Abstract
This chapter is about Grete Hermann, a philosopher-mathematician who productively and mutually beneficially interacted with the founders of quantum mechanics in the early period of that theory’s elaboration. Hermann was a neo-Kantian philosopher. At the heart of Immanuel Kant’s critical philosophy lay the question of the conditions under which we can be said to know something objectively, a question Hermann found to be particularly pressing in quantum mechanics. Hermann’s own approach to neo-Kantianism was neo-Friesian. Jakob Friedrich Fries, like Kant, had understood critical philosophy to be an essentially epistemic project. Fries departed from Kant in his account of the elements involved in our cognition. In this chapter it is discussed how, beginning from a neo-Friesian understanding of critical philosophy, Hermann is led to conclude that quantum mechanics shows us that physical knowledge is fundamentally split: that the objects of quantum mechanics are only objects from a particular perspective and in the context of a particular physical interaction. It will be seen how Hermann’s solution to the problem of objectivity in quantum mechanics is a natural one from a neo-Friesian point of view, even though it disagrees with those offered by more orthodox versions of Kantian doctrine.
My research for this chapter benefited substantially from discussions and correspondence with Guido Bacciagaluppi, Leah Henderson, Fedde Benedictus, Maura Burke, Elise Crull, Corey Dyck, Sean Gryb, Thijs Hemme, Samo Kutoš, Greg Lavers, Jamie Shaw, Sasa Stankovic, and Paul Ziche. My work has also benefited from the comments and questions I received during my presentations of preliminary versions of this chapter at the Canadian Philosophical Association meeting in Fredericton, the Canadian Society for History and Philosophy of Science meeting in Calgary, the International Society for the History of Philosophy of Science meeting in Minneapolis, from audiences at Concordia University, the University of Groningen, the University of Hannover, the University of Utrecht (on two different occasions), and the University of Wuppertal. I gratefully acknowledge financial support from the Alexander von Humboldt Stiftung, as well as funding I received while a postdoc at the Rotman Institute of Philosophy at the University of Western Ontario from 2016–2019, and from the Descartes Centre at the University of Utrecht during my stay there as a senior visiting fellow in the winter of 2020. Thanks are due again to Guido for being my academic host and guide during my stay in Utrecht, and to the other members of the Descartes Centre, not already named above, with whom I interacted and who helped to make my time at the Descartes Centre stimulating and productive. Thanks, finally, to my late friend and former professor Vladimir Zeman (1937–2014), who first introduced me to Kant and neo-Kantianism.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
“\(\dots \) sondern sie beabsichtigte nur, die Quellen unseres Wissens und den Grad seiner Berechtigung zu untersuchen, ein Geschäft, welches immer der Philosophie verbleiben wird, und dem sich kein Zeitalter ungestraft wird entziehen können” (Helmholtz, 1855, 5).
- 2.
See, for instance, Carnap’s summary of the prevailing attitude toward Kant in [Reichenbach 1958, vi].
- 3.
- 4.
For more on the Kantian aspects of Hilbert’s thought, see Kitcher (1976).
- 5.
I am of course not claiming that all (or even any) of the thinkers mentioned in this paragraph would have called themselves Kantians; in particular Schlick and (the later) Carnap certainly would not have done so, and nor should we. I nevertheless do think that their views on these matters as well as the views of the others I have mentioned can be seen as continuous with (in the sense of evolving continuously out of) a research programme that was begun by Kant. For more on these topics, see Coffa (1991), DiSalle (2002), Friedman (2009), Howard, (1994) and Murphey (2005).
- 6.
