## Abstract

This chapter aims to give substance to a contemporary understanding of emergence from the perspective of the philosophy of science. Looking at progress in the natural sciences, it draws on the concept of self-organization in order to provide a characterization of emergence. From the 1960s onward, theories of self-organization (including complex systems theory, nonlinear dynamics, chaos theory, synergetics, dissipative structures, fractal geometry, and autopoiesis theory) explicitly addressed emergent behavior. Referring to those theories, this chapter enquires into the ontological core as well as into the methodological and epistemological characteristics of self-organization—and, hence, of emergence. It is asked whether there is unity in the diversity of self-organizing phenomena in nature. It will be shown that instabilities constitute the ontological core of self-organization and are, therefore, central to any semantically meaningful understanding of emergence. Besides this ontological condition for the possibility of emergence (instability), the chapter also reveals that there are three further ontological characteristics of emergence, namely, (1) novelty, (2) processuality/temporality, (3) internality (“self”). In addition, related methodological and epistemological characteristics encompass: (4) limits in reproducibility/repeatability, (5) obstacles to predictability and (6) deficits in testability and reductive describability/explainability. In sum, since instabilities play a crucial role in nature, they are essential to any present-day concept of emergence.

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## Notes

- 1.
Well known in the Latin statement: Nihil sub sove novum (colloquial translation at Ecclesiastes 1:9).

- 2.
For instance: Conway Lloyd Morgan, Samuel Alexander, Roy W. Sellars, and William McDougall.

- 3.
The concepts are often used interchangeably, although “self-organization” is broader in content than “emergence”.

- 4.
This vagueness of the term has challenged philosophers such as Ansgar Beckermann, Hans Flohr, Jaegwon Kim and Manfred Stöckler to provide clarification.

- 5.
The main points of the list that follows can also be found in Stephan (2007) and in more detail in Schmidt (2015). However, Stephan (2007) distinguishes between different types of emergence. As we are here less interested in semantic details and more concerned with providing a conceptual framework, we will not make further differentiations at this point.

- 6.
The properties might also include aspects of information, dispositions, or risks.

- 7.
Including Nonlinear Dynamics, Chaos Theory, Synergetics, Dissipative Structures, Fractal Geometry, and Catastrophe Theory.

- 8.
In fact, we can observe a convergence of some sub-disciplines of physics, informatics, biology, chemistry, and medicine.

- 9.
I wish to stress here at the beginning of the chapter that the same holds for social or technical complex systems.

- 10.
For instance, as in a billiard system, which has become a paradigm in this regard.

- 11.
Instability has, therefore, to be regarded as an empirical fact of our life-world and beyond—not just as a contingent convention.

- 12.
In this regard, stability metaphysics precedes scientific methodology.

- 13.
As was seen in the 19th century in the debate on the heat death of the universe.

- 14.
Moreover, the various definitions and meanings of complexity—even if they do not refer to the genesis and evolution of a new pattern such as those in more geometric definitions of “complexity” via “dimensions”—refer directly or indirectly to instabilities (Atmanspacher et al. 1992; Wackerbauer et al. 1994).

- 15.
The term “organization” in “self-organization” emphasizes such characteristics.

- 16.
The priority of instability can also be shown for: symmetry breaking, phase transitions, time’s arrow/irreversibility, deterministic chance, randomness, chaos, turbulence, catastrophes, fractals, information loss or gain. In general, however, the same argument holds with respect to the essential role of nonlinearity in these phenomena. But nonlinearity per se does not challenge traditional physical methodology. Many systems are nonlinear but stable, for example, simple two-dimensional planetary systems. They are, like linear systems, without chaos and turbulence, without self-organization and symmetry breaking.

*Instability, and not nonlinearity by itself, makes the difference.* - 17.
Or, more precisely, we could speak of the “onto-nomological core” of emergence (cf. Schmidt 2015).

- 18.
Compare Maxwell’s (1991, p. 13) remark above, forty years earlier.

