Project

A New Logic for Complexity

Goal: Complexity and associated theories have brought about new understandings of change, growth, development, transformation, evolution... These new understandings, in turn, are prompting a rethinking of Aristotelian logic, dialectical logic, and the more recent inconsistency/paraconsistency logics (or dialetheism).

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Jeffrey Goldstein
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elaborates on theoretical advances in organizational processes with specific reference to self-organization, organizational learning, motivation, decision making, and implications for practice and intervention / [discuss dynamical systems school] and summarize the theoretical progress pertaining to organizational theory and OD [organizational development] theories of stability and change in organizations [beyond Lewin's force field, self-organization, organizational learning] / decision making [complex systems require complex controllers, beer distribution and workforce staffing] / motivation and conflict resolution / total quality management (PsycINFO Database Record (c) 2012 APA, all rights reserved)
Jeffrey Goldstein
added 2 research items
This volume offers a new and very different approach to exploring leadership, one based on the new sciences of complexity. What we are calling “Complex Systems Leadership Theory” posits that leadership can be enacted through any interaction in an organization. Far from being the sole province of managers and executives, we contend leadership is an emergent phenomenon within complex systems. As such, exploring the meaning and implications of “emergent” is one of the major issues taken up by the chapters in this book. Through advances in computational modeling and non-linear dynamics, the interactions which generate leadership can be “tracked” in a much more rigorous way, enabling managers to better understand and encourage those dynamics of interaction which prove to have beneficial effects on the organization. Overall, we see a Complex Systems Leadership Theory as the core of a new era in leadership studies; introducing and furthering this new era are the primary goals of the present volume. This
Policies to reduce urban poverty are increasingly important, not only in developing but also in developed countries. Yet, urban poverty seems invariant in relation to economic growth. Although different methodol- ogies and conceptual frameworks have surfaced to deal with poverty re- duction, the way to effectively achieve this objective is not clear. In this paper we develop a comprehensive approach to deal with urban poverty reduction policies by making up for the lack of attention to social net- works in nearly all poverty reduction programs or policies. We critically assess this neglect of social network connectivity in two case studies, Favela-Bairro, or slum revitalization, in the city of Rio de Janeiro and a program in workforce development in New York City. We then discuss several of the most important elements of a social network perspective. The aim here is to show why it is necessary for urban poverty production policies to incorporate social network connectivity with the marginal- ized and disenfranchised poor. We offer guidelines as to how this kind of social network connection of the poor with the non-poor populations of our urban environments may proceed.
Jeffrey Goldstein
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The concept of causality is revised in the light of the phenomenon of emergence as seen in chaos and complexity theories. Emergence is examined by taking a close look at the arising of new, more complex attractors in the logistic equation as the parameter k is increased. The "qualitative dynamics" of these attractors are understood in terms of a pattern- based causality. Philosophical issues associated with this revised view of causality are then discussed.
Jeffrey Goldstein
added 4 research items
This article examines recent attempts to gain insight into philosophical paradoxes through using NDS models employing iterated difference equations and resulting phase portraits and escape time diagrams. The temporal nature of such models is contrasted with an alternative approach based on the a-temporal and non-dynamical construct of a lattice. Finally, there is a discussion of how such strategies for understanding paradox transcend the realm of empirical research and enter territory in the philosophy of mathematics.
Jeffrey Goldstein
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After a long hiatus from this project, due to the interference of that multi-splendored thing called life, I am proposing to introduce a new logic for complexity over the next couple of weeks. This logic builds upon but transcends extant logical frameworks such as Aristotelian, dialectical, paraconsistent, and related logics. The tentative name that I have been using for this logic is "Self-transcending Constructional Logic" ("STCL"). This logic has been developing out of several major sources: 1. varied complexity constructs and mathematics, especially nonlinear dynamical systems theory; 2. set theory, particularly the method of anti-diagonalization (mistakenly called "diagonalization" as I shall explain later) which is a paramount proof method used in transfinite set theory; 3. category theory, notably the work of Ehresmann and Vanbremeersch on colimits, complexification, and multifoldedness; 4. the idea of noncomputability, both as proved by Turing with great help from earlier work by Godel, as well as found in later modifications (the latter as mostly interpreted by the mathematical logician Judson Webb); 5. various hints and intimations from the complexity theorists John Holland, James Crutchfield, Jack Cohen and Ian Stewart, John von Neumann, Charles Bennett, Walter Fontana and Leo Buss, Douglas Hofstadter (not usually considered a complexity theorist but whose amazing book Godel, Escher, Bach is rightly viewed as a long and difficult thesis on emergence), and others.
