Einstein

Responding in 1949 to the quantum orthodoxy that it is meaningless to speak of the definite disintegration time of an individual radioactive atom, Einstein pronounced the positivist attitude of the quantum physicists as scarcely distinct from Berkeley’s esse est percipi. Impugning subjective idealism as absurd, Einstein proceeded to elucidate how he understood claims of physical theory about unobserved objects and processes:

Brevity has not served Einstein well. It has led scholars to select one or another of these, or other similar, remarks in an attempt to identify a distinctive philosophical tendency. But there are difficulties in placing all in harmony together. How can the ostensibly realist retort to Schlick cited in the previous chapter be reconciled with the apparently idealist nuances of this passage? What is the significance of the fact that Einstein persistently places the term “real” in scare quotes? How is it possible to consider “existence” or “being” as an “intellectual construction”? What is meant by “free statute”?

An identifiable philosophical position, established by an earlier generation of philosopher-scientists, does encompass all these distinct aspects, but it is one familiar today perhaps only to historians of physics. Its incongruity with contemporary philosophical understandings of “realism” or “scientific realism” threatens to guarantee that efforts to assimilate Einstein’s views to contemporary positions remain anachronistic. The underpinnings of Einstein’s idea of physical theory as a conceptual construction aiming to grasp the real drew from, and built upon two related fin de siècle epistemological currents, one in pure mathematics, one in theoretical physics. The former, associated with George Cantor and Richard Dedekind, emphasized the freedom of concept formation in modern mathematics; the latter, stemming above all from Heinrich Hertz, sought to make precise the meaningful sense in which a physical theory could be said to be conceptual framework, an image (Bild) that seeks to “grasp” or “picture” – in short, “construct” – physical reality. Einstein’s assessment of the quantum theory as incomplete by 1930 implied it was incapable of being a physical theory of this kind. Even more, that the quantum physicists spurned as antiquated such a conception of physical theory elevated Einstein’s opposition to the quantum theory into a clash concerning the very meaning of physical theory.

Epistemological credo

Between 1930–1950, Einstein published two extensive expositions – the latter prefaced by remarks terming it “my epistemological credo” – of the philosophical considerations ostensibly underlying his practice as a theoretical physicist. The Latin term calls for comment. “Credo” means literally “I believe”, while a credo is an avowal of religious conviction. We may therefore presume intent, though tinged with gentle irony, to give expression to a resolute and fundamental faith. The question then is: what belief or set of beliefs could elicit such steadfast commitment from a theoretical physicist cognizant of the imperfect state of physical theory?

Unremarkably, it is a conviction regarding the core character of the scientific enterprise itself. And this is a persuasion that the methods, observational procedures, and theories of natural science have value insofar as they contribute to the overriding goal of finding out how the real external world is; that is, as it exists independently of any mode of perception. As Einstein will demonstrate, much in this declaration called for, and indeed received, clarification and epistemological qualification. But clothed even in vulgar dress, this is a motivational realism regarding the nature and purpose of natural science that was then, and remains today, perhaps the implicitly held principal reason for doing science of many, even most, scientists. Physicists other than Einstein, Duhem and Planck in particular, had recognized both the allure and purported necessity of this belief as well as the impossibility of ever completely justifying it. Yet quantum mechanics, particularly as portrayed by Bohr, renounced the project of seeking physical reality altogether, refusing to recognize as meaningful statements about what might be true of individual physical systems independently of devices for measurement of particular observables. As concordant positivist and non-realist philosophical currents swept over the physics community, Einstein felt compelled to articulate a new defense based upon his understanding of the development and transformation of physical theory since the turn of the century. A crucial component of this understanding is a retrospective reflection on his experience with the general theory of relativity. This reflection forms the backdrop of his criticism of the new quantum theory, not only because he regarded it as an incomplete description of individual physical systems but also since he considered it a theory of a new kind, surrendering and even dismissing the aim of science to find out how nature really is. Aided and abetted by logical positivism, these views had spread also into philosophy and beyond, into the lay understanding of science. To Einstein a view of science offering only positivism and instrumental control was both repugnant and false. In the face of this clearly perceived threat, he decided to respond.

The two presentations, affirming essentially the same viewpoint, were written some ten years apart during his residence in Princeton, the first in 1936 and the other in 1946. On each occasion, Einstein’s German text is published in its entirely, together with accompanying English translation. It may be presumed that Einstein insisted on this unusual format not only on account of his far greater confidence of expression in his native tongue but undoubtedly also because the peculiarly German language nuances of his epistemological views, inevitably coarsened in translation, would be available in the public record. The later and more diffuse presentation appeared in “Autobiographical Notes” (written 1946, published 1949, with facing page translation by philosopher Paul Schlipp) together with scattered remarks in the “Replies to Criticisms” at the end of the same volume. In this second version, he took care to observe that his credo evolved slowly over a lengthy period of time and “does not correspond with the point of view I held in younger years” (1946/1949, 11). This appears correct and in accord with an assessment that articulating a “credo” was itself prompted by the challenge posed by quantum mechanics to Einstein’s belief in the aim of physical science and the consequent task of the theoretician.

The 1936 presentation, prominently titled “Physik und Realität”, is the more systematic exposition. Thirty-four pages in length, it was published in a journal of engineering, popular science, and science education.³ Immediately follows a complete English translation (“Physics and Reality”) by Swiss-American chemist and engineer Jean Piccard, at the time a world-record-holding high altitude balloonist. The unusual venue was an indirect result of the award of the Franklin Medal to Einstein in March 1935.⁴ It would appear that Einstein already had conceived of the idea of writing such an essay. Today it is remembered mostly for a brief reiteration of the incompleteness argument against quantum theory given in the famous EPR paper, coincidentally published in the May 15, 1935 issue of The Physical Review.

In early summer 1935 two apparently striking recent results may well have fortified Einstein’s resolve to articulate his conception of physical theory: first, the famous EPR paper arguing for the incompleteness of quantum mechanics (see Chapter 4); then, the July 1 issue of The Physical Review contained a paper written together with his assistant Nathan Rosen (the “R” of EPR) claiming a solution to “the particle problem” in general relativity.⁵ For more than ten years, Einstein had considered the theory of general relativity as essentially an approximation to, and as a source of insight for, a further generalization to a unified theory of fields. The Einstein-Rosen paper of 1935 accordingly sought solutions of the now joint field equations of gravitation and electromagnetism corresponding to the particulate structure of matter and electricity. The difficulty had been to avoid point particles and the singularities associated with them. The Einstein-Rosen paper claimed to find such singularity-free solutions in discrete “bridges” connecting two congruent “sheets” of physical space; the bridges are portions of space representing both neutral and (massless) elementary electrical particles.⁶ The paper created little notice at the time, but since its revival in the 1980s, it has been celebrated in both popular and physical literature for originating the exotic concept of “wormholes” in space-time, topological “bridges” between distant regions of space-time that theoretically suggest the possibility of time travel. (Most recently, theorists have appealed to Einstein-Rosen bridges to resolve the so-called “firewall paradox” implying an inconsistency of general relativity with quantum mechanics; see Chapter 11.) Not surprisingly, Einstein invoked both the EPR incompleteness result and the Einstein-Rosen result at the corresponding strategic place in his 1935 essay. As with the Herbert Spencer Lecture in Oxford in June 1933 (discussed in Chapter 10), putative breakthroughs within his own research program encouraged Einstein to have the confidence for sustained philosophical pronouncement about the aim and future of theoretical physics.

