Natural law

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As natural law in the will of science regularity of transactions in the nature called. The plural form “laws of nature” also denotes the entirety of these regularities, including those that have not yet been discovered or formulated, regardless of their specific formulation. Natural laws differ from other laws in that they cannot be put into force or overridden by humans at their discretion. There is currently no precise, uniform, final definition of the term.

The demarcation from the laws of the individual sciences, such as in particular the physical laws as the basis of the natural sciences , the true nature of the natural laws - abstraction or ontological fact - as well as the question of whether axioms of scientific models and chemical, physical or cosmological constants also belong to them, are the subject of ongoing debate. Through the development of modern physics and the reductionism and naturalism associated with it, a paradigmatic understanding of natural laws has emerged as a necessary regularity in sequences of observable events which, without exception, determine all events of their respective type. As a result, some scientific rules were excluded from the existence of natural laws. Formally, both scientific and natural laws are expected to allow observable events to be explained and predicted. However, this criterion is not sufficient for the delimitation: The question of causality , especially in the case of confirmed statistical laws , and their verifiability is a further problem. In the debate about scientific laws, one camp (following David Hume ) emphasizes regularity, which enables an understanding of statistical laws as expressions of natural laws, or the need for an underlying cause-effect relationship.

There is at least one difference between the currently valid scientific laws of the individual sciences (even physics) and the laws of nature in the general sense. So z. In pragmatism or falsificationism , for example, it is assumed that the scientific laws are only an approximation of the natural laws that are the expression of a necessity that determines natural events. The logical positivism , however looking at the laws of nature only as derived from the observed natural phenomena rules that experience has shown are confirmed again and again; he assumes that no meaningful statement can be made beyond the experience ( criterion of meaning of empiricism ).

history

The concept of natural law in its modern conception goes back to the scientific revolution in the early modern period. In his work Principia philosophiae , published in 1644, René Descartes for the first time sets out three rules he called natural laws, which, in contrast to God as the general cause of all movements, are decisive for the particular movements on earth. His work is based on the writings of other authors from antiquity, the Middle Ages and the Renaissance . Galileo spoke, in the same sense, of “ theorems ”, “prepositions” or “rules”, in no published work of “laws”. For the first time in the works of Robert Boyle and Robert Hooke , i.e. scholars of the Royal Society , which was just being founded at that time , the laws of nature, in the sense of empirically observable regularities, are spoken of more regularly.

Antiquity

The concept of natural law was alien to the ancient Greek authors, it was not used in this form. The Greek term for law, nomos , was used specifically for voluntarily set norms and rules; it could also mean “habit”. The concept of nature (physis) was actually understood as a contradiction, it stood for the natural, unchangeable order, described by Heraclitus as logos (reason, sense) and by Anaximander Nous (spirit, reason). This went far beyond merely observed regularities, which no Greek thinker would have recognized as somehow relevant to such fundamental principles; this was not about the things themselves, but about the fundamentals, the ultimate determinations from which all things are formed (depending on philosophical school about fire, the elements, the atoms ...). The Greeks were familiar with the idea of ​​laws that were not set by humans ( agraphoi nomoi ), but these correspond more to natural law . In the extensively transmitted work of Plato and Aristotle , the expression of the law of nature is found once each, and also more in a referential context. In late antiquity, conveyed primarily by Roman authors, the philosophical school of the Stoa then used the term lex naturae , i.e. the law of nature, more often . This is conveyed by the fact that for the Stoic philosophers the world itself is God, so that the divine will, like a lawgiver, can make rules. Initially, this concerned moral rules, which were later transferred to natural regularities. In this way, the idea of ​​self-determined action or the determination of action through domination is transferred to nature. According to Zeno of Kition , the founder of the Stoa (narrated by Cicero ), the law of nature is divine and has the power to command what is right and to forbid the opposite.

