Fuzzy Epistemology: The Fuzziness of Experimental Systems*

Rudolf Seising Friedrich-Schiller-University Jena, Germany � Ernst-Haeckel-Haus, Institut für Geschichte der Medizin, Naturwissenschaft und Technik,

Berggasse 7, 07745 Jena, Germany Rudolf.seising@meduniwien.ac.at

* This work is partially supported by NSF Grant #2003168 and CNSF Grant #9972988.

Abstract – Fuzzy sets and systems (FSS) fill the gap between scientific theories and observable real systems and phenomena. In philosophy and history of science and technology this gap carries a great potential for epistemological discussions. A new approach in this area is Hans-Jörg Rheinberger’s “historical epistemology” dealing with the concept of “experimental systems”. In this paper we first summarize some facts on the theory of FSS and Computational Intelligence, then we give a brief sketch of Rheinberger’s “experimental systems”, “epistemic” and “technological things”, and finally we propose to combine Rheinberger’s approach with FSS methodologies.

I. INTRODUCTION

In history and philosophy of science and technology there is one mode of knowledge that has not been mentioned very often in textbooks and journal literature: unsharp or fuzzy knowledge. However, in the second half of the 20th century Lotfi A. Zadeh created successful tools to model this mode of knowledge: the theory of Fuzzy sets and systems (FSS) [1], [2], Computing with words (CW) [3], [4], and the Computational theory of perceptions (CTP) [5]. In 1996 he proposed CW as a potential replacement of exact computing with numbers based on the theory of Fuzzy sets and systems. Three years later he published the CTP that is based on the methodology of CW. In CTP, words play the role of labels of perceptions and, more generally, perceptions are expressed as propositions in natural language” ([4], p. 105). Fig. 1 shows these methodologies in a “stack hierarchy” and since the turn of the century Zadeh is intended to establish this hierarchy of methodologies as a new direction in of Artificial Intelligence (AI) � in Computational Intelligence (CI). [5].

Fig. 1 Left: Lotfi A Zadeh, right: The “stack hierarchy” of Zadeh’s methodologies in Computational Intelligence

In my research studies in history and philosophy of science concerning the genesis and philosophy of the theory of fuzzy sets and systems and its initial applications I have shown that it was the gap between exact mathematical formulated empirical theories at the one hand and observable real systems at the other hand that gave reason in the beginning 1960s to look for a new kind of mathematics [6], [7], [8], [9]. The electrical engineer and Berkeley-professor Lotfi A. Zadeh established this “fuzzy mathematics” in the second half of the 1960s [1], [2], [10]. Already in an article of the year 1962 he enunciated that “we need a radically different kind of mathematics, the mathematics of fuzzy or cloudy quantities which are not describable in terms of probability distributions.” ([11], p. 857) and in his seminal article on “Fuzzy Sets” in the year 1965 he presented his new mathematical theory [1]. Why was this needed? – Because there was “a fairly wide gap between what might be regarded as ‘animate’ system theorists and ‘inanimate’ system theorists at the present time, and it is not at all certain that this gap will be narrowed, much less closed, in the near future”, Zadeh wrote already in 1962, and to continue Zadeh’s line of thought: “There are some who feel that this gap reflects the fundamental inadequacy of conventional mathematics – the mathematics of precisely defined points, functions, sets, probability measures, etc. – for coping with the analysis of biological systems, and that to deal effectively with such systems, which are generally orders of magnitude more complex than man-made systems, we need a radically different kind of mathematics, the mathematics of fuzzy or cloudy quantities which are not describable in terms of probability distributions. Indeed, the need for such mathematics is becoming increasingly apparent even in the realm of inanimate systems, for in most practical cases the apriori data as well as the criteria by which the performance of a man-made system are judged are far from being precisely specified or having accurately known probability distributions.” ([11], p. 857). This gap carries a great potential for epistemological discussions in philosophy of science and technology! Scientific work has two components: in the theoretical part of scientific work scientists develop and formulate concepts, hypotheses and theories, sometimes they can confirm and

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sometimes they have to reject these theoretical things. In the other part of scientific work – let’s call it practical or experimental – the scientists design and plan experiments, they perform and control and replicate these experiments. To produce scientific knowledge in modern science and technology we need both parts: we need theoretical concepts and experimental systems. Scientists observe real systems or phenomena and they measure data, they establish laws and they introduce empirical theories that say that the laws hold for the data. That is to say: To study systems or phenomena in reality we connect them with a theoretical structure. To this end we give them self a structure. How to do that is not clear! – This is one of the central problems in philosophy of science. The German philosopher of science Wolfgang Balzer wrote in his book on empirical theories: “The problem is that we create a connection between real systems and theoretical structures. We assume that this can be done. Without this assumption it is senseless to talk about empirical science.” ([12], p. 289) In the so-called „structuralist view of scientific theories these real systems connected with a theoretical structure were called “intended systems” of the theory [12], [13], [14], [15]. In his scientific research based on an intended system the scientist gets a data structure and he builds a model, which represents the structure of the system. Frequently we say that we have by the theory a “picture of the reality” but this is a very simple expression for what we do in scientific work (see fig. 2).

