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Project summary.
table of contents
title, size, dates, readership, subject matter, organization, editor, contributors, foreword, related books
summaries of chapters
 
 

Title:

Thirdness. Sense as a complex phenomenon
 

Size:

Approximately 300 pages, including diagrams, graphical simulation data and some illustrations of works of art.
 

Dates:

Some papers have been written from 1995 through 2003. The editional task is still underway....
 

Readership:

The book is meant for students of complex systems who have an interest in biological and social manifestations of subjectivity; as well as for students of philosophical hermeneutics with an interest in complexity in biological and social systems.
 

Subject matter:

The term 'thirdness' alludes to Aristotle's dictum 'tertium non datur', there is no third. The book's central idea is that such a 'third' does exist, namely in the presence of sense and lived experiences in living beings. 'Thirdness', then, is a generic term that points towards a domain of existence beyond our capacities of dichotomous thinking and formal description. More specifically, qualities of aliveness and sensitivity can be put into words, but not into austere formalisms. They exist, but their complexity only enables descriptions relative to an act of measurement or observation. This book offers a variety of explorations, from various points of view and disciplines, of the domain of thirdness, and it aims to contribute to a cross-fertilization between the fields of hermeneutics and of complex systems.
 

Organization:

The University of Groningen (Netherlands), Dept. of Psychology, housed several symposia where most of the contributors presented their ideas, elaborated afterwards to the various contributing chapters. The University of Maastricht (Netherlands), Medical Dept., enabled and supported the editorial work.
 

Editor:

Arno L. Goudsmit, PhD (1955) has degrees in psychology and philosophy. He is an assistant professor at the School of General Practice, Medical Dept. of the University of Maastricht (Netherlands), and he is a psychotherapist in private practice. His major field of interest is the epistemology of autonomous social processes. He has edited Self-organization in psychotherapy; demarcations of a new perspective, Heidelberg: Springer Verlag, 1989 (recently appeared in an italian translation) and he is the author of various papers on self-referential and self-organizing systems and on epistemological issues in psychotherapy research.
 

Contributors:

The authors' names (alphabetically) and disciplines:

Pietro Barbetta (Milano/Bergamo/Venice; sociology, psychotherapy)
Arno Goudsmit (Maastricht, Netherlands; psychotherapy, philosophy)
Yukio-Pegio Gunji & Masaki Ishikawa (Kobe, Japan; mathematics, biology, model theory)
Marvin & Netta Kaplan (Nof Yam, Israel; psychology, psychotherapy)
Don Mikulecky (Richmond, Virginia; physiology, biology)
Joachim Mowitz (Amsterdam; mathematics)
Gordon Pask (1928-1996; cybernetics, psychology)
Robert Rosen (1934-1998; physics, biology)
Maxine Sheets-Johnstone (Yachats, Oregon; philosophy)
John Shotter (Durhan, New Hampshire; psychology)
Gertrudis Van de Vijver (Ghent, Belgium; philosophy, artificial intelligence)
 

Related books:

The following books can be taken as a frame of reference for situating the present one:

Bernstein, R.J., Beyond objectivism and relativism: science, hermeneutics, and praxis. Philadelphia: Philadelphia U.P., 1983.

Dreyfus, H.L., S.E. Dreyfus, Mind over machine, The power of human intuition and expertise in the era of the computer. New York: Free Press, 1986.

Rosen, R., Life itself. A comprehensive inquiry into the nature, origin and fabrication of life. New York: Columbia Univ. Press, 1991.

Shotter, J., Knowing of the third kind. Selected writings on psychology, rhetoric, and the culture of everyday social life. Utrecht, 1987-1990. Utrecht: ISOR, 1990.

Vijver, G. Van de, New Perspectives on Cybernetics. Self-Organization, Autonomy and Connectionism, Dordrecht: Kluwer Academic Publishers (Synthese Library), 1992.
 
 
 
 

TABLE OF CONTENTS


"Preface to a book on the question of all questions"
                              by professor Otto E. Rössler (Tübingen, Germany)
 

INTRODUCTION

Arno Goudsmit (Maastricht, Netherlands): The complex and the naive

ONE: FORM AND MEANING
Yukio-Pegio Gunji & Masaki Ishikawa (Kobe):  Symbolization from SIGN to SYMBOL

Gertrudis Van de Vijver (Ghent, Belgium):  The emergence of meaning in classical, connectionist and morphodynamical theories. Constituency and compositionality revisited

Joachim Mowitz & Arno Goudsmit (Amsterdam/Maastricht):  A tempered paradox: sensitive movement in dynamic geometry.

