Einstein’s Philosophy of Science (Stanford Encyclopedia of Philosophy)

Einstein’s Philosophy of Science (Stanford Encyclopedia of Philosophy)
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Einstein’s Philosophy of Science
First published Wed Feb 11, 2004; substantive revision Sun Feb 2, 2025
Albert Einstein (1879–1955) is well known as the most prominent
physicist of the twentieth century. His contributions to
twentieth-century philosophy of science, though of comparable
importance, are less well known. Einstein’s own philosophy of
science is an original synthesis of elements drawn from sources as
diverse as neo-Kantianism, conventionalism, and logical empiricism,
its distinctive feature being its novel blending of realism with a
holist, underdeterminationist form of conventionalism. Of special note
is the manner in which Einstein’s philosophical thinking was
driven by and contributed to the solution of problems first
encountered in his work in physics. Equally significant are
Einstein’s relations with and influence on other prominent
twentieth-century philosophers of science, including Moritz Schlick,
Hans Reichenbach, Ernst Cassirer, Philipp Frank, Henri Bergson,
Émile Meyerson (see Russo-Krauss and Laino 2024).
1. Introduction: Was Einstein an Epistemological “Opportunist”?
2. Theoretical Holism: The Nature and Role of Conventions in Science
3. Simplicity and Theory Choice
4. Univocalness in the Theoretical Representation of Nature
5. Realism and Separability
6. The Principle Theories—Constructive Theories Distinction
7. Conclusion: Albert Einstein: Philosopher-Physicist
Bibliography
Primary Literature: Einstein’s Work
Secondary Literature
Academic Tools
Other Internet Resources
Related Entries
1. Introduction: Was Einstein an Epistemological “Opportunist”?
Late in 1944, Albert Einstein received a letter from Robert Thornton,
a young African-American philosopher of science who had just finished
his Ph.D. under Herbert Feigl at Minnesota and was beginning a new job
teaching physics at the University of Puerto Rico, Mayaguez. He had
written to solicit from Einstein a few supportive words on behalf of
his efforts to introduce “as much of the philosophy of science
as possible” into the modern physics course that he was to teach
the following spring (Thornton to Einstein, 28 November 1944, EA
61–573). Here is what Einstein offered in reply:
I fully agree with you about the significance and educational value of
methodology as well as history and philosophy of science. So many
people today—and even professional scientists—seem to me
like somebody who has seen thousands of trees but has never seen a
forest. A knowledge of the historic and philosophical background gives
that kind of independence from prejudices of his generation from which
most scientists are suffering. This independence created by
philosophical insight is—in my opinion—the mark of
distinction between a mere artisan or specialist and a real seeker
after truth. (Einstein to Thornton, 7 December 1944, EA 61–574)
That Einstein meant what he said about the relevance of philosophy to
physics is evidenced by the fact that he had been saying more or less
the same thing for decades. Thus, in a 1916 memorial note for Ernst
Mach, a physicist and philosopher to whom Einstein owed a special debt
(see Norton 2010), he wrote:
How does it happen that a properly endowed natural scientist comes to
concern himself with epistemology? Is there no more valuable work in
his specialty? I hear many of my colleagues saying, and I sense it
from many more, that they feel this way. I cannot share this
sentiment. When I think about the ablest students whom I have
encountered in my teaching, that is, those who distinguish themselves
by their independence of judgment and not merely their
quick-wittedness, I can affirm that they had a vigorous interest in
epistemology. They happily began discussions about the goals and
methods of science, and they showed unequivocally, through their
tenacity in defending their views, that the subject seemed important
to them. Indeed, one should not be surprised at this. (Einstein 1916,
101)
How, exactly, does the philosophical habit of mind provide the
physicist with such “independence of judgment”? Einstein
goes on to explain:
Concepts that have proven useful in ordering things easily achieve
such an authority over us that we forget their earthly origins and
accept them as unalterable givens. Thus they come to be stamped as
“necessities of thought,” “a priori givens,”
etc. The path of scientific advance is often made impassable for a
long time through such errors. For that reason, it is by no means an
idle game if we become practiced in analyzing the long commonplace
concepts and exhibiting those circumstances upon which their
justification and usefulness depend, how they have grown up,
individually, out of the givens of experience. By this means, their
all-too-great authority will be broken. They will be removed if they
cannot be properly legitimated, corrected if their correlation with
given things be far too superfluous, replaced by others if a new
system can be established that we prefer for whatever reason.
