The book is about the development of the theory of epistemic fields with the corresponding relational and information fields as a framework for the understanding of strategies and tactics of the theory of knowing as the production of intellectual investment flows and the theory of knowledge accumulation as the production of intellectual capital stocks in systems of factories and departments providing the foundations for the development of open algorithms in the open space of problem-solution dualities. The concepts and the roles of thinking and reasoning with curiosity, creativity, hope, Ill-posed problems, phantom problems, unsolved problems, misinformation, disinformation, fake news, and courage are introduced, defined, and analyzed on the cognitive journeys over the space of ignorance-knowledge dualities, where dualistic-polar conflicts between duals in the space of ignorance-knowledge dualities are resolved with the instruments of fuzzy optimization, the results of which are used to induced the zones of ignorance, the zones of knowledge, and the zones of contentions. A complete development of the set of connecting paths of spaces and sub-spaces is provided, where all varieties, categories, and spaces reside in dualistic-polar structures with knowledge stock viewed as a single tree with the same roots, one trunk, many branches, and a fruit cocktail. The ontological space contains the space of actual-potential dualities as the primary category of knowing, and the epistemological space contains the space of imagination-reality dualities as the derived category of knowing within the space of primary-derived dualities. The space of potentials contains the space of imaginations which contains the sub-spaces of possibility-impossibility, probability-improbability, and possibility-probability dualities with corresponding spaces of necessity-freedom and anticipation-expectation dualities leading to the conception of the possible-world-impossible-world dualities in the space of semantic-non-semantic dualities. This book is also a continuation of the sequence of my works on the theories of paradigms of thought, rationality, info-statics, info-dynamics, entropy, problem-solution dualities in self-contained mathematics and philosophy, and their relational connectivity to information, language, knowing, knowledge, cognitive practices and open maching learning  relative to nominalism, and the space of construction-reduction dualities over the spaces of fundamental-applied, production-consumption, input-output, and cost-benefit dualities.

Although economic theory has increased our understanding of some economic problems, it has rendered others, including the problem of capital accumulation, growth, and development, more difficult to understand. Focusing on capitalist economic systems, this book develops a theoretical approach to the study of aggregate capital dynamics. The theory is developed within the Keynesian framework of aggregate thinking and builds on the work of such Cambridge economists as Robinson, Kaldor, and Pasinetti. The approach helps to resolve some theoretical difficulties within the Keynesian framework for studying aggregate investment behavior. Dompere also provides a criticism of the neoclassical investment theory and the general neoclassical theoretical framework for studying aggregate capital accumulation, investment, and growth. Reexamining some questions on investment that earlier theorists have tried to answer, this study develops some of the basic ideas of Keynes, Robinson, Kaldor, and Pasinetti into a general theoretical system that allows an optimal aggregate capital and investment to be determined for a given information set.

Building on his companion volume on closed economic systems, Dompere develops a theory of aggregate investment, optimal capital, and output dynamics for open economic systems under neo-Keynesian conditions with special reference to growth policy. By constructing and tracing the path of equilibrium aggregate investment, the study isolates and analyzes the internal and external factors that influence the adjusting of investment to aggregate finance and profit. It examines the role international trade and finance play in alleviating domestic technological and savings constraints on capital creation and growth. The theory's conclusions are used to analyze the rate of accumulation and finance needed to support a rate of output growth selected as part of an internal aggregate decision process. The analysis is extended to aggregrate development capital-output planning. The study goes on to discuss conceptual and aggregational problems of measures of economic openness implied in the data requirements across national economies. Here a unique set of theoretical measures of economic openness, different from the traditional, is developed. The book, further, presents a critique and appraisal of the essential capital elements implied by endogenous growth theory.

