Hailed by the Bulletin of the American Mathematical Society as "undoubtedly a major addition to the literature of mathematical logic," this volume examines the essential topics and theorems of mathematical reasoning. No background in logic is assumed, and the examples are chosen from a variety of mathematical fields. Starting with an introduction to symbolic logic, the first eight chapters develop logic through the restricted predicate calculus. Topics include the statement calculus, the use of names, an axiomatic treatment of the statement (...) calculus, descriptions, and equality. Succeeding chapters explore abstract set theory—with examinations of class membership as well as relations and functions—cardinal and ordinal arithmetic, and the axiom of choice. An invaluable reference book for all mathematicians, this text is suitable for advanced undergraduates and graduate students. Numerous exercises make it particularly appropriate for classroom use. (shrink)

Income inequality in the US has now reached levels not seen since the 1920s. Management, as a field of scholarly inquiry, has the potential to contribute in significant ways to our understanding of recent inequality trends. We review and assess recent research, both in the management literature and in other fields. We then delineate a conceptual framework that highlights the mechanisms through which business practice may be linked to income inequality. We then outline four general areas in which management scholars (...) are uniquely positioned to contribute to ongoing research: data and description, organizational dynamics, collective action, and value flows and tradeoffs. To stimulate future research, we highlight a number of relevant research questions and link these questions to existing management research streams that could be leveraged to address them. (shrink)

A collection of essays written in the field of feminist theory, this book reflects the social consequences of biological research and the political struggles waged by socialist and radical feminists. The contributors suggest that there is a pervasive racism within the feminist movement.

The work of feminists in science may seem less voluminous and less theoretical than the feminist scholarship in some humanities and social science disciplines. However, the recent burst of scholarship on women and science allows categorization of feminist work into six distinct but related categories: 1) teaching and curriculum transformation in science, 2) history of women in science, 3) current status of women in science, 4) feminist critique of science, 5) feminine science, 6) feminist theory of science. More feminists in (...) science are needed to further explore science and its relationships to women and feminism in order to change traditional science to a feminist science. (shrink)

considerable publicity in some of the leading general science journals such as Science and Nature. While most of this research has appeared in physics journals, some has appeared in economics journals as well, more often when at least one author is an economist. Strong claims have been made by some advocates regarding its reputed superiority to economics (McCauley, 2004), with arguments that in fact the teaching of microeconomics and macroeconomics as they are currently constituted should cease and be replaced by (...) appropriate courses in mathematics, physics, and some other harder sciences. The lack of invariance principles in economics and the failure of economists to deal properly with certain empirical regularities are held against it in this line of argument, although most econophysicists do not go as far as McCauley in proposing the complete replacement of economics as such by econophysics. (shrink)

“When demand and supply are in stable equilibrium, if any accident should move the scale of production from its equilibrium position, there will be instantly brought into play forces tending to push it back to that position; just as if a stone hanging by a string is displaced from its equilibrium position… But in real life such oscillations are seldom as rhythmical as those of a stone hanging freely from a string; the comparison would be more exact if the string (...) were supposed to hang in the troubled waters of a mill-race, whose stream was at one time allowed to flow freely and at another partially cut off. Nor are these complexities sufficient to illustrate all the disturbances with which the economist and the merchant alike are forced to concern themselves. (shrink)

We examine the “new comparative economics” as proposed by Djankov et al. (2003) and their use of the concept of an institutional possibilities frontier. While we agree with their general argument that one must consider a variety of institutions and their respective social costs, including legal systems and cultural characteristics, when comparing the performance of different economic systems, we find various complications and difficulties with the framework they propose. We propose that a broader study of clusters of institutions and such (...) newly emerging forms as the new traditional economy may be better suited as ways to approach the study of comparative economics in the era after the breakdown of the old comparison of market capitalism and command socialism that came to an end with the breakup of the Soviet Union. (shrink)

Relationships are studied between the non-observed economy, income inequality, corruption, social capital measured as trust, and various institutional quality, policy, and macroeconomic variables for a global data set of countries for two time periods accounting for social interactions. Tentative support is found for positive relations between the non-observed economy and income inequality, the non-observed economy and corruption, and a negative relation between corruption and trust. No significant relation was found between the nonobserved economy and tax rates, contrasting with previous studies (...) finding significant relations of opposite signs. Data difficulties and weak robustness tests suggest limits to our results. (shrink)

James Madison University Harrisonburg, VA 22807 USA Tel: 540-568-3212 Fax: 540-568-3010 E-mail: [email protected]..