The numerology of the Pythagoreans , a philosophical school and sectarian community, which invoked the predominantly secret teachings of Pythagoras , was effective for the ancient Greek understanding of nature . In the natural philosophy of the Pythagorean Philolaos , the order of the cosmos is based on ratios of numbers that establish harmony. This was triggered by the discovery of the integer relationships in musical harmony . The idea that the essence of nature could be expressed in numbers and their proportions subsequently proved to be very influential. Concepts of ancient Greek philosophy, which are now taken under the laws of nature, are based on mathematical proportions, according to Archimedes' laws of levers . Pythagorean thinking led to the essence of nature being sought more in theorems and axioms .

middle Ages

The ancient philosophical concepts were conveyed into Christian philosophy and theology of the Middle Ages through the writings of the Church Fathers. The most influential thinker was Augustine . This was strongly influenced by stoic ideas that were common to most philosophical thinkers in late antiquity. For Augustine there were two sources of human knowledge, both of which go back to God. Next to the Bible as the revealed scripture of God comes the book of nature . The stoic concept of natural law is transmitted by thinkers like himself or Basil and now denotes a law issued by God. The law of nature is here both prescriptive (prescriptive) and descriptive (descriptive). In the works of medieval thinkers, the term is regularly used in this sense. In the didactic poems of Alain von Lille , personified nature sets out its laws, Roger Bacon in the thirteenth and Wilhelm von Ockham in the fourteenth century use the term regularly. According to Heinrich von Langenstein , the comets move "secundum legem agencium naturaliter". In addition to the independence of natural phenomena, which, in addition to the revealed scriptures, which they always confirmed, was a legitimate source of knowledge, it turned out to be important for later development that they were convinced that God had created the world in such a way that it was human reason can be grasped. According to their self-understanding, Christian authors can not only use ancient wisdom, but even surpass it, since all new discoveries made since then are also available to them. Robert Grosseteste and Roger Bacon, building on the works of Arab scholars such as Hunain ibn Ishāq , made the laws of reflection and refraction known in the West as the first concrete physical laws . However, theorists like Wilhelm von Conches , who strongly emphasized the autonomy of the order of nature, were fiercely attacked by other theologians for this.

The scholastic scholars such as Albertus Magnus and Thomas Aquinas develop, building on the now rediscovered works of Aristotle and the Arab researchers in his successor, a synthesis that accepted by the official church and is binding for centuries Aristotelianism or, according to Thomas, Thomism called . For the sciencia naturalis , Aristotelian terms such as substance and essence are used as an explanatory approach. Although God in his omnipotence is not bound to these natural principles, in his relationship to the world he has created he adheres to the legal order that he himself has sovereignly established, which man can also explore through this. Since these only apply to natural things, but not to man-made ( artificalia ), this school of thought was skeptical of the value of experiments . The scholastic terminology was heavily criticized by the early scientists, for whom such explanations from substance and its forms are rejected as unproductive. The emerging natural sciences criticized medieval scholastic philosophy rather than Christian doctrine; most of its founders such as Galileo, Descartes, Newton and Boyle avoided any critical statements on Christian doctrines in their works.

Renaissance

The modern notion of a law of nature that brings observable quantities into context without restriction and exception can be traced back to three different lines of tradition that came together in René Descartes :

  • the idea of ​​a natural order established in creation, which was represented in Aristotelianism and also in Thomism,
  • the Pythagorean notion of harmonic numerical relationships that determine nature, which has also been important for Neoplatonism since the Renaissance and which was confirmed by Kepler's laws ,
  • as well as the tradition of technology and its rules of thumb, which arise from the craftsmanship and to which Francis Bacon had drawn attention.

Modern

Late 19th century, before Einstein's publication of the theory of relativity , it is generally understood in the natural sciences with natural laws, the laws by which the changes take place in nature. All changes that could be derived in mathematical formulas were considered to be scientifically explainable. The principle of causality was more indispensable for human cognitive reason , i.e. that every change had to have its cause. Changes were caused by the natural forces of gravity , heat , light , electricity , magnetism , chemical affinities and physical molecular forces in their complex interplay.

In the middle of the 20th century, natural laws were also defined as a legal connection or essential relationship between natural phenomena that exist outside of human consciousness, but can be adequately reflected by it. To a large extent, they can be verified and confirmed by experiments .

"By measuring the conditions and the legally occurring consequences, many natural laws can be represented in mathematical relationships and theoretically generalized"

- Meyer's New Lexicon, 1963

The following definition comes from the 1970s:

"Natural laws are inherent in nature, objectively necessary, general [specific] and [nd] essential [ies] connections between [ies] the phenomena of natural occurrences. A distinction is made between general natural laws, such as the conservation laws for energy and momentum, which apply in all of nature, and specific natural laws such as Maxwell's equations, which refer only to certain areas of nature. Furthermore, a distinction is made between [ischen] dyn. [Amish] N. [natural laws], which describe individual systems exactly, and [nd] statistical [isic] N. [natural laws], the probability statements about a multitude of individual systems of a totality do."