Both versions of the credo appear to have been composed with the same double purpose in mind: first, to articulate, clarify, and justify a “realist” (in the sense outlined in the previous chapter and to be further elucidated below) conception of physical theory; secondly, to show by reference to the history of physics that a reasonable course for future fundamental physical theory lay through a further generalization of field theory beyond the space-time geometry of general relativity, the geometry of a unified theory of fields. This path is presented as an evolutionary next step beyond general relativity and a continuation of the conception of theory presupposed in all previous attempts to find a “basis of physics”, i.e., a foundational theory universally valid at all scales, capable of embracing all natural phenomena. In contrast, Einstein casts the quantum theory as a significant and disagreeable departure from this conception. Einstein’s epistemological credo is not then a disquisition on sundry epistemological issues of natural science but rather as the title of the 1935 essay bluntly affirms, the expression of a deeply rooted conviction that “physics”, or rather physical theory, has a determinate relation to “reality” though the nature of that relation required both articulation and rather elaborate justification.

The structure of the argument is essentially the same in both versions of the credo. Einstein begins with epistemological fundamentals, a doctrine of concepts and of their relation to sense experience. Concepts, he insisted, are “free creations of the human mind” not inductively derivable from sense experience. Anti-inductivism is a recurrent theme in the credo. Next an axiomatic conception of physical theory is outlined, emphasizing first, the indirect relation of the theory’s basic concepts and relations to experience; and second, the dual criteria distinguishing a desirable theory: empirical adequacy and “inner perfection”, i.e., lack of superfluous or unnecessary elements in the theory’s formulation. There follows a chronicle of physical theories that, since 1900, were considered fundamental or universal in scope in the sense of providing explanation, at least in principle, of any physical phenomena. The search for “the basis of physics” informs the historical narrative: mechanics, thermodynamics, and electrodynamics had been successively proposed; each had been subsequently shown inadequate.

In the 1946 version, an autobiographical interlude interrupts the narrative at this point, discussing first the influence of Planck’s discovery of the quantum of energy, the use of Boltzmann’s conception of probability as entropy, and the inconsistency (pointed out by Einstein in 1906) in Planck’s derivation of his empirically justified radiation formula. The interlude provides occasion to refer to his 1905 work on Brownian motion in criticism of philosophical prejudices of positivist skeptics (Ostwald, Mach) of the reality of atoms: they mistakenly held that the facts themselves “can and should yield scientific knowledge without free conceptual construction”.

At this juncture, the common narrative resumes through consideration of the two theories of relativity, highlighting the needed revision in the concepts of time and space while stressing that already in the special theory, despite the unjustified concept of inertial frame, it appeared “unavoidable that physical reality must be described by continuous functions in space”. The quantum mechanics of Heisenberg, Born, de Broglie, Schrödinger, and Dirac, described in the 1946 version as “the most successful physical theory of our time”, is briefly characterized. Then follows a summary of Einstein’s reasons for the verdict that, considered as describing individual systems, that theory is incomplete, a defect that however can be removed in Einstein’s opinion by viewing it as an ensemble (purely statistical) theory. The narrative concludes by posing the question of “how the theoretical foundation of the physics of the future will appear” as lying in a choice between quantum mechanics and some kind of generally relativistic unified field theory mentioned above. As indicated above, this is also regarded as a choice between two opposing conceptions of physical theory, and in both the 1935 and 1946 versions of the credo, Einstein supports his decision to pursue the latter path, a choice that “departs most widely from that of contemporary physicists”, by invoking what he obviously considered to be significant theoretical results in his pursuit of a unified theory of fields. To be sure, the results appealed to in 1935 and in 1946 come from distinct proposals for such a theory.

The “constructing human mind”

The flat-footedly realist avowal that the scientific enterprise pursues the overriding goal of finding out how the real external world is independently of any mode of perception requires rather extensive epistemological tempering to be at all defensible, and this is the task assigned the two lengthy epistemological presentations. What immediately strikes the reader of the 1936 essay is the phrase “the constructing human mind” in its declaration of aim:

What is “constructive” about the human mind? It will be apparent this is a different sense of “construction” than that discussed in the Introduction between “principle” and “constructive” theories since both types of theory are the product of the “constructing human mind”. Rather the sense here is close to a variety of epistemological views, broadly termed constructivism, holding illusory any claim that there can be knowledge of mind-independent objects as they are in themselves, without significant tincture of mentation, what William James called “the trail of the human serpent”. According to constructivism, cognition of extra-mental objects is always to be understood as refracted through human conceptual, perceptual, and even cultural and social prisms. The object becomes an object of cognition (i.e., object as known) only insofar as it is constructed, constituted, made, or produced by the cognizing subject (singular or plural), that is, only insofar as it is recognized within the cognitive framework of the knowing subject or, as Kuhn has it, located within the governing paradigm of the scientific community. For constructivism there is, in principle, always a distinction to be drawn between object itself and the object as cognized, a distinction Kant captured as that between noumenal and empirical reality, and Planck between the physical Weltbild of the future and unadorned metaphysical reality. But though Kant is the most influential constructivist, the view itself is much older, going back to ancient Greek mathematics and the geometrical method of proof by construction of figures in the plane. The hurdle that any viable constructivism must cross is to reconcile the premise that constructing objects is an unavoidable condition of having knowledge of them with a claim that such knowledge is nonetheless objective, that the objects known are indeed “real” without lapsing into solipsism or subjective idealism. We saw Einstein alluding to this already in 2) in “The changing face of scientific realism” section of Chapter 8, in his remarks improving upon the quantum physicists and Berkeley’s esse est percipi.

The 1936 essay’s first section, entitled “General Considerations Concerning the Method of Science” (Allegemeines über die wissenschaftliche Methode), takes up this theme by expressing a conviction that thinking (or thought) in general is by its nature a constructive activity of mind. Einstein shies away from psychology in distinguishing thinking from other mental activities like free association and “dreaming” by the dominating cognitive role performed by concepts. This presupposes a core assumption about cognition, familiar in the Kantian tradition: a sharp distinction between an active, spontaneous conceptual faculty of mind and a largely receptive sensory part whose content is given as sensations or “complexes of sense impressions”, interconnected perceptual data whose external causes lie outside the mind. Cognition requires concepts that have a relative autonomy from sense experience; they are in general “constructs”, creative products of mentation or rather of imagination.

Thinking then is primarily discursive, operating with concepts, producing and applying determinate relations between concepts, and coordinating sense experience to the concepts employed in inquiry. Einstein pointed to the character of everyday thought as illustration. Through a mental process to some extent arbitrary and intuitive, from the “totality of sense experiences” certain patterns are selected for attention; to these the mind correlates a concept of bodily object (“the first step towards positing a real external world”); this concept then serves as a sign communicable to others for such patterns. The characteristics or extension of the concept is suggested by experience but by no means determined by experience since thinking is also imaginative, fueled by analogies, resemblances, figurative non-literal language, and simplifying idealizations. The activity of mind is creative in both the formation and the application of concepts. On the other hand, the justification for any concept lies in the totality of occurrences or fulfilled expectations of patterns of sense experience associated with the use of the concept. Application of the concept in new experiential situations continually changes the scope of the anticipated associations.