Furthermore, the major philosophical influence on the development of this complexity logic has been the conceptualization of natural complexes on the part of the American philosopher Justin Buchler (whose work I've found is unfortunately little known among complexity aficionados). Finally, there is the beguiling but enlightening philosophical method of Ludwig Wittgenstein, whose influence must be assumed on whatever I aver, having studied his work for close to 45 years.
As I have stated in earlier entries to this project, what I propose as a novel logic should not be taken as a novel mathematics. To be sure, the relation between logic and mathematics is a tangled and historically changing one. The way I am viewing that relation in this project is to conceive a logic as conceptual framework of foundation underlying any specific mathematical discipline, it is what supplies the conceptual "space", so to speak, which gives the permission to or provides allowance for mathematical methods/findings. Actually, logic does more than just permit specific mathematics, it opens the way, even points the way, to certain mathematics. Thus, a logic can be said to close off certain routes while opening up other routes for mathematics to proceed.
An example is how Aristotelian logic has notoriously rendered a cogent conceptualization of change (or transformation, or transition, or transmutation, or evolution, or...) quite problematic. One result of this has been the eruption of troublesome paradoxes in typical Aristotelian models of change, the infamous identity/change paradoxes. And once paradox arises, great effort has then been provoked to account for a requisite consistency so that we can trust in what is thought and said.
Moreover, the diremption wrought by paradox has led to a corresponding antithetical logic which supposedly "solves" any inconsistency brought by paradox by embracing paradox as on equal valuation of true and false, and so forth. This can be seen in an attenuated form in dialectical logics and in a full-blown form in dialethistic logics. In my estimation though, which I hope to adumbrate later on, dialethesis, to borrow a phrase from Bertrand Russell used in a different context, has all the benefits of theft over honest toil.
The self-transcending constructional logic being offered here, though, can be said to "flirt with" paradox but not embrace it. A flirtation and an embrace are a world apart, many a slip between the cup and the lip goes on here. As I hope to explicate, the logic of stcl can flirt with paradox in what I claim to be an insightful manner without at the same time succumbing to the temptations of embrace. I have borrowed this description using the metaphor of a flirtation with paradox from the aforementioned Douglas Hofstadter who wrote, during his elucidation of the method of diagonalization mentioned above,
  • “To some people, diagonalization seems a bizarre exercise in artificiality, a construction of a sort that would never arise in any realistic context. To others, its flirtation with paradox is tantalizing and provocative, suggesting links to many deep aspects of the universe" (Metamagical Themes, p. 335).
Although the inclusion of the word "transcending" in the name of this logic -- "self-transcending constructional" -- might sound portentous given its connotations in lofty circumstances, in actuality "transcending" as used here is a totally neutral term employed to describe the method of diagonalization on the part of the German historian and philosopher of mathematics Oskar Becker. Becker's phrase was in turn taken-up by the Austrian-American philosopher of law and mathematics, Felix Kaufmann, who believed it was an inherently absurd thing to posit since according to Kaufmann no mathematical procedure could transcend itself. I took the phrase from Kaufmann but reverted to the neutral way it was used by Becker because I think it is a much more appropriate and unbiased description of what can take place in complex systems. I will say much more on this later on.
As I hope to show, by flirting with paradox, the logic of stcl can help deal with those paradoxes that have been said to be present in conceptualizations of complex systems, specially, in ideas on bifurcations, phase transitions, self-organization, self-modification, criticalization phenomena such as self-organized criticality, and so on. Thus, it is a logic which opens a conceptual space for understanding certain very significant phenomena in complex systems.
Moreover, it needs to be stated that I am not using the term "complex" in the sense that earlier contributors to this project seemed to mean, namely, the incredible complex aka complicated and enmeshed diverse social networks all around us, i.e., networks mostly seen as bringing about unwanted, unintended consequences leading to the general decay and corruption of the social fabric of these post-modern times. Despite this pessimistic assessment (of which I am in more agreement than not), the development of the logic of stcl herein goes in a different direction since it implies that perhaps complex systems science can provide means for helping to ameliorate the general state of decline. This entry should be read as just the beginning salvo of my aim in explicating a novel logic for complexity. Of course, comments, questions, whatever, are most welcome.