In her illuminating chapter on Hermann’s philosophy, Elise Crull (2017) also understands Hermann’s project as, primarily, one of laying out these broader consequences of reflecting on quantum mechanics for our theoretical knowledge, as opposed to (merely) an attempt to reconcile quantum mechanics with Kant’s principle of causality (although, of course, reconciling quantum mechanics with causality is one part of Hermann’s broader project). Part of the contribution of my chapter is to further advance this basic take, which I share with Crull, on Hermann’s views, through a more in-depth conceptual investigation of Hermann’s Kantian and Friesian roots as these relate to transcendental idealism in particular. One point on which I disagree with the position put forward in Crull (2017), however, is her ontological reading of Hermann’s doctrine of the splitting-of-truth (ibid., 165). I do not have the space to discuss this issue further in this chapter, but it is discussed in depth in Cuffaro (2018, Sect. 10), and also, much more briefly, in footnotes 7 and 30 below. Recently, I have learned through personal correspondence that Crull has since (independently) come to change her view on this aspect of Hermann’s doctrine, and I believe we are now largely in agreement on the issue.
- 7.
I am asserting, without argument, that the so-called ‘epistemic reading’ of transcendental idealism is the correct one. There is a fair deal of controversy on this point, however. Interpreters of Kant such as Guyer (1987) and Langton (1998), for instance, prefer a reading of transcendental idealism that is in some sense ontic (for a summary of the controversy, see Stang, 2016, Sect. 4.4). I do not have enough space to defend the epistemic reading here, even though it could be defended on the basis of what we will be discussing in the sequel (see Cuffaro, 2018). Neo-Friesians as a rule subscribed to the epistemic reading in any case (even if they held Kant himself to be confused regarding its true significance) and that justifies our adopting it here (see Fries, 1828, xxiv–xxv; Hermann, 2017, 271; Nelson, 1970, 190–197; and Cuffaro, 2018, Sect. 10 for further discussion).
- 8.
References to the Critique of Pure Reason, or ‘first Critique’, will be to the Pluhar translation (1996). Page numbers for all of Kant’s works cited in this chapter (with the exception of the first Critique) will be as they are in the standard German edition. In the case of the first Critique, page numbers are as in the first (1781) and second (1787) edition, where “A” denotes the first and “B” the second, as usual.
- 9.
In the sequel I will (following Allison) be referring to transcendental idealism variously as an ‘epistemic interpretation’, ‘conceptual interpretation’, and ‘metaphilosophical interpretation’, in the senses in which those terms have been informally defined above. These descriptions of transcendental idealism are clearly not mutually exclusive.
- 10.
- 11.
Near the beginning of Kant’s so-called ‘silent decade’ in the 1770s (the period during which he produced the first Critique), he wrote this to Marcus Herz:
[Lambert objects that changes] are possible only on the assumption of time; therefore time is something real ... Then I asked myself: Why does one not accept the following parallel argument? Bodies are real (according to the testimony of outer sense). Now, bodies are possible only under the condition of space; therefore space is something objective and real that inheres in the things themselves. The reason lies in the fact that it is obvious, in regard to outer things, that one cannot infer the reality of the object from the reality of the representation ... (Zweig, 1967, 75).
- 12.
Kant writes, at B20: “In solving the above problem we solve at the same time another one, concerning the possibility of the pure use of reason in establishing and carrying out all sciences that contain theoretical a priori cognition of objects.” Cf. also (Kant, 2001, 4:280).
- 13.
Our focus in this chapter remains theoretical cognition, so we will not be discussing (except incidentally) the role of such methodological principles here. It is easy to find such discussions in the literature. See, for instance, McLaughlin (1990).
- 14.
For a more thorough discussion of this point, see (Harper 1984, 110–111).
- 15.
I have modified Pluhar’s translation of Vorstellung as ‘presentation’ to the more standard ‘representation’. As Allison (2001, 348) points out, Kant considered this term as equivalent to the Latin repraesentatio (A320/B376).
- 16.
The following example is adapted from Bacciagaluppi (2015, 381), as is my discussion of the analogous single-slit example involving quantum phenomena which follows. The quantum example is of course originally due to Bohr (1935). In his paper, Bohr actually discusses (successively) multiple variations of the single-slit experiment. The one discussed here and in Bacciagaluppi (2015) is the particular variation discussed on pp. 698–699: “In an arrangement suited for measurements of the momentum of the first diaphragm, it is further clear that even if we have measured this momentum before the passage of the particle through the slit, we are after this passage still left with a free choice whether we wish to know the momentum of the particle or its initial position relative to the rest of the apparatus”.