(Einstein 1916, 102)
One is not surprised at Einstein’s then citing Mach’s
critical analysis of the Newtonian conception of absolute space as a
paradigm of what Mach, himself, termed the
“historical-critical” method of philosophical analysis
(Einstein 1916, 101, citing Ch. 2, §§ 6–7 of
Mach’s
Mechanik
, most likely the third edition, Mach
1897).
The place of philosophy in physics was a theme to which Einstein
returned time and again, it being clearly an issue of deep importance
to him. Sometimes he adopts a modest pose, as in this oft-quoted
remark from his 1933 Spencer Lecture:
If you wish to learn from the theoretical physicist anything about the
methods which he uses, I would give you the following piece of advice:
Don’t listen to his words, examine his achievements. For to the
discoverer in that field, the constructions of his imagination appear
so necessary and so natural that he is apt to treat them not as the
creations of his thoughts but as given realities. (Einstein 1933,
5–6)
More typical, however, is the confident pose he struck three years
later in “Physics and Reality”:
It has often been said, and certainly not without justification, that
the man of science is a poor philosopher. Why then should it not be
the right thing for the physicist to let the philosopher do the
philosophizing? Such might indeed be the right thing at a time when
the physicist believes he has at his disposal a rigid system of
fundamental concepts and fundamental laws which are so well
established that waves of doubt can not reach them; but it can not be
right at a time when the very foundations of physics itself have
become problematic as they are now. At a time like the present, when
experience forces us to seek a newer and more solid foundation, the
physicist cannot simply surrender to the philosopher the critical
contemplation of the theoretical foundations; for, he himself knows
best, and feels more surely where the shoe pinches. In looking for a
new foundation, he must try to make clear in his own mind just how far
the concepts which he uses are justified, and are necessities.
(Einstein 1936, 349)
What kind of philosophy might we expect from the
philosopher-physicist? One thing that we should not expect from a
physicist who takes the philosophical turn in order to help solve
fundamental physical problems is a systematic philosophy:
The reciprocal relationship of epistemology and science is of
noteworthy kind. They are dependent upon each other. Epistemology
without contact with science becomes an empty scheme. Science without
epistemology is—insofar as it is thinkable at
all—primitive and muddled. However, no sooner has the
epistemologist, who is seeking a clear system, fought his way through
to such a system, than he is inclined to interpret the thought-content
of science in the sense of his system and to reject whatever does not
fit into his system. The scientist, however, cannot afford to carry
his striving for epistemological systematic that far. He accepts
gratefully the epistemological conceptual analysis; but the external
conditions, which are set for him by the facts of experience, do not
permit him to let himself be too much restricted in the construction
of his conceptual world by the adherence to an epistemological system.
He therefore must appear to the systematic epistemologist as a type of
unscrupulous opportunist: he appears as
realist
insofar as he
seeks to describe a world independent of the acts of perception; as
idealist
insofar as he looks upon the concepts and theories
as free inventions of the human spirit (not logically derivable from
what is empirically given); as
positivist
insofar as he
considers his concepts and theories justified
only
to the
extent to which they furnish a logical representation of relations
among sensory experiences. He may even appear as
Platonist
or
Pythagorean
insofar as he considers the viewpoint of logical
simplicity as an indispensable and effective tool of his research.
(Einstein 1949, 683–684)
But what strikes the “systematic epistemologist” as mere
opportunism might appear otherwise when viewed from the perspective of
a physicist engaged, as Einstein himself put it, in “the
critical contemplation of the theoretical foundations.” The
overarching goal of that critical contemplation was, for Einstein, the
creation of a unified foundation for physics after the model of a
field theory like general relativity (see Sauer 2014 for non-technical
overview on Einstein’s approach to the unified field theory
program). Einstein failed in his quest, but there was a consistency
and constancy in the striving that informed as well the philosophy of
science developing hand in hand with the scientific project.
Indeed, from early to late a few key ideas played the central, leading
role in Einstein’s philosophy of science, ideas about which
Einstein evinced surprisingly little doubt even while achieving an
ever deeper understanding of their implications. For the purposes of
the following comparatively brief overview, we can confine our
attention to just five topics:
Theoretical holism.