 
Jeffrey Goldstein
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Jeffrey Goldstein
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A key theme throughout this book, one that sharply distinguishes it from other works in the genre of leadership/management/ organizational theory, is that complexity is not something to be avoided or somehow damped down but instead is capable of yielding great dividends if it is embraced in the appropriate manner. In this chapter, we offer many insights from burgeoning research into social networks, one of the most intense and promising areas of complexity science, in order to show how leaders can reap benefits through transmuting their organizations’ complex social networks into smart networks that play a inimitable role in constructing ecologies of innovation. Smart networks contain this potential since it is through them that the identification and dissemination of experiments in novelty can become the requisite seeds of innovation. At the same time, smart social networks enable rapid adaptation to a relentlessly changing environment.
Emergence refers to the arising of unpredictable, nondeductible, and irreducible coherent structures, patterns, and properties in complex systems. Emergent phenomena are understood as collectivities or integrations occurring on a macro-level emerging out of less integrated substrates on a micro-level. The construct of emergence is turned to when the dynamics of a system can be better understood by focusing on across-system organization rather than by decomposition into parts. As the sciences of complex systems have rapidly expanded over the past three decades, the study of emergence has come forward as one of the most vital areas of research and theorizing, a dramatic shift from hovering on the edge of credibility as it was in the past to being embraced currently across a wide range of sciences and related fields of study.
Jeffrey Goldstein
added 2 research items
Innovation—it’s a buzzword for the twenty-first century. Creating new services, new products, new processes, new business models, new organizational forms, and new industries seems to be the key to success in this era of business. What drives innovation? Why do some companies achieve innovation more consistently than others? Is it the people? Is it the compensation? Is it the industry?
The elite sales managers at IBM in the early 1990s were proud to work at the world’s leading information technology (IT) company. But more recently, something had begun to change. Slowly at first, then far more quickly, it was becoming apparent that the company’s prospects had become increasingly bleak. A new technology, the microprocessor, entered the market a decade before, and IBM itself had helped define this new market when it launched the phenomenally successful IBM PC in 1981. All along, IBM’s experts had continued to counsel that the PC would never replace the vaulted IBM mainframe computer. They were wrong. During this period, low levels of interaction resonance (the important idea we described in the last chapter) among the product developers as well as the sales and services teams were setting the company up for a crisis.
Jeffrey Goldstein
added an update
I think the time has come to tighten some things up regarding this project. I want to reiterate some points made in the beginning. What I have meant by “logic” in this project does not equate to mathematics or even broad mathematical approaches. However, maths can point in certain directions that reveal the logic of complex systems or how the world appears different due to complexity constructs. Nor does the logic of complexity involve this or that “solution” to specific problems although, to be sure, any complexity construct involved in deriving a logic for complexity only attains its usefulness, confirmation, and fullest expression in relation to its encounters with specific problems which the world offers. This is where the “rubber meets the road” in laying-out which complexity constructs impact an overall logic for complexity. Thus I would expect that a logic for complexity contains complexity constructs that have been modified and refined through their applications. Consequently, a complexity construct worth its while in carving out a logic for complexity would have to demonstrate its usability in dealing with real world complex problems and not just because this or that construct is “cool” or “interesting” or whatever in terms of its pure mathematical or scientific roots. I am in the process of going through the varied comments to the projects (at least the ones I think are relevant to the goal of the project) in order to select and condense ideas from them if these ideas further the project. I welcome others to do so. I am not asking people to repeat anything, rather select and condense and even name some of the complexity logic pointers. I will be commenting as I go along. I start with something which may not have been mentioned in any specificity so far but is something I have been interested in for a long time. I hope this generates some comments: I’ve identified a kind of complexity construct associated with emergence which I don’t yet have a good name for and am seeking help. It is also related to nonlinearity in general and unpredictability/unexpectedness. One example of this complexity construct takes place in the case of low temperature superconductivity, a phenomena which is accepted as a case of emergence by the majority of solid state or condensed matter physicists as well as a number of philosophers of science. In particular, emergence in certain low temperature superconductive metals shows itself as a “unified collective quantum wave” of electric current flowing freely without resistance. Other effects are also seen relating to the magnetic field, etc. Perhaps the complexity construct have in mind is not best thought of as one construct but instead two or three or more acting together. A descriptive term for this construct might be “transformational” but I