economics and mathematics 7. Mathematics as the role model for neoclassical economics Nicola Giocoli 8. The role of econometric method in economic analysis: A reassessment of the Keynes-Tinbergen debate, 1938-43 Giovanna Garrone and Roberto Marchionatti IV. Economics and architecture 9. Economics and architecture Maurice Lagueux 10. Economic policies and urban development in Latin America Michele Alacevich and Andrea Costa V. Economics and geography 11. ‘Space’ in economic thought Giovanna Vertova 12. Economics, geography and colonialism in the writings of William Petty Hugh Goodacre Part VI. Economics and sociology 13. Economics and sociology: Gustav Schmoller and Werner Sombart on social differentiation Joachim Zweynert 14. Is Homo Oeconomicus a 'bad guy'? Isabelle This Saint-Jean -/- . (shrink)

Today, economic theory is a mathematical theory, but that was not always the case. Major changes in the ways economists presented their arguments to one another occurred between the late 1930s and the early 1950s; over that period the discipline became mathematized. Professor Weintraub, a noted scholar of the modern history of economic thought, argues that those changes were not merely cosmetic: The mathematical forms of the arguments significantly altered the substance of the arguments. Stabilizing Dynamics is (...) particularly concerned with the ways in which the rich and confusing talk of the 1930s evolved, over a fifteen-year period, into technical analysis of some mathematical structures. The author describes the context for the history of that change, locating it in the broader intellectual currents, and shows how the history of modern economics can be seen as a confluence of several disparate traditions. Historiographically, this book offers one of the first constructivist accounts of modern economic analysis. (shrink)

In Beyond Positivism, Behaviorism, and Neoinstitutionalism in Economics, Deirdre Nansen McCloskey zeroes in on the authoritarian cast of recent economics, arguing for a re-focusing on the liberated human. The behaviorist positivism fashionable in the field since the 1930s treats people from the outside. It yielded in Williamson and North a manipulative neoinstitutionalism. McCloskey argues that institutions as causes are mainly temporary and intermediate, not ultimate. They are human-made, depending on words, myth, ethics, ideology, history, identity, professionalism, gossip, movies, what (...) your mother taught you. Humans create conversations as they go, in the economy as in the rest of life. In engaging and erudite prose, McCloskey exhibits in detail the scientific failures of neoinstitutionalism. She proposes a "humanomics," an economics with the humans left in. Humanomics keeps theory, quantification, experiment, mathematics, econometrics, though insisting on more true rigor than is usual. It adds what can be learned about the economy from history, philosophy, literature, and all the sciences of humans. McCloskey reaffirms the durability of "market-tested innovation" against the imagined imperfections to be corrected by a perfect government. With her trademark zeal and incisive wit, she rebuilds the foundations of economics. (shrink)

The article presents a verbal and mathematical model of medium-term business cycles (with a characteristic period of 7–11 years) known as Juglar cycles. The model takes into account a number of approaches to the analysis of such cycles; in the meantime it also takes into account some of the authors' own generalizations and additions that are important for understanding the internal logic of the cycle, its variability and its peculiarities in the present-time conditions. The authors argue that the most (...) important cause of cyclical crises stems from strong structural disproportions that develop during economic booms. These are not only disproportions between different economic sectors, but also disproportions between different societal subsystems; at present these are also disproportions within the World System as a whole. The proposed model of business cycle is based on its subdivision into four phases: – recovery phase (which could be subdivided into the start sub-phase and the acceleration sub-phase); – upswing/prosperity/expansion phase (which could be subdivided into the growth sub-phase and the boom/overheating sub-phase); – recession phase (within which one may single out the crash/bust/acute crisis subphase and the downswing sub-phase); – depression/stagnation phase (which we could subdivide into the stabilization subphase and the breakthrough sub-phase). The article provides a detailed qualitative description of macroeconomic dynamics at all the phases; it specifies driving forces of cyclical dynamics and the causes of transition from one phase to another (including psychological causes); a special attention is paid to the turning point from the peak of overheating to the acute crisis, as well as to the turning point from the downswing to recovery. The proposed mathematical model of Juglar cycle takes into account the following effects that are typical for the market economy: • positive feedbacks between various economic processes; • presence of a certain inertia, time lags in reactions of the economic subsystem to the change in conditions; • amplification by the financial subsystem of positive feedbacks and time lags in the economic subsystem; • excessive reaction to changing conditions during the acute crisis sub-phase. The authors suggest that the current crisis turns out to be rather similar to classical Juglar crises; however, there is also a significant difference, as the current crisis occurs at a truly global scale. Yet, due to this truly global scale of the current crisis, the possibilities of regulation with the national state's measures have turned out to be ineffective,whereas the suprastate regulation of financial processes hardly exists. It is shown that all these have led to the reproduction of the current crisis according to a classical Juglar scenario. (shrink)

