Determinismus und Indeterminismus in der modernen Physik (DI) is one of Cassirer’s least known and studied works, despite his own assessment as “one of his most important achievements” (Gawronsky 1949, 29). A prominent theme locates quantum mechanics as a yet further step of the tendency within physical theory towards the purely functional theory of the concept and functional characterization of objectivity. In this respect DI can be considered an “update”, like the earlier monograph Zur Einsteinschen Relativitätstheorie: Erkenntnistheoretische Betrachtungen (1921), to Substanzbegriff und Funktionsbegriff (1910), a seminal work considering only classical and pre-relativistic physics. But how does DI cohere with the three volumes of The Philosophy of Symbolic Forms (1923–29) providing a systematic survey of symbolic meanings in diverse aspects of culture, each with its own mode of “objectification” via self-created signs and images? Cassirer’s “phenomenology of cognition” via distinct types of symbolic form locates Dirac’s Principles of Quantum Mechanics (1930) as an exemplar within physical theory of purely symbolic thought, a realm of pure relations and their correlated meanings. In particular, Dirac’s characterization of the new notion of “physical state” in quantum mechanics by a “symbolic algebra of observables” severed from particular representations points to a limiting pole of the Bedeutungsfunktion, the third and highest mode of symbolic formation.
Determinismus und Indeterminismus in der modernen Physik (DI) is one of Cassirer’s least known and studied works, despite his own assessment as “one of his most important achievements” (Gawronsky 1949, 29). A prominent theme locates quantum mechanics as a yet further step of the tendency within physical theory towards the purely functional theory of the concept and functional characterization of objectivity. In this respect DI can be considered an “update”, like the earlier monograph Zur Einsteinschen Relativitätstheorie: Erkenntnistheoretische Betrachtungen (1921), to Substanzbegriff und Funktionsbegriff (1910), a seminal work considering only classical and pre-relativistic physics. But how does DI cohere with the three volumes of The Philosophy of Symbolic Forms (1923–29) providing a systematic survey of symbolic meanings in diverse aspects of culture, each with its own mode of “objectification” via self-created signs and images? Cassirer’s “phenomenology of cognition” via distinct types of symbolic form locates Dirac’s Principles of Quantum Mechanics (1930) as an exemplar within physical theory of purely symbolic thought, a realm of pure relations and their correlated meanings. In particular, Dirac’s characterization of the new notion of “physical state” in quantum mechanics by a “symbolic algebra of observables” severed from particular representations points to a limiting pole of the Bedeutungsfunktion, the third and highest mode of symbolic formation.
This chapter examines Cassirer's view on contemporary science. It revisits Cassirer's lesser-known work Determinism and Indeterminism in Modern Physics and argues that it harbors a significantly new stage of his philosophy of physical science. On the one hand, this work presents the quantum formalism as a limiting pole of the Bedeutungsfunktion, the highest mode of symbolic formation according to Cassirer’s “phenomenology of cognition.” Inspired by Paul Dirac, Cassirer understands quantum mechanics as a symbolic calculus for deriving probabilistic predictions of measurement outcomes without regard to underlying wave or particle “images” – or, as an exemplar of abstract symbolic thought. On the other hand, Cassirer recognizes the philosophical significance of the use of group theory in quantum mechanics as advancing a purely structural concept of object in physics. Hence, Ryckman reveals that Cassirer drew epistemological consequences from the symbolic character of contemporary physical theory that retain relevance for philosophy of science today.
Die erste systematische Schrift, die Ernst Cassirer veröffentlicht hat, ist das Buch "Substanzbegriff und Funktionsbegriff" von 1910, in dem er sich mit dem Problem der mathematischen und naturwissenschaftlichen Begriffsbildung auseinandersetzt. Als "Faktum" legte er den damaligen Stand der Wissenschaft zugrunde, der das klassische System der Physik noch als unbestritten galt. Mit den Fortschritten der Wissenschaften, in diesem Fall der Entwicklung der theoretischen Physik, muß die Erkenntniskritik Schritt halten. Und so drängten sich im Laufe der Zeit neue Fragen auf, die der philosophischen Behandlung bedurften. Aus dieser Motivation heraus veröffentlichte Cassirer 1920 die Schrift "Zur Einsteinschen Relativitätstheorie" (ECW Bd. 10), in der er sich mit der Um- und Neubildung der modernen Physik durch die allgemeine und spezielle Relativitätstheorie beschäftigt. Um dem philosophischen Ideal der methodischen Analyse und erkenntniskritischen Grundlegung gerecht zu werden, ergab sich jedoch die Notwendigkeit, auch die Auswirkungen der Quantentheorie in die Reflexion mit einzubeziehen. Den historischen Ursachen und systematischen Gründen der Sprengkraft, die die Quantentheorie auf dem ganzen Gebiet der Physik entwickelte, geht Cassirer in der Schrift "Determinismus und Indeterminismus in der modernen Physik" nach, die er 1936 abschließt.