It is this view of thought and the relations of concepts to sense experience that undergirds Einstein’s statement that “all science is only a refinement of everyday thinking”, a notion of science differing considerably from the Newtonian or Cartesian tradition of natural philosophy. Yet regarding science as a sharpened continuation of “everyday thinking” was not a new perspective. It already was the core conception of science of American pragmatism, most prominently in theory of inquiry of Peirce and Dewey. Portraying science as a “refinement of everyday thinking” appears to have been the concomitant of a current of British 19th-century natural science whose most representative figures are the non-mathematicians Faraday and Darwin. T.H. Huxley (to become known as “Darwin’s bulldog”) expressed this conception in a picturesquely unequivocal manner from the perspective of natural history as early as 1854:

Huxley had explicitly in mind what he elsewhere termed the “unconscious logic of common sense” in everyday matters, for example, reasoning by simple analogy and inferences seeking to account for observed effects by appeal to causes known from experience to be competent to produce such effects. Presumably Einstein agreed, but he added to this conception a doctrine of concepts, an element completely foreign to Huxley’s notion.

There is a distinctive idealist and anti-inductivist cast to Einstein’s view of concepts as constructs that are, by their origin as it were, speculative. Even so, they enable (or should make possible) forecasting and prediction. In the now familiar Popperian sense, concepts are conjectures, and indeed Popper’s characterization of scientific method as that of conjectures and refutations arose from his reflection on Einstein’s general relativity. Einstein even charted the course of the development of the concepts of physical science along an axis showing accelerating distancing from sense experience. In the “childhood” of physical science, at the birth of classical mechanics, an inductive methodology was appropriated – urged by Newton as a corrective to Descartes’ rationalist physics. But in the course of the 19th century, particularly following Maxwell’s field theory of electromagnetism, the basic concepts of theory lie further and further from confirming observations. General relativity next showed that a speculative mathematical methodology of theory construction appeared necessary to advance the foundation of physics.

After the completion of general relativity, Einstein would occasionally argue that speculative methodology had always been part of physical science, going back to the early 17th century. In a 1930 essay commemorating the 300th anniversary of Kepler’s birth, Einstein identified Kepler as its most notable proponent:

This high praise of Kepler’s attempt to use the five Platonic solids to represent the distance relations between the known planets is further proof that reflection on the experience of completing general relativity convinced Einstein that the only way forward in pursuit of a fundamental physical theory capable of unifying widely disparate realms of phenomena in a common theoretical framework lay in mathematical speculation. This belief resounds in repeated admonitions that concepts (and the conceptual structures into which they enter) are “free creations of the human mind” and in an avowal that scientific knowledge itself arises only through “free conceptual construction”.

The adjective “constructive” is then Einstein’s generic term for the theoretical physicist’s balancing act or continual pivot between the opposing tendencies of rationalism and empiricism. From the standpoint of physics, empiricism requires the distinction of “primary concepts” from “all other notions”; the former alone are directly connected to typical patterns of sense experience. The validity or justification of all physical concepts consists in their connection, however indirect, to the “primary concepts”. If not explicitly definitional in nature, they have physical meaning only insofar as they can be linked in various ways, however remotely by deduction, to the primary concepts, and so to experience. In a letter to Solovine in 1952, Einstein clearly portrayed his conception of the “eternally problematic connection between everything intellectual (alles Gedanklichen) and what is tangible (sense experience)” in a diagram with four articulated steps (Figure 9.1).

The diagram, and accompanying elucidating remarks, are an almost textbook presentation of confirmational holism in the method of hypothetico-deductive testing of theories.

A rationalist moment enters with the axiomatic conceptual structures that are contemporary physical theories. Here speculative abstract concepts or principles may stand at considerable deductive remove from any sense experience, and so are implicated or condemned by observation only indirectly. In this balancing sense of “constructive”, Einstein fashioned a “constructive” epistemological framework to attempt to justify his conviction about the character of physical theory and the inherently realist aim of science. The constructive framework is not a purely philosophical imposition but stems from, and is traceable to, two distinct currents arising within the previous half-century of exact science. The first comes from pure mathematics but is easy to identify in Einstein’s doctrine of concepts by use of Richard Dedekind’s locution, “free creations of the human mind”. The other arises within physics, but is only implicitly indicated and so must be inferred: this is the Bild conception of physical theory first formulated by Heinrich Hertz, reiterated by Ludwig Boltzmann, and extended by Max Planck. These are considered in turn.

Free creations of the human mind

As noted in Chapter 7, in the lecture “Geometry and Experience” at the Berlin Academy in January 1920, Einstein characterized axioms in the modern axiomatic treatment of geometry as “free creations of the human mind” (“freie Schöpfungen des menschlichen Geistes”). In his lectures at Princeton in May 1921, he returned to this expression to signal a relative but not complete autonomy of concepts from experience:

The accolade “free inventions of the human mind” is applied to both concepts and basic laws of physics in the Herbert Spencer lecture at Oxford in June 1933.¹² In “Physics and Reality”, the concept of bodily object is “a free creation of the human (or animal) mind” (“eine freie Schöpfung des menschlichen [oder tierischen] Geistes”) and so distinct from the totality of relevant sense impressions.¹³ The pattern continues in The Evolution of Physics where “Physical concepts are free creations of the human mind” (“freie Schöpfungen des menschlichen Geistes”),¹⁴ and in “Remarks on Bertrand Russell’s Theory of Knowledge”: “The concepts arising in our thought and linguistic expressions are all – logically considered – free creations of thought” (“freie Schöpfungen des Denkens”).¹⁵ In “Autobiographical Notes” written in 1946, the locution (“eine Schöpfung des Menschen”) is extended broadly to conceptual systems in general, i.e., to “the conceptual system together with the syntactic rules comprising the structure of the system”;¹⁶ whereas Einstein’s last publication affirmed that “logically considered”, the concepts of space and time are “free creations of human intelligence (“freie Schöpfungen des menschlichen Intelligenz”).¹⁷ Clearly this is a view of concepts deeply rooted in Einstein’s epistemology. What is its significance? Against what view or doctrine is it directed?

The Einstein texts are unequivocal in refusing any positivist or empiricist theory of concepts according to which meaning or content is inductively derived or abstracted from sense experience. The rejection extends to the only probabilistic meaning (in terms of measurement outcomes) given by quantum mechanical orthodoxy to the core kinematical or dynamical concepts of “position”, “momentum”, or “energy”. Emphasis is placed instead on the cleft between sense experience and concept, rendering the latter “logically independent” (i.e., not inductively derivable) from the former. As seen above, Einstein also employed the metaphor of “free creation” to underscore a denial that any concepts (archetypically those of space or time) are immutable “necessities of thought”. At times the metaphor is accompanied, as in his 1916 obituary of Mach¹⁸ and the quotation from 1921 above, with an admonition to not forget the “earthly origin” of all concepts. In short, the doctrine of “free creation” is a bulwark against positivist phenomenalism, empiricist inductivism and Kantian a priorism. But what positive construal might the doctrine have?