- 19.
A special case of static instability is one that shows sensitive dependence of

*all*points in the state space. A prominent example is compound interest. Tiny differences in seed capital grow exponentially into enormous differences years later. The linear differential equation dx/dt = ax yields a solution that can be determined analytically: x(t) = x(0) · e^{at}, with a constant Lyapunov coefficient: a > 0. Trajectories starting from a neighborhood reveal a static continuous divergence. In an open-ended state space, they need never converge to each other again. However, a closed solution does not exist for this linear differential equation. If the initial conditions are known, a calculation for all times is feasible and a prediction is possible. - 20.
Translation from German (JCS).

- 21.
Today, we utilize Poincaré’s fundamental ideas to construct a specific map in order to obtain insights into the time evolution of a dynamical system—the so-called “Poincaré map”.

- 22.
The term “butterfly effect”, central to the notion of “chaos”, was coined by Lorenz (1963, 1989). In addition, and in more detail, more than 15 competing notions and definitions of “chaos” exist (cp. Brown and Chua 1996, 1998). One of the most relevant chaos definitions nowadays has been suggested by Devaney (1987). Devaney requires a system’s dynamics to exhibit three features in order to be called chaotic: (a) sensitive dependence on initial conditions (unpredictability); (b) topological transitivity (non-decomposability, wholeness); and (c) denseness of periodic points (elements of regularity). Banks et al. (1992) show from a mathematical perspective for one-dimensional maps that sensitivity (a) follows from properties (b) and (c). Thus, sensitivity does not seem to be a fundamental requirement for providing an adequate understanding of dynamical instability. From an empirical perspective, Devaney’s and Banks’ definitions—focusing on (b) and (c)—are regarded as interesting but hard to determine. Unlike mathematicians, physicists mostly advocate an understanding of chaos based on sensitivity coefficients. A classical sensitivity coefficient is Lyapunov’s exponent that measures the average divergence of trajectories (“chaos coefficient”). For physics and its methodological need to deal with experimental uncertainties, a positive Lyapunov exponent is one major characteristic of dynamical instability.

- 23.
Depending on the initial model class, altering a model can be performed by varying the model’s equations, the system parameters or exponents, by adding mathematical functions or by modifying the state space.

- 24.
Such as trigonometric stability, stability of the first order, permanent stability, semi-permanent stability, unilateral stability, regions of stability, stability in the sense of Poisson (cp. Birkhoff 1927).

- 25.
It is important to stress, as Janich does convincingly, the experimental/engineering aspects of physics: physics aims to produce experimentally reproducible phenomena, and it is based on experimentation (cp. Hacking 1983).

- 26.
Bunge believes that instabilities and nonlinearity make it too difficult to assign determinism to unstable dynamics.

- 27.
In the case of

*static instability,*if the watershed is not fractal or the initial states are not located within the neighborhood of the watershed, numerical integration is feasible. Small perturbations do not make any difference in the final result. In other cases, two initial states differing by imperceptible amounts may evolve into two considerably different states. Then, if any observation error of the present state is made, an acceptable prediction of the state (to within only small tolerances) in the distant future may well be impossible. Similar conclusions hold for*structural instability*. - 28.
Feigenbaum cited in Gleick (1987, p. 174f). The differential equation of a deterministic system is effectively worthless since reliable predictions would require exact information.

- 29.
In particular, they drive a wedge between (deterministic) laws and (prediction-relevant, single) trajectories.

- 30.
It is still an ongoing debate whether testability is to be understood as a normative requirement or merely as a description of what in fact happens in science.

- 31.
In this line, Woodward (2000, p. 197) has very recently claimed: “Explanation in the special sciences involves subsumption under general laws.”

- 32.
In the history of the philosophy of science, there has been a strong focus on these challenges, in particular on ontological, epistemological, and methodological types of reductionism. The unification of three of the four fundamental theories in physics shows the success of explanatory reductionism.

- 33.
By referring to earthquakes Hume also supports his arguments against anti-naturalist positions since phenomena that appear irregular can be generated by regular laws.

- 34.
This point is, in fact, the nucleus of the classic deductive-nomological account of explanation (cp. Hooker 2004).

- 35.
- 36.
- 37.
Of course, nonlinear techniques such as nonlinear data analysis, phase space reconstruction, surrogate data analysis, and other tools provide some options to find deterministic structures and separate them from white noise.