TWO: COMPLEXITY AND AESTHETICS

Maxine Sheets-Johnstone (Yachats, Oregon): Surface sensitivity and the density of flesh

Don Mikulecky (Richmond, Virginia):  Art, science and the mind: cubism as a form of complexity

Marvin Kaplan & Netta Kaplan (Nof Yam, Israel):  The organization of experience: human psychological functioning as a self-organizing system.


THREE: SENSE AND SOCIAL PRAXIS

John Shotter (Durhan, New Hampshire): From within the event: a rhetorical-responsive version of social constructionism

Pietro Barbetta (Milano/Bergamo): Le conflit des interprétations in family therapy: different models for different issues

EPILOGUE

Arno Goudsmit: Complexity and the 'via negativa'.

APPENDIX
  Gordon Pask (1928-1996): Causality and relations (abstract only)
  Robert Rosen (1934-1998): Foldings and unfoldings (abstract only)
 

SUMMARIES OF CHAPTERS
 

CHAPTER 1
 
 

Arno Goudsmit
 
 

Introduction: The complex and the naive

'Thirdness' is a generic term that points towards a domain of thinking beyond the dichotomies of formalized description. The present introductory chapter relates 'thirdness' to the notions of 'sense' and
'complexity'. Sense occurs in living beings, and it is maintained that the complexity of the living organization resides in its capacity to be sentient and to have lived experiences. Furthermore, it is argued that sense can be regarded as a tertium, an event occurring between living beings, as such being not only the locus of identification between observer and observed, but also their common source. At this locus there is a non-distinction between what is sensed and how it is sensed. This non-distinction cannot be formalized, but it is a substantial property of what is called 'naive perception'.

 

PART ONE: FORM AND MEANING

CHAPTER 2
 

Yukio-Pegio Gunji & Masaki Ishikawa
 

Symbolization from SIGN to SYMBOL

In starting from biosemiotics, the process of symbolization is discussed by focusing on the aspect of an observer. Because of indefiniteness of an observer, both a negative expression of normal form of the code (SIGN) and a positive expression of indefinite code (SYMBOL) are found in the aspect of signs.  In this scheme, symbolization can be expressed by the revolution from SIGN to SYMBOL, which is formalized as the perpetual invalidation of adjunction (formal definite code) generating indefinite limits and co-limits.  This is illustrated by a particular dynamical model of which the adjunction between grammars and languages is perpetually invalidated and a grammar is transformed in time development.
 
 

Yukio-Pegio Gunji  is professor at Kobe University (Department of Earth & Planetary Sciences,
Faculty of Science), and researches theoretical models of evolution, development, self-organization and emergence. He graduated at the faculty of Science, Tohoku University in 1981, and he received his
Dr. Sc. degree from Tohoku University in 1986. He has published in 1997 a book entitled "Internal Measurement", together with Professor K. Matsuno and with Professor O.E. Rossler (Seido-sha Pub., Tokyo,
in Japanese), and he is the author of many papers in technical journals.

Masaki Ishikawa was born in 1970, and studied at the faculty of applied biological school, Hiroshima
University in 1994. He received his Master's degree from the graduate school of education, Osaka-Kyoiku University, and received his Doctor of Science degree from the graduate school of science and technology Kobe University in 2000. His main research is on the studies of ethology and ecology of fish.

CHAPTER 3
 

Gertrudis Van de Vijver
 
 The emergence of meaning in classical, connectionist and morphodynamical theories. Constituency and compositionality revisited

The problem of the emergence of meaning is today crucial in the two dominant paradigms of cognition. In the classical cognitivist approach, it is attempted to understand and explain cognition on a formal basis in purely symbolic terms, without taking into account the levels underlying cognitive phenomena (subsymbolic, perceptual, neural, biological, ...). In the connectionist approach, on the contrary, the automatisms which are described at the symbolic level in the classical paradigm on the basis of discrete structures (symbols, symbolic expressions, rules, inferences, ...) are considered as formal macrostructures emerging from an underlying dynamics at the lower, subsymbolic level. As a consequence, the relation between syntax and semantics is interpreted in current connectionism in a way fundamentally different from that of classical cognitivism.