Fig. 2 Two layers of structures in scientific research.

In some earlier papers I examined Zadeh’s methodology stack (see fig. 1) for bridging the gap between real and theoretical systems from a philosophical point of view. To this end, I reviewed the structuralist approach of scientific theories and then modified or “fuzzified” this approach by extending the structuralist framework with fuzzy sets and fuzzy relations to model perceptions of observers. This approach provides a new view of the “fuzzy” relationship between empiricism and theory. Empiricism is represented by the so-called “empirical layer”, where we find real systems and phenomena, whereas theories are represented by (potential) models in the so-called “theoretical layer” (see fig. 3). For this purpose see also [16], [17], [18].

Fig. 3 Three layers of structures in scientific research.

The proposed fuzzy modification of the structuralist

approach to philosophy of science pertains to the empirical layer. A distinction can be made between real systems and phenomena, on the one hand, and perceptions of these entities, on the other. Thus a lower layer – the real layer – is introduced and the former empirical layer is renamed the “fuzzy layer”, as a minimal (fuzzy) structure is imposed by the scientist’s observations. These are perception-based systems and thus must be distinguished from real systems and phenomena that have no structure before someone imposes one upon them. In the following sections of the paper we will present a more sophisticated view.. For this reason we give in section II of this paper a brief sketch of a new view. in history and philosophy of science that was proposed by the Swiss historian of science and molecular biologist Hans-Jörg Rheinberger in the last decade of the 20th century. Rheinbergers proposal for “historical epistemology” means a turnaround in philosophy and history of science. He made allowance for the situation that historians and philosophers of science in the 1980s and 1990s concentrated their attention to the experiments in science. Rheinberger’s approach is a historical epistemology of modern experimentation that deals with the concept of so-called “experimental systems”, “epistemic things” and “technological things”. In the next sections we follow his arguments to show that “epistemic things” are vague or fuzzy and that they “move the world of science” ([20], p. 220). Rheinberger considered these “fluctuating objects” and “imprecise concepts” – as he also called them - in detail in his historical work. We will give one example of his results: the fluctuating object “gene”. In section IV we try to combine Rheinberger’s approach with Zadehs methodologies (respectively theories) of FSS, CW, and CTP and the fuzzy structuralism I mentioned in this introduction already. We show that this combination could be very fruitful in the epistemological thinking of the 21st century!

II. EXPERIMENTAL SYSTEMS

A. Basics of the Theory of Experimental Systems What is an experimental system? � Hans-Jörg Rheinberger illustrated: “This notion is firmly entrenched in the everyday practice and vernacular of the twentieth-century life scientists, especially of biochemists and molecular biologists. Scientists use the term to characterize the scope, as well as the limits and the constraints, of their research activities. Ask a laboratory scientist what he is doing, and he will speak to you about his “system”. Experimental systems constitute integral, locally manageable, functional units of scientific research.” ([19], p. 246) In Rheinberger’s epistemology we find again two parts of scientific research, that he named epistemic and technical, respectively, but he emphasizes that there is no sharp boundary between, moreover this boundary is vague or fuzzy. Here is a brief sketch of his approach: “If there are concepts endowed with organizing power in a research field, they are embedded in experimental operations. The practices in which the sciences are grounded engender epistemic objects, epistemic things as I call them, as targets of research.” He considered these “fluctuating objects” and “imprecise concepts” – as he also called them - in detail in his historical work [19], [20], [23], [24], [25], [26], [29], [30]. Rheinberger’s starting point is the research process in science. From his point of view the scientific activity goes on in an experimental system. – Of course, philosophers of science often say that experiments have the role to proof or confirm or to refute scientific theories but since Ludwig Fleck’s Genesis and Development of a Scientific Fact [21] philosophers of science have to bear also in mind that a single experiment is only the degeneration of an elementarily complex situation – the experimental system, that was described by Fleck with these words: “Every experimental scientist knows just how little a single experiment can prove or convince. To establish proof, an entire system of experiments and controls is needed, set up according to an assumption … and performed by an expert.” ([21], p. 96.) A more important point stated by Fleck in his book is the following: “If a research experiment were well defined, it would be altogether unnecessary to perform it. For the experimental arrangements to be well defined the outcome must be known in advance; otherwise the procedure cannot be limited purposeful.” ([21], p. 86.) For Fleck’s work see also [7].