ArgumentIn the decades following World War II, the Cowles Commission for Research in Economics came to represent new technical standards that informed most advances in economic theory. The public emergence of this community was manifest at a conference held in June 1949 titledActivity Analysis of Production and Allocation. New ideas in optimization theory, linked to linear programming, developed from the conference's papers. The authors’ history of this event situates the Cowles Commission among the institutions of postwar science in-between National (...) Laboratories and the supreme discipline of Cold War academia, mathematics. Although the conference created the conditions under which economics, as a discipline, would transform itself, the participants themselves had little concern for the intellectual battles that had defined prewar university economics departments. The authors argue that the conference signaled the birth of a new intellectual culture in economic science based on shared scientific norms and techniques un-interrogated by conflicting notions of the meaning of either science or economics. (shrink)

Eleventh-century Europe was dominated by a single political and economic elite with position based on control of the means of coercion; by the end of the fifteenth. century there were various elites with power based on control of some form of production. Theories based on trade, population, and the class struggle have been advanced to account for this change but are inadequate because they posit causal relationships running from some single independent factor. A different form of explanation emphasizes the network (...) of relationships among economic and political units. Here economic power is crucial. The development of new technology shifted the economic leverage of the nobility to the mer chants, then to town craftsmen, with detailed effects on all other economic relationships. The argument is primarily theoretical, not a reconstruction of events, and a mathematical model is provided. (shrink)

Every price is set by someone; this is where economics begins. Building on that fundamental idea and on Ayn Rand's philosophy of Objectivism, Objective Economics transforms economics. The thesis of this book is that Ayn Rand's concept of "objective" is the indispensible base of valid economic thought. Consistently applying this idea across the board, the author reaches a general theory of price for the first time in the history of economic thought. This theory of price then provides a valid (...) base for explaining how a free economy functions. Based on facts everyone knows, presented without graphs or higher mathematics, Objective Economics makes accessible to the intelligent layman a clear understanding of how the economy works. For everyone who found college economics impenetrable--and that is just about everyone--this is the book.The thesis of Objective Economics changes everything about economics, including economics' method, the conception of the economy, the meaning of competition, the idea of price, the nature of business costs, the concept of supply, the concept of demand, the law of supply and demand, the theory of price, and the theory of total national output. Overall, as the result of all the preceding, Objective Economics demonstrates that capitalism is the practical economic system. (shrink)