We propose to analyze here the relation between syntax and semantics in the two paradigms on the basis of the current debate on constituent and compositional structure. The criticisms which are put forward in the current morphodynamic theories, in particular that of Jean Petitot, will be used to clarify the epistemological status of emergence in connectionism, and will help to show the fundamental shortcomings that are prevalent in both paradigms with regard to the interpretation of the relation between emergence, causality and explanation.
 
 

Gertrudis Van de Vijver is a Senior Research Associate at the Belgian Fund for Scientific Research, affiliated to the Department of Philosophy and Moral Science at the University of Ghent, Blandijnberg 2, 9000 Ghent. She has been working in the field of epistemology on the problems of teleology and self-organization in cybernetics, cognitive sciences and connectionism. She published a.o.: Van cybernetica naar connectionisme. Een epistemologische studie van doelgerichtheid, Ghent, Akademia Press, 1991. She is the editor of New Perspectives on Cybernetics. Self-Organization, Autonomy and Connectionism, Dordrecht, Kluwer Academic Publishers, 1992, and co-editor of Proceedings of the International Seminar on Evolutionary Systems, Vienna 1995, 1996 (to appear as: Evolutionary Systems, G. Van de Vijver, S. Salthe and M. Delpos, eds.).

 

CHAPTER 4
 
Joachim Mowitz & Arno Goudsmit
 
 

A self-modifying process in dynamical geometry

Self-referential structures are often considered to result in paradoxes. However, if the development of self-reference toward paradox is taken as a process in time, then such temporization permits the study of structures that contain self-reference within dynamically evolving systems that are capable of forestalling the trap of paradox. The present paper aims at describing a class of such systems.

We will introduce a process that generates a particular topological space in which this kind of network is defined. Special attention will be given to the moments at which the self-modifications occur. It will be maintained that at these moments processes are at work that emerge, fully context-dependent, from the configurations generated thus far, without their rule being specified in advance. These transient moments of self-modification are instances of 'thirdness': they are events that transcend the set of constraints thus far in operation. They can be claimed to follow an aesthetic principle. Here some crucial differences with cellular automata or genetic algorithms can be recognized: the latter follow rules at every step and they do not re-design themselves in a way that is specified as the process goes on. It is for that reason that, next to presenting results of recent computer simulations, also some logical limits to these simulations will be discussed.
 
 

Joachim Mowitz (1944) studied mathematics (B.A.) in Hamburg and pure and applied mathematics, with specialization in algebraic topology (M.A.), in Heidelberg. He has worked as a scientific programmer at the department of biochemistry of the German Cancer Research Center, and at various scientific programmer's positions at the University of Amsterdam. He has published papers and written computer programs a.o. on autonomous processes and dynamical geometries in topological spaces.

 
 

PART TWO: COMPLEXITY AND AESTHETICS

CHAPTER 5
 
 

Maxine Sheets-Johnstone

Surface sensitivity and the density of flesh

Skin and other animate coverings are sensitive to touch and movement. This essay spells out the profound epistemological significance of surface sensitivities in terms of an in-depth morphology. It surveys the evolutionary import of tactility in the lives of animate forms, introducing in this context the intimate linkage between what existential philosophers have called "the flesh of objects" and our own flesh. It demonstrates this linkage concretely in a consideration of paleolithic cave art, showing in particular how a sense of surface and a density of meaning derive from nonlinguistic corporeal understandings of ourselves as animate forms. It concludes by putting these insights into critical twentieth-century cultural perspective, and by pinpointing in particular the challenge of an in-depth morphology.
 
 

Maxine Sheets-Johnstone is an independent scholar who teaches periodically in the Department of Philosophy at the University of Oregon, and who recently occupied the yearly Endowed Chair in the Humanities at Albright College. She has published numerous articles in philosophy, humanities, art, and science journals. She is the author of The roots of power: animate form and gendered bodies (1994); The roots of thinking (1990); The phenomenology of dance (1966/1980); and The primacy of movement (1999). She is the editor of Giving the body its due (1992), and Illuminating dance: philosophical perspectives (1984).

