Generalizing is necessary or even unavoidable

The problems of geometry and mechanics have driven forward the generalization of the concepts of number and function. This shows how application and generalization together prevent that mathematics becomes a mere formalism. Thoughts are signs and signs have meaning within a certain context. Meaning is a function of a term: This function produces a pattern. Algebra or modern axiomatic come to mind, as examples. However, strictly formalistic mathematics did not pay sufficient attention to the fact that modern axiomatic theories require a complementary element, in terms of intended applications or models, not to end up in a merely formal game.La generalización es necesaria o incluso inevitableLos problemas de geometría y mecánica han motivado la generalización de los conceptos de número y función. Esto muestra cómo la aplicación y la generalización previenen que las matemáticas sean un mero formalismo. Los pensamientos son signos y los signos tienen un significado dentro de un cierto contexto. El significado es una función de un término: esta función produce un patrón. El álgebra o la moderna axiomática vienen a la mente como ejemplos. Sin embargo, las matemáticas estrictamente formales no prestaron suficiente atención al hecho de que las teorías axiomáticas modernas requieren un elemento complementario, en términos de aplicaciones intencionadas o modelos, para no terminar en un juego meramente formal.Handle: http://hdl.handle.net/10481/34987WOS-ESCINº de citas en WOS (2017): 1 (Citas de 2º orden, 1

La generalización es necesaria o incluso inevitable

The problems of geometry and mechanics have driven forward the generalization of the concepts of number and function. This shows how application and generalization together prevent that mathematics becomes a mere formalism. Thoughts are signs and signs have meaning within a certain context. Meaning is a function of a term: This function produces a pattern. Algebra or modern axiomatic come to mind, as examples. However, strictly formalistic mathematics did not pay sufficient attention to the fact that modern axiomatic theories require a complementary element, in terms of intended applications or models, not to end up in a merely formal game.Los problemas de geometría y mecánica han motivado la generalización de los conceptos de número y función. Esto muestra cómo la aplicación y la generalización previenen que las matemáticas sean un mero formalismo. Los pensamientos son signos y los signos tienen un significado dentro de un cierto contexto. El significado es una función de un término: esta función produce un patrón. El álgebra o la moderna axiomática vienen a la mente como ejemplos. Sin embargo, las matemáticas estrictamente formales no prestaron suficiente atención al hecho de que las teorías axiomáticas modernas requieren un elemento complementario, en términos de aplicaciones intencionadas o modelos, para no terminar en un juego meramente formal

Emergent Design

Explorations in Systems Phenomenology in Relation to Ontology, Hermeneutics and the Meta-dialectics of Design SYNOPSIS A Phenomenological Analysis of Emergent Design is performed based on the foundations of General Schemas Theory. The concept of Sign Engineering is explored in terms of Hermeneutics, Dialectics, and Ontology in order to define Emergent Systems and Metasystems Engineering based on the concept of Meta-dialectics. ABSTRACT Phenomenology, Ontology, Hermeneutics, and Dialectics will dominate our inquiry into the nature of the Emergent Design of the System and its inverse dual, the Meta-system. This is an speculative dissertation that attempts to produce a philosophical, mathematical, and theoretical view of the nature of Systems Engineering Design. Emergent System Design, i.e., the design of yet unheard of and/or hitherto non-existent Systems and Metasystems is the focus. This study is a frontal assault on the hard problem of explaining how Engineering produces new things, rather than a repetition or reordering of concepts that already exist. In this work the philosophies of E. Husserl, A. Gurwitsch, M. Heidegger, J. Derrida, G. Deleuze, A. Badiou, G. Hegel, I. Kant and other Continental Philosophers are brought to bear on different aspects of how new technological systems come into existence through the midwifery of Systems Engineering. Sign Engineering is singled out as the most important aspect of Systems Engineering. We will build on the work of Pieter Wisse and extend his theory of Sign Engineering to define Meta-dialectics in the form of Quadralectics and then Pentalectics. Along the way the various ontological levels of Being are explored in conjunction with the discovery that the Quadralectic is related to the possibility of design primarily at the Third Meta-level of Being, called Hyper Being. Design Process is dependent upon the emergent possibilities that appear in Hyper Being. Hyper Being, termed by Heidegger as Being (Being crossed-out) and termed by Derrida as Differance, also appears as the widest space within the Design Field at the third meta-level of Being and therefore provides the most leverage that is needed to produce emergent effects. Hyper Being is where possibilities appear within our worldview. Possibility is necessary for emergent events to occur. Hyper Being possibilities are extended by Wild Being propensities to allow the embodiment of new things. We discuss how this philosophical background relates to meta-methods such as the Gurevich Abstract State Machine and the Wisse Metapattern methods, as well as real-time architectural design methods as described in the Integral Software Engineering Methodology. One aim of this research is to find the foundation for extending the ISEM methodology to become a general purpose Systems Design Methodology. Our purpose is also to bring these philosophical considerations into the practical realm by examining P. Bourdieu’s ideas on the relationship between theoretical and practical reason and M. de Certeau’s ideas on practice. The relationship between design and implementation is seen in terms of the Set/Mass conceptual opposition. General Schemas Theory is used as a way of critiquing the dependence of Set based mathematics as a basis for Design. The dissertation delineates a new foundation for Systems Engineering as Emergent Engineering based on General Schemas Theory, and provides an advanced theory of Design based on the understanding of the meta-levels of Being, particularly focusing upon the relationship between Hyper Being and Wild Being in the context of Pure and Process Being