Over the years, mathematics and statistics have become increasingly important in the social sciences1 . A look at history quickly confirms this claim. At the beginning of the 20th century most theories in the social sciences were formulated in qualitative terms while quantitative methods did not play a substantial role in their formulation and establishment. Moreover, many practitioners considered mathematical methods to be inappropriate and simply unsuited to foster our understanding of the social domain. Notably, the famous Methodenstreit (...) also concerned the role of mathematics in the social sciences. Here, mathematics was considered to be the method of the natural sciences from which the social sciences had to be separated during the period of maturation of these disciplines. All this changed by the end of the century. By then, mathematical, and especially statistical, methods were standardly used, and their value in the social sciences became relatively uncontested. The use of mathematical and statistical methods is now ubiquitous: Almost all social sciences rely on statistical methods to analyze data and form hypotheses, and almost all of them use (to a greater or lesser extent) a range of mathematical methods to help us understand the social world. Additional indication for the increasing importance of mathematical and statistical methods in the social sciences is the formation of new subdisciplines, and the establishment of specialized journals and societies. Indeed, subdisciplines such as Mathematical Psychology and Mathematical Sociology emerged, and corresponding journals such as The Journal of Mathematical Psychology (since 1964), The Journal of Mathematical Sociology (since 1976), Mathematical Social Sciences (since 1980) as well as the online journals Journal of Artificial Societies and Social Simulation (since 1998) and Mathematical Anthropology and Cultural Theory (since 2000) were established. What is more, societies such as the Society for Mathematical Psychology (since 1976) and the Mathematical Sociology Section of the American Sociological Association (since 1996) were founded. Similar developments can be observed in other countries. The mathematization of economics set in somewhat earlier (Vazquez 1995; Weintraub 2002). However, the use of mathematical methods in economics started booming only in the second half of the last century (Debreu 1991). Contemporary economics is dominated by the mathematical approach, although a certain style of doing economics became more and more under attack in the last decade or so. Recent developments in behavioral economics and experimental economics can also be understood as a reaction against the dominance (and limitations) of an overly mathematical approach to economics. There are similar debates in other social sciences. It is, however, important to stress that problems of one method (such as axiomatization or the use of set theory) can hardly be taken as a sign of bankruptcy of mathematical methods in the social sciences tout court. This chapter surveys mathematical and statistical methods used in the social sciences and discusses some of the philosophical questions they raise. It is divided into two parts. Sections 1 and 2 are devoted to mathematical methods, and Sections 3 to 7 to statistical methods. As several other chapters in this handbook provide detailed accounts of various mathematical methods, our remarks about the latter will be rather short and general. Statistical methods, on the other hand, will be discussed in-depth. (shrink)

Leveraging, according to David M. Anderson and his colleagues, is both a basic principle of human conduct and the most dominant strategy in recent years that individuals, organizations and countries use to pursue their ends. Although many scholars agree that a crisis of "over-leveraging" caused the financial crisis of 2008-2010, it has not been appreciated that an "over-leveraging" crisis has existed in American politics and the American family system as well. This book addresses the need for a "Leverage Mean" (falling (...) between the extremes of too much leverage and too little leverage) in the economy, politics, family life, and international relations. It identifies three different kinds of leveraging-bargaining, resource, and investment and provides an explanatory and normative theory which draws on the fields of economics, political science, sociology, history, psychology, international relations, law, and philosophy. Moreover, it shows how the dissolution of the Cold War, the dismantling of the modern family, and the rise of the Internet along with the deregulation of the financial services industry led to the diffusion of power which has made leveraging of the first importance for everyone. This book should be of interest to social scientists, philosophers, political theorists, public policy makers and politicians. David Anderson and his colleagues are the first to characterize and assess one of the major instruments of power of the contemporary era. This volume represents the best work on leverage since Archimedes and will be widely read and discussed. Benjamin Ginsberg, David Bernstein Professor of Political Science and Chair, Center for Advanced Governmental Studies, Johns Hopkins University Leverage might literally be the operative word of the 21st century. Anderson's volume is a wide-ranging and illuminating study of this fundamental and dynamic concept. Parag Khanna, Senior Fellow, New Amer ica Foundation, author of The Second World: How Emerging Powers Are Redefining Global Competition in the Twenty-first Century. (shrink)

