1 Introduction
Writing on the role of physics in the rise of logical empiricism, Thomas Ryckman has expressed the prevalent view: âLogical empiricism was conceived
I want to suggest that this picture of the relation of philosophy to science and of the path to logical empiricism does indeed some justice to the importance of relativity theory. But it also leaves out the way electromagnetic theory, with its historical formulations, applications and developments, played a role. In particular, it leaves out the role it played in the paths different thinkers such as Carnap and Neurath took to the logical empiricist movement, both in their shared and their differentiating problems and positions.
Prior to the works of Carnap, Frank, Schlick and Neurath, Maxwellâs electromagnetic theory had also been the subject of philosophical consideration and criticism in the hands and minds of a number of influential scientist-philosophers such as Hertz, Mach, Boltzmann, Duhem and Poincaré. Their appeal to it by members of the movement of logical empiricism reflected and extended the theoryâs dual life, its evolving philosophical and scientific significance.
2 Scientific and Meta-scientific Lives of Maxwellâs Equations
I begin with the historical background, with an emphasis on its dual theoretical and methodological dimensions.
Maxwellâs equations were introduced by James Clerk Maxwell in 1856 to provide a unified mathematical field theory of electrical and magnetic phenomena. In a subsequent development, in 1861, he used them to suggest the identity of light with electromagnetic waves. The result was an even more significant turning point in the history of physics. With it, Maxwellâs theory was opening the door to the possibility of reducing optics to electromagnetism. In a more methodological twist, he also linked different mathematical representations of electric and magnetic phenomena to particular mechanical models of the ether. Maxwell called this cognitive and methodological heuristic the method of physical analogy.3 In this way, Maxwellâs equations had entered, then, both the history of physics and the history of scientific epistemology and methodology, in fact raising controversies in both.
Hertz also gave the physical theory a broader epistemological significance when in the Principles of Mechanics he identified a physical theory with a consistent system of appropriate clear symbols or pictures that would denote facts, make observable predictions and be appropriate in the avoidance of arbitrary terms or symbols such as âforceâ denoting nothing.5 Hertzâs foundational ideas and scientific example had wider scientific and philosophical implications. For instance, they resonated in Vienna with Ernst Machâs anti-metaphysical and economy-centered philosophical analysis of science, prompting both thinkers to refer to each other.6 Also in Vienna, they had a significant influence on Ludwig Boltzmann and Ludwig Wittgenstein, especially philosophical. Boltzmann, who had followed in the footsteps of Maxwellâs researches on molecular theory of gases, had published the first lectures in Germany on Maxwellâs electromagnetic theory.7 In subsequent, more philosophical discussions that included references to Hertz and Mach, Boltzmann endorsed a restricted standard of models as mental pictures, after Maxwellâs analogies, without Machâs or Hertzâs phenomenological or monistic axiomatic constructions.8
In Germany, Hertzâs views also might have provided a key catalyst in David Hilbertâs formulation and pursuit of his formalist axiomatic program, first in geometry and subsequently in physics.9 In Hertzâs and Hilbertâs views,
Maxwellâs theory extended its dual scientific and methodological life in the hands, among others, of French conventionalists such as Poincaré and Duhem. Poincaré led the way with a technical study of Maxwellâs theory in 1890 that prompted a more critical one by Duhem in 1902.10 The critique continued in their more philosophical works. Both Poincaré and Duhem defended a privileged role for intersubjective, historically continuous and invariant mathematical structures. Poincaré pointed to persistent elements in the evolution of mathematical theories of light from the theory of motion to the theory of electricity. Duhem simply denounced its historical discontinuity. Both also appealed to allegedly French methodological standards of simplicity, precision and logical structure to reject Maxwellâs disunified collection of provisional and independent but often contradictory constructs. Duhem notoriously declared that model-building was the product of neither reason nor experiment, only of imagination, the proverbial weakness of the English mind.
Not surprisingly, Duhem acknowledged Hertzâs separation of Maxwellâs equations from Maxwellâs models. The interpretation helped Maxwellâs electromagnetic theory meet Duhemâs logical and, especially in Helmholtzâs classificatory theory, also historical standards.