think that specific term is too general although the complexity construct I have in mind is about a radical kind of transformation. Here is a description of this construct in operation in superconductivity by viewing it as made of three interlocked phenomena: 1. The metals exhibiting superconductivity at low temperature do not sure any greater conductivity than other metals at normal temperatures whereas those metals which are better conductors of electricity at normal temperatures are not the ones which become superconductive at very low temperatures; this is curious since it means that one cannot extrapolate from the properties of conductivity at normal temperature or the structure of metals at normal temperature to what happens in the case of the metals when superconductivity emerges at low temperatures, that is, it is not any kind of linear elongation or piece-meal process but rather a radical transformation of the superconductors metals’ electron structure; 2. Superconductivity at low temperatures involves the transformation of electrons from their status as fermions which cannot occupy the same quantum state at room temperature to actually becoming a different kind of particle, the boson, which have the property of being able to occupy the same quantum state (and hence follow Bose-Einstein statistics, hence the name “boson”); the emergent quantum state is a collective integration because the superconducting electrons as bosons are in the same quantum state (hence the description of “quantum wave”); 3. Related to 2.) is that superconductivity at low temperature involves the formation of a pairing or coupling of electrons, a strange situation given the fact that electrons normal repel each other. What I am looking for here is not any more stipulated technical “mechanisms” responsible for superconductivity as an emergence. I have been studying the BCL theory and am well aware of these explanations. Instead I am looking for the complexity construct s here that are pertinent to the logic for complexity.
 
Jeffrey Goldstein
added 2 research items
The authors present a new approach to leadership based on findings from complexity science. Integrating real case studies with rigorous research results, they explore the biggest challenges being faced in fast-paced organizations, and provide a host of concrete tools for leading during critical periods. © Jeffrey Goldstein, James K. Hazy, and Benyamin B. Lichtenstein, 2010. All rights reserved.
Jeffrey Goldstein
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This paper lays-out an approach for probing the nature of complex systems through focusing on parameters in relation to variables and understanding parameters in terms of contexts and constraints. Rather than starting from a set of preconceived abstract principles in order to build up a philosophical conceptualization of complex systems, the paper instead starts with the praxis of working with complex system through the means of modeling, intervening, and leading them. From this grounding in praxis, the paper offers a set of conceptual tools for more effectively understanding and hence working with complex systems, including guidelines into a philosophy of complex systems. This paper is meant to the first of two related papers. The first, the one presented here, looks primarily at the role of parameters in mathematics and the relation of parameters to contexts and constraints. The paper turns to the study of semantics in linguistics as to help unpack the role of parameters and contexts in complex systems. The second paper will present case studies utilizing the conceptual tools developed in the first paper. In particular the follow-up paper will look at various aid programs around the world being used to fight poverty and low quality of life conditions. It is hoped that a complexity science lens can make such programs more effective.
Jeffrey Goldstein
added 2 research items
This paper concludes a three part series by reimagining processes of emergence along the lines of a formal "blueprint" for the "logic" of these processes, a topic surprisingly neglected even within the camp of those advocating some form of emergence. This formalism is presented according to the following conceptual strategy. First, the explanatory gap of emergence, the presence of which is one of the main defining characteristics of emergent phenomena, is interpreted in terms of uncomputability, an idea introduced in complexity science in order to supplement the more traditional features of unpredictability, nondeducibility, and irreducibility. Uncomputability is traced back to a method devised by Georg Cantor in a very different context. I label Cantor's formalism a type of "self-transcending construction" (STC), a phrase coined by an early commentator on Cantor's work. Next, I examine how Cantor's STC was appropriated, respectively, in the work of Gödel and Turing on undecidability and uncomputability. Next, I comment on how self-transcending constructions derive a large measure of their potency via a kind of "firtation" with paradox in a manner similar to what Gödel and Turing had done. Finally, I offer some suggestions on how the formalism of an STC can shed light on the nature of macro-level emergent wholes or integrations. This formalism is termed a "self-transcending construction" a term derived from the anti-diagonalization method devised by George Cantor in 1891 and then utilized in the limitative theorems of Godel and Turing.
Jeffrey Goldstein
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Some general comments about understanding complex systems, perhaps with some significance to the development of a logic of complexity.
 
Jeffrey Goldstein
added a project goal
Complexity and associated theories have brought about new understandings of change, growth, development, transformation, evolution... These new understandings, in turn, are prompting a rethinking of Aristotelian logic, dialectical logic, and the more recent inconsistency/paraconsistency logics (or dialetheism).