- 17.
Note, however, the caveat mentioned in Hughes (1989, Sect. 2.4).
- 18.
Note that if we choose not to measure the diaphragm at all, then the joint state of the diaphragm and photon will be describable as an entangled quantum superposition. Hermann (2017, Sect. 10) makes this point in the context of a different thought-experiment (the \(\gamma \)-ray microscope experiment). The role played by the diaphragm in our example is in that context played by a photon which has collided with an electron (the system of interest) in order to determine the latter’s state. In place of a pointer connected to a diaphragm, we have in that context a photographic plate which can be set up in various ways (or not at all) in order to measure the state of the photon. See also footnote 26 below.
- 19.
The mathematical principles are the Axioms of Intuition and Anticipations of Perception; the dynamical principles are the Analogies of experience and the Postulates of empirical thought as such.
- 20.
Here, I only consider the Analogies, as the Postulates are not directly relevant for our discussion.
- 21.
- 22.
As we will see in more detail later, ‘deduction’ is being used here in a specific technical sense that is relevant to Friesian critical philosophy. Her essay was originally published in the Friesian journal Abhandlugen der Fries’schen Schule.
- 23.
Regarding the occurrence of a measurement outcome, she writes: “It would \(\dots \) be pointless to wish to seek the cause of its occurrence in new physical features hitherto overlooked \(\dots \) The theory of measurement already contains a sufficient basis for explanation” (ibid., 255, emphasis in original).
- 24.
- 25.
This is just the statement that (perfect) quantum measurements are repeatable.
- 26.
In Sect. 10 of her exposition, Hermann explores the microscope example alluded to here at length. Besides being a concrete illustration of the more abstract discussion of Sect. 9, Sect. 10 additionally contains (among other things) one of the earliest discussions of quantum entanglement in either the physical or philosophical literature. For more on the particulars of Hermann’s microscope example, see Filk (2017), Frappier (2017), and for a detailed comparison of it with the ‘diaphragm and slit’ example, see Bacciagaluppi (2017).
- 27.
- 28.
For a detailed account of Fries’s method of deduction see Nelson (1971, 164–196). We will be considering part of Nelson’s exposition in more detail below.
- 29.
This illustration of how one may learn about an axiomatic system ‘via observation’ is not actually a part of Nelson’s discussion, but it is fully in the spirit of that discussion.
- 30.
Friesians (including Hermann in 1935) as a rule criticised Kant’s doctrine of formal idealism (see Hansen-Schaberg (2017, 6), and also Cuffaro (2018, Sect. 10) for further discussion, as well as footnote 7 above). As Bacciagaluppi (2020) discusses, however, in her later career she backed away from this Friesian criticism of Kant, which she (rightly) came to view as a misinterpretation of his doctrine.
- 31.
Cf. Harper’s (2011) account of ‘theory-mediated measurements’.
- 32.
It is possible that the view represented by the hypothetical objector here may actually be that of Nelson. In the context of practical philosophy, for instance, Nelson maintained that the moral law, although only discoverable empirically and ‘subjectively’, was nevertheless objective. This was a conclusion with which Hermann disagreed (Leal, 2017).
References
Allison, H. E. (2001). Kant’s Theory of Taste. Cambridge University Press.
Allison, H. E. (2004). Kant’s Transcendental Idealism, an Interpretation and Defense (Enlarged). Yale University Press.
Ameriks, K. (2003). Interpreting Kant’s Critiques. Clarendon Press.
Bacciagaluppi, G. (2015). Did Bohr understand EPR? Series M-Mathematica et Physica, Scientia Danica. In F. Aaserud & H. Kragh (Eds.), One Hundred Years of the Bohr Atom (Vol. 1, pp. 375–394). Royal Academy of Sciences and Letters.
Bacciagaluppi, G. (2017). Bohr’s slit and Hermann’s microscope. In Crull & Bacciagaluppi (Eds.) (pp. 135–148).
