Skip to main content
Log in

Johannes von Kries’s Objective Probability as a Semi-classical Concept. Prehistory, Preconditions and Problems of a Progressive Idea

  • Special Section Article: Kries and Objective Probability
  • Published:
Journal for General Philosophy of Science Aims and scope Submit manuscript

Abstract

Johannes von Kries’s Spielraum-theory is regarded as one of the most important philosophical contributions of the nineteenth century to an objective interpretation of probability. This paper aims at a critical and contextual analysis of von Kries’s approach: It is contextual insofar as it reconstructs the Spielraum-theory in the historical setting that formed his scientific and philosophical outlook. It is critical insofar as it unfolds systematic tensions and inconsistencies which are rooted in this context, especially in the grave change of mechanism which took place in the late nineteenth century. In this regard, the paper focuses on von Kries’s understanding of natural laws and nomological knowledge in relation to his concept of objective probability. While the formal approach of the Spielraum-theory—as far as developed by von Kries—seems sound, his epistemological claims with respect to nomological knowledge sustain classical mechanism and are hence difficult to substantiate from the point of view of modern science.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Notes

  1. Von Kries (1925, 34). All translations from German are mine unless indicated otherwise.

  2. I will put ‘ontological’ in simple quotation marks in order to allude to von Kries’s use of the word; see part 4 for his meaning of this term.

  3. My ‘practitioner’s-view’ is highlighted amongst others by the Festschrift dedicated to him on the occasion of his 70th birthday, which appeared in two parts: one part with 26 papers was published in Pflüger’s Archiv für die gesamte Physiologie (Festschrift 1923a). Another part with 11 papers appeared in Psychologische Forschung. Zeitschrift für Psychologie und ihre Grenzwissenschaften (Festschrift 1923b). Only two papers of his colleagues and disciples touch philosophical topics and no paper deals with probability or other mathematical and philosophical concepts. Von Kries was obviously an academic outsider both in philosophy and in mathematics. While this finding does not say too much about his philosophical rank, the weak reception of his scientific work within philosophy of science of his days seems more revealing in this respect.

  4. According to Lakatos, Euclideanism expresses the view that the “ideal theory is a deductive system with an indubitable truth-injection at the top (a finite conjunction of axioms)—so that truth, flowing down from the top through the safe truth-preserving channels of valid inferences, inundates the whole system”; its basic aim “is to search for self-evident axioms—Euclidean methodology is puritanical, anti-speculative” (Lakatos 1978, 28–29). Euclideanism in this sense is epistemologically neutral insofar as it is applicable to different foundational programs like rationalism, empiricism and transcendental philosophy: Whether the axioms at the top are revealed by the ‘light of reason’ (Descartes and others) or ‘deduced from phenomena’ (Newton and others) or are understood as synthetic principles a priori (Kant and his followers) is irrelevant. Only their status as indubitable axioms of the deductive system is decisive.

  5. See von Kries (1925, 129–130). An exemplary analysis of Helmholtz’s transition from a classical to a modern understanding of science is provided by Schiemann (1997). This book also discusses earlier investigations (of A. Diemer, G. König, H. Schnädelbach and others) which make use of the distinction of classical and modern science in order to better understand the development of philosophy of science in the modern age.

  6. Wundt published in 1866 the booklet Die physikalischen Axiome und ihre Beziehung zum Kausalprinzip (Wundt 1866), which is a manifesto of Mechanical Euclideanism par excellence. More than four decades later, a revised edition of this booklet appeared under the title Die Prinzipien der Naturlehre. Ein Kapitel aus einer Philosophie der Naturwissenschaften (Wundt 1910). The change that took place in the meantime and the subsequent change in Wundt’s philosophy of science are highlighted by this remark to the principles of mechanics and of (pure) mathematics: “What had been accepted as an axiom in former times was now labeled as ‘hypothesis’, thereby expressing that also alternative systems of premises—perhaps deviating essentially from the established system—can be chosen, as long as they serve the purpose of linking the phenomena which have to be described” (Wundt 1910, 2).