The adjective “free” underscores that concepts are constructed, neither determined by nor derivable from experience nor necessities of thought. “Creation” also connotes freedom in the sense of imaginative pluralism, that distinct concepts may be equally compatible within some domain of experience. The different ways these two aspects are expressed often manifests the language of conventionalism: concepts are “posits” (Setzungen), or “creations” (Schöpfungen). Logical empiricists and others more recently have interpreted Einstein’s remarks about “free creation” as accordingly indicating a strong current of conventionalism in his philosophy of science. A classic attempt along these lines is that of Phillip Frank, physicist, philosopher and Einstein biographer. Frank attempted to characterize Einstein’s philosophy, as well as logical positivism as a whole, as resting upon a coherent integration of Machian positivism (on the “extreme empiricist side”) with the conventionalism of Henri Poincaré (on the “extreme logical side”). This involves something of a delicate balancing act stressing, with Mach, that concepts must have an interpretation in the realm of observable facts while holding, as did Poincaré, that the meaning of certain general principles of physics or geometry, including terms such as “force”, “energy” and “straight line”, are established not by experience but through stipulation (“disguised definition”). A section of Frank’s Einstein biography, subtitled “The General Laws of Physics Are Free Creations of the Human Mind”, is accordingly devoted to Poincaré.¹⁹

On the other hand, Einstein frequently emphasized, against conventionalism, that that the mind’s “liberty of choice” in creatively choosing or constructing concepts “is of a special kind”. In the 1936 essay “Physics and Reality”, the analogy of a crossword puzzle is invoked to underscore Einstein’s conviction that only one choice “really solves the puzzle in all its parts”. A conviction that physical reality has the character of a well-formulated puzzle or logical ordering (or in Duhem’s sense, a “natural classification”)²⁰ is a matter of faith that transcends all evidence, in short, a metaphysical postulate. In the April 1918 tribute to Planck on his 60th birthday discussed in the previous chapter, Einstein continues the passage quoted there to affirm a deeply anti-conventionalist view of physical theory:

While in the writings of Poincaré conventions are described as “disguised definitions” the expression “free creations of the human mind” is a well-known locution in Richard Dedekind’s 1888 monograph, Was sind und was sollen die Zahlen? (The Nature and Meaning of Numbers). Maurice Solovine, Einstein’s lifelong friend and fellow member in Bern of the so-called Olympia Academy, published a considerable number of Einstein’s letters and postcards after Einstein’s death from a correspondence extending nearly fifty years (a letter from 1952 was cited above). In the “Introduction”, Solovine listed Dedekind’s book as among those read and discussed by the Academy. Both in the “Preface” and in section 73 of that work, Dedekind characterized natural numbers as “free creations of the human mind” (“freie Schöpfungen des menschlichen Geistes”). By this Dedekind meant not only, as stated in the Preface, that the number concept is independent of the notions or intuitions of space and time, but more importantly (in section 73) that it is justifiable to regard the natural numbers as a free creation of the human mind (“eine freie Schöpfung des menschlichen Geistes”) since as the merely distinguishable elements of a simply infinite system, they are free from every other content, in particular, from subjective ideas and extraneous connotations.

In Dedekind’s account the natural numbers are mathematical objects whose only properties are completely determined by the totality of truths of arithmetic. Since the latter are infinite in number, they require axiomatic characterization, and so Dedekind’s characterization of the number concept as a “free creation of the human mind” goes hand in hand with abstract, structural axioms for simply infinite systems (sometimes called the Dedekind-Peano axioms). Simply infinite systems are unique up to isomorphism which means that the laws and relations of arithmetic obtain for any system of objects satisfying the Dedekind axioms, no matter what designations may be given to the system’s individual elements. (For example: Is the first element of the system designated “0” or “1”?) An archetypal example of “creation” is the statement (one of Dedekind’s axioms) that every natural number has a successor. Any collection of objects encountered in experience is finite, but it is possible to “abstract” from any collection its finite cardinality, increase it by one and then indefinitely continue the process. The possibility of indefinite iteration undergirds the meaning of the statement that there is no largest natural number. Nothing in experience licenses the induction that given any finite number, there is a larger one. The consequent is a conceptual not an empirical conclusion. The successor function, explicitly in Einstein-Infeld (1938, p. 311; see the discussion below) is then a paradigm “free creation of the human mind”.

Dedekind deemed a structural characterization of the concept of number in terms of the existence and uniqueness of simply infinite systems to be justification for the claim of “free creation” since it freed the concept of number from any subjective connotations imposed by individual minds while retaining only what must be common to all. This structuralist sense of free creation has nothing to do with conventionalism. It pertains not to creation of individual concepts but to an objective, because isomorphic, system of concepts capable of expressing all arithmetic truths. An analogue showed up above in Einstein’s characterization of the method of physics as the search for “a logically simplest unified conceptual basis of physics”.

Bildtheorie

By the early 1850s in Germany the epoch of Naturphilosophie, the a priori philosophies of nature of German idealism (Fichte, Schelling, Hegel, and lesser epigoni), had run its course. But by so doing, it had badly tarnished the purport of philosophy to speak at all with authority about empirical natural science. Just as a century before in France, when the materialism of Holbach, La Mettrie, and Diderot developed in reaction to the theological metaphysics of Leibniz, within German philosophical circles the speculative metaphysics of the Naturphilosophien antagonistically prompted the crude mechanistic materialism of Vogt, Moleschott, Dühring, and Büchner, largely unknown names today except for the pillory received at the hands of Marx and Engels. On the other hand, in England and France, where Naturphilosophie found but few adherents, empiricism and positivism were firmly rooted among both philosophers and scientists. J.S. Mill sought to encapsulate what he saw as the inductive method of the natural sciences within the scope of A System of Logic (1838, and many later editions), while in France the positivism of August Comte became dominant, especially in the social sciences.

Meanwhile in Germany, philosophical rejection of mechanistic materialism by the 1860s led to the “Back to Kant” movement that gave rise to the different schools of Neo-Kantianism enduring up until the end of WW I. But as a result of speculative excesses of both idealist and materialist philosophers, the overriding tendency among German-speaking natural scientists after 1850 was to ignore all “school philosophy” as simply irrelevant to science. Almost by default, among natural scientists an austere form of positivism emerged that prized exact description of observed facts while remaining inherently skeptical or dismissive of theory. The most influential form of this positivism was that of physicist Ernst Mach. Mach framed positivism within a gradualist evolutionary account of mind according to which scientific hypotheses were considered merely further developments of primitive and instinctual thought serving as “economical” standins or abbreviations of scientific facts. But positivism proved a too-impoverished view of science for some philosophically minded scientists. Foremost in this group was Hermann von Helmholtz, Germany’s greatest natural scientist and one of the few scientists who championed the “Back to Kant” tendency in philosophy. With the one exception of Mach, the most influential philosopher-scientists within a generation were Helmholtz’s student Heinrich Hertz and the Viennese physicist Ludwig Boltzmann, who also had studied under Helmholtz. In their scientific and philosophical writings, a “scientific philosophy” autonomously appeared in relative isolation from professional philosophy. By 1900, this renewed “scientific philosophy” was in full flower, including now the prominent French mathematician Henri Poincaré as well as physicist and physical chemist Pierre Duhem. While naturally there were differences, of both substance and emphasis, in the respective philosophical perspectives of these philosopher-scientists, there were also broad similarities in outlook on certain core matters. Again with the exception of Ernst Mach who retained positivism’s skepticism of theory, the kinship in viewpoint extended to the general characterization of the aims and value of physical theory.