Bacciagaluppi, G. (2020). Physics and beyond: Essay review of Kay Herrmann (Ed.), Grete Henry-Hermann: Philosophie–Mathematik–Quantenmechanik. Journal for General Philosophy of Science, 51, 595–610.
Bächtold, M. (2017). On Bohr’s epistemological contribution to the quantum-classical cut problems. In Faye & Folse (Eds.) (pp. 235–252).
Bai, T., & Stachel, J. (2017). Bohr’s diagrams. In R. E. Kastner, J. Jeknić-Dugić, & G. Jaroszkiewicz (Eds.), Quantum Structural Studies: Classical Emergence from the Quantum Level (pp. 23–52). World Scientific Publishing Europe.
Banks, E. C. (2017). Grete Hermann as neo-Kantian philosopher of space and time representation. Journal for the History of Analytical Philosophy, 6, 245–263.
Beiser, F. C. (2014). The Genesis of Neo-Kantianism. Oxford University Press.
Bell, J. L. (2017). Continuity and infinitesimals. In E. N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy (Summer 2017 Edition). https://plato.stanford.edu/archives/sum2017/entries/continuity/
Bitbol, M. (2017). On Bohr’s transcendental research program. In Faye & Folse (Eds.) (pp. 47–66).
Bohr, N. (1928). The quantum postulate and the recent development of atomic theory. Nature, 121, 580–590.
Bohr, N. (1935). Can quantum-mechanical description of physical reality be considered complete? Physical Review, 48, 696–702.
Bohr, N. (1937). Causality and complementarity. Philosophy of Science, 4, 289–298.
Bohr, N. (1949). Discussion with Einstein on epistemological problems in atomic physics. In P. A. Schilpp (Ed.), Albert Einstein: Philosopher-Scientist. The Library of Living Philosophers (Vol. 7, pp. 199–241). Open Court.
Bohr, N. (1958). Atoms and human knowledge. In Atomic Physics and Human Knowledge (pp. 83–93). John Wiley & Sons, Inc.
Born, M. (1929). Über den Sinn der physikalischen Theorien. Die Naturwissenschaften, 17, 109–118.
Cassirer, E. (1956[1936]). Determinism and Indeterminism in Modern Physics In O. T. Benfey (Trans). Yale University Press.
Chevalley, C. (1994). Niels Bohr’s words and the Atlantis of Kantianism. In J. Faye & H. J. Folse (Eds.), Niels Bohr and Contemporary Philosophy (pp. 33–55). Kluwer Academic Publishers.
Coffa, J. A. (1991). The Semantic Tradition from Kant to Carnap. Cambridge University Press.
Crull, E. (2017). Hermann and the relative context of observation. In Crull & Bacciagaluppi (Eds.) (pp. 149–172).
Crull, E., & Bacciagaluppi, G. (2017). Grete Hermann: Between Physics and Philosophy. Springer.
Cuffaro, M. E. (2010). The Kantian framework of complementarity. Studies in History and Philosophy of Modern Physics, 41, 309–317.
Cuffaro, M. E. (2012). Kant and Frege on existence and the ontological argument. History of Philosophy Quarterly, 29, 337–354.
Cuffaro, M. E. (2018). Kantian and neo-Kantian first principles for physical and metaphysical cognition. philsci-archive.pitt.edu/15350/.
Dieks, D. (2017). Von Neumann’s impossibility proof: Mathematics in the service of rhetorics. Studies in History and Philosophy of Modern Physics, 60, 136–148.
DiSalle, R. (2002). Conventionalism and modern physics: A re-assessment. Noûs, 36, 169–200.
Faye, J. (2017). Complementarity and human nature. In Faye & Folse (Eds.) (pp. 115–132).
Faye, J., & Folse, H. (2017). Niels Bohr and the Philosophy of Physics: Twenty-First-Century Perspectives. Bloomsbury.
Feyerabend, P. (2015). Determinism and quantum mechanics (1954). In S. Gattei & J. Agassi (Eds.), Physics and Philosophy: Philosophical Papers (pp. 25–45). Cambridge University Press.