Rheinberger considers an experimental system as an “experimental arrangement designed to produce knowledge that we do not yet have” and – like Fleck – he considers them “as the smallest functional unit of research, designed to give answers to questions which we are not yet able clearly to ask. It is a ‘machine for making the future’. It is not only a device that generates answers; at the same time, and as a prerequisite, it shapes the questions that are gong to be answered. An experimental system is a device to materialize questions. It co-generates, so to speak, the phenomena or material entities and the concepts they embody.” ([23]), p. 309) B. Epistemic things and technical objects Let’s look to an experimental system more closely: Rheinberger discerns “two different yet inseparable structures or components”. The first he called “epistemic thing” and the second he called “technical object”. Epistemic things are not necessarily “objects” in the narrow sense; an epistemic thing is “a physical structure, a chemical reaction, a biological function whose elucidation is at the centre of the investigative effort. Since it is not and cannot be fixed from the beginning, it represents itself in a characteristic, irreducible vagueness, which is inevitable since it translates the fact that one does not exactly know what one is looking for.” ([23]), p. 310) The epistemic thing has “a fragile status to be in a certain way absent in its experimental presence; not that it were only hidden and could just be brought to light entirely by sophisticated manipulations. As a scientific object, it does not exist ready made; it is only in the process of its own material definition. How does this work?” ([25], p. 282) “In order to work, one needs an arrangement to which to refer for the experimental conditions or the technological [or technical] objects. In contrast to the former they are characteristically determined. They perform, at least for the purposes and within the conditions of their use, according to known regularities. They contain the scientific object in the double sense of the word: They embed it and they restrict it.” ([25], p. 310) But the constellation of epistemic and technical things in this constellation is not that simple: epistemic and technical things or objects are engaged in a non-trivial interaction. “The discrimination of these two types of things is a functional not a material one. They do not describe well-defined, fixed parts of the system. They rather define ‘places’ within it, and they are able to change places.” ([23], p.310). Or in other words: “Both elements are intertwined so closely as is the case with placing fusing at their borders, and the different terms can be assigned to one and the same material entity occupying those places. Nevertheless, their distinctness is clearly perceived in scientific practice. It does not only serve as a criterion for organization of laboratory work, it also organizes the standard scientific text.” ([25], p. 282) Thus, both components of scientific research, theory and empiricism, we find in Rheinberger’s historical epistemology, “epistemic” and “technical things”, and particularly he characterized them both as “vague”, “imprecise”, “fluctuation”, and. “fuzzy”.

Fig. 3 Left: L Fleck (1896-1961), right: H.-J. Rheinberger (born 1946.

B. Fluctuating Objects Rheinberger could show that experimental systems” operate most prolifically at the fuzzy boundary between the trivial and the complex. Experimental systems are machines for reducing complexity but to escape triviality, they must remain connected to the complexity of an “epistemic horizon”. It is the network of surrounding experimental systems that makes each of its elements take on its epistemic value. If ontic complexity has to be reduced in order to make experimental research possible, this very complexity is epistemically retained in the rich context of an experimental landscape, in which new connections and disconnections ca happen at any time, and where the boundaries of a scientific object continually fluctuate.”([19], p. 247.) In his article on Gene Concepts, published in the year 2000, he argued more detailed: “If there are concepts endowed with organizing power in a research field, they are embedded in experimental operations. The practices in which the sciences are grounded engender epistemic objects, epistemic things as I call them, as targets of research. Despite their vagueness, these entities move the world of science. As a rule, disciplines become organized around one or a few of these “boundary objects” that underlie the conceptual translation between different domains.” ([20], p. 220)