By the end of the century, electromagnetic theory had reached new heights of theoretical and methodological significance. In 1895 Hendrik Antoon Lorentz made a crucial contribution by introducing the so-called Lorentz-Maxwell equations for the electrodynamics and optics of moving bodies. With the equations taken axiomatically, Lorentzâs theory broke away from the mechanical world-picture and provided a broader unification of electromagnetism and optics with a new electron theory. It postulated new relations between locations, times and motions and a hypothesis of contraction of electrons when moving through the ether. The growing success of Lorentzâs theory explaining new phenomena prompted him in 1900 to speculate on the possibility of reducing gravitation to electromagnetism. As a result, at a conference in Lorentzâs honor of the same year, Wilhelm Wien announced officially the project of an electromagnetic world-picture unifying all matter and forces. The proposal was promptly and widely endorsed and enlisted new theorists and experimenters.
Any credibility left for the mechanical world-picture was further shattered by Planckâs statistical proposal of the quantum of radiation, also in 1900. The
Along the way, Einsteinâs electromagnetic path to the theory of relativity ended up placing Maxwellâs equations further at the core of modern physics, only now alongside a new image of space and time whose job was to protect them.
3 Logical Empiricism
Where do logical empiricists enter the picture? The older scientifically-trained generation of logical empiricists included Philipp Frank, Otto Neurath and Moritz Schlick. Maxwellâs equations and electromagnetic theory were in the focus of Schlickâs doctoral thesis of 1904 under Planck in Berlin, and Frankâs habilitation of 1908 in Vienna. Frank had studied with Boltzmann in Vienna and with Klein and Hilbert in Göttingen and received a doctorate with a thesis on dynamics. Schlickâs dissertation in optics investigated the application of Maxwellâs equations to inhomogenous media without ether models.
Frank, Neurath and the mathematician Hans Hahn, among others, met regularly in Vienna between 1907 and 1912 to discuss current issues in science and philosophy. Their readings included recent foundational work in logic, mathematics and physics and the philosophy of science of Mach and French conventionalists such as Duhem, Poincaré and Rey. As Frank reported, much of their discussions revolved around the crisis in physics associated with the failure of the atomistic mechanical worldview and the proliferation of alternative
In an extended version of this paper, I offer a more detailed discussion of Schlickâs and especially Frankâs attention to the significance of Maxwellâs equations and electromagnetic theory.12 Here, I focus on Neurath and Carnap.
4 Otto Neurath
The association of Neurath with electromagnetism is more surprising than Carnapâs. So, I begin with his particular electromagnetic path to the scientific world-conception. Neither his interest in political economy nor his contributions to logical empiricism can be fully understood in isolation from considerations of physics and technology. The Vienna discussion group only added to his earlier science education.
One context for the relevance of physics and its applications to economics is the history of political economy itself. The so-called Industrial Revolution had taken place on the basis of a new organization of labor and the use of machines and engines. Marx and others promptly analyzed its significance for economic theory.
Neurath even considered valuable the economic role for machines supplementing labor shortages in war economies.13 In the same spirit, he didnât omit references to the economic relevance of the steam engine, but he drew special attention to the social and political significance of the use of electricity (already noted by Lenin), especially noting its superior socializing effect and its power to set up networks of production.14
In the history of economics, also physical as well as organic analogies were dangerously common. Throughout the 1910s, Neurath began introducing mechanical, thermodynamic and engineering analogies to illustrate the distinctive holistic, modal and constructive features of his own model of planned
The consideration of possibilities was for Neurath part even of the historical methodology of political economy. His view resulted from engaging two different but related debates over unity still ongoing at that time: one, over the relation of the historical and cultural sciences, including economics, to the natural sciences; and the other, over the different economic methods and perspectives. During the same period, Neurath extended his critical investigation to the methodological unity and cooperation in history and chose the case of the history of optics.