Over Plato's Academy in ancient Athens, it is said, hung a sign: "Let no one ignorant of geometry enter here." Plato thought no one could do philosophy without also doing mathematics. In The Waltz of Reason, mathematician and philosopher Karl Sigmund shows us why. Charting an epic story spanning millennia and continents, Sigmund shows that philosophy and mathematics are inextricably intertwined, mutual partners in a reeling search for truth. Beginning with-appropriately enough-geometry, Sigmund explores the power and beauty of numbers and (...) logic, and then shows how those ideas laid the ground work for everything from the theory of a fair election, to modern conceptions of governance, cooperation, morality, and even of reason itself. Did you know, for example, that John Locke, author of some of the most important texts in the Western theory of government, was motivated in his work by his study of geometry? Or, that Locke was actually terrible at geometry, a seventeenth-century mathematical laughingstock? He was, a fact that might want us to think again about the logic of his life's work. And Locke wasn't the only one! Sigmund reveals how many of our modern ideas about what is true and what is reasonable are based on similarly shaky grounds. The economists and other thinkers who promulgated game theory, classical economics, and behavioral economics-the basis of so much in modern life-were not necessarily good at either math or philosophy, or both. The result is a remarkable book: accessible, funny, and wise, it tells an engrossing history of ideas that spins as dizzyingly and beautifully as a ballroom full of expert dancers. But it doesn't just celebrate the past. Instead, by making all these great ideas accessible to all, The Waltz of Reason empowers as it entertains, giving each of us the tools to ask, what do we know, how do we know it, and what do we want to do, with all these ideas? (shrink)

This paper elaborates the hypothesis that the unique demography and sociology of Ashkenazim in medieval Europe selected for intelligence. Ashkenazi literacy, economic specialization, and closure to inward gene flow led to a social environment in which there was high fitness payoff to intelligence, specifically verbal and mathematical intelligence but not spatial ability. As with any regime of strong directional selection on a quantitative trait, genetic variants that were otherwise fitness reducing rose in frequency. In particular we propose that the (...) well-known clusters of Ashkenazi genetic diseases, the sphingolipid cluster and the DNA repair cluster in particular, increase intelligence in heterozygotes. Other Ashkenazi disorders are known to increase intelligence. Although these disorders have been attributed to a bottleneck in Ashkenazi history and consequent genetic drift, there is no evidence of any bottleneck. Gene frequencies at a large number of autosomal loci show that if there was a bottleneck then subsequent gene flow from Europeans must have been very large, obliterating the effects of any bottleneck. The clustering of the disorders in only a few pathways and the presence at elevated frequency of more than one deleterious allele at many of them could not have been produced by drift. Instead these are signatures of strong and recent natural selection. (shrink)

Augustin Cournot (1801-1877) a marqué l'histoire de la pensée économique en introduisant la modélisation des phénomènes économiques, et non leur seule quantification. Ce constat appelle une double question : 1° Comment la rupture opérée par Cournot s'inscrit-elle dans l'histoire et l'évolution des méthodes de l'économie? La question se pose d'autant plus que les Recherches sur les principes mathématiques de la théorie des richesses passèrent d'abord presque inaperçues. 2° Que reste-t-il aujourd'hui de ce tournant effectué par le «philosophe-géomètre»? Autrement dit, comment (...) penser l'actualité de l'œuvre économique de Cournot? Or, avant d'être un économiste, Cournot est d'abord mathématicien et philosophe. Comment son œuvre économique s'accorde-t-elle alors avec son activité de mathématicien, et comment prend-elle place dans sa réflexion philosophique, c'est-à-dire à la fois dans sa théorie de la connaissance et dans sa philosophie de l'action et de la décision? Comprendre la portée de l'œuvre économique de Cournot et sa place dans son œuvre multiforme, tel est le projet qui anime le présent ouvrage où économistes, philosophes, historiens des sciences et sociologue entrecroisent leurs approches de celui qui demeure l'un des économistes et des philosophes majeurs du XIXe siècle."--Page 4 of cover. (shrink)

Edgeworth's original mathematical formalization of utilitarianism as presented in his works of 1877–81 illustrates an intriguing phase in the mutually intertwined history of economics and utilitarianism. In this article I analyse Edgeworth's motivations and point to its interesting implications. In particular, it is pointed out that the starting point of Edgeworth's project had little to do with the field of economics, but formed part of an attempt to present utilitarianism in the most scientific way possible; an attempt made (...) in the context of intensive dispute between the three opposing camps in the field of ethics at the time. Nevertheless, the project concluded with the monograph Mathematical Psychics (1881) that embodied an original relationship between economics and utilitarianism. (shrink)