- 38.
See the six characteristics described in the first part of this article, in particular the methodological and epistemological characteristics 4–6, such as non-reproducibility/non-repeatability (4), unpredictability (5), and irreducibility (6).

- 39.
Prediction and time’s arrow are twins. And time is a necessary condition for the possibility of scientific experience.

- 40.
- 41.
An analysis of the historical development can be found in Aubin and Dalmedico (2002).

- 42.
For an introduction to Duhem’s philosophy of instability see, Schmidt (2017).

- 43.
“Deduction is sovereign mistress, and everything has to be ordered by the rules she imposes” (ibid., 266). A “deduction is of no use to the physicist so long as it is limited to asserting that a given

*rigorously true*proposition has for its consequence the*rigorous accuracy*of some other proposition” (Duhem 1991, p. 143). - 44.
Further, Prigogine stresses that Duhem was pioneering in his reflection on instabilities, but–according to Prigogine–Duhem went too far in his general critique concerning the ultimate uselessness of “unstable deductions”. Duhem assessed instabilities in a negative sense only, as a threat to classical-modern physical methodology.

- 45.
However, a proper methodology of the sort that works for stable objects is, and will always remain, impossible.

- 46.
The traditional quantitative, metrically oriented stability dogma has been replaced by weaker, more qualitative topological characteristics.

- 47.
Some of these deserve to be mentioned: entropies, information theory parameters, Lyapunov exponent, scaling exponents, lengths of transients, fractal dimensions, renormalization theory parameters, topological characteristics, structure of stable and unstable periodic trajectories, existence of chaos or hyper-chaos, parameters of basin boundaries, types of bifurcations, parameters of chaos control theory, power and Fourier spectra, phenomenological analysis of patterns, etc. Some of these properties are well known from solid state physics, fluid and plasma physics, meteorology, or statistical thermodynamics. What is new is (a) that these properties are necessary to empirically test (complex dynamical) models with just a few degrees of freedom and (b) that the model-theoretical discussion is deepened by the acceptance that nature can be structurally unstable.

- 48.
The assumption required for the existence of such shadow trajectories is that the system is hyperbolic. How serious this restriction to hyperbolicity might be is still a matter of ongoing research.

- 49.
The shift in terminology is not just rhetoric. Rather, it indicates a modeling turn in the sciences. For a philosophical account of models, see Redhead (1980), Morgan and Morrison (1999), and Hartmann and Frigg (2006). However, these authors already diagnose such a model-orientation in the realm of non-unstable objects.

- 50.
It is interesting that an epistemological and methodological discussion on the structure of mathematical models is taking place

*within*the sciences today, as part of the progress of the sciences themselves. Well-established ideas of philosophy of science are not an add-on—they can be considered as an intrinsic element of sciences. Instability and complexity carry philosophical thought, such as the reflection on the criteria for scientific evidence, truth or objectivity, into the very heart of sciences. - 51.
In his seminal book “Knowledge and Human Interest”, Habermas (1972) exemplifies this point and encourages a broader perception of the value dimension of research programs in general and among the public. However, in spite of its relevance to our late-modern technoscientific age, in the mainstream of the philosophy of science, Habermas’ central point was—and still is—neglected and disregarded.

## References

Abarbanel HD, Brown R, Sidorowich JJ, Tsimring LS (1993) The analysis of observed chaotic data in physical systems. Rev Mod Phys 65:1331–1392

Andronov A, Pontryagin L (1937) Systèmes Grossiers. Dokl. Akad. Nauk. (Doklady) SSSR 14, pp 247–251

Andronow A, Witt AA, Chaikin SE (1965/1969) Theorie der Schwingungen, Part I + II. Berlin, Akademie Verlag

Atmanspacher H, Kurths J, Scheingraeber H, Wackerbauer R, Witt A (1992) Complexity and meaning in nonlinear dynamical systems. Open Syst Inform Dyn 1(2):269–289

Aubin D, Dalmedico AD (2002) Writing the history of dynamical systems and Chaos: Longue Durée and revolution. Discipl Cultures Hist Math 29:273–339