Simplicity and theory choice.
Univocalness in the theoretical representation of nature.
Realism and separability.
The principle theories-constructive theories distinction.
The emphasis on the continuity and coherence in the development of
Einstein’s philosophy of science contrasts with an account such
as Gerald Holton’s (1968), which claims to find a major
philosophical break in the mid-1910s, in the form of a turn away from
a sympathy for an anti-metaphysical positivism and toward a robust
scientific realism. Holton sees this turn being driven by
Einstein’s alleged realization that general relativity, by
contrast with special relativity, requires a realistic ontology.
However, Einstein was probably never an ardent “Machian”
positivist,
and he was never a scientific realist, at least not in the sense
acquired by the term “scientific realist” in later
twentieth century philosophical discourse (see Howard 1993). Einstein
expected scientific theories to have the proper empirical credentials,
but he was no positivist; and he expected scientific theories to give
an account of physical reality, but he was no scientific realist.
Moreover, in both respects his views remained more or less the same
from the beginning to the end of his career.
Why Einstein did not think himself a realist (he said so explicitly)
is discussed below. Why he is not to be understood as a positivist
deserves a word or two of further discussion here, if only because the
belief that he was sympathetic to positivism, at least early in his
life, is so widespread (for a fuller discussion, see Howard 1993).
That Einstein later repudiated positivism is beyond doubt. Many
remarks from at least the early 1920s through the end of his life make
this clear. In 1946 he explained what he took to be Mach’s basic
error:
He did not place in the correct light the essentially constructive and
speculative nature of all thinking and more especially of scientific
thinking; in consequence, he condemned theory precisely at those
points where its constructive-speculative character comes to light
unmistakably, such as in the kinetic theory of atoms. (Einstein 1946,
21)
Is Einstein here also criticizing his own youthful philosophical
indiscretions? The very example that Einstein gives here makes any
such interpretation highly implausible, because one of
Einstein’s main goals in his early work on Brownian motion
(Einstein 1905b) was precisely to prove the reality of atoms, this in
the face of the then famous skepticism of thinkers like Mach and
Wilhelm Ostwald:
My principal aim in this was to find facts that would guarantee as
much as possible the existence of atoms of definite size.… The
agreement of these considerations with experience together with
Planck’s determination of the true molecular size from the law
of radiation (for high temperatures) convinced the skeptics, who were
quite numerous at that time (Ostwald, Mach), of the reality of atoms.
(Einstein 1946, 45, 47)
Why, then, is the belief in Einstein’s early sympathy for
positivism so well entrenched?
The one piece of evidence standardly cited for a youthful flirtation
with positivism is Einstein’s critique of the notion of absolute
distant simultaneity in his 1905 paper on special relativity (Einstein
1905c). Einstein speaks there of “observers,” but in an
epistemologically neutral way that can be replaced by talk of an
inertial frame of reference. What really bothers Einstein about
distant simultaneity is not that it is observationally inaccessible
but that it involves a two-fold arbitrariness, one in the choice of an
inertial frame of reference and one in the stipulation within a given
frame of a convention regarding the ratio of the times required for a
light signal to go from one stationary observer to another and back
again. Likewise, Einstein faults classical Maxwellian electrodynamics
for an asymmetry in the way it explains electromagnetic induction
depending on whether it is the coil or the magnet that is assumed to
be at rest. If the effect is the same—a current in the
coil—why, asks Einstein, should there be two different
explanations: an electrical field created in the vicinity of a moving
magnet or an electromotive force induced in a conductor moving through
a stationary magnetic field? To be sure, whether it is the coil or the
magnet that is taken to be at rest makes no observable difference, but
the problem, from Einstein’s point of view, is the asymmetry in
the two explanations. Even the young Einstein was no positivist.
First generation logical empiricists sought to legitimate their
movement in part by claiming Einstein as a friend. They may be
forgiven their putting a forced interpretation on arguments taken out
of context. We can do better.