The book contains thirty original articles dealing with important aspects of theoretical as well as applied economic theory. While the principal focus is on: the computational and algorithmic nature of economic dynamics; individual as well as collective decision process and rational behavior, some contributions emphasize also the importance of classical recursion theory and constructive mathematics for dynamical systems, business cycles theories, growth theories, and others are in the area of history of thought, methodology and behavioural economics. The contributors range (...) from Nobel Laureates to the promising new generation of innovative thinkers. This volume is also a Festschrift in honour of Professor Kumaraswamy Vela Velupillai, the founder of Computable Economics, a growing field of research where important results stemming from classical recursion theory and constructive mathematics are applied to economic theory. The aim and hope is to provide new tools for economic modelling. This book will be of particular appeal to postgraduate students and scholars in one or more of the following fields: computable economics, business cycles, macroeconomics, growth theories, methodology, behavioural economics, financial economics, experimental and agent based economics. It might be also of importance to those interested on the general theme of algorithmic foundations for social sciences. (shrink)

This book argues that we can only understand transformations of nature studies in the Scientific Revolution if we take seriously the interaction between practitioners and scholars. These are not in opposition, however. Theory and practice are end points on a continuum, with some participants interested only in the practical, others only in the theoretical, and most in the murky intellectual and material world in between. It is this borderland where influence, appropriation, and collaboration have the potential to lead to new (...) methods, new subjects of enquiry, and new social structures of natural philosophy and science. The case for connection between theory and practice can be most persuasively drawn in the area of mathematics, which is the focus of this book. Practical mathematics was a growing field in early modern Europe and these essays are organised into three parts which contribute to the debate about the role of mathematical practice in the Scientific Revolution. First, they demonstrate the variability of the identity of practical mathematicians, and of the practices involved in their activities in early modern Europe. Second, readers are invited to consider what practical mathematics looked like and that although practical mathematical knowledge was transmitted and circulated in a wide variety of ways, participants were able to recognize them all as practical mathematics. Third, the authors show how differences and nuances in practical mathematics typically depended on the different contexts in which it was practiced: social, cultural, political, and economic particularities matter. Historians of science, especially those interested in the Scientific Revolution period and the history of mathematics will find this book and its ground-breaking approach of particular interest. (shrink)

A newly emerged field within economics, known as geographical economics claims to have provided a unified approach to the study of spatial agglomerations at different spatial scales by showing how these can be traced back to the same basic economic mechanisms. We analyze this contemporary episode of explanatory unification in relation to major philosophical accounts of unification. In particular, we examine the role of argument patterns in unifying derivations, the role of ontological convictions and mathematical structures in shaping unification, (...) the distinction between derivational and ontological unification, the issue of how explanation and unification relate and finally the idea that unification comes in degrees. (shrink)

This article expands Michel Foucault's genealogy of liberalism and neoliberalism by analysing the concept of competition. It addresses four key liberal conceptions of competition in turn: the idea of competition as a destructive but progressive and thus necessary force (roughly 1830–90); economic theories of market equilibrium that theorize competition mathematically (1870 onwards); socio-biological ideas of competition as something natural (1850–1900); and sociological arguments that see competition as adding value to the social (1900–20). From this starting point, the article considers the (...) ways in which three main trajectories of neoliberal thought that emerged from the early 1920s onwards – Austrian, German and American – developed and responded to these conceptualizations of competition. In conclusion, it is argued that this history of the concept of competition leads to a new understanding of the tensions that lie at the heart of neoliberal thought, and which are largely missing from Foucault's account. (shrink)

More Heat Than Light is a history of how physics has drawn some inspiration from economics and also how economics has sought to emulate physics, especially with regard to the theory of value. It traces the development of the energy concept in Western physics and its subsequent effect upon the invention and promulgation of neoclassical economics. Any discussion of the standing of economics as a science must include the historical symbiosis between the two disciplines. Starting with the philosopher Emile (...) Meyerson's discussion of the relationship between notions of invariance and causality in the history of science, the book surveys the history of conservation principles in the Western discussion of motion. Recourse to the metaphors of the economy are frequent in physics, and the concepts of value, motion, and body reinforced each other throughout the development of both disciplines, especially with regard to practices of mathematical formalisation. However, in economics subsequent misuse of conservation principles led to serious blunders in the mathematical formalisation of economic theory. The book attempts to provide the reader with sufficient background in the history of physics in order to appreciate its theses. The discussion is technically detailed and complex, and familiarity with calculus is required. (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)