This paper presents a view of the process of transition from planned command socialism to mixed market capitalism involving nonlinear complex dynamical phenomena. After the former institutional structure disappears a coordination failure can bring about macroeconomic collapse as in almost all of the former Soviet bloc or macroeconomic boom as in China. A closely linked phenomenon is the rise of the underground economy as inflation and income inequality increase. This can lead to a jump from one equilibrium to a very (...) different one as nonlinear social feedback processes operate in the transition. (shrink)

Various complex dynamics in ecologic-economic systems are presented with an emphasis upon models of global warming dynamics and fishery dynamics. Chaotic and catastrophic dynamic patterns are shown to be possible, along with other complex dynamics arising from nonlinearities in such combined systems. Problems associated with amplified oscillations due to these nonlinear interactions in the combined interactions of human economic decisionmaking with ecological dynamics are identified and discussed. Implications for policy are examined with strong recommendations for greater emphasis in particular upon (...) the precautionary principle to avoid catastrophic collapses beyond critical thresholds and the scale-matching principle to ensure that efforts to manage complex nonlinear dynamics are directed at the appropriate levels of ecologiceconomic interaction. Key Words: complex dynamics, chaos, catastrophe, fisheries, global warming.. (shrink)

Economies making a transition from centrally planned socialism to market capitalism can experience chaotic hysteresis. This can arise from elements of the previous system persisting even as institutions are transformed with the system possibly experiencing chaos during this conflict. A model of investment cycles accompanied by technological stagnation shows this phenomenon which can be viewed from a cusp catastrophe perspective. Empirical tests of Soviet investment and construction data provide incomplete support for the cusp structure with chaos. Nonlinear structures are found (...) with bifurcation effects for all cases and possibly chaotic dynamics for five-year lagged construction data. (shrink)

Increasingly in economics what had been considered to be unusual and unacceptable has come to be considered usual and acceptable, if not necessarily desirable. Whereas it had been widely believed that economic reality could be reasonably described by sets of pairs of linear supply and demand curves intersecting in single equilibrium points to which markets easily and automatically moved, now it is understood that many markets and situations do not behave so well. Economic reality is rife with nonlinearity, discontinuity, and (...) a variety of phenomena that are not so easily predicted or understood. At the same time the broad coherence of economic systems is more impressive than ever in the face of such phenomena. The order of the economy appears to emerge from the complex interactions that constitute the evolutionary process of the economy. These phenomena have come to be labeled as complexity in economics. Even what seems simple in economics generally arises from behavior not reflecting rational expectations; we live in a world that reflects the enormous variety and diversity of humanity in their knowledge, attitudes, and behaviors, interacting with each other in an enormous range of institutional frameworks. What emerges in the aggregate may have little to do with what happens at the individual level. But this aggregate cannot be simply described by some set of aggregate equations. It emerges out of the soup of the individual and particular with all its multiform interactions and peculiarities. (shrink)

“The ‘fallacy of composition’ that drives a felicitous wedge between micro and macro, between the individual and the aggregate, and gives rise to emergent phenomena in economics, non-algorithmic ways – as conjectured originally by John Stuart Mill…, George Herbert Lewes … , and codified by Lloyd Morgan … in his popular Gifford Lectures - may yet be tamed by unconventional models of computation.” --K. Vela Velupillai (2008, p. 21).

“A ‘Public Domain,’ once a velvet carpet of rich buffalo-grass and grama, now an illimitable waste of rattlesnake-bush and tumbleweed, too impoverished to be accepted as a gift by the states within which it lies. Why? Because the ecology of the Southwest happened to be set on a hair trigger.”.