- Meyer's Universal Lexicon 1979

To this day, the specification and delimitation of the term natural law is discussed:

“What the sufficient and necessary conditions are so that a certain statement is actually recognized as a law of nature has not yet been fully clarified in the philosophy of science. Most physicists take the pragmatic stance that a statement has the character of a law if it is acceptable without checking all individual cases, but at the same time its acceptance does not depend on checking only certain individual cases. When classifying natural laws, a distinction is made between the division into deterministic and statistical laws, often microscopic and macroscopic laws, although the limit is not clear, and quantum mechanical phenomena also cause macroscopic effects ... "

- Lexicon of Physics, 2000

Contemporary positions

Ontological naturalism

The advancing scientific knowledge seems to indicate a unit of empirical sciences on a physical basis. Murray Gell-Mann wrote: "Sometimes a theory succeeds in a remarkable synthesis by compressing the regularities of a broad spectrum of phenomena that were previously described separately ... into a concise and elegant representation."

One possible approach for a consistent, uniform view of the empirical sciences on nature is ontological naturalism , as it is e.g. B. Bernulf Kanitscheider represents. Gerhard Vollmer cannot yet make up his mind to deprive philosophy of "air sovereignty" in this matter, although he too presents a number of arguments in favor of an empirical naturalism, among others. a. the attribute "evolutionary". He thinks it is “... obvious to expand the concept of evolution and the theory of evolution upwards and downwards”, in other words towards physics and towards the social order.

There are first approaches to connecting metaphysics within the framework of the process-oriented model of emergent (i.e. developing) self-organization . In addition to evolution, this model incorporates other related concepts such as synergetics , symbiosis , holism , autopoiesis, and complexity theory . Such a metaphysics extends into human society to the spontaneous social order and the invisible hand of the market. Starting with the Big Bang , there is a chain of emergent processes from the development of inanimate nature to animate nature and the mental abilities of humans.

Regularity, DTA and Dispositional Theory

In current, naturalistic natural philosophy, three main approaches are discussed which are intended to describe natural laws in the modern physical sense: The regularity theory , which is formulated by David Kellogg Lewis based on David Hume , the anti-Humean theory by Fred Dretske , Michael Tooley and David Armstrong (DTA theory), as well as the dispositional theory , which is represented by Alexander Bird . Among other things, the debate is about whether laws of nature have a modal force , i.e. whether they can force a certain effect due to a certain cause or whether they are actually mere descriptions of observed, but ultimately arbitrary, regularities in the world. The regularity theory takes the latter standpoint. Metaphorically, she sees the world as a mosaic of isolated individual facts, which may indeed result in a pattern overall, in which the individual facts are nevertheless not in any necessary, i.e. H. in the strict sense of the law, are related. Supporters of the DTA theory take a contrary position. The dispositionalists, on the other hand, understand natural laws as dispositions; H. as the natural tendencies of the individual objects to show certain behaviors. In methodical form, i.e. H. to standardize scientific work, naturalism combined with scientific realism is common regardless of these debates.

Closely related to the discussion about the understanding of natural laws is the debate about the relationship between cause and effect and the modern understanding of natural science: For example, the so-called Russell-Mach problem describes the apparent contradiction between the intuitive assumption of a temporally irreversible causality and the principle of causality Reversibility and timelessness of modern physical laws.

A well-known and often discussed approach to depicting the way in which natural laws explain individual events is the Hempel-Oppenheim scheme .