  7. Von Kries (1882, 1886, 1888, 19161920, 1925), respectively. As his understanding of natural laws and nomological knowledge does not change noticeable, I will mainly refer to the Logik (von Kries 1916) as his most elaborated presentation of the ‘nomological context’.

  8. This seems to be the deeper reason for his special use of ‘ontological’ with respect to physical initial and boundary states (cf. note 2 and part 4): For von Kries, these states always have to be understood as real among possible alternatives, i.e. alternatives conformal to the same laws.

  9. Therefore, the denotation ‘ontological’ seems a bit high-flying and immoderate in this context and is put in quotation marks (cf. note 2). Given von Kries’s leaning towards Kant’s philosophy, one might say that the ontological determination of nature has to include all aspects which cannot be grasped by ‘nature according to its formal meaning’ according to Kant. In this sense, ‘ontological’ determination demands the identification of positions, forms and movements of matter, which themselves are in fact outcomes of law-like behaviour of matter, but are taken from the point of view of nomological determination as mere ‘historical facts’, to which laws are first applied. This is why I prefer to use the term ‘initial conditions’ for these given facts.

  10. “According to what has been said, the claim that the success is possible under certain general circumstances always articulates a knowledge with nomological content, a cognition with respect to the laws of the events” (von Kries 1886, 88; cf. also 37).

  11. Referring again to his ‘percussion game’, for example, von Kries convincingly argues that several formal requirements must be imposed on the whole arrangement: strong continuity of the introduced probability function and avoidance of a certain periodicity of this function, among others (von Kries 1886, 50–60).

  12. Regardless of the fact that von Kries rejects (‘subjective’) probability ascriptions to laws (cf. part 4) his theory would not work if the initial states would be related to probabilities by rules implying probability: “One could try to generalize the approach by considering processes in which an initial state does not fix an outcome, but only a probability distribution over the possible outcomes. But this distribution would have to be interpreted in turn, and if this were done according to the range approach, one could in principle eliminate these probability distributions by moving to another, higher-dimensional initial-state space. Therefore, the range approach is indeed restricted to deterministic contexts, or else becomes dependent on a different interpretation of probability” (Rosenthal 2010, 77, n. 4).

  13. And according to the restrictions of classical mechanical laws which govern his random experiments, these questions cannot be answered in principle in other relevant scientific areas (like quantum physics, for example).

  14. An anonymous referee of this journal called my attention to the fact that this critique (recurrence of subjectivism) can already be found in early receptions of the Spielraum-theory in the context of discussions on the foundations of (mathematical) probability. Two representative findings may do in order to confirm this parallel: Reichenbach (1916, 215–220 and von Mises 1919, 55).

References

  • Bayertz, K., Gerhard, M., & Jaeschke, W. (Eds.). (2007). Weltanschauung, Philosophie und Naturwissenschaft, Bd. 3: Der Ignorabimus-Streit. Hamburg: F. Meiner.

    Google Scholar 

  • DuBois-Reymond, E. (1848). Über die Lebenskraft. Aus der Vorrede zu den ‘Untersuchungen über tierische Elektrizität‘vom März 1848. In E. DuBois-Reymond (Ed.), Reden in zwei Bänden (Vol. 1, pp. 1–26). Leipzig: Von Veit & Comp.

    Google Scholar 

  • DuBois-Reymond, E. (1872). Über die Grenzen des Naturerkennens. In der zweiten allgemeinen Sitzung der 45. Versammlung Deutscher Naturforscher und Ärzte zu Leipzig am 14. August 1872 gehaltener Vortrag. In E. DuBois-Reymond (Ed.), Reden in zwei Bänden (Vol. 1, pp. 441–473). Leipzig: Von Veit & Comp.

  • Festschrift (1923a). Für J. v. Kries. Pflüger’s Archiv für die gesamte Physiologie, 201, 1–332.

    Article  Google Scholar 

  • Festschrift (1923b). Für Johannes von Kries. Psychologische Forschung. Zeitschrift für Psychologie und ihre Grenzwissenschaften, 3, 209–318.