September 2008 Abstract: We consider the precursors to the discovery of sensitive dependence on initial conditions by Edward Lorenz (1963) in his model of climatic fluid dynamics. This will focus on work in various disciplines that imply either such sensitivity, irregular endogenous dynamic patterns, or fractal nature of an attractor, as is also found in the attractor underlying the model Lorenz studied. Going from ancient hints in Anaxagoras through nineteenth century mathematics and physics, the main areas of such development will (...) be argued to have been in celestial mechanics, oscillators, and economics. (shrink)

Among the most striking developments in the process of economic transition has been the very diverse paths these economies have taken with respect to income distribution, with some maintaining degrees of equality similar to the socialist era while others now exhibit degrees of inequality noticeably greater than any advanced market capitalist economies. We argue that these outcomes reflect divergent dynamics with multiple equilibria wherein the pattern of income distribution interacts with the level of corruption and the breakdown of the public (...) sector and social safety nets, with the possibility of societies going sharply in one direction or another. This argument is supported by empirical data linking income inequality and measures of the size of the unofficial economy in a set of fifteen transitional economies. (shrink)

Large increases unofficial economies in many transition economies arise from a dynamic interaction with rising income inequality and public sector changes in multiple equilibria system. Returns to unofficial activity are first increasing and then decreasing, implying two distinct stable equilibria, with changes in inequality possibly causing a jump from one to the other. Multiple regressions of data from 18 transition economies find income inequality significantly correlated with the size of the unofficial economy, with the maximum annual rate of inflation also (...) significantly correlated. The latter appears to be the only significant correlate with the increase in the size of the unofficial economy. (shrink)

“A Public Domain, once a velvet carpet of rich buffalo-grass and grama, now an illimitable waste of rattlesnake-bush and tumbleweed, too impoverished to be accepted as a gift by the states within which it lies. Why? Because the ecology of the Southwest happened to be set on a hair trigger.”.

To acquaint the student with the problems of open-economy macroeconomics. These include the theory and policy issues related to the international balance of payments, the determination of foreign exchange rates, the functioning of the macroeconomy under different exchange rate regimes, the operation of macroeconomic policy under different exchange rate regimes, and the evolution and future of the international monetary system as a whole.

This paper will focus upon the confluence of two strands of discussion and debate that have been developing for some time and their interaction and mutual implications. One involves the nature of economic complexity, how it is to be defined, what is the best way of thinking about it, both theoretically and empirically. The other is the question of the nature and relevance for economics of the recently developed sub-discipline of econophysics. Debates over both of these strands have become more (...) intensified in recent years, and this observer sees the debates as having. (shrink)

Fishery dynamics are considered within the context of an integrated ecologiceconomic, or bioeconomic, approach. The possibility of complex dynamics is examined, both of the chaotic as well as the catastrophic variety. Issues involving learning and convergence by fishers are considered. Complications arising from multi-species interactions are considered as are complications arising from the hierarchical nature of fisheries. Policy responses to these problems are seen to involve the precautionary..

This paper presents a stylized overview of the process of transition from planned command socialism to mixed market capitalism in stages, each involving nonlinear complex dynamical phenomena. The end of the command form arises out of a chaotic hysteretic long wave investment cycle. After the former institutional structure disappears a coordination failure brings about macroeconomic collapse. As recovery emerges various complex fluctuations of employment appear as government labor policies oscillate.

The most important fact about 21st century economics is that it is the post-neoclassical era in terms of the frontiers of economic research. One can still find orthodox, neoclassical theory in most textbooks, especially those at the upper undergraduate level. However, this no longer reflects the reality of how economists at the cutting edge of economics are thinking, including those who are in the mainstream of the profession. The intellectual orthodoxy of neoclassicism has died (Colander, 2000) and the current thrust (...) of research at the cutting edge of the frontier is the search for the appropriate alternative to replace it. (shrink)

James Madison University Harrisonburg, VA 22807 Tel: 540-568-3212 Fax: 540-568-3010 Email: [email protected].

Roger Koppl (2009, p. 1) argues that “Austrian economics is a school of thought within the broader complexity movement in economics.” Is he correct? While there are many who have argued for some overlapping between the two, I shall argue that this is probably an overly strong statement. The main reason is that there are substantial elements and strands within Austrian economics that do not fit in with any of the multiple varieties of complexity theory, even though there are some (...) that clearly do. While I have some disagreements with Koppl’s argument, I think that he does a good job of identifying some of the main strands of Austrian economics that are consistent with complexity thought. The most important of these are associated with the work of Friedrich A. Hayek, who.. (shrink)