From logos to bios : Hellenic philosophy and evolutionary biology

This thesis deals with the relation of Hellenic philosophy to evolutionary biology. The first part entails an explication of Hellenic cosmology and metaphysics in its traditional understanding, as the Western component of classical Indo-European philosophy. It includes an overview of the relevant contributions by the Presocratics, Plato, Aristotle, and the Neoplatonists, focusing on the structure and origin of both the intelligible and sensible worlds. Salient aspects thereof are the movement from the transcendent Principle into the realm of Manifestation by means of the interaction between Essence and Substance; the role of the Logos, being the equivalent of Plato’s Demiurge and Aristotle’s Prime Mover, in the cosmogonic process; the interaction between Intellect and Necessity in the formation of the cosmos; the various kinds of causality contributing to the establishment of physical reality; and the priority of being over becoming, which in the case of living organisms entails the primacy of soul over body. The first part of the thesis concludes with a discussion of the implications of Hellenic cosmology and metaphysics for evolutionary biology, including an affirmation of final and formal causality over and against its rejection by the modern scientific project. The second part commences with a delineation of organic form and transformation, emphasizing the mathematical foundations thereof. It continues with a critical consideration of the modern evolutionary theory on both scientific and philosophical grounds. In the process a fundamental distinction is made between micro- and macro-evolution, involving the reshuffling of existing genetic material which is acted upon by natural selection, and the production of new genetic material by means of macro-mutations, respectively. In the remainder of the thesis the macro-evolutionary process is described as mainly lawful, directed and convergent, instead of contingent, undirected and divergent as postulated in the modern evolutionary synthesis. This approach does not preclude the recognition of exceptions, due to the limitation of Intellect by Necessity – that is to say, of teleology by mechanism.Religious Studies and ArabicD.Litt. et Phil. (Religious Studies

A Bricolage of Critical Hermeneutics, Abductive Reasoning, and Action Research for Advancing Humanistic Values through Organization Development Practice

