Chaos and Stochastic Models in Physics: Ontic and Epistemic Aspects

  • Sergio CapraraEmail author
  • Angelo Vulpiani
Part of the Studies in Applied Philosophy, Epistemology and Rational Ethics book series (SAPERE, volume 25)


There is a persistent confusion about determinism and predictability. In spite of the opinions of some eminent philosophers (e.g., Popper), it is possible to understand that the two concepts are completely unrelated. In few words we can say that determinism is ontic and has to do with how Nature behaves, while predictability is epistemic and is related to what the human beings are able to compute. An analysis of the Lyapunov exponents and the Kolmogorov-Sinai entropy shows how deterministic chaos, although with an epistemic character, is non subjective at all. This should clarify the role and content of stochastic models in the description of the physical world.


Lyapunov Exponent Deterministic System Deterministic Chaos Suspension Point Deterministic Nature 
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  1. Atmanspacher, H.: Determinism is ontic, determinability is epistemic’. In: Atmanspacher, H., Bishop, R. (eds.) Between Chance and Choice. Imprint Academic, Thorverton (2002)Google Scholar
  2. Boyd, R.: Determinism, laws and predictability in principle. Phylosophy Sci. 39, 43 (1972)Google Scholar
  3. Campbell, L., Garnett, W.: The Life of James Clerk Maxwell. MacMillan and Co., London (1882)Google Scholar
  4. Cencini, M., Cecconi, F., Vulpiani, A.: Chaos: From Simple Models to Complex Systems. World Scientific, Singapore (2009)CrossRefGoogle Scholar
  5. Chibbaro, S., Rondoni, L., Vulpiani, A.: Reductionism, Emergence and Levels of Reality. Springer-Verlag, Berlin (2014)CrossRefGoogle Scholar
  6. Dyson, F.: Birds and frogs. Not. AMS 56, 212 (2009)Google Scholar
  7. Franceschelli, S.: Some remarks on the compatibility between determinism and unpredictability. Prog. Biophys. Mol. Biol. 110, 61 (2012)CrossRefGoogle Scholar
  8. Galilei, G.: Dialogues Concerning Two New Sciences. MacMillan, New York (1914)Google Scholar
  9. Koertge, N.: Galileo and the problem of accidents. J. Hist Ideas 38, 389 (1977)CrossRefGoogle Scholar
  10. Lorenz, E.N.: Deterministic nonperiodic flow. J. Atmos. Sci. 20, 130 (1963)CrossRefGoogle Scholar
  11. Ma, S.K.: Statistical Mechanics. World Scientific, Singapore (1985)CrossRefGoogle Scholar
  12. Onsager, L., Machlup, S.: Fluctuations and irreversible processes. Phys. Rev. 91, 1505 (1953)CrossRefGoogle Scholar
  13. Pais, A.: Subtle is the Lord: The science and the life of Albert Einstein. Oxford University Press, Oxford (2005)Google Scholar
  14. Poincaré, H.: Les méthodes nouvelles de la mécanique céleste. Gauthier-Villars, Paris (1892)Google Scholar
  15. Popper, K.R.: The open universe: An argument for indeterminism. From the Postscript to the Logic of Scientific Discovery. Routledge, London (1992)Google Scholar
  16. Popper, K.R.: The Logic of Scientific Discovery. Routledge, London (2002)Google Scholar
  17. Prigogine, I., Stengers, I.: Les Lois du Chaos. Flammarion, Paris (1994)Google Scholar
  18. Primas, H.: Hidden determinism, probability, and times arrow. In: Bishop, R., Atmanspacher, H. (eds.) Between Chance and Choice, p. 89. Imprint Academic, Exeter (2002)Google Scholar
  19. Shannon, C.E.: A note on the concept of entropy. Bell Syst. Tech. J. 27, 379 (1948)CrossRefGoogle Scholar
  20. Stone, M.A.: Chaos, prediction and Laplacean determinism. Am. Phylos. Q. 26, 123 (1989)Google Scholar
  21. Takens, F.: Detecting strange attractors in turbulence. In: Rand, D., Young, L.S. (eds.) Dynamical Systems and Turbulence, Lecture Notes in Mathematics 898. Springer-Verlag, New York (1981)Google Scholar
  22. van Kampen, N.G.: Determinism and predictability. Synthese 89, 273 (1991)CrossRefGoogle Scholar
  23. von Plato, J.: Creating Modern Probability. Cambridge University Press, Cambridge (1994)Google Scholar
  24. Vauclair, S.: Elémentes de Physique Statistique. Interéditions, Paris (1993)Google Scholar

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© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Dipartimento di FisicaUniversità SapienzaRomaItaly

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