In terms of control of composition, the fabrication of money was arguably the most demanding of all pre-Industrial Revolution metallurgical practices. The calculations involved in such control needed arithmetical computations involving repeated multiplications and divisions, not only of integers but also of mixed numbers. Such computations were possible using Roman numerals, but with some difficulties. The advantages gained by employing arithmetic using Indo-arabic numerals for alloying calculations would have been the same as for other types of commercial calculations. A method (...) of calculating the proportions of two coinage alloys of different compositions that were needed to produce a third alloy of specified intermediate composition, eventually known as the rule of alternate alligation, was however, a specific requirement in the minting of money. This requirement made a particular demand on medieval mathematics, as a solution was not possible using arithmetic alone. Furthermore, the problem became indeterminate when more than two components were available for mixing. All the necessary methods of calculation were described by Fibonacci in his Liber abbaci. These methods are to be found in a sequence of practical arithmetics that stretch through the trattati d'abbaco of the Italian city states during the fourteenth and fifteenth centuries, to the first printed books of Continental authors such as Pacioli. Of the earliest sixteenth-century printed English books on practical arithmetic, The Grounde of Artes by Robert Recorde contained the first advance in the methodology of alternate alligation since Fibonacci. In the seventeenth century, formal proof of the rule of alternate alligation was given by Kersey in his practical arithmetics and his treatise on algebra. The topic was also addressed by several authors of academic algebras. It was in this century that the problem of indeterminacy in the solution of alternate alligation involving the mixture of more than two components, was finally resolved. English mint accounts provide little direct information on the alloying calculations carried out, and nothing on the methods used. However, the continued description of such calculations in other mint documents, merchants notebooks, and in goldsmiths' handbooks spanning four centuries imply that the calculations described in practical arithmetics were used in practice. Monetary matters had high economic and political profiles during the whole of the time span covered in this study. The influence of such considerations pervades the history of the technology of minting and the mathematics on which it called, and is discussed in context. (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)

During his long and continuing scholarly career, Patrick Suppes contributed significantly both to the sciences and to their philosophies. The volume consists of papers by an international group of Suppes colleagues, collaborators, and students in many of the areas of his expertise, building on or adding to his insights. Michael Friedman offers an overview of Suppes accomplishments and of his unique perspective on the relation between science and philosophy. Paul Humphreys, Stephen Hartmann, and Tom Ryckman present essays in the philosophy (...) of physics. Jens-Erik Fenstad, Harvey Friedman, and Jaako Hintikka consider problems in the foundations of mathematics, while the late Duncan Luce, Jean-Claude Falmagne, Brian Skyrms, and Hannes Leitgeb have contributed essays in theory of measurement, decision theory and probability. Foundations of economics and political theory are addressed by Adolfo Garcia de la Sienra, Russell Hardin, and Kenneth Arrow. Psychology, language, and philosophy of language are addressed by Elizabeth Loftus, Anne Fagot-Largeault, Willem Levelt, Dagfinn Follesdal, and Marcos Perreau-Guimares and some of Suppes most recent research in neurobiology is addressed in essays by Colleen Crangle, Acadio de Barros and Claudio Carvalhes. Finally Nancy Cartwright and Alexandre Marcelles consider the alignment (or misalignment) of method and policy. Each of the essays is accompanied by a response from Suppes.". (shrink)