This book focuses on the development of a theory of info-dynamics to support the theory of info-statics in the general theory of information. It establishes the rational foundations of information dynamics and how these foundations relate to the general socio-natural dynamics from the primary to the derived categories in the universal existence and from the potential to the actual in the ontological space. It also shows how these foundations relate to the general socio-natural dynamics from the potential to the possible to give rise to the possibility space with possibilistic thinking; from the possible to the probable to give rise to possibility space with probabilistic thinking; and from the probable to the actual to give rise to the space of knowledge with paradigms of thought in the epistemological space. The theory is developed to explain the general dynamics through various transformations in quality-quantity space in relation to the nature of information flows at each variety transformation. The theory explains the past-present-future connectivity of the evolving information structure in a manner that illuminates the transformation problem and its solution in the never-ending information production within matter-energy space under socio-natural technologies to connect the theory of info-statics, which in turn presents explanations to the transformation problem and its solution. The theoretical framework is developed with analytical tools based on the principle of opposites, systems of actual-potential polarities, negative-positive dualities under different time-structures with the use of category theory, fuzzy paradigm of thought and game theory in the fuzzy-stochastic cost-benefit space. The rational foundations are enhanced with categorial analytics. The value of the theory of info-dynamics is demonstrated in the explanatory and prescriptive structures of the transformations of varieties and categorial varieties at each point of time and over time from parent-offspring sequences. It constitutes a general explanation of dynamics of information-knowledge production through info-processes and info-processors induced by a socio-natural infinite set of technologies in the construction-destruction space.

This book presents the development of a theory of social goal-objective formation and its relationship to national interest and social vision under a democratic decision-choice system with imperfect information structure. It provides a framework for the application of fuzzy logic and its mathematics to the analysis in resolving conflicts in individual preferences in the collective decision-choice space without violence. The book demonstrates how to use fuzzy logic and its mathematics in the study of economics, social sciences and other complex systems. It also presents the use of collaborative tools of opposites, duality, polarity, continuum in fuzzy paradigm with its logic, laws of thought and mathematics in developing a new approach to the theory of political economy in order to enhance the constructs of social decision-choice theory.

We do not perceive the present as it is and in totality, nor do we infer the future from the present with any high degree of dependability, nor yet do we accurately know the consequences of our own actions. In addition, there is a fourth source of error to be taken into account, for we do not execute actions in the precise form in which they are imaged and willed. Frank H. Knight [R4.34, p. 202] The "degree" of certainty of confidence felt in the conclusion after it is reached cannot be ignored, for it is of the greatest practical signi- cance. The action which follows upon an opinion depends as much upon the amount of confidence in that opinion as it does upon fav- ableness of the opinion itself. The ultimate logic, or psychology, of these deliberations is obscure, a part of the scientifically unfathomable mystery of life and mind. Frank H. Knight [R4.34, p. 226-227] With some inaccuracy, description of uncertain consequences can be classified into two categories, those which use exclusively the language of probability distributions and those which call for some other principle, either to replace or supplement.

Philosophy involves a criticism of scientific knowledge, not from a point of view ultimately different from that of science, but from a point of view less concerned with details and more concerned with the h- mony of the body of special sciences. Here as elsewhere, while the older logic shut out possibilities and imprisoned imagination within the walls of the familiar, the newer logic shows rather what may happen, and refuses to decide as to what must happen. Bertrand Russell At any particular stage in the development of humanity knowledge comes up against limits set by the necessarily limited character of the experience available and the existing means of obtaining knowledge. But humanity advances by overcoming such limits. New experience throws down the limits of old experience; new techniques, new means of obtaining knowledge throw down the limits of old techniques and old means of obtaining knowledge. New limits then once again appear. But there is no more reason to suppose these new limits absolute and final than there was to suppose the old ones absolute and final.

This book discusses the development of a theory of info-statics as a sub-theory of the general theory of information. It describes the factors required to establish a definition of the concept of information that fixes the applicable boundaries of the phenomenon of information, its linguistic structure and scientific applications. The book establishes the definitional foundations of information and how the concepts of uncertainty, data, fact, evidence and evidential things are sequential derivatives of information as the primary category, which is a property of matter and energy. The sub-definitions are extended to include the concepts of possibility, probability, expectation, anticipation, surprise, discounting, forecasting, prediction and the nature of past-present-future information structures. It shows that the factors required to define the concept of information are those that allow differences and similarities to be established among universal objects over the ontological and epistemological spaces in terms of varieties and identities. These factors are characteristic and signal dispositions on the basis of which general definitional foundations are developed to construct the general information definition (GID). The book then demonstrates that this definition is applicable to all types of information over the ontological and epistemological spaces. It also defines the concepts of uncertainty, data, fact, evidence and knowledge based on the GID. Lastly, it uses set-theoretic analytics to enhance the definitional foundations, and shows the value of the theory of info-statics to establish varieties and categorial varieties at every point of time and thus initializes the construct of the theory of info-dynamics.