This is an emergent and auto-ethnographic study to find ways for the practice of organization development (OD) to recover and sustain humanism in the workplace. It begins with a literature review hermeneutically exploring the history and relevance of three modes of inquiry—hermeneutics, abductive reasoning, and action research—paratactically, which is to say, separately without overlap or reference to each other—to future OD practice. These three modes were selected from an extended literature search for non-reductive modes of inquiry that could address the range of human interests and workplace disease as I understand them. I combined my strong background reading on hermeneutics with the abductive reasoning of C. S. Peirce as two of the modes for review and also reflexively as part of my own methodology. The third mode, action research, is borrowed from the work of Kurt Lewin and his tradition in OD, known for its humanistic and democratic aims. Also included in the literature review is a report on the some of the more salient challenges and opportunities currently confronting the practice of organization development (OD) to provide a context for practical expression of my emerging discoveries. Following the literature review, I hermeneutically surfaced submerged, tacit (hidden-from-consciousness) generative connections from the confluence (flowing together) of the three modes, as they abductively emerged from within my expanding hermeneutic experience (known as a horizon) with the literature review. I then interpret the tacit relevance of that confluence through my life experience, for illuminating those OD challenges and opportunities. Finally this study integrates a sequence of critical hermeneutic and abductive processes in a participatory action research (PAR) pathway leading to plateaus of discovery and renewal through facilitation by humanistically oriented OD praxis. I conclude with five abduced interventions hypothetically drawn from personal case studies. My audience are OD practitioners inclined to develop wholistic humanism in the workplace through facilitative immersion with small groups and micro-cultures. Here they may find enlarged conceptual frames to reconceptualize OD, engage clients in transformative dialogue, and create actionable knowledge in their practice

The Routledge Handbook of Philosophy of Economics

The most fundamental questions of economics are often philosophical in nature, and philosophers have, since the very beginning of Western philosophy, asked many questions that current observers would identify as economic. The Routledge Handbook of Philosophy of Economics is an outstanding reference source for the key topics, problems, and debates at the intersection of philosophical and economic inquiry. It captures this field of countless exciting interconnections, affinities, and opportunities for cross-fertilization. Comprising 35 chapters by a diverse team of contributors from all over the globe, the Handbook is divided into eight sections: I. Rationality II. Cooperation and Interaction III. Methodology IV. Values V. Causality and Explanation VI. Experimentation and Simulation VII. Evidence VIII. Policy The volume is essential reading for students and researchers in economics and philosophy who are interested in exploring the interconnections between the two disciplines. It is also a valuable resource for those in related fields like political science, sociology, and the humanities.</p

Pattens of Human Knowing in the Information Society : A Philosophical Study of the Epistemological Implications of the Information Revolution

The aim of this thesis is to introduce a dynamic and integrative epistemology based on the notion of information. This thesis is mainly a critique of normative epistemology on the grounds that normative epistemology through its adoption of the assumptions of methods of modern sciences, models all processes of human knowing to the physical sciences and henceforth upholds a mechanical model of the universe which is indistinctly applied to natural phenomena and human behavioral and cognitive processes; (2) reduces human knowing to logical-deductive processes in the attempt to achieve a degree of certainty that is comparable to the one achieved by mathematics; (3) reduces knowing to achieving accurate representations of reality (true-justified-beliefs or clear and distinct ideas) with the assumption that the knower is a passive and impartial spectator of reality. The dynamic and integrative model of epistemology that this thesis advocates rejects the modeling of all processes of human knowing on the physical sciences basing itself on evidence from neurophysiology, cognitive and behavioral sciences. The knower is not a passive spectator of reality but an active agent who (1) is continuously in relation with his or her environment; and who (2) is involved processes of meaning and value creation as the knower pursues various goals. Dynamic and integrative epistemology defines knowing not in terms of achieving accurate representations (true-justified-beliefs or clear and distinct ideas) but as accumulating insights through information processing i.e. enriching the immediate data of experience with value and meaning for the purposes of decision-making and problem-solving. Dynamic and integrative epistemology is only possible in the context of a paradigm shift from mechanical (causal) to cybernetics (information processing) models. It overcomes the analysis and synthesis dichotomy characteristic of mechanical models and upholds systems thinking as a way of tackling in inherent complexity of reality. Dynamic and integrative epistemology rejects the reduction of wisdom to certainty or knowing to thinking that led to top-down logical deductive systems. It advocates a bottom-up approach that aims at wisdom in experiencing, understanding, judging and acting within the limits of a human “bounded rationality” i.e. subject to humanly attainable pre-determined goals (satisficing rather than optimizing), complexity of the subject matter and the limited human computational abilities. This is possible through processes that apply the methods of heuristics rather than clearly determined algorithms in processes that span at Lonergan’s four levels of consciousness (the empirical, the intellectual, the rational, the responsible) and that require attention, intelligence, reasonableness and responsibility as resources

Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education

International audienceThis volume contains the Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education (ERME), which took place 9-13 February 2011, at Rzeszñw in Poland