The relationship between physical notions and the structures expressing them is an issue of primary importance the history and philosophy of pre-modern natural philosophy and of modern science. Historical evidence suggests that, when investigating the relationship between physics and mathematics, one should pay attention to the material, sensually perceivable forms mediating it: spoken or written words, drawings, artefacts, descriptions of experimental set-ups or, as the case discussed the present paper, symbolic notation. The reason for this is that, historically, physical notions and their expressions have very often been developed as one, and only distinguished from each other at a later stage. This was for example the case with what we today regard as mathematical and classical mechanics, which were developed the course of the eighteenth century as the discipline of the analysis of motion. When considered from a later point of view, both the physical notions and the concepts involved historical developments appear as being in flux, vague, and, as far as the side is concerned, non-rigorous. In such cases, verbal description, mechanical artefacts or symbols do not simply mediate between physical notions and structures, as might be the case at a later stage, but represent both of them one, allowing the historical actors to construct and manipulate physical-mathematical meaning by following, at times, their physical reasoning and, at times, their criteria of rigour. The history of quantum mechanics offers many examples of how new physics and new mathematics can emerge as one, with symbolic notation playing a central role shaping both. Among the many creators of quantum theory, Paul Dirac was particularly sensitive to questions of notation:
Ernst Cassirer's Determinism and Indeterminism in Modern Physics (DI; Cassirer, 1936/1956) constitutes a major but systematically overlooked transformation in the philosophy of quantum mechanics. Against interpretations that treat the text as a late application of his earlier structuralism, this article argues that quantum mechanics forces a fundamental reconstruction of causal order and scientific objectivity. Following the dissolution of Laplacean determinism, causality is no longer directed at ‘things’ in the world, but functions as a regulative demand that experience be rendered intelligible. Accordingly, causal order does not map to a pre-given reality but is progressively constituted from within experience through recursive processes of functional co-ordination (Zuordnung). This reconstruction culminates in a participatory account of objectivity organised through three mutually conditioning levels – measurements, laws, and principles. The upshot is that physical objects emerge as invariant nodes within relational structure; objects are fixed as objective relations. On this basis, the article shows that neither epistemic nor ontic structural realism adequately captures Cassirer's position and develops in response a provisional functional ontology in which a co-ordinating subject and an indeterminate relational domain jointly constitute the transcendental conditions of objectivity. The article concludes by situating DI within a broader participatory tradition in the foundations of physics, arguing that Cassirer's recursive and observer-dependent account of objectivity anticipates key developments in second-order cybernetics and participatory approaches to quantum mechanics.
Cet article revient sur la philosophie de la physique quantique d’Ernst Cassirer telle que développée dans son dernier ouvrage épistémologique Determinismus und Indeterminismus in der modernen Physik (1936), et sa thèse principale selon laquelle la causalité est conservée dans la théorie quantique, moyennant une re-conceptualisation de son objet. Il étudie la place du principe de causalité dans la hiérarchie de la connaissance physique selon Cassirer, et montre son rôle à la fois constitutif et régulateur, qui est lié à la disparition de la faculté kantienne de l’intuition chez Cassirer. Il passe en revue d’autres caractéristiques (holisme notamment) de la conception cassirérienne de la théorie physique. Il revient en détail sur la manière dont Cassirer parvient à passer d’une interprétation observationnaliste (négative, en tant que manque d’information) à une interprétation constitutive (positive, en tant que nouvelle définition de l’objet) des relations de Heisenberg. Il conclut avec le caractère prometteur de la conception de Cassirer pour faire droit à la théorie quantique, par rapport à une conception du type « relativized a priori » à la Friedman-Kant.
This paper compares Cassirer´s and Bohr´s views on symbolic knowledge in quantum physics. Although both of them consider quantum physics as symbolic knowledge, for Cassirer this amounts to a complete renunciation to intuition in quantum physics, while according to Bohr only spatio-temporal images may provide the mathematical formalism of the theory with physical reference. We show the Kantian roots of Bohr´s position and we claim that his Kantian concept of symbol enables Bohr to account for the sensible content of quantum theory as well as for its systematic relation to classical physics.