The appearance of a physical theory of any entirely different kind from mechanics, the Maxwell theory of the electromagnetic field, prompted Heinrich Hertz in the early 1890s to write a highly influential epistemological reflection on what, in general, a physical theory can be, and what are its attainable goals. Hertz’s conception was laid out in a lengthy “Introduction” to his Principles of Mechanics (1894), a book in press when Hertz perished from a blood infection on January 1, 1894. Despite the title, Hertz had not written a textbook, but an ambitious attempt to reformulate mechanics by eliminating the concept of force that Hertz regarded as logically obscure. In place of action-at-distance forces, Hertz substituted purely hypothetical networks of hidden masses and hidden motions connected to observable masses and motions in such a way as to simulate the contiguous transmission of action of electromagnetic theory.

Hertz’s approach to mechanics did not find widespread acceptance. Far more influential was the Introduction, a philosophical discussion of the nature of physical theory that, as Königsberg physicist-philosopher Paul Volkmann observed in 1901, was “read with equal enthusiasm by philosophers and physicists” and was considered a “new gospel” exercising “great influence … in particular on the younger generation”.²³ Among that younger generation was Albert Einstein for the Bild conception informs Einstein’s view of physical theory throughout his lifetime. From his biographer Philipp Frank, it is known that Einstein read and studied Hertz’s Mechanics as a student at the ETH in Zurich, as well as in Bern with his friends Habicht and Solovine, co-members of the “Olympia Academy”. Decisive methodological aspects of Einstein’s epistemological credo are reflections or implications of Hertz’s Bild conception of physical theory.

Hertz had been the student of Hermann von Helmholtz, and a rapidly rising star in a growing international community of physics. A renowned experimenter, his generation and detection of radio waves in 1888 gave dramatic confirmation to the 1865 prediction of Maxwell that electromagnetic waves propagate with the speed of light and that light itself is such a wave. It was this expertise with Maxwell’s electromagnetic theory that led to Hertz’s oft-repeated characterization of that theory as “Maxwell’s system of equations”. In this way, Hertz swept aside Maxwell’s own presentation of his theory via the complicated path of empirical discovery of various electromagnetic phenomena, the theory of which Maxwell sought to heuristically illustrate through construction of elaborate purely mechanical analogies to the electromagnetic ether. Though Maxwell explicitly stated he did not believe in the existence in nature of such hypothetical mechanisms, he nonetheless considered them to be helpful means by which electromagnetic phenomena might be reproduced. Hertz renounced the theoretician’s supposed need of heuristic resemblances or visualizable models and promoted a new abstract conception of physical theory in which the sole relation between the premises of theory and entities or processes in nature need be only symbolic.

According to Hertz, the office of physical theory cannot be that of capturing the nature of the physical world lying behind the appearances but rather more modestly that of providing only Bilder (images or pictures) or even Scheinbilder (apparent images) of nature, i.e., models of unobservable aspects of reality. To be sure, scientific pedagogy traditionally instructed students to imagine or picture unobserved objects and processes (e.g., a sound wave) with “the eye of the mind”, i.e., to represent the unobserved through analogy to objects and processes both observed and familiar. Maxwell’s mechanical models of the electromagnetic ether were heuristic devices of this kind. But in the new sense, the “picture” or “image” of nature provided by a physical theory is of a considerably more abstract genus, dependent on the theory’s mathematical assumptions and intellectual posits. Above all, the Bild conception underscored Hertz’s epistemological assumption that it is not possible to know whether theoretical representations, the mental images comprising physical theories, are “in conformity with the things themselves”, i.e., outside of the conditions and conventions imposed by their mathematical representation. That was Hertz’s principal philosophical message.

The Bild conception of theory is outlined in two widely quoted paragraphs of the “Introduction”, articulating the theme of a double parallelism: that between thought and nature, and between theory and phenomena. The first parallelism is that of hypothetical theoretical structures and unobserved causal mechanisms in nature, and the second that between predictions derivable from the theory (observation statements) and observed causal effects of the hidden mechanisms:

A diagram makes Hertz’s Bild conception of physical theory more readily comprehended (Figure 9.2).

The innere Scheinbilder or Symbole are hardly synonyms but emphasize different aspects of representational freedom. The term innere clearly means “mental”, while Scheinbild is borrowed from German aesthetic or theatrical discourse; it has no exact English equivalent but connotes something like “appearance” or “apparent image”, while also suggesting illusion or mirage. Scheinbild roughly connotes an image (Bild) suspected of, or understood as having, an illusory (schein), or at least not-to-be-taken-as-literal, character. Hertz’s readers and followers largely jettisoned the adjectival use of Schein while tacitly retaining its non-descriptive nuances, simply referring to physical theories as pictures or images (Bilder, Abbilder).

The reference to signs or Symbole brings out representational freedom in a different way, signifying that physical theories are stated in terms of algebraic relations between symbols of a calculus or formalism that stand for physical quantities and processes; the term carries the connotations of “conventional” and “abstractness”: i.e., as a sign, the particular symbol chosen to stand for some physical quantity or process has no “natural” connection to what it designates. Pierre Duhem, much more familiar to philosophers of science today, followed Hertz in employing precisely this sense of “symbol” when characterizing physical theories as purely symbolic and so neither true nor false.

No positivist, Hertz enjoined that in order to attempt to complete the parallelism between thought and nature, the theorist is free to invoke invisible entities – “clandestine partners (heimliche Mitspieler) behind the limits of our senses” (p. 25; p. 30 German original) – in order to formulate a Bild of the laws governing physical reality. Thus the main theme of Hertz’s “Introduction” is to articulate the sense in which a physical theory may be legitimately said to be a representation (Vorstellung) of unobservable aspects of the external world. His signature philosophical contribution, drawing upon his formal assessment of Maxwell’s theory and upon a contemporary proliferation of theoretical proposals for electrodynamics, is that physical theories are representative of the external world in the sense of being images (Bilder) of this world, valuable but not perhaps entirely trustworthy.

Whatever term (Scheinbild, Bild, Abbild, Symbol) employed, Hertz’s intent was to embed the constructivist transformation in the concept of knowledge initiated by Kant into the very conception of a physical theory. Since, as Hertz emphasized, “we do not know, nor have we any means of knowing” whether physical theories thus constructed are in actual conformity with the mind-independent world, theories can at best project various images of this mind-independent reality, to be compared and evaluated according to antecedently adopted normative criteria. Hertz drew attention to the contexts, conventions, and constraints presupposed by any conceptual representation, observing that different images (Bilder) of mechanics are not only possible but also desirable, so long as certain criteria governing representation were satisfied. These are 1) permissibility (they must not contradict the laws of our thought – die Gesetze unseres Denkens); 2) correctness, i.e., empirical correctness; and 3) appropriateness (Zweckmäßigkeit), by which Hertz meant both simplicity (the theory must contain no superfluous elements) and completeness (the theory omits no known phenomena in its domain). Substituting “consistency” for “permissibility” (which has inflexible Kantian connotations), these criteria are also characteristic guidelines for theory construction according to Einstein.