Criticism is the habitus of the contemplative intellect, whereby we try to recognize with probability the genuine quality of a l- erary work by using appropriate aids and rules. In so doing, c- tain general and particular points must be considered. The art of interpretation or hermeneutics is the habitus of the contemplative intellect of probing into the sense of somewhat special text by using logical rules and suitable means. Note : Hermeneutics differs from criticism as the part does from the whole. Antonius Gvilielmus Amo Afer (1727) There is no such thing as absolute truth. At best it is a subj- tive criterion, but one based upon valuation. Unfortunately, too many people place their fate in the hands of subjective without properly evaluating it. Arnold A. Kaufmann and Madan M. Gupta The development of cost benefit analysis and the theory of fuzzy decision was divided into two inter-dependent structures of identification and measurement theory on one hand and fuzzy value theory one the other. Each of them has sub-theories that constitute a complete logical system.

The genus of definitions for the theoretical sciences is (the province of) the habitus of the intellective intention, for the practical sciences, however, that of the effective intention; the objects and ends constitute the specific differ ence There is nothing in the intellect that has not already been in the senses, that is, in the sensory organs, that has not already been in sensible things from which are distinguished things not perceptible to the senses. Nothing can be of the mind, sensation and the thing inferred therefrom except the operation itself. Real learning is cognition of things in themselves. It thus has the basis of its certainty in the known thing. This is established in two ways: by demon stration in the case of contemplative things, and by induction in the case of things perceptible to the senses. In contrast with real learning there is pos sible, probable and fictive learning. Antonius Gvilielmus Amo Afer (1827) This research has been long in the making. Its conception began in my last years in the doctoral program at Temple University, Philadelphia, Pa. It was simultaneously conceived with my two books on the Neo Keynesian Theory of Optimal aggregate investment and output dynamics [201] [202] as well as reflections on the methodology of decision-choice rationality and development economics [440] [441]. Economic theories and social policies were viewed to have, among other things, one impor tant thing in common in that they relate to decision making under different.

This volume presents an analysis of the problems and solutions of the market mockery of the democratic collective decision-choice system with imperfect information structure composed of defective and deceptive structures using methods of fuzzy rationality.

The book is devoted to the political economy of rent-seeking, rent-protection and rent-harvesting to enhance profits under democratic collective decision-choice systems. The toolbox used in the monograph consists of methods of fuzzy decision, approximate reasoning, negotiation games and fuzzy mathematics. The monograph further discusses the rent-seeking phenomenon in the Schumpeterian and Marxian political economies where the rent-seeking activities transform the qualitative character of the general capitalism into oligarchic socialism and making the democratic collective decision-choice system as an ideology rather than social calculus for resolving conflicts in preferences in the collective decision-choice space without violence.

The monograph is an examination of the fuzzy rational foundations of the structure of exact and inexact sciences over the epistemological space which is distinguished from the ontological space. It is thus concerned with the demarcation problem. It examines exact science and its critique of inexact science. The role of fuzzy rationality in these examinations is presented. The driving force of the discussions is the nature of the information that connects the cognitive relational structure of the epistemological space to the ontological space for knowing. The knowing action is undertaken by decision-choice agents who must process information to derive exact-inexact or true-false conclusions. The information processing is done with a paradigm and laws of thought that constitute the input-output machine. The nature of the paradigm selected depends on the nature of the information structure that is taken as input of the thought processing. Generally, the information structure received from the ontological space is defective from the simple principles of acquaintances and the limitations of cognitive agents operating in the epistemological space. How then do we arrive and claim exactness in our knowledge-production system? The general conclusion of this book is that the conditions of the fuzzy paradigm with its laws of thought and mathematics present a methodological unity of exact and inexact sciences where every zone of thought has fuzzy covering.