Aurell E, Boffetta G, Crisanti A, Paladin G, Vulpiani A (1997) Predictability in the large: an extension of the concept of Lyapunov exponent. J Phys A 30:1–26

Badii R (1991) Quantitative characterization of complexity and predictability. Phys Lett A 160:372–377

Banks J, Brooks J et al (1992) On Devaney’s definition of chaos. Am Math Monthly 99:332–334

Batterman R (2002) The devil in the detail: asymptotic reasoning in explanation, reduction and emergence. Oxford University Press, Oxford/New York

Bergé P, Pomeau Y, Vidal C (1984) Order within chaos. Towards a deterministic approach to turbulence. Wiley, New York

Birkhoff GD (1927) Dynamical systems. AMS Colloquium Publications, New York

Böhme G, van den Daele W (1977) Erfahrung als Programm—Über Strukturen vorparadigmatischer Wissenschaft. In: Böhme G, van den Daele W, Krohn W (eds) Experimentelle Philosophie. Frankfurt, Suhrkamp, pp 166–219

Brown R, Chua LO (1996) Clarifying chaos: examples and counterexamples. Int J Bif Chaos 6(2):219–249

Brown R, Chua LO (1998) Clarifying Chaos II: Bernoulli chaos, zero Lyapunov exponents and strange attractors. Int J Bif Chaos 8(1):1–32

Bunge M (1987) Kausalität. Geschichte und Probleme. Mohr, Tübingen

Carnap R (1928) Der logische Aufbau der Welt. Weltkreisverlag, Berlin

Cartwright N (1983) How the laws of physics lie. Oxford University Press, Oxford

Cartwright N (1994) Nature’s capacities and their measurement. Oxford University Press, Oxford

Chaitin GJ (1971) Computational complexity and Gödel’s incompleteness theorem. ACM SIGACT News 9:11–12

Chaitin GJ (1987) Algorithmic information theory. Cambridge University Press, Cambridge

Chaitin GJ (2001) Exploring randomness. Springer, London

Comte A (2006) Cours de Philosophie positive (1830–1842). Bachelier, Paris

Coven E, Kan I, Yorke JA (1988) Pseudo-orbit shadowing in the family of tent maps. Trans Am Math Soc 308(1):227–241

Crutchfield J, Farmer JD, Packard NH, Shaw RS (1986) Chaos. Sci Am 12:46–57

Darrigol O (2006) Worlds of flow. A history of hydrodynamics from Bernoulli to Prandtl. Oxford University Press, Oxford

Descartes R (1979) Regeln zur Ausrichtung der Erkenntniskraft. Felix Meixner, Hamburg

Devaney RL (1987) An introduction to chaotic dynamical systems. Addison Wesley, Redwood City

Drieschner (2002) Moderne Naturphilosophie. Eine Einführung. Paderborn, Mentis

Duhem P (1991) The aim and structure of physical theory (1906). Princeton Uni Press, Princeton

Ebeling W, Feistel R (1990) Physik der Evolutionsprozesse. Akademie Verlag, Berlin

Einstein A (1917) Kosmologische Betrachtungen zur allgemeinen Relativitätstheorie. Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften, physikalisch-mathematische Klasse, pp 142–152

Einstein A, Podolsky B, Rosen N (1935) Can quantum-mechanical description of physical reality be considered complete? Phys Rev 47:777–780

Gierer A (1981) Physik der biologischen Gestaltbildung. Naturwiss 68:245–251

Gleick J (1987) Chaos: making a new science. Viking Penguin, New York

Guckenheimer J, Holmes P (1983) Nonlinear oscillations, dynamical systems, and bifurcations of vector fields. Springer, New York

Habermas J (1972) Knowledge and human interest (1968). Heinemann, London

Hacking I (1983) Representing and intervening. Introductory topics in the philosophy of natural sciences. Cambridge University Press, Cambridge

Haken H (ed) (1977) Synergetics. A workshop. Springer, Berlin

Harrell M, Glymour C (2002) Confirmation and chaos. Philos Sci 69:256–265

Hartmann S, Frigg R (2006) Models in science. In: Zalta EN (ed) Stanford encyclopedia of philosophy. Stanford University Press, Stanford