Einstein’s philosophy of science is an original synthesis
drawing upon many philosophical resources, from neo-Kantianism to
Machian empiricism and Duhemian conventionalism. Other thinkers and
movements, most notably the logical empiricists, drew upon the same
resources. But Einstein put the pieces together in a manner
importantly different from Moritz Schlick, Hans Reichenbach, and
Rudolf Carnap, and he argued with them for decades about who was right
(however much they obscured these differences in representing Einstein
publicly as a friend of logical empiricism and scientific philosophy).
Starting from the mid-1920s till the end of the decade Einstein show
some interest in the rationalistic realism of Émile Meyerson
(Einstein, 1928; cf. Giovanelli 2018; on the contemporary debate
between Einstein and Bergson, see Canales 2015). Understanding how
Einstein puts those pieces together therefore sheds light not only on
the philosophical aspect of his own achievements in physics but also
upon the larger history of the development of the philosophy of
science in the twentieth century.
2. Theoretical Holism: The Nature and Role of Conventions in Science
Any philosophy of science must include an account of the relation
between theory and evidence. Einstein learned about the historicity of
scientific concepts from Mach. But his preferred way of modeling the
logical relationship between theory and evidence was inspired mainly
by his reading of Pierre Duhem’s
La Théorie physique:
son objet et sa structure
(Duhem 1906). Einstein probably first
read Duhem, or at least learned the essentials of Duhem’s
philosophy of science around the fall of 1909, when, upon returning to
Zurich from the patent office in Bern to take up his first academic
appointment at the University of Zurich, he became the upstairs
neighbor of his old friend and fellow Zurich physics student,
Friedrich Adler. Just a few months before, Adler had published the
German translation of
La Théorie physique
(Duhem
1908), and the philosophy of science became a frequent topic of
conversation between the new neighbors, Adler and Einstein (see Howard
1990a).
Theoretical holism and the underdetermination of theory choice by
empirical evidence are the central theses in Duhem’s philosophy
of science (on Einstein’s and theory choice, see Oberheim 2016).
His argument, in brief, is that at least in sciences like physics,
where experiment is dense with sophisticated instrumentation whose
employment itself requires theoretical interpretation, hypotheses are
not tested in isolation but only as part of whole bodies of theory. It
follows that when there is a conflict between theory and evidence, the
fit can be restored in a multiplicity of different ways. No statement
is immune to revision because of a presumed status as a definition or
thanks to some other a priori warrant, and most any statement can be
retained on pain of suitable adjustments elsewhere in the total body
of theory. Hence, theory choice is underdetermined by evidence.
That Einstein’s exposure to Duhem’s philosophy of science
soon left its mark is evident from lecture notes that Einstein
prepared for a course on electricity and magnetism at the University
of Zurich in the winter semester of 1910/11. Einstein asks how one can
assign a definite electrical charge everywhere within a material body,
if the interior of the body is not accessible to test particles. A
“Machian” positivist would deem such direct empirical
access necessary for meaningful talk of a charge distribution in the
interior of a sold. Einstein argues otherwise:
We have seen how experience led to the introd. of the concept of the
quantity of electricity. it was defined by means of the forces that
small electrified bodies exert on each other. But now we extend the
application of the concept to cases in which this definition cannot be
applied directly as soon as we conceive the el. forces as forces
exerted
on electricity
rather than on material particles. We
set up a conceptual system the individual parts of which do not
correspond directly to empirical facts. Only a certain totality of
theoretical material corresponds again to a certain totality of
experimental facts.
We find that such an el. continuum is always applicable only for the
representation of el. states of affairs in the interior of ponderable
bodies. Here too we define the vector of el. field strength as the
vector of the mech. force exerted on the unit of pos. electr. quantity
inside a body. But the force so defined is no longer directly
accessible to exp. It is one part of a theoretical construction that
can be correct or false, i.e., consistent or not consistent with
experience, only
as a whole
. (
Collected Papers of Albert
Einstein
, hereafter CPAE, Vol. 3, Doc. 11 [pp. 12–13])
One can hardly ask for a better summary of Duhem’s point of view
in application to a specific physical theory. Explicit citations of
Duhem by Einstein are rare (for details, see Howard 1990a). But
explicit invocations of a holist picture of the structure and
empirical interpretation of theories started to prevail at the turn of
the 1920s.