    Article  Google Scholar 

  • Galaty, D. G. (1974). The philosophical basis of mid-nineteenth century German reductionism. Journal of the History of Medicine and Allied Sciences, 29, 259–316.

    Google Scholar 

  • Heidelberger, M. (1993). Die innere Seite der Natur. Gustav Theodor Fechners wissenschaftlich-philosophische Weltauffassung. Frankfurt a.M.: Klostermann.

  • Heidelberger, M. (2001). Origins of the logical theory of probability: von Kries, Wittgenstein, Waismann. International Studies in the Philosophy of Science, 15, 177–188.

    Article  Google Scholar 

  • Henrich, J. (2010). Die Fixierung des modernen Wissenschaftsideals durch Laplace. Berlin: Akademie.

    Book  Google Scholar 

  • Lakatos, I. (1978). In J. Worrall, & G. Gurrie (Eds.) Philosophical papers, Vol. 2. Cambridge: University Press.

  • Laplace, P. S. D. (1886). Oevures. Publiées sous les auspieces de l‘Académie des Science. Tome Septième, Paris: Gauthier-Villars.

  • Lübbe, Weyma. (1993). Die Theorie der adäquaten Verursachung. Journal for General Philosophy of Science, 24, 87–102.

    Google Scholar 

  • Neumann, C. (1870). Ueber die Principien der Galilei-Newton’schen Theorie. Akademische Antrittsrede gehalten in der Aula der Universität Leipzig am 3. November 1869. Leipzig: Teubner.

    Google Scholar 

  • Neumann, M. (2002). Die Messung des Unbestimmten. Die Geschichte der Konstruktion und Dekonstruktion eines Gegenstandsbereichs der Wahrscheinlichkeitstheorie. Frankfurt a. M: Hänsel-Hohenhausen.

    Google Scholar 

  • Pulte, H. (2004). Wahrheitsähnlichkeit. In. J. Ritter, K. Gründer und G. Gabriel (Hgg.), Historisches Wörterbuch der Philosophie, Bd. 12, (pp. 170–177). Basel: Schwabe.

  • Pulte, H. (2005). Axiomatik und Empirie. Eine wissenschaftstheoriegeschichtliche Untersuchung zur Mathematischen Naturphilosophie von Newton bis Neumann. Darmstadt: Wissenschaftliche Buchgesellschaft.

  • Pulte, H. (2009). From Axioms to Conventions and Hypotheses: The Foundations of Mechanics and the Roots of Carl Neumann's 'Principles of the Galilean-Newtonian Theory'. In M. Heidelberger & G. Schiemann (Eds.), The Significance of the Hypothetical in the Natural Sciences (pp. 77–98). Berlin: de Gruyter.

  • Pulte, H. (2015). Emil du Bois-Reymond in Context: Kantianism and 'Mechanical' Limitations of Knowledge in the Second Half of the 19th century. In M. Anacker & N. Moro (Eds.), Limits of Knowledge. The Nineteenth Century Epistemological Debate and Beyond (pp. 57–73). Milano: Polimetrica.

  • Reichenbach, H. (1916). Der Begriff der Wahrscheinlichkeit für die mathematische Darstellung der Wirklichkeit. Zeitschrift für Philosophie und philosophische Kritik, 161, 209–239.

    Google Scholar 

  • Rosenthal, J. (2004). Wahrscheinlichkeiten als Tendenzen. Eine Untersuchung objektiver Wahrscheinlichkeitsbegriffe. Paderborn: Mentis.

    Google Scholar 

  • Rosenthal, J. (2010). The natural-range conception of probability. In G. Ernst & A. Hüttemann (Eds.), Time, chance and reduction. Philosophical aspects of statistical mechanics (pp. 71–91). Cambridge: University Press.

    Chapter  Google Scholar 

  • Rower, G., & Pötter, U. (2002). Wahrscheinlichkeit. Begriff und Rhetorik in der Sozialforschung. Weinheim/München: Juventa.

    Google Scholar 

  • Schiemann, G. (1997). Wahrheitsgewissheitsverlust. Hermann von Helmholtz‘Mechanismus im Anbruch der Moderne. Eine Studie zum Übergang von klassischer zu moderner Naturphilosophie. Darmstadt: Wissenschaftliche Buchgesellschaft.