Heidegger M (1986) Nietzsches metaphysische Grundstellung im abendländischen Denken—die ewige Wiederkehr des Gleichen. Vittorio Klostermann, Frankfurt

Hempel CG (1965) Aspects of scientific explanation. Free Press, New York

Hertz H (1963) Die Prinzipien der Mechanik. In neuem Zusammenhang dargestellt (1894). Wiss. Buchgesellschaft, Darmstadt

Hirsch M (1984) The dynamical systems approach to differential equations. Bull Am Math Soc 11:1–64

Holmes P (2005) Ninety plus thirty years of nonlinear dynamics: more is different and less is more. Int J Bif Chaos 15(9):2703–2716

Hooker CA (2004) Asymptotics, reduction and emergence. Brit J Phil Sci 55(3):435–479

Hume D (1990) Enquiries concerning human understanding (1748). Clarendon Press, Oxford

Hund F (1972) Geschichte der physikalischen Begriffe. BI, Mannheim

Jackson EA (1989) Perspectives of nonlinear dynamics. Cambridge University Press, Cambridge

Janich P (1997) Kleine Philosophie der Naturwissenschaften. Beck, München

Kellert S (1993) In the wake of chaos: unpredictable order in dynamical systems. University Chicago Press, Chicago

Krohn W, Küppers G (eds) (1992) Selbstorganisation. Aspekte einer wissenschaftlichen Revolution. Vieweg, Braunschweig/Wiesbaden

Küppers B-O (1992) Naturals Organismus. Schellings frühe Naturphilosophie und ihre Bedeutung für die moderne Biologie. Suhrkamp, Frankfurt

Langer JS (1980) Instabilities and pattern formation. Rev Mod Phys 52:1–28

Lenhard J (2007) Computer simulations: The cooperation between experimenting and modeling. Philos Sci 74:176–194

Lewes GH (1875) Problems of life and mind, first series, vol 2. Trubner, Kegan and others, London

Li T-Y, Yorke JA (1975) Period three implies chaos. Am Math Monthly 82(10):985–992

Lorenz EN (1963) Deterministic nonperiodic flow. J Atmos Sci 20:130–141

Lorenz EN (1989) Computational chaos—a prelude to computational instability. Phys D 35:299–317

Mach E (1988) Die Mechanik in ihrer Entwicklung (1883). Akademie Verlag, Leipzig/Darmstadt

Mainzer K (1996) Thinking in complexity. The complex dynamics of matter, mind, and mankind. Heidelberg/New York: Springer

Mandelbrot B (1991) Die fraktale Geometrie der Natur (1977). Basel: Birkhauser

Maxwell JC (1873) Does the progress of physical science tend to give any advantage to the opinion of necessity (or determinism) over that of the contingency of events and the freedom of the will? In: Campbell L, Garnett W (eds) The life of James Clerk Maxwell. Johnson, New York, pp 434–444

Maxwell JC (1991) Matter and motion (1877). Dover Publications, New York

Meinhardt H (1995) The algorithmic beauty of seashells. Springer, Berlin

Mitchell SD (2002) Integrative Pluralism. Biol Philos 17:55–70

Mittelstraß J (1998) Die Haeuser des Wissens. Suhrkamp, Frankfurt

Morgan MS, Morrison M (eds) (1999) Models as mediators. Perspectives on natural and social sciences. Cambridge University Press, Cambridge

Newton I (1770) Opticks: or, a treatise of the reflections, refractions, inflections and colours of light. Innys, New York, 1730 (1717)

Nicolis G, Prigogine I (1977) Self-organization in nonequilibrium systems. From dissipative structures to order through fluctuations. Wiley, New York/London

Nietzsche F (1930) Die fröhliche Wissenschaft (1887). Leipzig: Kroener

Parker TS, Chua LO (1989) Practical numerical algorithms for chaotic systems. Springer, New York

Pauli W (1961) Aufsaetze und Vortraege über Physik und Erkenntnistheorie. Vieweg, Braunschweig

Peitgen H-O, Jürgens H, Saupe D (1992) Bausteine des Chaos: Fraktale. Springer/Klett-Cotta, Berlin