The subject of discussion is still to what extent there are in principle only physical laws of nature or whether rules and laws of other sciences can also be laws of nature with comparable, strict validity claims. Attempts to understand independent natural laws, for example in biology or psychology, as special cases of general physical laws are referred to in the literature as a type of reductionism . One argument in favor of reductionism is, for example, that physics claims to be valid in all of reality, while the other sciences only deal with limited special areas of the world, i.e. so-called special sciences . A modern representative of a reduction of this kind is the scientific theorist Ernest Nagel . The question of how the knowledge and rules of the other sciences are to be classified in a physicalistic worldview leads in philosophy to the formulation of different concepts of emergence and supervenience . The central subject of discussion is the idea of ​​multiple realizability of similar biological or social phenomena, based on different physical principles. One of two churches can be made of wood and one of stone, so obviously have different physical bases. Nevertheless, from a sociological, religious or theological point of view, they are considered to be two representatives of the same genus of research object. A book can also be available as a printed copy, as an e-book or as an audio book, but can still be viewed as the same work in literary terms. A moderate form of physicalism assumes that identical physical principles lead to the same non-physical consequences, but conversely different physical principles can lead to objects of the same kind in other sciences, i.e. can be implemented in multiple ways. This position, known as functionalism , is widespread in the philosophy of science today and was originally formulated by Hilary Putnam and Jerry Fodor to understand the relationship between psychological events such as feelings and thoughts through neurological processes. Based on the arguments of Putnam and Fodor, Elliott Sober , for example, advocates a moderate form of reductionism in biology.

Presentation and types

In a narrower epistemological description, a law of nature in the real sciences represents a description of regularities in the behavior of objects that is abstracted from the behavior of individual objects and that applies regardless of a human evaluation.

Laws of nature are often part of a scientific theory and can be expressed using mathematical formulas . These abstractions describe possible worlds; which of these correspond to the real world is an empirical question.

Laws of nature apply regardless of human observation. You can not man- made , but only of them discovered be. The laws of nature are explored in order to understand the world on the one hand and to apply and use the knowledge gained on the other. Not the mere perception of nature with our senses, but only the “laws of nature create reality”. "Direct experience only reveals a fraction of natural phenomena."

The laws of nature are structured in areas and build hierarchically on one another. Along with the development of their objects and systems, the associated laws also develop. As far as possible, individual laws are grouped into theories. The interpretation of the laws and theories of the empirical areas as laws of nature is called ontological naturalism . However, it is questionable whether all scientific laws can be traced back to physical laws governing elementary particles and forces. This problem, which affects both sub-areas of physics and the relationship to the other natural sciences , is dealt with under the heading of " emergence ". In some empirical sciences outside of physics it has therefore become customary - also because of the limited scope of application - to dispense with the expression "law" and instead speak of "rules".

There are different types of natural laws: deterministic cause-effect relationships that can be represented as mathematical functions and numbers (examples: laws of mechanics and electrodynamics), statements about static mean values ​​(examples: thermodynamics, theory of ideal gases), statements about collective probabilities (Quantum theory) or deterministic-chaotic behavior in emergent self-organized processes. Laws of nature apply always and everywhere, but their formulation can only be correct with restrictions. It must therefore be further developed as soon as new, reliable knowledge is obtained or its scope is to be expanded. To research and review of the laws of nature and the laws of other empirical science is empirical science working method applied, consisting of the phase observations, recognizing regularities hypothesis, measurements, forecasts, verification, development of a theory and so on. The predictions of a hypothesis that have not yet been observed must also be checked as far as possible.

Examples (selection)

Demarcation

The demarcation between natural laws and other confirmed or formally derived theorems is not always sharp.

Many mathematical theorems have implications and applications that are central to science or engineering. So the sentence The sum of the angles in the triangle in the plane is 180 degrees is not a law of nature, but a mathematical theorem, which is based on certain basic axioms of geometry .

In the applied branches of science and technology, numerous formulas are also used that describe certain relationships between physical measured variables with sufficient accuracy without the underlying relationships being unambiguously clear. For the known applications, they result in approximate values ​​with an accuracy that is sufficient for the application purpose ( empirical values ). Such formulas are called empirical formulas or empirical laws . These formulas are not laws in the physical sense, they lack a theoretical basis. So-called rules of thumb form an extreme case of this .

Laws of nature outside of natural science

Many scientists equate natural laws with physical laws. Although the physical laws apparently also work in living nature, according to another opinion there are laws of the development of life that can no longer only be explained nano- , micro- or macrophysical . The conditions under which a chemical reaction leads to life have not yet been formulated. But the search for these regularities, the existence of which is not doubted, now leads to the cosmos and other planets. The search for the causes and conditions under which instincts , reflexes and human consciousness arise is even more complicated .