By 1900 the Bild view of physical theory had been taken up by the leading theoreticians of the day. Boltzmann explicitly invoked Hertz’s name when lecturing to a gathering of natural scientists in Munich on September 22, 1899, on the recent development of methods of theoretical physics:

Other evidence of Hertz’s significant influence is an address of February 8, 1900, by Dutch physicist H. A. Lorentz, of whom Einstein wrote in tribute in 1953, “He meant to me more than all the others I’ve encountered on life’s path”.²⁶ Celebrating the 325th anniversary of the University of Leiden, H.A. Lorentz, then university rector as well as perhaps the world’s foremost theoretical physicist, sought to characterize the theoretician’s method to his largely lay audience. Though speaking in Dutch, Lorentz used the German term in describing that task as producing “ ‘innere Scheinbilder’ ” (“apparent mental images”) of external objects; that is, of positing mathematically characterized physical mechanisms or structures capable of producing the phenomena the theory sought to explain.²⁷ The expression, as Lorentz expressly noted, originated with the recently deceased Heinrich Hertz.

In the Bild conception, physical theories are regarded as axiomatic systems constructed for the purpose of representation of certain aspects of nature. The modern conception of axiomatic system arose not in physics but from developments in 19th-century mathematics, reaching its highest refinement in David Hilbert’s influential Grundlagen der Geometrie (1899), an axiomatic analysis (not simply presentation) of Euclidean geometry based on five groups of cognate abstract axioms. In this modern sense, one no longer thought of axioms as a priori truths, as in Euclid’s own treatment of geometry, but simply as hypothetical postulates, chosen for their mutual consistency, independence from one another, and deductive fecundity. From a recently published lecture of Hilbert in 1894, Hilbert reports that his inspiration for this conception of axioms derived from reading Hertz’s Mechanics.

Since in Hilbert’s conception axioms are not to be regarded as true, the only applicable sense of truth for a proposition of an axiomatized system lay in the requirement of consistency, that the derived consequences of the axioms do not yield a contradiction. Similarly, with Hertz, since Bilder concern “images of our own creation not of nature’s”, the axioms of a physical theory are not to be regarded as true, and so the only meaningful sense of the truth of a physical theory lies in the most complete agreement of deductive consequences of the theory with observable phenomena, i.e., in the theory’s empirical adequacy. Along similar lines, Boltzmann, the leading proponent of atomism among physicists, observed at the beginning of his Lectures on Gas Theory (1896) that the question “Are atoms real?” was really to ask, “Is the atomistic theory of gases empirically successful?”²⁹ As only the deductive consequences of an axiomatically formulated theory can be compared with observation, those speculative concepts, postulates and theorems that lie at considerable deductive distance from observation have only an indirect empirical meaning. Although Pierre Duhem drew conspicuous attention to the epistemological and semantic holism associated with the axiomatic conception of physical theory, it was earlier and explicitly recognized by Hertz:

As seen above, this expression of confirmational holism very well characterizes Einstein’s understanding of physical theory.

From Bildtheorie to physical world picture (physikalischen Weltbild)

Bildtheorie’s pluralism – that is, tolerance for and encouragement of construction of empirically equivalent alternative “pictures” of a domain of phenomena – is an aspect Einstein emphatically did not adopt. In recognizing pluralism as a virtue, Hertz had been inspired by alternative theories of electrodynamics, each claiming empirical equivalence to Maxwell’s. In the Hertzian conception of physical theory, any permissible (i.e., consistent) physical image can be considered correct (richtig) only if the logical relations between symbols do not contradict observed relations among the phenomena. Selection of one or another of these images was to be made through application of Hertz’s third criterion, appropriateness, but Hertz allowed considerable latitude in interpreting this principle, admitting that different physicists might apply it differently. In general Hertz deemed theoretical pluralism to encourage novel modes of thought; his reformulation of classical mechanics is a prime illustration of this belief. However, there is little evidence that Einstein endorsed this kind of theoretical pluralism at any stage of his career, and, after 1918, much evidence that he rejected it. Naturally, avowal of belief in theoretical uniqueness brought Einstein closer to a realist outlook on physical theories. But what might realism look like within the Bild conception of theory?

As discussed in the previous chapter, an answer was supplied by Max Planck, reluctant discoverer of the quantum of action, in his 1908 Leiden lecture. Planck took the further step in distinguishing natural scientific research by the goal of creating a stable and unified “world picture”:

The condition of constancy mandates use of concepts of universal validity not dependent on particular individuals, circumstances or times, i.e., independent of the peculiarities of particular peoples, periods, and cultures. The condition of unity required that the Weltbild must, at least in principle, extend all physical phenomena, no matter how disparate or varied, as derivable consequences from a de-anthropomorphized basis of principles, concepts and laws. Planck had taken a sizeable step towards this goal in 1899 in showing that physical constants may be freed from anthropocentric arbitrariness through definition in terms of fundamental physical theories, rather than as interchangeable experimental parameters.

A physical world picture is then a projected theoretical representation of the totality of physical phenomena freed from the taint of particular persons, cultures or points of view. As previously discussed, Planck certainly recognized that a completely unchanging picture did not then and even perhaps may never exist. At the same time he argued that it remained a necessary goal of physical theory and even that in referring to “the world”, physicists intend just an unchanging “ideal future picture” (ideale Zufunftsbild). This usage, according to Planck, gives the physicists’ notion of “the real”, not the significance of the world as it is, independently of experience or conceptions, but rather that portrayed by an ideal future picture. The former remains merely a Grenzbegriff, or limiting concept. The physikalischen Weltbild accordingly retains the ontological modesty of Hertz’s constructivist Bild conception, namely, that “we do not know, nor have we any means of knowing” whether physical theories as constructed are in actual conformity with the mind-independent world. The world in itself remains an abstract concept, beyond epistemic accessibility and the possibility of ever confirming any ideal future picture as uniquely correct. Planck highlighted this incommensurability in 1908, expressly attributing the point to Kant that there is no method of proving the existence of such a difference between ideal future picture and world in itself:

In epistemological writings over four decades, Planck returned to the theme of this incommensurability, portraying it as an irremovable source of tension, even irrationality, within theoretical physics. In the depths of World War II, Planck at age 84 reiterated the message:

Planck, in 1905–1906, had been the first theoretical physicist of international repute to place the special theory of relativity within his own research agenda. He initiated bringing Einstein to Berlin in 1914. Admiration between Planck and Einstein rapidly became reciprocal. Post general relativity, Einstein surely appreciated that his public endorsement in 1918 of the search for the Weltbild as “the highest task of the physicist” would be understood as a deliberate alignment with Planck over Mach and positivist conceptions of physical theory. Essentially from that time forward, Einstein’s own search for the yet-to-be-completed world picture, seeking a theoretical structure of greatest possible logical unity capable of comprehending the complete and exhaustive description of all individual events, would be based on a field-theoretic generalization of his theory of gravity.