Pietschmann H (1996) Phaenomenologie der Naturwissenschaft. Springer, Berlin

Poincaré H (1892) Les méthodes nouvelles de la mécanique céleste. Gauthier-Villars et fils, Paris, p 1892

Poincaré H (1914) Wissenschaft und Methode (1908). Teubner, Leipzig

Popper KR (1934) Logik der Forschung. Wien: Julius Springer (English translation: the logic of scientific discovery. Routledge, London)

Poser H (2001) Wissenschaftstheorie. Reclam, Stuttgart

Prigogine I, Glansdorff P (1971) Thermodynamic theory of structure, stability and fluctuation. Wiley, New York/London

Prigogine I (1980) From being to becoming. Time and complexity in the physical sciences. Freeman, New York

Psillos S (1999) Scientific realism. How science tracks truth. Routledge, London/New York

Redhead M (1980) Models in physics. Brit J Phil Sci 31:145–163

Rueger A, Sharp AD (1996) Simple theories of a messy world: truth and explanatory power in nonlinear dynamics. Brit J Phil Sci 47:93–112

Ruelle D (1989) Elements of differentiable dynamics and bifurcation theory. Academic Press, London, p 1989

Ruelle D, Takens F (1971) On the nature of turbulence. Commun Math Phys 20:167–192

Salmon W (1989) Four decades of scientific explanation. In: Kitcher P, Salmon W (eds) Scientific explanation. Minnesota: University Minnesota Press, pp 3–219

Sauer T, Yorke JA, Casdagli M (1991) Embedology. J Stat Phys 77(3/4):579–616

Schmidt JC (2003) Zwischen Berechenbarkeit und Nichtberechenbarkeit. Die Thematisierung der Berechenbarkeit in der aktuellen Physik komplexer Systeme. J Gen Phil Sci 34:99–131

Schmidt JC (2008a) From symmetry to complexity: on instabilities and the unity in diversity in nonlinear science. Int J Bif Chaos 18(4):897–910

Schmidt JC (2008b) Instabilität in Natur und Wissenschaft. Eine Wissenschaftsphilosophie der nachmodernen Physik. De Gruyter, Berlin

Schmidt JC (2015) Das Andere der Natur. Neue Wege zur Naturphilosophie, Stuttgart

Schmidt JC (2017) Science in an unstable world. On Pierre Duhem’s challenge to the methodology of science. In: Pietsch W, Wernecke J, Ott M (Hg.) (eds) (2017) Berechenbarkeit der Welt? Philosophie und Wissenschaft im Zeitalter von big data. Springer, Berlin, pp 403–434

Stephan A (2007) Emergenz. Von der Unvorhersagbarkeit zur Selbstorganisation (1999). Mentis, Paderborn

Swinney HL, Gollub J (eds) (1981) Hydrodynamic instabilities and the transition to turbulence. Springer, Berlin

Takens F (1985) Distinguishing deterministic and random systems. In: Barenblatt GI, Ioss G, Joseph D (eds) (1985) Nonlinear dynamics and turbulence. Pitman, Boston, pp 314–333

Thom R (1975) Structural stability and morphogenesis. An outline of a general theory of models. Benjamin, Reading/MA

Vuillemin J (1991) Introduction. In: Duhem P (ed) (1991) The aim and structure of physical theory (1906). Princeton University Press, Princeton, pp xv–xxxiii

Wackerbauer R, Witt A, Atmanspacher H, Kurths J, Scheingraber H (1994) A comparative classification of complexity measures. Chaos, Solit Fract 4(1):133–174

Weizsäcker CFv (1974) Die Einheit der Natur. München: dtv

Wiggins S (1988) Global bifurcations and chaos. Analytical methods. Springer, New York

Woodward J (2000) Explanation and invariance in the special sciences. Brit J Phil Sci 51:197–254

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Schmidt, J.C. (2019). Is There Anything New Under the Sun?. In: Wegner, L., Lüttge, U. (eds) Emergence and Modularity in Life Sciences. Springer, Cham. https://doi.org/10.1007/978-3-030-06128-9_1

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