The modern works on African philosophy have not been integrated and fully connected to Africa's antiquity in order to provide a foundational unity for further intellectual refinement. The philosophical dimensions of humanism, Nkrumah's concept of categorial conversion, African concepts of duality, polarity, unity, continual creation and democratic ideals must be shown their African-centered origins. In considering African philosophy, there arise conceptual and logical gaps that require the development of fundamental cognitive unity from the available data with judicious interpretation and restructuring in order to define the parameters of African philosophical unity that will allow these gaps to be closed for intellectual continuity. This monograph is devoted to the establishment of the foundations for the development of Africa's intellectual continuity and cognitive unity from antiquity to the present. Its main premise is that there is African philosophy with its own method of reasoning, analysis and synthesis. The monograph initiates self-contained philosophical foundations for African intellectual unity that is required to support African cultural unity, African personality, African essence and humanism needed for the creation of Greater Africa that is implied by African Union. These philosophical foundations, it is argued, formed the thinking system for Africa's social construct, law, economics, politics and governance of empires, kingdoms and social units that have come to pass. These philosophical foundations constitute the thinking system that must guide current and future Africa's socioeconomic dynamics. The monograph discusses also Africa's contributions to the global intellectual heritage by showing the relationships among foundations of African philosophical tradition and other philosophical systems that lead to rediviva Africana. It presents the principles of cognitive unity and continuity on the held position that without clearly developed Africa's philosophical foundations from its antiquity providing intellectual unity and cognitive continuity complete emancipation of Africa will be a mere mimicking of intellectual faults of other nations and philosophical systems. The research by African scholars and others on specific philosophical thoughts from different areas of Africa is useful materials that must be integrated into cognitive unity by accepting those that fit and rejecting those that do not fit by a defined logical process. Mindful of this, a case is thus made in this monograph for African cognitive unity and supporting reasoning methods. The system of ideas and perceptive interpretations of relevant data is, here, referred to as Africentricity, and its philosophical foundations that project thought as polyrhythmicity while the study of logic of reasoning about methodological and epistemic problems of polyrhythmicity and Africentricity is referred to as polyrhythmics. On practical level these philosophical foundations are shown to support the conceptual basis of Nguzo Saba (the Seven Principles of Kwanzaa). The monograph would be of interest to philosophers in general, professionals, researchers and students engaged in African philosophy, African studies, Black studies, socio-political philosophy and those interested in knowing the thinking system on the basis of which African essence arises and African social formations were constructed and governed from antiquity. _______________________ Kofi Kissi Dompere is a professor of economics at Howard University, USA. He has authored a number of scientific and scholarly works in economics, philosophy and decision theory. He is the producer and host of a radio program "African Rhythms and Extensions" on WPFW 89.3fm in Washington D.C., USA.

This book is concerned with the development of the understanding of the relational structures of information, knowledge, decision-choice processes of problems and solutions in the theory and practice regarding diversity and unity principles of knowing, science, non-science, and information-knowledge systems through dualistic-polar conditions of variety existence and nonexistence. It is a continuation of the sequence of my epistemic works on the theories on fuzzy rationality, info-statics, info-dynamics, entropy, and their relational connectivity to information, language, knowing, knowledge, cognitive practices relative to variety identification-problem-solution dualities, variety transformation-problem-solution dualities, and variety certainty-uncertainty principle in all areas of knowing and human actions regarding general social transformations. It is also an economic-theoretic approach in understanding the diversity and unity of knowing and science through neuro-decision-choice actions over the space of problem-solution dualities and polarities. The problem-solution dualities are argued to connect all areas of knowing including science and non-science, social science, and non-social-science into unity with diversities under neuro-decision-choice actions to support human existence and nonexistence over the space of static-dynamic dualities. The concepts of diversity and unity are defined and explicated to connect to the tactics and strategies of decision-choice actions over the space of problem-solution dualities. The concepts of problem and solution are defined and explicated not in the space of absoluteness but rather in the space of relativity based on real cost-benefit conditions which are shown to be connected to the general parent-offspring infinite process, where every solution generates new problem(s) which then generates a search for new solutions within the space of minimum-maximum dualities in the decision-choice space under the principle of non-satiation over the space of preference-non-preference dualities with analytical tools drawn from the fuzzy paradigm of thought which connects the conditions of the principle of opposites to the conditions of neuro-decision-choice actions in the zone of variety identifications and transformations. The Monograph would be useful to all areas of Research, Learning and Teaching at Advanced Stages of Knowing and Knowledge Production.