III. FOR EXAMPLE: THE GENE

As an example for these “fluctuating objects” Rheinberger considered in many publications the “gene”. Thus, in [20] he further wrote: “For a long time in physics, such an object has been the atom; in chemistry, the molecule; in classical genetics, it became the gene. It is the historically changing set of epistemic practice that gives contours to these objects. According to received accounts, that I need not question here in depth, the boundary object of classical genetics has worked as a formal unit: That which, in an ever more sophisticated context of breeding experiments, accounts for the appearance or disappearance of certain characters that can be traced through subsequent generations. Accordingly, what has made classical genetics different from nineteenth-century inquiries in heredity is that its practice allowed combining the notion of character discreteness, rooted in the Darwinian and early Vriesian traditions, with Weisman’s distinction between germ plasm and body substance. The result, read back into Mendel’s experiments, was a deliberate distinction between genetic unit characters, taken in their entirety, between genotype and phenotype, respectively.” ([20], p. 220f) However, Rheinberger also considered the way of the fluctuating object “gene” through the history of molecular genetics: “At the beginning, molecular genetics, with its set of biochemical practices and genetic manipulations, was characterized by switching from higher plants and animals to bacteria and phages as model organisms.” ([20], p221) There are two transformations of the object “gene”:

1. The transformation of the formal gene into a material, physicochemical entity. Before, in classical genetics, there was the problem of the stability of genes; now, in molecular genetics, genes consist of metastable macromolecules of such as nucleic acids.

2. The transformation of the gene into unit endowed with informational qualities with from the object. Before, in classical genetics there were the problems of the gene’s mode of reproductions and the connection between genotype and phenotype; now, in molecular genetics we say: “Nucleotide sequences, and DNA in particular, can be replicated specifically and faithfully by virtue of stereochemical properties of their building blocks. In addition, DNA stretches specify traits by virtue of the ordered sequence of nucleotides they contain for being translated, with the help of a complex cytoplasmic machinery, into corresponding sequences of amino acids that yield structural proteins or enzymes catalysing all ,sort of metabolic reactions.” ([20], p. 221)

But, against this schematic and simple-looking outline, “so suggestive in its clarity and distinctness after the event”, Rheinberger stressed “that the fruitfulness of boundary objects in research does not depend on whether they can be given a precise and codified meaning from the outset. Stated otherwise, it is not necessary, indeed it can be rather counterproductive, to try to sharpen the conceptual boundaries of vaguely bounded research objects while in operation. As long as objects are in flux, too, the corresponding concepts must remain in flux, too.” In other words, he wrote: “Boundary objects require boundary concepts.” ([20], p. 221) which we will interpret as Fuzzy objects require fuzzy concepts. However, this was only a very brief sketch of what happened with the concept of gene in classical genetics and molecular genetics. Rheinberger showed in much greater details, that the “spectacular rise of molecular biology has come about without a comprehensive, exact, and rigid definition of what a gene is” in his article on Gene Concepts ([20], p. 225-235). We are not able to retrace this history of the gene in this paper. Let’s steady that he considered the gene as a vague or fluctuating or fuzzy object in the history of genetics and let’s have a look to his resume. (For the field of “fuzzy genomes” see also [22]

IV. EPISTEMIC THINGS AND FUZZY SETS AND SYSTEMS

“The gene has been a powerful epistemic entity in the history of heredity, in all the vagueness that is characteristic for such entities.” Without despising the value of precision in science, “but precision itself has historically changing boundaries”, Rheinberger accentuates the value of imprecision, vagueness or fuzziness in science: “Assessing what it means to be fuzzy, instead if eliminating vagueness altogether and implementing precision, has become a major

concern in fields such as AI-research. Lofti† Zadeh claims that “there is a rapidly growing interest in inexact reasoning and processing of knowledge that is imprecise, incomplete, or totally reliable. And it is in this connection that it will become more and more widely recognized that classical logical systems are inadequate for dealing with uncertainty and that something like fuzzy logic is needed for that purpose” ([20], p. 236). Rheinberger referred this excerpt from [33] and then he went back to the question “whether we need, in order to understand conceptual tinkering in research, more rigid metaconcepts than those first-order concepts that we, as epistemologists, analyze. I am inclined to deny this. Why should historians and epistemologists be less imprecise, less operational, and less opportunistic after all, than scientists?” ([20], p. 236) This is an argument to establish fuzzy epistemology in philosophy of science as it is briefly sketched in the introduction of this paper and in more details in also [16], [17], [18] and also for special subjects, in particular evolutionary biology [34] and quantum mechanics [35]. Epistemology has to deal not only with empiricism and theoretical structures but with the observing scientists perceptions and fuzzy concepts that can be represented by fuzzy sets. Epistemologists, philosophers and historians of science should consider entities and relations in the fuzzy layer shown in figure 3, these are representations of fluctuating or fuzzy concepts, e. g. the gene, the atom etc. Fuzzy epistemology could help to manage complexity in the field of science.