The British philosopher Alfred North Whitehead in particular dealt intensively with this problem in his philosophy. According to Whitehead, the requirement for general validity and its description as a mathematical formulation does not do justice to the essential characteristics of natural laws. For Whitehead, a law of nature is above all (also) a characteristic of behavior that is not imposed on things from outside (in the form of cause and effect), but rather represents an essential characteristic. According to this consideration, a law of nature is inherent in things. For Whitehead, natural laws do not have an absolute, but rather a statistical validity. This in turn is a view, writes Michael Hauskeller, that corresponds to modern quantum physics.

theology

In theology , natural laws are ultimately interpreted as God's will , God's plan. The discourse between materialism and idealism , atheism and theism is still current.

Starting from the recognition of a comprehensive divine plan, fatalism developed , which sees all events in the world and all activities of earthly individuals as predetermined. This also applies to the development in the future and the fate of every individual.

Philosophy of history

The laws observed in the development of human society are controversial. To what extent these comparable developmental sequences should be classified as laws of the nature of human societies remains to be examined.

literature

  • Gerhard Vollmer : What are and why are natural laws valid? In: Philosophia naturalis . Journal for the Philosophy of Nature. Volume 37/2, 2000 ( summary ; PDF file; 426 kB)
  • Erwin Schrödinger : What is a law of nature? - Contributions to the scientific worldview - 5th edition - Munich: Oldenbourg, 1997. (Scientia nova) - ISBN 3-486-56293-2
  • David Armstrong : What Is a Law of Nature? , Cambridge University Press, 1983 SL Goldman: Review
  • Alfred Jules Ayer : What is a law of nature? , in: Revue Internationale de Philosophie 10 (1956), 144-65, also in: Curd / Cover 1998
  • Helen Beebee : The Non-Governing Conception of Laws of Nature , in: Philosophy and Phenomenological Research 61 (2000), 571-594.
  • Nancy Cartwright : How the Laws of Physics Lie , Oxford University Press 1983
  • M. Curd, JA Cover (ed.): Philosophy of Science: The Central Issues , WW Norton & Company 1998, v. a. 808-877
  • Fred Dretske : Laws of Nature , in: Philosophy of Science 44 (1977), 248-268.
  • John Foster: The Divine Lawmaker: Lectures on Induction, Laws of Nature, and the Existence of God , Oxford: Clarendon Press, 2004. Evan Fales: Review , in: Notre Dame Philosophical Reviews 2004
  • RN Giere: Science Without Laws , Chicago: University of Chicago Press 1999
  • Carl Gustav Hempel : Aspects of Scientific Explanation , New York: Free Press 1965
  • William Kneale : Natural Laws and Contrary-to-Fact Conditionals , in: Analysis 10 (1950), 121-25.
  • M. Lange: Natural Laws in Scientific Practice . Oxford: Oxford University Press 2000
  • John Leslie Mackie : The Cement of the Universe , Oxford University Press 1974
  • S. Mumford: Laws in Nature , Routledge Stathis Psillos: Review
  • Karl Popper : A Note on Natural Laws and So-Called Contrary-to-Fact Conditional , in: Mind 58 (1949), 62–66.
  • Patrick Suppes (ed.): The Structure of Scientific Theories , Urbana: University of Illinois Press 2nd A. 1977
  • Michael Tooley : The Nature of Laws , in: Canadian Journal of Philosophy 7 (1977), 667-698
  • Bas van Fraassen : Laws and Symmetry , Oxford: Clarendon Press 1989
Popular literature