This article portrays unification of physics as a central tenet of ErnstMach’s thought, and organizes some of the focal issues in philosophy of science around the process of unification of science. Mach finds a natural place in the history. Newton’s Principia marked the beginning of the era of mathematical physics, which developed triumphantly in the eighteenth century, until new phenomena were discovered in the nineteenth century whose explanations went over and above Newtonian physics. Also Positivism emerged in the (...) nineteenth century. This was the setting where Mach entered. The notion that a central function of physics is to give mathematical descriptions of perceptions is all over Mach’s work, but in Mach’s thought mathematics comes together with hypothetical laws of nature and an overall world-view, similarly as in Newtonian physics where mathematics comes together with the laws of motion. Mach’s criticism of Newtonian absolute time and space was in line with positivism, and his suggestions about an overall holistic worldview were to function as an intuitive background for the new physics. Thus, as a physicist and a philosopher of physics, Mach should be seen primarily as a unifier, and his famous anti-metaphysics should be seen as derivative from this unificationist project: he did not intend to banish the metaphysical core that he himself proposed, but only metaphysics that is not needed in unified science. (shrink)

In Bettering Humanomics: A New and Old Approach to Economic Science, Deirdre Nansen McCloskey offers a critique of contemporary economics and a proposal for a better humanomics. McCloskey argues for an economic science that accepts the models and mathematics, the statistics and experiments of the current orthodoxy, but also attests to the immense amount we can still learn about human nature and the economy. From observing human actions in social contexts, to the various understandings attained by studying history, philosophy, (...) and literature, McCloskey presents the myriad ways in which we think about life and how we justify and understand our actions in a synergistically human approach towards economic theory and practice. (shrink)

This major work of reference is an indispensable resource for anyone conducting research or teaching in philosophy. An international team of over 100 leading scholars has been brought together under the general editorship of Alan Schrift and the volume editors to provide authoritative analyses of the continental tradition of philosophy from Kant to the present day. Divided, chronologically, into eight volumes, "The History of Continental Philosophy" is designed to be accessible to a wide range of readers, from the scholar (...) looking for original insight and the latest thinking to the student wishing for a masterly encapsulation of a particular thinker's views. By placing continental philosophy within a historical context, "The History of Continental Philosophy" helps define what the continental tradition has been and where it is moving. It will become a landmark publication in its field. Volume 1 covers the period from 1780 until 1848, focusing primarily on the main philosophical figures and developments in Germany during that period, but also including a description of economic and social theories in France that set the stage for the philosophical and social movements that predominated in Germany and France during the second half of the nineteenth century. Volume 2 examines what is often referred to as the 'Age of Revolution' as various responses to Hegel, while also attending to developments in science, mathematics, sociology and aesthetics during the second half of the nineteenth century that would set the stage for the twentieth century. Volume 3 examines the earliest developments in the twentieth century: while attending to a number of key thinkers, it also discusses the emergence of French sociology in the Durkheim school, developments in modern science, the philosophical response to evolution, and the schools of phenomenology and neo-Kantianism. Volume 4, as the title indicates, charts the various responses to phenomenology that appeared in the years following Husserl, with particular attention to the emergence of existentialism and existential theology, as well as its relations with philosophy of science, aesthetics and ethics. Volume 5 surveys some of the main continental movements and philosophers associated with social and political philosophy and philosophy of the human sciences during the period from 1940 through to 1968. Volume 6 looks at the major figures associated with the two dominant movements that emerge in the 1960s - poststructuralism and critical theory - while also attending to the emergence of philosophical feminism and some influential figures in those years not easily situated in the "standard" histories of the period. Volume 7 examines the developments in Continental philosophy in the years, roughly, 1980-95, the period immediately after the hegemony of poststructuralism in France and of Habermas in Germany. Volume 8 attempts to situate the present scene in continental philosophy in terms of various new developments that are framed as attempts to rethink some of the classic themes with which the history of continental philosophy has been more or less consistently engaged. (shrink)

In chapter 3, we reflected on the view that the fallacies on the traditional list are inherently dialectical. The answer proposed there was that, with the possible exception of, e.g., begging the question and many questions, they are not. The aim of the present chapter is to cancel theispossibility by showing that begging the question and many questions are not in fact dialectical fallacies. The reason for this is not that question-begging and many questions aren’t (at least dominantly) dialectical practices. (...) The reason is that, dialectical or not, they are not fallacies. That begging the question, BQ for short, is a fallacy is an idea which originates with Aristotle. Given logic’s already long history, it should not be surprising that Aristotle’s views of these matters have in some ways been superseded. But the traditional view retains the original connection between conception and instantiation. Whereas BQ in Aristotle’s sense is said to be a fallacy in Aristotle’s sense, so too is BQ in the modern sense said to be a fallacy in the modern (i.e., EAUI) sense.[1] As currently conceived of, BQ and fallacies can be characterized in the following ways. (shrink)