Reprise: “Physics” and “reality”

For Einstein linking the two terms is a belief in the conception of physical theory as seeking to “grasp” reality, i.e., constructing the picture of a reality law-governed in the manner affirmed in fundamental physical theory. “Grasping” remains a metaphor: The sense in which the theorist speaks of the “physically real” is as a reality “pictured” or “imagined” by the conceptual constructions of a fundamental physical theory. As these conceptual constructions are “free inventions of the human mind”, no strong sense of mind independence can be involved. From the theoretician’s perspective, the supposition of a conceptionless strongly mind-independent reality is strictly speaking meaningless:

As seen above, Einstein’s credo emphasized a speculative, anti-inductivist – or better, constructivist – view of concepts, axioms, principles, and theories. There is no determinate inductive route from facts of observation to the fundamental concepts and relations of physical theories; the latter are neither inductive generalizations of empirical data, nor based on relative frequencies of outcomes of repeated measurements, nor mere economical compressions of data, nor “a priori necessities of thought”. Rather they are hypothetical posits, “free creations of the human mind”. With the success of general relativity, Einstein constrained the freedom of the Bild conception with a notable rationalist amendment, the criterion of “logical simplicity” requiring a minimum of primary concepts and relations in the basis of a theory as a determinative factor in its choice. Yet the sine qua non hurdle to be met by any theory remained constructivist: the sole justification (and so “truth”) of any theory lies in conformity of its derived consequences with observation.

The abstract character of axiomatic representation of theories permits further and further degrees of deductive separation between the fundamental concepts and relations of a theory and observable confirmation. The result of this distancing is that it is impossible to associate a clear empirical (observational) meaning with each fundamental concept or relation; experimental tests can only pertain to the theory as a whole. An empirical holism in physical theory was an essential component of Hertz’s Bild conception particularly emphasized by Duhem. At this juncture looms the problem of underdetermination of theory by empirical evidence, opening the door to theoretical pluralism. Einstein sought to circumvent pluralism, at least in part, by a Planckian-like commitment to the permanence of the core constituents of his physikalischen Weltbild.

Finally, the Bild and Weltbild conceptions of theory give rise to a weakened semantics for physical theories. Reference to unobservable theoretical entities (using Arthur Fine’s term³⁵, see the discussion in Chapter 11), is entheorized, i.e., reference of a theoretical term is not a context-independent primitive and irreducible semantic relation between name and object (like designation) but a function of the term’s explanatory role in the setting of the entire theory’s success or lack of success in attaining overall empirical adequacy. A prime example of an entheorized term is the concept of space within the general theory of relativity,

The theory-functional characterization of reference is then another aspect of regarding empirically successful physical theories as Bilder. Just as the meaning of a theoretical concept is given by its occurrences in an axiomatically formulated theoretical system, so a theoretical term has reference only insofar as it remains essential to the empirical success of the theory. Contextual reference cements the truth of referential claims to the constructivist requirement of epistemic access, even though the route from one to other may be highly indirect. It implies that it is not really admissible to state without qualification that e.g., the term “atom” refers to atoms, posited mind-independent particulate entities that are constituents of matter. As entities they may be deemed to exist independent of mind but as “atoms”, they are theoretical constructs serving to establish order among sense impressions. To return to Boltzmann’s example, the posit of certain entities termed “atoms” in the kinetic theory (possessing the mechanical properties of mass, elasticity, velocity, and mean free path) is justified to the extent that the term serves as a necessary explanatory posit in deductively accounting for the empirical successes of gas theory. This was also the view of Einstein for whom atoms are physically real in the sense that they are posited conceptual objects, the properties of which are not directly perceptible but are assigned hypothetically in the explanation of phenomena.

Similarly, the Bild conception entheorizes truth (see also Chapter 11). The significance of the term “physical reality” is always theory-internal, the conception of reality projected from a fundamental theory satisfying the constraints of empirical adequacy and logical parsimony. As did Planck, Einstein regarded it necessary to formulate the very aim of science as an aspiration to seek a “picture of reality” Weltbild – that ideal limit of physical knowledge to which the human mind may aspire. No reconciliation with the quantum theory was possible so long as it surrendered this quest to represent a mind-independent reality.

Perhaps the clearest expression of what Einstein meant by conjoining “Physics” and “Reality” occurs in the semi-popular book of Einstein and Leopold Infeld, The Evolution of Physics (1938). The book came about, Einstein wrote to Solovine on April 1, 1938, in order “to provide for Mr. Infeld, who was refused a fellowship” at the Institute of Advanced Study. But there was also an ulterior motive. Of his collaboration with Infeld, Einstein reported to Solovine: “We worked out the subject very carefully together, giving particular attention to the epistemological point of view”. The declared intent, reminding of Einstein’s response to Schlick in 1930, was to counter the “mood of the present”, dominated by “the subjective – positivist point of view” that “explains the demand for comprehension of nature as an objective reality as an antiquated prejudice”. The credo is essentially stated in the book early on:

In the book’s final subsection, entitled “Physics and Reality” (pp. 310–13), Einstein’s view of physical theory is again schematically summarized, while the concept of natural number, as in Dedekind, is denominated one of the “creations of the thinking mind”. Four now familiar points are given particular emphasis:

Summary

Near universal acceptance of the quantum theory after 1930 and its apparent alignment with positivism prompted Einstein to articulate and defend an ostensibly realist conception of the aim and meaning of physical theory. Scrutiny of his “epistemological credo”, however, shows that in doing so, Einstein drew from a philosophical current, prominent within the previous generation of physical theorists, whose constructivist elements significantly temper the claims of realism. These constructive elements are most significant in understanding Einstein’s use of the metaphor that a physical theory is an attempt to “grasp reality”. Above all, the metaphor signals a faith that comprehension of nature through theoretical construction is possible. The response to positivism, coupled with a speculative methodology employed in seeking a “theory of the total field”, a unified representation of gravitation and electromagnetism, produced extensive epistemological engagement in his last decades. The ensuing philosophy of physical theory combines elements of realism, idealism-constructivism, and as will be seen in the next chapter, rationalism.

Notes

1“Autobiographical Remarks”, p. 81.

2“Replies to Criticisms”, p. 669; German 1951, p. 496.

3Einstein, “Physik und Realität”, The Journal of the Franklin Institute v. 221, no. 3 (March 1936), pp. 313–47; English translation, pp. 349–82. Translation reprinted in Einstein, Ideas and Opinions. New York: Crown Publishers, 1954, pp. 290–323.

4In March 1935 the Franklin Institute, a venerable museum of science education in Philadelphia dating to 1824, awarded its Franklin Medal jointly to Einstein and to Sir Ambrose Fleming, the inventor of the vacuum tube. At the ceremony Einstein, not expecting the request, was asked to speak. An embarrassed pause followed. In correspondence with the Institute’s director a few days later, Einstein confessed to being “sincerely ashamed” (“redlich geschämt”) by his silence on that occasion. To make amends, he offered to contribute a “dissertation” to the Franklin Institute’s Journal that eventually appeared in the March 1936 issue. Reporting the appearance of Einstein’s essay, Time Magazine (March 16, 1936) tells the story of what happened a year before. “A throng of scientists and dignitaries was assembled to hear what the medalist had to say. Einstein genially informed the chairman that he had nothing to say, that inspiration which he had awaited until the last moment had failed him. The chairman, much more embarrassed than the medalist, conveyed this information to the audience. In atonement, Einstein wrote a 44-page essay entitled ‘Physics and Reality’ ”.

5Einstein and Nathan Rosen, “The Particle Problem in the General Theory of Relativity”, Physical Review, v. 48 (July 1, 1935), pp. 73–77.

6In the Einstein-Rosen solutions, electrical charge and mass appear as independent constants of integration.