Filk, T. (2017). Carl Friedrich von Weizsäcker’s ‘Ortsbestimmung eines Elektrons’ and its influence on Grete Hermann. In Crull & Bacciagaluppi (Eds.) (pp. 71–84).
Folse, H. J. (2017). Complementarity and pragmatic epistemology: A comparison of Bohr and C. I. Lewis. In Faye & Folse (Eds.) (pp. 91–114).
Frappier, M. (2017). ‘In the No-Man’s-Land between Physics and Logic’: On the dialectical role of the microscope experiment. In Crull & Bacciagaluppi (Eds.) (pp. 85–106).
Frege, G. (1980[1884]). The Foundations of Arithmetic (J. Austin, Trans). Northwestern University Press.
Friedman, M. (2009). Einstein, Kant, and the relativized a priori. In M. Bitbol, P. Kerszberg, & J. Petitot (Eds.), Constituting Objectivity: Transcendental Perspectives on Modern Physics (pp. 253–268). Springer.
Fries, J. F. (1828). Neue oder Anthropologische Kritik der Vernunft (2nd ed.). Christian Friedrich Winter.
Guyer, P. (1987). Kant and the Claims of Knowledge. Cambridge University Press.
Hansen-Schaberg, I. (2017). A biographical sketch of Prof. Dr. Grete Henry-Hermann (1901–1984). In Crull & Bacciagaluppi (Eds.) (pp. 3–16).
Harper, W. (1984). Kant’s empirical realism and the distinction between subjective and objective succession. In W. Harper & R. Meerbote (Eds.), Kant on Causality, Freedom and Objectivity (pp. 108–137). University of Minnesota Press.
Harper, W. L. (2011). Isaac Newton’s Scientific Method. Oxford University Press.
Helmholtz, H. (1855). Ueber das Sehen des Menschen. Leopold Voss.
Hermann, G. (2017). Natural-philosophical foundations of quantum mechanics (1935). (E. Crull, & G. Bacciagaluppi, Trans). In Crull & Bacciagaluppi (Eds.) (pp. 239–278). The German version is reprinted in Herrmann (2019) (pp. 185–204).
Herrmann, K. (2019). Grete Henry-Hermann: Philosophie—Mathematik—Quantenmechanik. Springer.
Hilbert, D. (1902). The Foundations of Geometry (E. Townsend, Trans.). Open Court Publishing Company. Reprint Edition (1950)
Howard, D. (1994). Einstein, Kant, and the origins of logical empiricism. In W. Salmon & G. Wolters (Eds.), Language, Logic, and the Structure of Scientific Theories (pp. 45–105). University of Pittsburgh Press.
Hughes, R. I. G. (1989). The Structure and Interpretation of Quantum Mechanics. Harvard University Press.
Jammer, M. (1974). The Philosophy of Quantum Mechanics. John Wiley & Sons.
Kaiser, D. (1992). More roots of complementarity: Kantian aspects and influences. Studies in History and Philosophy of Science, 23, 213–239.
Kant, I. (1981). Grounding for the Metaphysics of Morals (1785) (J. W. Ellington, Trans.). Hackett Publishing Company.
Kant, I. (1996). Critique of Pure Reason (W. S. Pluhar, Trans.). Hackett Publishing Company.
Kant, I. (2001). Prolegomena to any Future Metaphysics that will be Able to come Forward as Science, with Kant’s Letter to Marcus Herz, February 27, 1772, 2nd edn. (J. W. Ellington, Trans.). Hackett Publishing Company.
Kant, I. (2002a). Inquiry concerning the distinctness of the principles of natural theology and morality (1763). In Walford (Ed.), (pp. 243–286).
Kant, I. (2002b). A new elucidation of the first principles of metaphysical cognition (1755). In Walford (Ed.), (pp. 1–46).
Kant, I. (2002c). On the form and principles of the sensible and intelligible world (1770). In Walford (Ed.), (pp. 373–416).