He wrote two overlapping papers, âOn the Foundations of the Theory of Opticsâ and âOn the Classification of Systems of Hypothesesâ.16 It is in these works, especially in the second, that electromagnetic theory and Maxwellâs equations play a role. To begin with, Maxwellâs theory put an end to the isolation of optics. By the mid-19th century, as Neurath observed, optics entered a unification with electrical theory introduced by Maxwell to order phenomena of electricity and magnetism.17
Neurath proposed an objective, unifying method of classification in history of science that he modeled after the method of analysis and synthesis in physical theory, also chemistry, even after the algebraic logic of the political economist and mathematician Stanley Jevons â in addition to what he had learned and critiqued from Ernst Schröderâs Algebra der Logik.18 Jevonsâ technique offered a combinatorial mechanical approach to composition applied to duals of conceptual components and their negations. As a result, it could systematically explore and classify realized and unrealized possible combinations. Neurath adopted as elementary notions, periodicity, polarization, interference and diffraction.
But what was the required form of the analyzed theories? Neurath introduced a weighted criterion of physical theory as a system of hypotheses. One criterion, which he attributed to modern physicists including Duhem and Poincaré, gave almost exclusive priority to mathematical form, with a role in logical argument. The alternative granted superior educational and methodological value to the role of imagery and analogy.19 For the methodological
Without explicitly endorsing Maxwellâs method of analogies or dismissing Duhemâs criticism, he declared the heuristic value of analogies to present, guide and extend the imaginable systems of relations; and this, he added, must be done âpurely logicallyâ and by deducing further consequences.20 Here Neurath provided several explicitly Maxwellian examples: (1) Mechanical analogies for electric and magnetic phenomena;21 (2) analogies between the large and the small such as the application of Maxwellâs equations for electrical fields to the field of electrons;22 and analogies between different fields and their kinds of phenomena such as the ones that led to the successive unification of light, electricity, magnetism and radiating heat, the very achievement attributed to Maxwellâs theory.23
For Neurath the significance of the formal criterion of theory was historical: it tracked changes in the history of science â and not just in the 20th century â, a method he also attributed to Duhem and Poincaré and used to 0discuss with Frank and others. Accordingly, he also mentioned Hertz explicitly on two accounts, as having developed Maxwellâs theory of light24 and as having identified the theory with its mathematical field equations. On this occasion, Neurath also made sure to note that Hertz had justified the identification in Neurathâs own Duhemian historical way, on the basis of the convergence and continuity of results.25 He quoted Hertz accordingly, beyond the famous identity statement: âTo the question, âWhat is Maxwellâs theory?â I know of no shorter or more definite answer than the following: â Maxwellâs theory is Maxwellâs systems of equations. Every theory which leads to the same system of equations, and therefore comprises the same possible phenomena, I would consider as being a form of or special case of Maxwellâs theory.â26
The collective efforts of the Vienna circle manifesto would give expression to the goal of unity. The manifesto emphasized a rigorous linguistic framework prominently featuring the axiomatic method and logical analysis, and an emphasis on intersubjective, neutral constructed systems of formula with precise symbolic relations.27 Hertzâs interpretation of Maxwellâs theory met
In the wake of the manifesto, Neurath would still make occasional reference to electromagnetic theory, but now to serve the purposes of illustrating and supporting his own views, and marking out differences from the manifestoâs ideals.
His well-known proposal was an anti-metaphysical, materialist account of unified language characterized by the interconnected doctrines of syntacticism and physicalism.29
The unified language of empirical science would have to be intersubjective and, from the empirical standpoint, inter-sensory. And such features depended, according to Neurath, on relations of order,30 for instance, in statements of spatio-temporal data, that is, of spatio-temporal order â or âspace-time linkagesâ31 â, so that protocol statements would consider only material things or events in space and time. Neurath sought to enforce the social and scientific requirement of objectivity and to challenge Carnapâs reliance on subjective experience in the epistemology of the Aufbau. His brand of physicalism also provided a new solution to his old problem of unifying the natural and the human sciences.