A time series of the Shanghai stock index in China for the 1990s is studied for the possible existence of nonlinear speculative bubbles. Three alternative specifications of fundamentals are estimated using VAR models of domestic and international variables. These are subjected to regime switching tests and rescaled range analysis tests. Nulls of no persistence were mostly rejected, suggesting the strong possibility of bubbles. Nonlinearities beyond ARCH effects using the BDS test could not be rejected. The paper also discusses the special (...) circumstances of the stock market in an emerging transition economy. (shrink)

We present three arguments regarding the limits to rationality, prediction, and control in economics, based on Morgenstern's analysis of the Holmes-Moriarty problem. The first uses a standard metamathematical theorem on computability to indicate logical limits to forecasting the future. The second provides possible nonconvergence for Bayesian forecasting in infinite dimensional space. The third shows the impossibility of a computer perfectly forecasting an economy with agents knowing its forecasting program. Thus, economic order is partly the product of something other than calculative (...) rationality. The joint presentation of these existing results should introduce the reader to implications of these concepts for certain shared concerns of Keynes and Hayek. (shrink)

This paper examines how institutions for managing environmental resources change over time with economic development and the seriousness of environmental problems. Different problems tend to be more serious at different levels of development requiring different approaches. A major point is that traditional systems of management in poorer countries were often effective at managing common good resources, and institutions that replicate their advantages should be encouraged at higher levels of economic development as well.

This paper examines how institutions for managing environmental resources change over time with economic development and the seriousness of various environmental problems. Different problems tend to be more serious at different levels of development requiring different approaches. Traditional systems of management in poorer countries were often effective at managing common good resources, and institutions that replicate their advantages may work at higher levels of economic development as well. Problems of inter-level relations are also be considered.

Fishery dynamics are considered within the context of an integrated ecologiceconomic, or bioeconomic, approach. The possibility of complex dynamics is examined, both of the chaotic as well as the catastrophic variety. Issues involving learning and convergence by fishers are considered as are complications arising from the hierarchical nature of fisheries. Policy responses to these problems are seen to involve the precautionary principle to mitigate the threat of catastrophic discontinuities and the scalematching principle to ensure that management and property rights system (...) are properly.. (shrink)

For transition economies, income inequality is positively correlated with the share of output produced in the informal economy. Increases in income inequality also tend to be correlated with increases in the share of output produced in the unofficial economy. These hypotheses are supported significantly by empirical data for sixteen transition economies between 1987 to 1989 and 1993 to 1994. Various causal mechanisms may operate in both directions, an increasingly large informal economy causing more inequality due to falling tax revenues and (...) weakened social safety nets, and increasing inequality causing more informal activity as social solidarity and trust decline. (shrink)

Nobody has died yet as a result of the ongoing trials for transferring money internationally without a license of four Harrisonburg men from Kurdish parts of Iraq: Rashid Qambari, Ahmed Abdullah, Amir Rashid, and Fadhil Noroly. However, before coming here they were threatened because of their work for groups associated with the United States, and they were brought here by the United States government as part of Operation Pacific Haven. Saddam Hussein killed members of local Kurdish families. Qambari, convicted on (...) January 30, 2006, has stated, “If I get deported back to Iraq, I will be a nice gift to the insurgents. I will be dead.” Deportation is a possible outcome of his conviction. (shrink)

James Madison University Harrisonburg, VA 22807 USA tel: 540-568-3212 fax: 540-568-3010 email: [email protected]..

We investigate how stochastic asset price dynamics with herding and financial constraints in heterogeneous agents’ decisions explain the presence of a period of financial distress (PFD) following the peak and preceding the crash of a bubble, documented by Kindleberger [2000, Appendix B] as common among most major historical speculative bubbles. Simulations show the PFD is due to agents’ wealth distribution dynamics, selling because of financial constraints after the bubble’s peak in relation to switching behavior of agents. An increase in switching (...) tendency increases the length of the PFD and decreases bubble amplitude, while increasing strength of interaction between the agents increases bubble amplitude. (shrink)

Large increases unofficial economies in many transition economies arise from a dynamic interaction with rising income inequality and public sector changes in multiple equilibria system. Returns to unofficial activity are first increasing and then decreasing, implying two distinct stable equilibria, with changes in inequality possibly causing a jump from one to the other. Multiple regressions of data from 18 transition economies find income inequality significantly correlated with the size of the unofficial economy, with the maximum annual rate of inflation also (...) significantly correlated. The latter appears to be the only significant correlate with the increase in the size of the unofficial economy. (shrink)