Kant, I. (2002d). The only possible argument in support of a demonstration of the existence of God (1763). In Walford (Ed.), (pp. 107–202).
Kauark-Leite, P. (2017). Transcendental versus quantitative meanings of Bohr’s complementarity principle. In Faye & Folse (Eds.) (pp. 67–90).
Kitcher, P. (1976). Hilbert’s epistemology. Philosophy of Science, 43, 99–115.
Langton, R. (1998). Kantian Humility. Oxford University Press.
Leal, F. (2017). Grete Hermann as a philosopher. In Crull & Bacciagaluppi (Eds.) (pp. 17–34).
Leary, D. E. (1982). The psychology of Jakob Friedrich Fries (1773–1843): Its context, nature, and historical significance. Storia E Critica Della Psicologia, 3, 217–248.
McLaughlin, P. (1990). Kant’s Critique of Teleology in Biological Explanation: Antinomy and Teleology. The Edwin Mellen Press.
Merrick, T. (2006). What Frege meant when he said: Kant is right about geometry. Philosophia Mathematica (III), 14, 44–75.
Murphey, M. G. (2005). C. I. Lewis: The Last Great Pragmatist. State University of New York Press.
Nelson, L. (1970). Progress and Regress in Philosophy, Vol. I. (H. Palmer, Trans.). Basil Blackwell.
Nelson, L. (1971). Progress and Regress in Philosophy, Vol. II. (H. Palmer, Trans.) Basil Blackwell.
Pitowsky, I. (1994). George Boole’s ‘conditions of possible experience’ and the quantum puzzle. British Journal for the Philosophy of Science, 45, 99–125.
Pringe, H. (2009). A transcendental account of correspondance and complementarity. In M. Bitbol, P. Kerszberg, & J. Petitot (Eds.), Constituting Objectivity (pp. 317–327). Springer.
Reichenbach, H. (1958). The Philosophy of Space & Time (M. Reichenbach, & J. Freund, Trans.). Dover Publications Inc. English edition, with introductory remarks by Rudolf Carnap.
Schlick, M. (1961[1931]). Causality in contemporary physics (I) (D. Rynin, Trans.). The British Journal for the Philosophy of Science, 12, 177–193.
Schlick, M. (1962[1931]). Causality in contemporary physics (II) (D. Rynin, Trans.). The British Journal for the Philosophy of Science, 12, 281–298.
Schnädelbach, H. (1984). Philosophy in Germany 1831–1933. Cambridge University Press.
Soler, L. (2017). The convergence of transcendental philosophy and quantum physics: Grete Hermann’s 1935 pioneering proposal. In Crull & Bacciagaluppi (Eds.) (pp. 55–70).
Stang, N. (2016). Kant’s transcendental idealism. In E. N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy. Spring 2016 Edition. https://plato.stanford.edu/archives/spr2021/entries/kant-transcendental-idealism/
Stein, H. (1967). Newtonian space-time. In R. Palter (Ed.), The Annus Mirabilis of Sir Isaac Newton, 1666–1966 (pp. 258–284). The M.I.T. Press.
Walford, D. (2002). Theoretical Philosophy 1755–1770. Cambridge University Press.
Zeman, V. (1997). Hermann Cohen’s concept of the transcendental method. In T. Rockmore & V. Zeman (Eds.), Transcendental Philosophy and Everyday Experience (pp. 111–124). Humanities Press.
Zweig, A. (Ed.). (1967). Kant, Philosophical Correspondance 1759–99. (A. Zweig, Trans.). The University of Chicago Press.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Cuffaro, M.E. (2022). Grete Hermann, Quantum Mechanics, and the Evolution of Kantian Philosophy. In: Peijnenburg, J., Verhaegh, S. (eds) Women in the History of Analytic Philosophy. Women in the History of Philosophy and Sciences, vol 15. Springer, Cham. https://doi.org/10.1007/978-3-031-08593-2_6
Download citation
DOI: https://doi.org/10.1007/978-3-031-08593-2_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-08592-5
Online ISBN: 978-3-031-08593-2
eBook Packages: HistoryHistory (R0)