To illustrate and support his physicalist doctrine of empiricism, in âSociology in the Framework of Physicalismâ32 Neurath considered the use of the everyday term âblueâ to report an experience. One way to provide a physicalist, inter-sensory and intersubjective formulation, Neurath suggested, was to have recourse to electromagnetic theory, namely, the physical concept of âthe number of oscillations of electromagnetic wavesâ.33 Carnap had introduced the same correspondence in 1923. The appropriateness of the choice was obviously based on Maxwellâs theoryâs reduction to electromagnetic theory of optics and the associated concepts for qualities such as color. The statement âhere is a blue cubeâ could then be replaced, according to Neurath, by âa physical formula in which place is defined by coordinates.â34
Also one later appeal to electromagnetic theory in 1936, in âIndividual Sciences, Unified Science, Pseudorationalism,â illustrated his anti-reductionistic approach to unity.36 Now it did so from an extended Duhemian standpoint of methodological holism across different disciplines, not just different hypotheses. In addition to the familiar example of the forest fire, here Neurath mentioned electromagnetic theory much in the way Einstein had introduced it in 1905. The theory, stated Neurath, cannot be empirically âcontrolled in isolation,â without predictions integrating statements of different disciplinary sources: âThe theory speaks of electric currents that originate when closed conductors and magnetic fields move relative to each other in a certain way whereas a prediction has to speak of a dynamo in a certain laboratory and of the behavior of an experimenter.â37
5 Rudolf Carnap
Carnap intended and presented his pre-Aufbau works as contributions to the theory of science. In particular, he applied recent formalist, axiomatic and psychological perspectives. The goal was to investigate the sources of physical knowledge in terms of the construction and organizations of concepts, and, derivatively, the evaluation of theories.
In âOn the Task of Physicsâ (âÃber die Aufgabe der Physikâ),38 for instance, Carnap investigated the decisions he considered involved in evaluating and selecting physical theories according to principles. Extending the scope of the conventionalism he had encountered in Poincaré and Dingler, he now argued that the relevant decisions concerned, first, three stipulations: a system of space, a system of time and an action law fixing the dynamics and the description of
I want to draw attention to the fact that Carnap required the three elements to accommodate the concepts and laws of electromagnetic theory. Why? Without them, the elements of Carnapâs ideal of physics and thereby his own account lacked a necessary credible scientific image of the physical world, one with the epistemic authority of actual science. In the case of the axiom system, he considered three possible kinds.41 All included Maxwellâs equations either as axioms or required theorems, including those systems with Einsteinâs space-time equations.
If in the first element of the ideal of completed construction of physics, the equations of electromagnetic theory illustrated and grounded the formal structure of the unified ideal of physics, in the second element, they also illustrated and grounded the empirical, phenomenological dimension. Carnap pointed to the case of colors, which would be recognized only within an ordered color system â he mentioned the example of Ostwaldâs. The corresponding physical object or process is electromagnetic, but it would vary according to the chosen axiom system for physical theory. Thus, for the case of blue, also Neurathâs choice, he observed that the color would correspond in the second kind of system to a periodical movement of electrons denoted by the frequency of oscillation.42 Similarly with smells â despite the caveat, he noted, of the lack of a clear classificatory system â and sensations of warmth; Carnap associated them, within a system of the second kind, for example, with different properties of electron complexes.43
Now, where in the Aufbau48 is next the theory of electrons and electromagnetic fields? They featured more discreetly in the set of choices of a physical basis. Carnap listed only a selection from the examples of axiom systems for natural laws that he had introduced in âOn the Task of Physicsâ. The narrower set of available projects still illustrated and supported the conventional nature of the required choice.
