Marriages of Mathematics and Physics: A Challenge for Biology

The human attempts to access, measure and organize physical phenomena have led to a manifold construction of mathematical and physical spaces. We will survey the evolution of geometries from Euclid to the Algebraic Geometry of the 20th century. The role of Persian/Arabic Algebra in this transition and its Western symbolic development is emphasized. In this relation, we will also discuss changes in the ontological attitudes toward mathematics and its applications. Historically, the encounter of geometric and algebraic perspectives enriched the mathematical practices and their foundations. Yet, the collapse of Euclidean certitudes, of over 2300 years, and the crisis in the mathematical analysis of the 19th century, led to the exclusion of “geometric judgments” from the foundations of Mathematics. After the success and the limits of the logico-formal analysis, it is necessary to broaden our foundational tools and re-examine the interactions with natural sciences. In particular, the way the geometric and algebraic approaches organize knowledge is analyzed as a cross-disciplinary and cross-cultural issue and will be examined in Mathematical Physics and Biology. We finally discuss how the current notions of mathematical (phase) “space” should be revisited for the purposes of life sciences

Platonic model of mind as an approximation to neurodynamics

Hierarchy of approximations involved in simplification of microscopic theories, from sub-cellural to the whole brain level, is presented. A new approximation to neural dynamics is described, leading to a Platonic-like model of mind based on psychological spaces. Objects and events in these spaces correspond to quasi-stable states of brain dynamics and may be interpreted from psychological point of view. Platonic model bridges the gap between neurosciences and psychological sciences. Static and dynamic versions of this model are outlined and Feature Space Mapping, a neurofuzzy realization of the static version of Platonic model, described. Categorization experiments with human subjects are analyzed from the neurodynamical and Platonic model points of view

A cognitive view of relevant implication

Relevant logics provide an alternative to classical implication that is capable of accounting for the relationship between the antecedent and the consequence of a valid implication. Relevant implication is usually explained in terms of information required to assess a proposition. By doing so, relevant implication introduces a number of cognitively relevant aspects in the denition of logical operators. In this paper, we aim to take a closer look at the cognitive feature of relevant implication. For this purpose, we develop a cognitively-oriented interpretation of the semantics of relevant logics. In particular, we provide an interpretation of Routley-Meyer semantics in terms of conceptual spaces and we show that it meets the constraints of the algebraic semantics of relevant logic

Moral Intuitions and Organizational Culture

Many efforts to understand and respond to a succession of corporate scandals over the last few years have underscored the importance of organizational culture in shaping the behavior of individuals. This focus reflects appreciation that even if an organization has adopted elaborate rules and policies designed to ensure legal compliance and ethical behavior, those pronouncements will be ineffective if other norms and incentives promote contrary conduct. Responding to the call for creating and sustaining an ethical culture in organizations requires appreciating the subtle ways in which various characteristics of an organization may work in tandem or at cross-purposes in shaping behavior. The idea is to identify the influences likely to be most important, analyze how people are apt to respond to them, and revise them if necessary so that they create the right kinds of incentives when individuals are deciding how to act. This can be a tall order even if we assume that most behavior is the result of a deliberative process that weighs multiple risks and rewards. It’s even more daunting if we accept the notion that conscious deliberation typically plays but a minor role in shaping behavior. A focus on what two scholars describe as “the unbearable automaticity of being” posits that most of a person’s everyday life is determined not by conscious intentions and deliberate choices but by mental processes outside of conscious awareness. In this article, I discuss a particular strand of research that is rooted in the study of non-conscious mental processes, and consider its implications for ethics and culture in the organizational setting. This is work on the process that we use to identify and respond to situations that raise what we think of as distinctly moral questions. A growing body of research suggests that a large portion of this process involves automatic non-conscious cognitive and emotional reactions rather than conscious deliberation. One way to think of these reactions is that they reflect reliance on moral intuitions. When such intuitions arise, we don’t engage in moral reasoning in order to arrive at a conclusion. Instead, we do so in order to justify a conclusion that we’ve already reached. In other words, moral conclusions precede, rather than follow, moral reasoning. If this research accurately captures much of our moral experience, what does it suggest about what’s necessary to foster an ethical organizational culture? At first blush, the implications seem unsettling. The non-conscious realm is commonly associated with irrational and arbitrary impulses, and morality often is characterized as the hard-won achievement of reason over these unruly forces. If most of our moral judgments are the product of non-conscious processes, how can we hope to understand, much less influence, our moral responses? Are moral reactions fundamentally inscrutable and beyond appeals to reason? If reason has no persuasive force, does appreciation of the non-conscious source of our moral judgments suggest that any effort to promote ethical conduct must rest on a crude behaviorism that manipulates penalties and rewards? I believe that acknowledging the prominent role of non-conscious processes in shaping moral responses need not inevitably lead either to fatalism or Skinnerian behaviorism. Research has begun to shed light on how these processes operate. Related work has suggested how our moral responses may be rooted in human evolution. This perspective focuses on the ways in which our capacity for moral judgment is embedded in physical and mental processes that have provided an adaptive advantage in human evolution. These bodies of research contribute to a richer portrait of human cognition and behavior that can be valuable in thinking about how to promote ethical awareness and conduct. As Owen Flanagan has put it, “seeing clearly the kinds of persons we are is a necessary condition for any productive ethical reflection.” If there were such a thing as a normative theory of human movement, it would be futile if it exhorted us to fly. Efforts to create an organizational culture that encouraged people to fly would be doomed as well. In thinking about ethics, we need to have a sense of what lies between simply accommodating what we tend to do and demanding that we fly. My hope is that this article takes a small step in that direction