This paper traces missing links in the history of economic thought. In outlining Hume's concept of 'the reflexive mind' it shows that this opened frontiers between philosophy and psychology which Bertrand Russell denied and which logical positivism in philosophy and positive economics displaced. It relates this to Hume's influence not only on Smith, but also on Schopenhauer and the later Wittgenstein, with parallels in Gestalt psychology and recent findings from neural research and cognitive psychology. It critiques Kant's reaction to (...) Hume's claim that one may assume but cannot prove cause and effect and how Samuelson's Foundations of Economic Analysis has been Kantian but wrong in claims for axioms that are universal truths. It illustrates how Samuelson's presumption that language and mathematics are 'identical' was as mistaken as the logical atomism of Russell and the early Wittgenstein, relates this to Kleinian splitting, denial and projective identification and suggests that recovery of greater realism in economics needs to regain links with such philosophy and psychology. (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)

Quantitative assessments of when infectious disease outbreaks end are crucial, as resources targeted towards outbreak responses typically remain in place until outbreaks are declared over. Recent improvements and innovations in mathematical approaches for determining when outbreaks end provide public health authorities with more confidence when making end-of-outbreak declarations. Although quantitative analyses of outbreaks have a long history, more complex mathematical and statistical methodologies for analysing outbreak data were developed early in the 20th century and continue to be (...) refined. Historically, such methodologies focused primarily on factors affecting the early and middle phases of an outbreak, with less attention given to determining how and when outbreaks end. This review discusses mathematical modelling methods from the last 20 years that have been developed for determining the ends of infectious disease outbreaks, and considers factors that affect the accuracy of such determinations. When disease surveillance systems provide timely and representative data to inform models, the timings of end-of-outbreak declarations can be fine-tuned to allow outbreaks to be declared over quickly and with a low risk of being incorrect. Premature declarations that outbreaks are over can undermine earlier achievements in disease control and may result in a resurgence of cases, but unnecessary delays in declaring outbreaks over can cause significant economic and social harm. Appropriate declarations that balance the benefits of relaxing control measures against the risk of a surge in cases allow public health resources to be conserved (and economic and social pressures to be reduced) while limiting the potential for additional transmission. (shrink)

This paper shows that William Stanley Jevons was not precursor of logical positivism despite his attempt to build up a unified science. His mechanical reductionism was directed towards this project, and Jevons tried to found mathematics on logic through the development of a theory of number. We show that his attempts were unsuccessful, and that his errors remain visible within the totality of his mechanical system, including his economics. We argue that both his logic and his economics are comprehensible only (...) when interpreted in terms of extent of meaning, and that Jevons? system gives rise to difficulties when interpreted in terms of intent of meaning. We argue that Jevons? methodological recommendations were intended to bridge the gap between extent and intent of meaning. Although Jevons did not succeed in establishing a unified science, his flawed methodology resulted in one of the first applications of statistics to the social sciences. (shrink)

ABSTRACT This paper examines the evolution of Michael Polanyi’s critique of economic planning. It portrays how the focal point of his critique shifted from addressing the ‘spirit,’ ‘social consciousness,’ and ‘public emotion’ of the people supporting planned economies to addressing the administrative ‘unmanageability’ and the logical impossibility of economic planning. Polanyi developed thought experiments of imaginary economies, contrasted the ‘pyramid of authority’ with the polygons of liberty, and explained organic and inorganic ways of adjusting economic relations. He attempted to relax (...) the Leviathan of Soviet economics, and drew the conclusion that mathematics is not sufficient in itself to properly address the economy. Eventually, Polanyi developed an institutionalist approach in order to be able to address both the variability of market economies and the failures of socialist ‘super-planners’ who claimed to eliminate the drift of individual economic adjustments. (shrink)