ACKNOWLEDGMENT

The author thanks Prof. Dr. Wolfgang Balzer, Julia Limberg, Prof. Dr. Jerry Mendel, Prof. Dr. Hans-Jörg Rheinberger, Prof. Dr. Kazem Sadegh-Zadeh, and Prof. Dr. Lotfi A. Zadeh for discourses and conversations, and the availability of their writings.

REFERENCES [1] L. A. Zadeh: Fuzzy Sets, Information and Control, 8, 1965, pp. 338-353. [2] L. A. Zadeh: Fuzzy Sets and Systems. In: Fox, J. (ed.): System Theory.

Microwave Res. Inst. Symp. Ser. XV, Brooklyn, New York: Polytech. Pr. 1965, pp. 29-37.

[3] L. A. Zadeh: Fuzzy Logic = Computing with Words, IEEE Transactions on Fuzzy Systems, Vol. 4, No. 2, 1996, pp. 103-111.

[4] L. A. Zadeh: From Computing with Numbers to Computing with Words – From Manipulation of Measurements to Manipulation of Perceptions, IEEE Trans. on Circuits and Systems-I: Fundamental Theory and Appl., 45, 1, 1999, pp. 105-119.

[5] L. A. Zadeh: A New Direction in AI. Toward a Computational Theory of Perceptions. AI-Magazine, 22, 1, 2001, pp. 73-84.

[6] R. Seising: The Fuzzification of Systems. The Genesis of Fuzzy Set Theory and Its Initial Applications � Developments up to the 1970s (Studies in Fuzziness and Soft Computing Vol. 216) Berlin, New York, [u.a.]: Springer 2007.

† Rheinberger wrote erroneously “Lofti” instead of „Lotfi“ – what happened in many times before, too.

[7] R. Seising: From Vagueness in Medical Thought to the Foundations of Fuzzy Reasoning in Medical Diagnosis. Artificial Intelligence in Medicine Vol. 38, November 2006, S. 237-256.

[8] R. Seising: Pioneers of Vagueness, Haziness, and Fuzziness in the 20th Century. In: M. Nikravesh, J. Kacprzyk, L. A. Zadeh (Eds.): Forging the Frontiers: Fuzzy Pioneers I. (Studies in Fuzziness and Soft Computing, Vol. 217) Berlin, New York, [u.a.]: Springer 2007, S. 55-83

[9] R. Seising: On the Absence of Strict Boundaries � Vagueness, Haziness, and Fuzziness in Philosophy, Medicine, and Science, Applied Soft Computing Vol. 8, January 2008. Special Issue: Forging the Frontiers (available online: doi:10.1016/j.asoc.2007.02.017).

[10] R. E. Bellman, R. Kalaba, L. A. Zadeh: Abstraction and Pattern Classification. Journal of Mathematical Analysis and Applications 13 (1966), pp. 1-7.

[11] L. A. Zadeh: From Circuit Theory to System Theory, Proceedings of the IRE, Vol. 50, Nr. 5, May 1962, pp. 856-865

[12] W. Balzer: Empirische Theorien: Modelle – Strukturen – Beispiele. Die Grundzüge der modernen Wissenschaftstheorie. Braunschweig/ Wiesbaden: Fr. Vieweg & Sohn 1982.

[13] J. D. Sneed: The Logical Structure of Mathematical Physics, Dordrecht: Reidel 1971.

[14] W. Balzer, C. U. Moulines, J. D. Sneed: An Architectonic for Science. The Structuralist Program. Dordrecht: Reidel 1987.

[15] W. Balzer: Die Wissenschaft und ihre Methoden. Grundsätze der Wissen-schaftstheorie. Ein Lehrbuch. München: Verlag Karl Alber 1997..

[16] R. Seising: Scientific Theories and the Computational Theory of Perceptions � A Structuralist View including Fuzzy Sets. In: M. Štepni�ka, V. Novák, U. Bodenhofer (eds.): New Dimensions in Fuzzy Logic and Related Technologies. Proceedings of the 5th EUSFLAT Conference (European Society for Fuzzy Logic and Technology), Volume I, Ostrava, Czech Republic, 2007, p. 401-408.