    Google Scholar 

  • Vidoni, F. (1991). Ignorabimus! Emil Du Bois-Reymond und die Debatte über die Grenzen wissenschaftlicher Erkenntnis im 19. Jahrhundert. Frankfurt a. M./Bern/New York: Peter Lang.

    Google Scholar 

  • von Helmholtz, H. (1847). Über die Erhaltung der Kraft. Eine physikalische Abhandlung. In H. von Helmholtz (Ed.), Wissenschaftliche Abhandlungen, Bd. 1 (pp. 12–75). Berlin: Reimer.

    Google Scholar 

  • von Helmholtz, H. (1867). Handbuch der physiologischen Optik. Leipzig: Voss.

    Google Scholar 

  • von Kries, J. (1882). Ueber die Messung intensiver Grössen und über das sogenannte psychophysische Gesetz. Vierteljahresschrift für wissenschaftliche Philosophie, 6, 257–294.

    Google Scholar 

  • von Kries, J. (1886). Die Principien der Wahrscheinlichkeitsrechnung. Eine logische Untersuchung. Freiburg: Mohr.

    Google Scholar 

  • von Kries, J. (1888). Ueber den Begriff der objektiven Möglichkeit und einige Anwendungen desselben. Vierteljahresschrift für wissenschaftliche Philosophie 12, (pp. 179–240) [1. Artikel], (pp. 287–323) [2. Artikel], (pp. 393–428) [3. Artikel].

  • von Kries, J. (1916). Logik. Grundzüge einer kritischen und formalen Urteilslehre. Tübingen: Mohr.

    Google Scholar 

  • von Kries, J. (1919). Über Wahrscheinlichkeitsrechnung und ihre Anwendung in der Physik. Die Naturwissenschaften 7, 2–7 [I, II], 17–23 [III].

  • von Kries, J. (1920). Über die zwingende und eindeutige Bestimmtheit des physikalischen Weltbildes. Die Naturwissenschaften, 8, 237–247.

    Article  Google Scholar 

  • von Kries, J. (1921). Helmholtz als Physiolog. Die Naturwissenschaften, 9, 673–693.

    Article  Google Scholar 

  • von Kries, J. (1925). Johannes von Kries. In L. R. Grote (Ed.), Die Medizin der Gegenwart in Selbstdarstellungen (pp. 1–63). Leipzig: Meiner.

    Google Scholar 

  • von Kries, J. (1927). Die Principien der Wahrscheinlichkeitsrechnung. Eine logische Untersuchung. Freiburg: Mohr. (Reprint of von Kries 1886, with an additional Preface: “Vorwort zum zweiten Abdruck”).

  • von Mises, R. (1919). Grundlagen der Wahrscheinlichkeitsrechnung. Mathematische Zeitschrift, 5, 52–99.

    Article  Google Scholar 

  • von Plato, J. (1994). Creating modern probability. Its mathematics, physics and philosophy in historical perspective. Cambridge: University Press.

    Book  Google Scholar 

  • Wundt, W. (1866). Die physikalischen Axiome und ihre Beziehung zum Kausalprinzip. Heidelberg: Enke.

    Google Scholar 

  • Wundt, W. (1910). Die Prinzipien der mechanischen Naturlehre. Ein Kapitel aus einer Philosophie der Naturwissenschaften. Stuttgart: Enke.

    Google Scholar 

Download references

Acknowledgments

I would like to thank Gerhard Wagner (Frankfurt) and two anonymous referees of this journal for helpful comments on an earlier version of this paper. Many thanks also to Bernd Buldt (Fort Wayne) for providing me with a useful bibliography of von Kries’s publications.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Helmut Pulte.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pulte, H. Johannes von Kries’s Objective Probability as a Semi-classical Concept. Prehistory, Preconditions and Problems of a Progressive Idea. J Gen Philos Sci 47, 109–129 (2016). https://doi.org/10.1007/s10838-015-9317-5

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10838-015-9317-5

Keywords

Navigation