 

CHAPTER 6
 

Don Mikulecky
 

Art, science and the mind: cubism as a form of complexity

Cubism was a significant "paradigm shift" in painting just after the turn of the century. It has been associated with changes in science which were happening in parallel with its advent. However, the thesis of this work is that the nature of the paradigm shift, of which cubism was the transitional representation, had a new notion of space and time as its "trademark", but, in fact was a deeper transition than even that. In order to demonstrate this, certain parallels between art and science are developed. In particular, the way the human mind deals with both art and science are shown to have certain similar characteristics, which are best formulated in terms of the modeling relationship. The modeling relationship concept is used to emphasize the interactive nature between human cognition and the subject matter of both art and science. Having established this, it is then shown that cubism introduced an artistic equivalent of complexity into the modeling relation underlying painting. The term complexity is defined with some care and its applicability to art as well as science is established. Finally, the fact that cubism was actually the introduction of complexity into painting at the turn of the century, is shown to make this art form a forerunner of some of our most recent breakthroughs in scientific thinking. In order to do this, it is shown that the difference between non- computable formalisms and computable formalisms in scientific complexity has a strong parallel in the difference between pictorial painting and representational painting. It is this character of cubism rather than the mere change in space-time perception which it entails which is its major contribution to our current intellectual situation. The use of computers in art and, in particular, the use of fractal geometry in art, will be shown as a retrogressive intellectual step when viewed in this context. The computability of this form of art makes it "simple" and "mechanistic" when compared to cubism as a complex art form.
 
 

Donald C. Mikulecky (1936) is Professor of Physiology and Affiliate Professor of Biology at Virginia Commonwealth University, Richmond, VA. He is the author of Application of Network Thermodynamics to Problems in biomedical Engineering, NYU Press, NY, 1993, and of numerous papers on network thermodynamics and on the complexity of the living organization. CHAPTER 7
 

Marvin L. Kaplan & Netta R. Kaplan
 
 

The organization of experience: human psychological functioning as a self-organizing system.

The development of human psychological functioning in an individual is described in terms of the development of an autonomous self-organizing system. It is that which emerges as the organizational activity that is securing the system's coherence and continuity. Organizational activity exists in present time; ongoing psychological functioning evolves as it is creating experiential existence which is spanning the immediate past and the immediate future.

Recent developments in scientific thinking have challenged traditional understandings of the nature of the universe and of how natural phenomena function. Rather than assuming a fixed universe in which functioning occurs according to universal laws of linear dynamics the newer concepts pose a continually changing universe in which qualities of orderliness and stability are no longer taken as anchored in fixed properties of physical composition but these qualities exist as they are actively ordering and stabilizing themselves through their own ongoing non-linear activity.

This understanding opens new ways of appreciating how complex systems such as human psychological functioning arise and exist. In this article we examine the traditional orientation that underlies contemporary theorizing and research in psychology and cite some basic difficulties. We then define self-organizational functioning and show how this perspective avoids these difficulties and provides a means of describing the emergence and evolution of human psychological functioning in a unified and comprehensive theory.

Marvin L. Kaplan received his Ph.D. in Clinical Psychology from the State University of New York at Buffalo, in 1956. Netta R. Kaplan received her Ph.D. in Communication Disorders and Speech Sciences from Wayne State University, in 1972. After having been affiliated to the dept. of Psychology, University of Windsor, Ontario, both are currently working in Nof Yam, Israel, as consultants, educators, writers and clinicians, with an emphasis upon training individuals in the helping professions in experiential psychotherapy. PART FOUR: SENSE AND SOCIAL PRAXIS
 

CHAPTER 8
 

John Shotter
 
From within the event: a rhetorical-responsive version of social constructionism

Common to all versions of social constructionism, is the central assumption that - instead of the study of the inner dynamics of the individual psyche (romanticism and subjectivism), or the already determined characteristics of the external world (modernism and objectivism), the two polarities in terms of which we have thought about ourselves in recent times (Gergen, 1991; Taylor, 1989) - it is the contingent flow of continuous communicative interaction between human beings which becomes the central focus of concern. It is from within this not wholly orderly (i.e., chaotic) flow of relational, self-other relationships, constructionists maintain, that all the other socially significant dimensions of interpersonal and person-world interaction - with their associated modes of being: either subjective or objective - originate and are formed.

Our central topic of study, then, is the making of social relations. They are formed, constructionists maintain, not automatically, according to already established rules or principles, but by different, particular, practical negotiations, conducted at-the-time, on-the-spot, constrained but not determined by the 'resources' different socio-historical contexts make available, or afford. Social constructionism thus gives rise to a concern, not only with the nature of social relations, but also with their temporal development, i.e., with how historically they become 'in-formed' with the 'living ideologies' of the society in which they subsist.