[17] R. Seising: Between Empiricism and Rationalism: A Layer of Perception Modeling Fuzzy Sets as Intermediary in Philosophy of Science. In: O. Castillo, P. Melin, O. Montiel Ros, R. Sepúlveda Cruz, W. Pedrycz, J. Kacprzyk (Eds.): Theoretical Advances and Applications of Fuzzy Logic and Soft Computing (Proceedings of the IFSA 2007 World Congress Theory and Applications of Fuzzy Logic and Soft Computing, Cancun Mexico, June 18-21, 2007), Berlin, Heidelberg: Springer-Verlag (Advances in Soft Computing 42) 2007, pp. 101-108.

[18] R. Seising: A Philosophy of Science with Fuzzy Structures In: M. Reformat and M. R. Berthold (eds.): Proceedings of the 2007 Annual Meeting of the North American Fuzzy Information Processing Society NAFIPS 2007, San Diego, California, June 24-27, 2007.

[19] H.-J. Rheinberger: Experimental complexity in biology: Some Epistemological and historical remarks. Philosophy of Science, Proceedings of the 1996 Biennial Meeting of the Philosophy of Science Association, Supplement to Vol. 64, No. 4, pp. 245-254 (1997).

[20] H.-J. Rheinberger: Gene Concepts. Fragments from the Perspective of Molecular Biology. In: P. Beurton, R. Falk and H.-J. Rheinberger (eds.): The Concept of the Gene in Development and Evolution, Cambridge University Press, Cambridge, pp. 219-239, 2000.

[21] Fleck L. Entstehung und Entwicklung einer wissenschaftlichen Tatsache. Einführung in die Lehre vom Denkstil und Denkkollektiv, Basel: Schwabe & Co, 1935. Citations from the American Edition: Trenn TJ, Robert KM, (eds): Fleck, L.udwik, Genesis and Development of a Scientific Fact. Chicago/London: The University of Chicago Press, 1979.

[22] J. Limberg, Fuzzy Concepts in Human Biology (in this volume). [23] H.-J. Rheinberger: Experiment, Difference, and Writing I. Tracing protein

synthesis. Stud. Hist. Phil. Sci. 23, pp. 305-331 (1992). [24] H.-J. Rheinberger: Experiment, Difference, and Writing II. The laboratory

production of transfer RNA. Stud. Hist. Phil. Sci. 23, pp. 389-422 (1992). [25] H.-J. Rheinberger: The “epistemic thing” and its technical conditions -

from biochemistry to molecular biology. In: B. Gremmen (ed.): The Interaction between Technology and Science. Wageningen/The Netherlands, pp. 281-298 (1991).

[26] H.-J. Rheinberger: Toward a History of Epistemic Things: Synthesizing Proteins in the Test Tube. Stanford: Stanford University Press, 1997. (German edition: Experimentalsysteme und epistemische Dinge. Eine Geschichte der Proteinsynthese im Reagenzglas. Göttingen: Wallstein Verlag 2001.

[27] H.-J. Rheinberger: Die Evolution des Genbegriffs – Perspektiven der Molekularbiologie, 1999. In: H.-J. Rheinberger: Epistemologie es Konkreten. Studien zur Geschichte der modernen Biologie, Frankfurt: Suhrkamp 2006.

[28] H.-J. Rheinberger: Zur Historizität wissenschaftlichen Wissens: Ludwik Fleck, Edmund Husserl. In: H.-J. Rheinberger: Epistemologie des Konkreten. Studien zur Geschichte der modernen Biologie, Frankfurt: Suhrkamp 2006.

[29] H.-J. Rheinberger: Experiment and Orientation: Early Systems of in vitro Protein Synthesis. J. Hist. Biol. 26, pp. 443-471 (1993).

[30] H.-J. Rheinberger: Experimental systems: Historiality, narration, and deconstruction. Science in Context 7, pp. 65-81 (1994).

[31] H.-J. Rheinberger: From Microsomes to Ribosomes: 'Strategies' of 'Representation'. Journal of the History of Biology 28, pp. 49-89 (1995)

[32] H.-J. Rheinberger: Beyond nature and culture: A note on medicine in the age of molecular biology. Science in Context 8, pp. 249-263 (1995).

[33] L. A. Zadeh: Coping with the imprecision of the real world. In: R. R. Yager, S. Ovchinnikov, R. M. Tong, and H. T. Nguyen (eds.), Fuzzy Sets and Applications: Selected papers by Lotfi Zadeh. New York: John Wiley, 1987, pp. 9-28.

[34] R. Seising, Fuzziness in Evolutionary Biology (in this volume. [35] R. Seising, From Principles of Mechanics to Quantum Mechanics � A

Survey on Fuzziness in Scientific Theories (in this volume).