7Einstein, “Physik und Realität”, The Journal of the Franklin Institute v. 221, no. 3 (March 1936), pp. 313–47; p. 318.

8Huxley, Thomas Henry, “On the Educational Value of the Natural History Sciences”, 1854; reprinted in Collected Papers v. III (“Science and Education”). New York: D. Appleton and Co., 1897, pp. 38–65; p. 45.

9Einstein, “Johannes Kepler”, originally published 1930; as translated by Sonia Bargmann in Albert Einstein: Ideas and Opinions. Ideas and Opinions. New York: Crown Publishers, 1954, pp. 262-66; p. 266.

10Einstein, letter to Solovine of May 7, 1952, in Albert Einstein Letters to Solovine, with an introduction by Maurice Solovine. New York: Philosophical Library, 1987, pp. 138–9.

11Einstein, Vier Vorlesungen über Relativitätstheorie gehalten im Mai 1921 an der Universität Princeton. Braunschweig: Friedrich Vieweg & Sohn, 122; CPAE 7 (2002), Doc 71; translated by Edwin P. Adams, The Meaning of Relativity. Fifth edition. Princeton: Princeton University Press, 1956, p. 6.

12Einstein, “On the Method of Theoretical Physics”, Philosophy of Science v. 1, no. 2 (April, 1934), pp. 163–9; p. 165.

13Einstein, “Physik und Realität”, The Journal of the Franklin Institute v. 221, no. 3 (March, 1936), pp. 313–47; English translation, pp. 349–82. Translation reprinted in Einstein, Ideas and Opinions. New York: Crown Publishers, 1954, pp. 290–323; p. 314.

14Einstein and Leopold Infeld, The Evolution of Physics: The Growth of Ideas from Early Concepts to Relativity and Quanta. New York: Simon and Schuster, 1938, p. 33.

15Einstein, “Bemerkungen zu Bertrand Russells Erkenntnis-Theorie”, in Paul A. Schilpp (ed.), The Philosophy of Bertrand Russell. Evanston, IL: Northwestern University Press, 1944, pp. 278–91; p. 286.

16Einstein, “Autobiographical Notes”, in Paul A. Schilpp (ed.), Albert Einstein: Philosopher-Scientist. Evanston IL: Northwestern University Press, 1949, pp. 2–95; p. 81.

17Einstein, “Relativität und Raumproblem”, in Einstein, Über die spezielle und die allgemeine Relativitätstheorie. Erweiterte Auflage. Braunschweig: Friedrich Vieweg & Sohn Verlagsgesellschaft mbH, 1954, pp. 91–109; pp. 95–6. Translation by Robert Lawson as Appendix V of Albert Einstein Relativity: The Speical and the General Theory. New York: Bonanza Books, 1961, pp. 135–57; p. 141.

18“Ernst Mach”, Physikalische Zeitschrift, v. 17 (1916), pp. 101–104; CPAE 8, Doc. 29; English translation supplement, pp. 141–145.

19Frank, Phillip, Einstein: His Life and Times. New York: Alfred Knopf, 1947; fourth printing January 1953, pp. 40–42.

20Duhem, Pierre. The Aim and Structure of Physical Theory. Second edition. Translated by Philip P. Wiener from orginal 1914 French edition. Princeton: Princeton University Press, 1991, chapter 2.

21Einstein, “Motive des Forschens” (“Motives of Research”), April 26, 1918. CPAE 7 (2002), Doc. 7.

22Frank, Einstein: His Life and Times, p. 218.

23Volkmann, Paul. “Die gewöhnliche Darstellung der Mechanik und ihre Kritik durch Hertz”, Zeitschrift für den physikalischen und chemischen Unterricht Bd.14 (1901), 266–93; p. 266.

24Hertz, Heinrich. Die Prinzipien der Mechanik in neuem zusammenhänge dargestellt. Leipzig, Germany: Johann Ambrosius Barth, 1894. “Einleitung”, pp. 1–2.

25Boltzmann, Ludwig, “Über die Entwicklung der Methoden der theoretischen Physik in neuerer Zeit”, Münchener Naturforscherversammlung (September 22, 1899), as reprinted in Ludwig Boltzmann, Populäre Schriften, ausgewählt von Engelbert Broda. Braunschweig/Wiesbaden, Germany: Friedrich Vieweg & Sohn, 1979, pp. 120–49; p. 138.

26Einstein, Albert, H.A. Lorentz als Schöpfer und als Persönlichkeit. Leiden: Mededeling van het Rijksmuseum voor de Geschiedenis der Natuurwetenschappen te Leiden, Netherlands, no. 91. 1953.

27Lorentz, Hendrik A., “Electromagnetische theorieën van natuurkundige verschijnselen”, Jaarb. Rijksuniv. Leiden, Bijlagen 1. German translation in Collected Papers, vol. 8 (1935), pp. 333–52; p. 337.

28Hilbert, David, “Die Grundlagen der Geometrie”, 1894 lecture in M. Hallett and U. Majer (eds.), David Hilbert’s Lectures on the Foundations of Geometry 1891–1902. Berlin, Heidelberg, and New York: Springer, 2004, p. 74.

29Boltzmann, Ludwig, Vorlesungen über Gastheorie. I Theil. Leipzig: Ambrosius Barth, 1896, p. 6; as translated by Steven G. Brush, Ludwig Boltzmann: Lectures on Gas Theory. Berkeley: University of California Press, 1964, p. 28, translation modified: “The question of the appropriateness (Zweckmässigkeit) of atomistic representations (Anschauungen) is of course … really whether mere (blossen) differential equations or atomistic views (Ansichten) will one day be established as complete descriptions of the phenomena.”

30Hertz, Heinrich, “On the Fundamental Equations of Electromagnetics for Bodies at Rest”, (Göttinger Nachr. 19 March 1890; Wiedemann’s Ann. 40, p. 577) as translated in Electric Waves. New York: Dover, 1962, p. 197.

31Planck, “Die Einheit des physikalischen Weltbildes”, as reprinted in Wege zur physikalischen Erkenntnis: Reden und Vorträge. Zweite Auflage. Leipzig, Germany: S. Hirzel Verlag, 1934, pp. 1–32; p. 30.

32Ibid., p. 32.

33Planck, “Sinn und Grenzen der exakten Wissenschaft”, Die Naturwissenschaften Bd. 30, Heft 9/10 (27 February 1942), pp. 125–33; p. 130.

34Einstein, “Physik und Realität”, The Journal of the Franklin Institute v. 221, no. 3 (March 1936), pp. 313–47; p. 315. Translation in Albert Einstein, Ideas and Opinions. New York: Crown Publishers, 1954, pp. 290–323, p. 292.

35Fine, The Shaky Game, pp. 93 ff.

36Einstein, “On the Generalized Theory of Gravitation”, Scientific American v. 182, no. 4 (April 1950), p. 13.

37Einstein and Leopold Infeld, The Evolution of Physics: The Growth of Ideas from Early Concepts to Relativity and Quanta. New York: Simon and Schuster, 1938, p. 33.

Nine

Philosophy of science – constructivism

Introduction

Epistemological credo

The “constructing human mind”

Free creations of the human mind

Bildtheorie

From Bildtheorie to physical world picture (physikalischen Weltbild)

Reprise: “Physics” and “reality”

Summary

Notes

Further reading