Past concentration upon one or the other of the two polarities above (subjectivism or objectivism) gave rise to an ambition to locate a world beyond the social and historical, and to attempts to discover this world, either in the depths of the organic, perhaps, or in abstract principles or systems. The rhetorical-responsive version of social constructionism that I want to discuss - drawing upon the work of Billig (1987) and Bakhtin (1984, 1986) - takes the living utterances of particular individuals, voiced in concrete social contexts, addressed to particular audiences, as its analytic unit. Such a unit, in being 'shaped' by different speakers, in different ways, in different contexts, is revealing (in that 'shaping' process) of many of the important influences making people who they are, and provides an instrument through which to 'see' such influences at work, from within the processes concerned.

Professor John Shotter is currently at the Department of Communication, University of New Hampshire. His long term concern has been with the social conditions conducive to the development of autonomous personhood, social identities, and responsible action - especially with the metamethodological issues involved in their study. He is the author of Images of Man in Psychological Research (Methuen, 1975), of Human Action and is Psychological Investigation (with Alan Gauld, Routledge, 1977), of Social Accountability and Selfhood (Blackwell, 1984), and Knowing of the Third Kind: Essays on Rhetoric, Psychology, and the Culture of Everyday Social Life (ISOR, Utrecht, 1990). He is also the editor with Kenneth J. Gergen of Texts of Identity (Sage, 1989), and with Ian Parker the editor of Deconstructing Social Psychology (Routledge, 1990). More recently he published Cultural politics of everyday life: social constructionism, rhetoric and knowing of the third kind (Univ. Of Toronto Press, 1993) and Conversational realities: constructing life through language (Sage, 1993)

CHAPTER 9
 
 Pietro Barbetta
 
 Le conflit des interprétations in family therapy: different models for different issues

Following an expositive methodology used by Paul Ricoeur (1969), I will propose different hermeneutics for therapeutic conversation.

The first one is a constructivist hermeneutics. According it, the therapy systems are conceived as "observer systems", in search of autopoiesis and organizational closure of family systems. Their main focus is to produce "perturbations" in order to help family systems to re-organize themselves. This approach has found a concrete application in counterparadoxical interventions (Selvini Palazzoli et al., 1978).

The second one is constructionist hermeneutics, that considers the therapist as a "co-constructor" of stories. The therapist is like a storyteller, meeting other storytellers (the members of the family), and they try to change the old stories, constructing together new stories. Externalization of symptoms is one of the clearest examples of this approach (White, 1988).

The last hermeneutics I will propose, is that of the therapist as a "de-constructor". This approach focuses upon two aspects, generally considered disparate, viz. cultural patterns and emotions. The main idea is that individual emotions are based on the "moral order" of a particular cultural pattern, and that both emotions and moral order coexist in language. In this sense "curiosity" (Cecchin, 1987, 1992 - Cecchin et al., 1992), as a way to get strange taken-for-granted "data", is the most important source of the therapist.

We will see that these three different approaches give rise to different (often irreconcilable) interpretations (Ricoeur, 1969) about the "same story". I will argue that the choice among those different approaches is an undecidable question at a theoretical level, and has mainly to do with "praxis" and "phronesis" of the therapists. After having analyzed the differences, I will propose a dialogue among those differences.

References:

Cecchin, G., "Hypothesizing, circularity and neutrality revisited: an invitation to curiosity", Family Process, 26, 205-13, 1987.

Cecchin, G., "Constructing therapeutic possibilities", S. McNamee and K. Gergen (eds.), Therapy as Social Construction. Sage, London, 1992.

Cecchin, G., G. Lane and W.A. Ray, Irreverence. A strategy for therapist's survival. Karnac Books, London, 1992.

P. Ricoeur, Le conflit des interprétations. Essais d'hermeneutique. Paris, 1969.

Selvini Palazzoli, M., L. Boscolo, G. Cecchin and G. Prata, Paradox and Counterparadox. Jason Aronson, New York, 1978.

White, M., "The externalizing of the problem and the reauthoring of lives and relationships. Dulwich Centre Newsletter. Summer, 1988.
 
 

Pietro Barbetta (PhD) is a family therapist and Professor of Family Therapy and Counselling at the Centro Milanese di Terapia della Famiglia (Milano), Professor of Developmental Psychology at Venice University, and Professor of Intercultural Communication at Bergamo University.