The effective use of development economic theories in practice is limited, the authors contend, by the lack of explicit criterion for judging their scientific content. The directional progress of critical research and teaching is also constrained by this deficiency. This study advances a meta-theory designed to assist in evaluating the scientific validity of theories in economic development and how these theories can be improved to assist social practice. Using this model, the study then examines existing theories, dividing them into explanatory and prescriptive theories. The explanatory theories include the stage-based theories of Marx, Schumpeter, and Rostow, and factor-based theories, including capital-based, human-capital-based, and technology-based theories. The prescriptive theories include explanatory-theory-based prescriptions, interventionist prescriptive theories, and theories of economic planning. In conclusion, the authors contend that modern analysis of development economics is plagued with logical ills, misleading notions, and a weak theoretical structure that lacks scientific appeal. Most of the theories, except for those of Marx and Schumpeter, neglect an analysis of the mechanism of change.

This book presents an epistemic framework for dealing with information-knowledge and certainty-uncertainty problems within the space of quality-quantity dualities. It bridges between theoretical concepts of entropy and entropy measurements, proposing the concept and measurement of fuzzy-stochastic entropy that is applicable to all areas of knowing under human cognitive limitations over the epistemological space. The book builds on two previous monographs by the same author concerning theories of info-statics and info-dynamics, to deal with identification and transformation problems respectively. The theoretical framework is developed by using the toolboxes such as those of the principle of opposites, systems of actual-potential polarities and negative-positive dualities, under different cost-benefit time-structures. The category theory and the fuzzy paradigm of thought, under methodological constructionism-reductionism duality, are used in the fuzzy-stochastic and cost-benefit spaces to point to directions of global application in knowing, knowledge and decision-choice actions. Thus, the book is concerned with a general theory of entropy, showing how the fuzzy paradigm of thought is developed to deal with the problems of qualitative-quantitative uncertainties over the fuzzy-stochastic space, which will be applicable to conditions of soft-hard data, fact, evidence and knowledge over the spaces of problem-solution dualities, decision-choice actions in sciences, non-sciences, engineering and planning sciences to abstract acceptable information-knowledge elements.

It is necessary to practice methodological doubt, like Descartes, in - der to loosen the hold of mental habits; and it is necessary to cultivate logical imagination, in order to have a number of hypotheses at c- mand, and not to be the slave of the one which common sense has r- dered easy to imagine. These two processes, of doubting the familiar and imagining the unfamiliar, are corrective, and form the chief part of the mental training required for a philosopher. Bertrand Russell At every stage and in all circumstances knowledge is incomplete and provisional, conditioned and limited by the historical circumstances under which it was acquired, including the means and methods used for gaining it and the historically conditioned assumptions and categories used in the formulation of ideas and conclusions. Maurice Cornforth This monograph is the second in the series of meta-theoretic analysis of fuzzy paradigm and its contribution and possible contribution to formal reasoning in order to free the knowledge production process from the ridge frame of the classical paradigm that makes its application to soft and inexact sciences d- ficult or irrelevant. The work in the previous monograph was strictly devoted to problems of theory of knowledge and critique of classical, bounded and other rationalities in decision-choice processes regarding the principles of verification, falsification or corroboration in knowledge production. This monograph deals mostly with epistemic decision-choice models and theories and how they are related to both the classical and fuzzy paradigms.

This volume presents an analysis of the problems and solutions of the market mockery of the democratic collective decision-choice system with imperfect information structure composed of defective and deceptive structures using methods of fuzzy rationality. The book is devoted to the political economy of rent-seeking, rent-protection and rent-harvesting to enhance profits under democratic collective decision-choice systems. The toolbox used in the monograph consists of methods of fuzzy decision, approximate reasoning, negotiation games and fuzzy mathematics. The monograph further discusses the rent-seeking phenomenon in the Schumpeterian and Marxian political economies where the rent-seeking activities transform the qualitative character of the general capitalism into oligarchic socialism and making the democratic collective decision-choice system as an ideology rather than social calculus for resolving conflicts in preferences in the collective decision-choice space without violence.

This book presents the development of a theory of social goal-objective formation and its relationship to national interest and social vision under a democratic decision-choice system with imperfect information structure. It provides a framework for the application of fuzzy logic and its mathematics to the analysis in resolving conflicts in individual preferences in the collective decision-choice space without violence. The book demonstrates how to use fuzzy logic and its mathematics in the study of economics, social sciences and other complex systems. It also presents the use of collaborative tools of opposites, duality, polarity, continuum in fuzzy paradigm with its logic, laws of thought and mathematics in developing a new approach to the theory of political economy in order to enhance the constructs of social decision-choice theory.