In addition, appeal to physical theory in the epistemological or experiential system allows for the objects of perception constructed out of experiences in the autopsychological basis, to be used in the construction of physical objects. Carnap referred to the explication of the physical-qualitative correlation he had offered in the earlier essays I have presented.49
The new manifesto had already pointed to the linguistic nature and unity of science. In âPhysics as a Universal Scienceâ (âPhysikalische Sprache als Universalsprache der Wissenschaftâ)50 Carnap heeded Neurathâs call for
More importantly, he argued, with Neurath, that the mathematical determination allowed by the equation had the virtue of being both intersubjective and inter-sensory, independent of color perception and visual perception altogether. In fact, the technological arrangement that would make the cross-modality possible involved the use of electricity, so that, by a further application of Maxwellâs theory (or a modern development), the information about the set of frequencies associated with a certain color could have its ordering or structural property expressed in the motion of a palpable pointer or the audible frequency of acoustic waves.53
He also pointed out that the formal sameness of content of qualitative and physical representations or propositions was independent of the images and conceptions associated with them.54 Now, notice that the rejection of associated images or conceptions and the emphasis on the common numerical determination constitute precisely, as I have already mentioned, the sort of epistemic decoupling that Neurath had identified in Hertzâs restrictive conception of Maxwellâs theory and that Duhem had noted and approved.
Finally, I want to conclude this brief examination of the enduring and significant role of electromagnetic theory in Carnapâs philosophical evolution
The argument also illustrated the kind of foundational investigation that should characterize what he called non-metaphysical philosophy, the logic analysis of science. The task he now declared syntactical was the analysis of scientific statements, of so-called language-forms, expressed by formal statements about other statements, that is, in the formal mode. He called these syntactical statements; the others he called descriptive. However, he also warned against assuming that the distinction between the logical or syntactical analysis of science and the specific sciences rests on the distinction between syntactical and descriptive statements.58 He offered a detailed example from the empirical sciences, namely, the analysis of Einsteinâs discussion of Maxwellâs equations for moving bodies and the propagation of light. Beginning with Einsteinâs opening statement, he offered a paraphrase that allowed for the identification of descriptive and syntactical statements. Maxwellâs equations, however, appear as primitive and not linguistic rules and, as such, would be retained as a matter of convenience. This view is consistent with his earlier conventionalism, although it weakens the commitment to the formalistic interpretation of the equations adopted by Hertz and Neurath â and Neurathâs attention to analogies.59
The evolving significance of Maxwellâs equations and electromagnetic theory reappears here now in the syntactic analysis, one also of the recent significant new place in Einsteinâs argument for his special theory of relativity. Attention to relativity, in fact, requires attention to electromagnetic theory. In the earlier discussions, among examples of actual projects of axiom systems, he had recognized the place of Maxwellâs equations also in every unified theory of physics based on the space-time structure of general relativity.
Ryckman 2007, p. 194.
Ibid., p. 195.
Hertz 1892/1893, p. 21.
See Hertz 1894, introduction.
Boltzmann 1891 and 1893.
See Corry 2006 for the suggestion.
I am grateful to Iulian Toader for this qualification.
See Neurath 1910/2004, p. 169.
See Neurath 1925/2004, p. 449; also Neurath 1973, pp. 8â9.
Neurath 1919/1973, p. 151.
Neurath 1916/1983, 16â17.
See Neurath 1915, pp. 102â103, 1916, p. 25.
Ibid., p. 25.
Ibid., pp. 26â27.
Ibid., p. 27.
Ibid.
Ibid., p. 17.
Ibid., p. 29.
Ibid.
See Carnap, Neurath and Hahn 1929/1973, p. 306.
See Frank 1941, p. 10.
Cf. Neurath 1931a/1983 and 1931b/1983.
Neurath 1931b/1983, p. 62.
Neurath 1931a/1983, p. 49.
Neurath 1931b/1983.
Neurath 1931b, p. 63.
Ibid.
Ibid.
Neurath 1936/1983, p. 133.
Ibid., p. 211 and 239.
Ibid., pp. 221â233.
Ibid., pp. 223â227.
Ibid., p. 227.
Ibid.
Cf. ibid., p. 405.
Ibid., 407.
Ibid., 409.
Ibid., p. 182, art. 136.
Ibid., pp. 52â53.
See ibid., p. 56.
Ibid., p. 60.
Ibid., p. 91.
See Carnap 1934/1937, pp. 316â318.
Ibid., p. 319.
Ibid., p. 331.
I am grateful to Iulian Toader for suggesting the qualification.
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