CHAPTER 10

Arno Goudsmit
 
 Epilogue. Complexity and the 'via negativa'
 
 

There is a link from Nicolaus Cusanus' fifteenth century De docta ignorantia to Merleau-Ponty's (1964) Le Visible et l'Invisible. Both works define a negative way. Cusanus deals with man's incapacity to know God. It is from from our failures to know, that we attain some understanding of God. Likewise, Merleau-Ponty defined a 'negative philosophy', as a discipline that reflects upon the impossibility of consciousness to grasp itself and have itself, in its acts of reflection, as an object of these reflections.

These negative disciplines are of interest to students of complex systems. Especially the self-referentiality that is intrinsic to some complex systems, such as living beings, cannot be approached but by accepting our incapacity to know them in an encompassing way. It is maintained that a 'negative' conceptualization of complexity would shed some positive light upon our capacities, as living beings and as humans, to create sense and to assign meanings.
 
 

APPENDIX

editor's addendum:
Professor Pask died on the 29th of March, 1996, and professor Rosen on the 30th of December, 1998. The summaries they submitted for this book are included here as a tribute to their genius.
 

Gordon Pask
 

Causality and relations

There is a prevailing tendency to ascribe a cause to each effect, it is almost the same as ascribing a blame to each event encountered. The idea of multiple causality as in Singer's logic is of course ubiquitous, but seldom appreciated. As a matter of fact I know of no causality which can be blamed, even upon Nature, which is unique so that there is nobody to blame. Only causalities which occur as a result of many events and it is of these events and their outcomes that I would like to speak.

There is an understandable, but couterfactual idea that relations are n-adic where n=2, or even n=1. I mean, of course, irreducibly, relations which are of higher adicity and cannot be reduced to 2-adic relations by some tree-like procedure such as is common in computer programming. I may contest this on formal grounds by appeal to Borromean rings, a triadic relation which, by slicing one ring of any of the three will yield three rings, not as you might expect, a chain and a ring, as a 2-adic relation would do. 3-adicity may also be demonstrated by the fact that if you adhere to the von Neumann and Morgenstern theory of games, i.e. zero sum games in particular, one has to invoke at least three players in order to obtain the required actuality of a cooperative game since one cannot have a coalition of less than two players. I can appeal to many other sources at this level, but my intention is to show that the great majority of relations are of very much higher adicity.

This is an elusive matter, since if I wish to obtain a certain kind of result I may pretend to a 2-adic binary relation and the statistics based upon it. For example, if I am a wine vendor I may try out which of many mixtures of wine, ethyl alcohol, water, flavouring, colouring matter are most saleable. But, you see I have examined not what is called taste. I have shown nothing about taste, only about saleability, which may be related to taste, but if nothing to do with the taste of the wine connoisseur. The same applies to more social variables. It applies to hope, fear, aggression, submission, persuasion, endeavour, entreaty. It applies a fortiori to happiness, to any pretence we have to be doing "good".
 
 

Gordon Pask (1928-1996), B.A., M.A., Ph.D., D.Sc. Professor Pask is considered as one of the 'founding fathers' of cybernetics, in particular the cybernetics of self-steering systems. He has published a vast amount of papers on this subject matter. His major work is the trilogy on 'conversation theory' (The cybernetics of human learning and performance, 1975; Conversation, cognition and learning, 1975; Conversation theory: applications in education and epistemology, 1976).
 

Robert Rosen
 

Foldings and unfoldings

"Folding" is a familiar process in the biology of polypeptide biochemistry. It produces entities ("sites") which play essential functional roles (recognition, specificity, catalysis) which, once formed, cannot be fractionated or separated from the larger system in which they are embedded. "Unfoldings" provide ways to systematically explore what kinds of things are near a singularity of some kind. Both of these notions lead, in separate ways, out of small, mechanistic, simple worlds which we ultimately inherit from Newtonian mechanics, and from pure syntax, into a larger world, in which contexts and referents are basic. We shall discuss some of the impacts of these ideas, with particular attention to the nature of organisms, and the structure of mathematics.
 
 

Robert Rosen (1934-1998). Education: BS (Mathematics), Brooklyn College 1955; MA (Mathematics, Columbia University 1956; PhD (Mathematical Biology, University of Chicago 1959. Professor Rosen published 300 papers, five monographs (among which Fundamentals of measurement and representation in natural systems, 1978 and Life itself, 1991. Editor of series Progress in Theoretical Biology (seven volumes), etc.