The monograph is an examination of the fuzzy rational foundations of the structure of exact and inexact sciences over the epistemological space which is distinguished from the ontological space. It is thus concerned with the demarcation problem. It examines exact science and its critique of inexact science. The role of fuzzy rationality in these examinations is presented. The driving force of the discussions is the nature of the information that connects the cognitive relational structure of the epistemological space to the ontological space for knowing. The knowing action is undertaken by decision-choice agents who must process information to derive exact-inexact or true-false conclusions. The information processing is done with a paradigm and laws of thought that constitute the input-output machine. The nature of the paradigm selected depends on the nature of the information structure that is taken as input of the thought processing. Generally, the information structure received from the ontological space is defective from the simple principles of acquaintances and the limitations of cognitive agents operating in the epistemological space. How then do we arrive and claim exactness in our knowledge-production system? The general conclusion of this book is that the conditions of the fuzzy paradigm with its laws of thought and mathematics present a methodological unity of exact and inexact sciences where every zone of thought has fuzzy covering.

The genus of definitions for the theoretical sciences is (the province of) the habitus of the intellective intention, for the practical sciences, however, that of the effective intention; the objects and ends constitute the specific differ ence There is nothing in the intellect that has not already been in the senses, that is, in the sensory organs, that has not already been in sensible things from which are distinguished things not perceptible to the senses. Nothing can be of the mind, sensation and the thing inferred therefrom except the operation itself. Real learning is cognition of things in themselves. It thus has the basis of its certainty in the known thing. This is established in two ways: by demon stration in the case of contemplative things, and by induction in the case of things perceptible to the senses. In contrast with real learning there is pos sible, probable and fictive learning. Antonius Gvilielmus Amo Afer (1827) This research has been long in the making. Its conception began in my last years in the doctoral program at Temple University, Philadelphia, Pa. It was simultaneously conceived with my two books on the Neo Keynesian Theory of Optimal aggregate investment and output dynamics [201] [202] as well as reflections on the methodology of decision-choice rationality and development economics [440] [441]. Economic theories and social policies were viewed to have, among other things, one impor tant thing in common in that they relate to decision making under different.

Criticism is the habitus of the contemplative intellect, whereby we try to recognize with probability the genuine quality of a l- erary work by using appropriate aids and rules. In so doing, c- tain general and particular points must be considered. The art of interpretation or hermeneutics is the habitus of the contemplative intellect of probing into the sense of somewhat special text by using logical rules and suitable means. Note : Hermeneutics differs from criticism as the part does from the whole. Antonius Gvilielmus Amo Afer (1727) There is no such thing as absolute truth. At best it is a subj- tive criterion, but one based upon valuation. Unfortunately, too many people place their fate in the hands of subjective without properly evaluating it. Arnold A. Kaufmann and Madan M. Gupta The development of cost benefit analysis and the theory of fuzzy decision was divided into two inter-dependent structures of identification and measurement theory on one hand and fuzzy value theory one the other. Each of them has sub-theories that constitute a complete logical system.

It is necessary to practice methodological doubt, like Descartes, in - der to loosen the hold of mental habits; and it is necessary to cultivate logical imagination, in order to have a number of hypotheses at c- mand, and not to be the slave of the one which common sense has r- dered easy to imagine. These two processes, of doubting the familiar and imagining the unfamiliar, are corrective, and form the chief part of the mental training required for a philosopher. Bertrand Russell At every stage and in all circumstances knowledge is incomplete and provisional, conditioned and limited by the historical circumstances under which it was acquired, including the means and methods used for gaining it and the historically conditioned assumptions and categories used in the formulation of ideas and conclusions. Maurice Cornforth This monograph is the second in the series of meta-theoretic analysis of fuzzy paradigm and its contribution and possible contribution to formal reasoning in order to free the knowledge production process from the ridge frame of the classical paradigm that makes its application to soft and inexact sciences d- ficult or irrelevant. The work in the previous monograph was strictly devoted to problems of theory of knowledge and critique of classical, bounded and other rationalities in decision-choice processes regarding the principles of verification, falsification or corroboration in knowledge production. This monograph deals mostly with epistemic decision-choice models and theories and how they are related to both the classical and fuzzy paradigms.