Natural and Artificial Systems: Compare, Model or Engineer?

Some areas of biological research use artificial means to explore the natural world. But how the natural and artificial are related across wide-ranging research areas is not always clear. Relations differ further for bioengineering fields. We propose a taxonomy which would serve to elucidate distinct relations; there are three ways in which the natural is linked to the artificial, corresponding with distinct methods of investigation: i) a comparative approach (natural vs artificial) in which artificial systems are treated in the same way as natural systems, ii) a modeling approach (natural via artificial) in which we use artificial systems to learn about features of natural ones, and iii) an engineering approach (natural pro artificial) in which natural systems are used to draw inspiration for artefacts. Ambiguities about and between these approaches limit the development of fields and impact negatively on interdisciplinary communication

Facts, skills and intuition : A typology of personal knowledge

This paper introduces a knowledge model in which the types of knowledge are formed according to the nature of knowledge. First we use Ryle’s distinction of “that” and “how” knowledge, to which we add further three types. The five knowledge types are then synthesized using Polanyi’s distinction of focal and subsidiary awareness. The resulting model distinguishes three types of knowledge, the facts, the skills, and the intuition; all three having focal and subsidiary parts. We believe that this knowledge model is comprehensive in the sense that can classify any knowledge and it also has great explanatory power, as it is demonstrated through illustrative examples. Moreover, the model is elegant and easy to use, which facilitates our understanding of the domain of personal knowledge. Therefore we expect our findings to be useful for both researchers and educators in the field of knowledge and knowledge management

Beyond Desartes and Newton: Recovering life and humanity

Attempts to ‘naturalize’ phenomenology challenge both traditional phenomenology and traditional approaches to cognitive science. They challenge Edmund Husserl’s rejection of naturalism and his attempt to establish phenomenology as a foundational transcendental discipline, and they challenge efforts to explain cognition through mainstream science. While appearing to be a retreat from the bold claims made for phenomenology, it is really its triumph. Naturalized phenomenology is spearheading a successful challenge to the heritage of Cartesian dualism. This converges with the reaction against Cartesian thought within science itself. Descartes divided the universe between res cogitans, thinking substances, and res extensa, the mechanical world. The latter won with Newton and we have, in most of objective science since, literally lost our mind, hence our humanity. Despite Darwin, biologists remain children of Newton, and dream of a grand theory that is epistemologically complete and would allow lawful entailment of the evolution of the biosphere. This dream is no longer tenable. We now have to recognize that science and scientists are within and part of the world we are striving to comprehend, as proponents of endophysics have argued, and that physics, biology and mathematics have to be reconceived accordingly. Interpreting quantum mechanics from this perspective is shown to both illuminate conscious experience and reveal new paths for its further development. In biology we must now justify the use of the word “function”. As we shall see, we cannot prestate the ever new biological functions that arise and constitute the very phase space of evolution. Hence, we cannot mathematize the detailed becoming of the biosphere, nor write differential equations for functional variables we do not know ahead of time, nor integrate those equations, so no laws “entail” evolution. The dream of a grand theory fails. In place of entailing laws, a post-entailing law explanatory framework is proposed in which Actuals arise in evolution that constitute new boundary conditions that are enabling constraints that create new, typically unprestatable, Adjacent Possible opportunities for further evolution, in which new Actuals arise, in a persistent becoming. Evolution flows into a typically unprestatable succession of Adjacent Possibles. Given the concept of function, the concept of functional closure of an organism making a living in its world, becomes central. Implications for patterns in evolution include historical reconstruction, and statistical laws such as the distribution of extinction events, or species per genus, and the use of formal cause, not efficient cause, laws