Web links

Wikiquote: Law of Nature  - Quotations

Individual evidence

  1. N. Swartz: Laws of Nature . In: Internet Encyclopedia of Philosophy and its Authors . ISSN  2161-0002 (English, utm.edu ).
  2. “From the same immutability of God we can infer certain rules as laws of nature, which are the second and special causes of the various movements that we notice in the individual bodies. ". René Descartes: Principia Philosophiae. Amsterdam, 1644. German The principles of philosophy. Translated by Christian Wohlers. Meiner, Hamburg 2005, ISBN 3-7873-1697-3 .
  3. a b c John R. Milton (1981): The origin and development of the concept of the 'laws of nature'. European Journal of Sociology / Archives Européennes de Sociologie / European Archives for Sociology 22 (2): 173-195.
  4. Brigitte Falkenburg: Natural law, causality, determinism. In Thomas Kirchhoff, Nicole C. Karafyllis: Natural Philosophy: A Text and Study Book. Mohr Siebeck, Tübingen 2017, UTB Volume 4769, ISBN 978-3-8252-4769-0
  5. Dieter Bremer (1989): From physique to nature. A Greek concept and its fate. Journal of Philosophical Research 43: 241-264.
  6. Nomos. in Anthony Preus: Historical dictionary of ancient Greek philosophy. Scarecrow Press, Lanham 2007. ISBN 978-0-8108-5487-1
  7. Wolfgang Kullmann: Natural law in the conception of antiquity, especially the Stoa. A conceptual examination. (Philosophy of Antiquity 30.) Franz Steiner, Stuttgart 2010. ISBN 978-3-515-09633-1
  8. a b Holm Tetens , entry “Natural Law” in: Jürgen Mittelstraß , Gereon Wolters (ed.): Encyclopedia Philosophy and Philosophy of Science , JB Metzler 2004, Volume 2: HO, ISBN 978-3-476-02012-3 , p. 968 -970.
  9. ^ Wiebrecht Ries: The philosophy of antiquity. Scientific Book Society, Darmstadt 2005. ISBN 3-534-17480-1
  10. ^ Samuel Sambursky: Nature and Number. in The Physical World of the Greeks. Princeton University Press, 1956 (translated 1987). ISBN 0-691-08477-7
  11. Hubert Herkommer (1986): Book of writing and book of nature. On the spirituality of world experience in the Middle Ages, with an outlook on its change in modern times. Journal for Swiss Archeology and Art History 43 (1): 167-178.
  12. ^ A b Yael Kedar: Laws of Nature. In Henrik Lagerlund (editor): Encyclopedia of Medieval Philosophy. Philosophy between 500 and 1500. Springer, 2011 ISBN 978-1-4020-9728-7
  13. ^ AC Crombie & JD North: Roger Bacon. in AC Crombie: Science, Art and Nature in medieval and modern thought. Hambledon Press, London 1996. ISBN 1-85285-067-1
  14. ^ AC Crombie: Infinite Power and the Laws of Nature: A Medieval Speculation. In: Science, Art and Nature in medieval and modern thought. Hambledon Press, London 1996. ISBN 1-85285-067-1
  15. Christoph Kann (2003): Signs, Order, Law: To the understanding of nature in medieval philosophy. In Peter Dilg (editor): Nature in the Middle Ages, Concepts - Experiences - Effects. Akademie Verlag, Berlin 2003, ISBN 3-05-003778-4 .
  16. ^ Andreas Hüttemann (2006): Matter, Chaos and Law - The Concept of Natural Law in the 17th Century. in: Karin Hartbecke and Christian Schütte (editors): Natural Laws . Mentis, Paderborn 2006: 193-205.
  17. ^ Meyers Konversations-Lexikon, 4th edition, 12th volume, Verlag des Bibliographisches Institut Leipzig 1888, p. 11
  18. ^ Meyers Neues Lexikon, Volume 6, VEB Bibliographisches Institut Leipzig 1963, p. 58
  19. ^ Meyers Universallexikon, Volume 3, 1st edition, VEB Bibliographischen Insxtitut Leipzig 1979, p. 223
  20. Lexicon of Physics in six volumes, Vol. 4, Heidelberg Berlin, Spektrum Akad. Verl. 2000, ISBN 3-86025-294-1 , p. 68
  21. See e.g. B. Edward O. Wilson: The Unity of Knowledge, Siedler 1998
  22. Murray Gell-Mann: The Quark and the Jaguar; Piper 1994, p. 134
  23. a b Bernulf Kanitscheider: The matter and its shadow, Alibri 2007
  24. Gerhard Vollmer: In search of order, Hirzel 2013, p. 32
  25. Günter Dedié: The Power of Natural Laws - Emergence and Collective Abilities from Elementary Particles to Human Society, 2nd edition, tredition 2015
  26. Mario Bunge, Martin Mahner: About the nature of things, Hirzel 2004, p. 207ff
  27. Henning Genz: How the laws of nature create reality, rororo science 2004
  28. Richard P. Feynman: Vom Wesenischer physical laws, Piper 2007, p. 157
  29. ^ Michael Hauskeller: Alfred North Whitehead for an introduction . Junius, Hamburg 1994, ISBN 3-88506-895-8 , p. 199 .