During the decade 1905–1915, Einstein had more or less
explicitly assumed that in a good theory there are certain
individual parts
that can be directly coordinated with the
behavior of physically-existent objects used as probes. A theory can
be said to be ‘true or false’ if such objects respectively
behave or do not behave as predicted. In special relativity, as in
classical mechanics, the fundamental geometrical/kinematical
variables, the space and time coordinates, are measured with rods and
clocks separately from the other non-geometrical variables, say,
charge electric field strengths, which were supposed to be defined by
measuring the force on a charge test particle. In general relativity,
coordinates are no longer directly measurable independently from the
gravitational field. Still, the line element \(ds\) (distance between
nearby spacetime points) was supposed to have a ‘natural’
distance that can be measured with rods and clocks. In the late 1910s,
pressed by the epistemological objections raised by different
interlocutors—in particular Hermann Weyl (Ryckman 2005) and the
young Wolfgang Pauli (Stachel, 2005)—Einstein was forced to
recognize that this epistemological model was at most a provisional
compromise. In principle rod- and clock-like structures should emerge
as solutions of a future relativistic theory of matter, possibly a
field theory encompassing gravitation and electromagnetism. In this
context, the sharp distinction between rods and clocks that serve to
define the geometrical/kinematical structure of the theory and other
material systems would become questionable. Einstein regarded such
distinction as provisionally necessary, give the current state of
physics. However, he recognized that in principle a physical theory
should construct rods and clocks as solutions to its equations (see
Ryckman 2017, ch. VII for an overview on Einstein view on the relation
between geometry and experience).
Einstein addressed this issue in several popular writings during the
1920s, in particular, the famous lecture
Geometrie und
Erfahrung
(Einstein 1921, see also Einstein, 1923, Einstein,
1924, Einstein 1926; Einstein 1926; see Giovanelli 2014 for an
overview).
Sub specie temporis
, he argued, it was useful to
compare the geometrical/kinematical structures of the theory with
experience separately from the rest of physics.
Sub specie
aeterni
, however, only geometry and physics taken together can be
said to be ‘true or false.’ This epistemological model
became more appropriate, while Einstein was moving beyond general
relativity in the direction of theory unifying the gravitational and
the electromagnetic field. Einstein had to rely on progressively more
abstract geometrical structures which could not be defined in terms of
the behavior of some physical probes. Thus, the use of such structures
was justified because of their role in the theory as a whole. In the
second half of the 1920s, in correspondence with Reichenbach
(Giovanelli 2017) and Meyerson (Giovanelli 2018), Einstein even denied
that the very distinction between geometrical and non-geometrical is
meaningful (Lehmkuhl 2014, Giovanelli 2016, 2022).
A different, but especially interesting example of Einstein’s
reliance on a form of theoretical holism is found in a review that
Einstein wrote in 1924 of Alfred Elsbach’s
Kant und
Einstein
(1924), one of the flood of books and articles then
trying to reconcile the Kant’s philosophy. Having asserted that
relativity theory is incompatible with Kant’s doctrine of the a
priori, Einstein explains why, more generally, he is not sympathetic
with Kant:
This does not, at first, preclude one’s holding at least to the
Kantian
problematic
, as, e.g., Cassirer has done. I am even
of the opinion that this standpoint can be rigorously refuted by no
development of natural science. For one will always be able to say
that critical philosophers have until now erred in the establishment
of the a priori elements, and one will always be able to establish a
system of a priori elements that does not contradict a given physical
system. Let me briefly indicate why I do not find this standpoint
natural. A physical theory consists of the parts (elements) A, B, C,
D, that together constitute a logical whole which correctly connects
the pertinent experiments (sense experiences). Then it tends to be the
case that the aggregate of fewer than all four elements, e.g., A, B,
D,
without
C, no longer says anything about these
experiences, and just as well A, B, C without D. One is then free to
regard the aggregate of three of these elements, e.g., A, B, C as a
priori, and only D as empirically conditioned. But what remains
unsatisfactory in this is always the
arbitrariness in the
choice
of those elements that one designates as a priori,
entirely apart from the fact that the theory could one day be replaced
by another that replaces certain of these elements (or all four) by
others. (Einstein 1924, 1688–1689)
Einstein’s point seems to be that while one can always choose to
designate selected elements as a priori and, hence, non-empirical, no
principle determines which elements can be so designated, and our
ability thus to designate them derives from the fact that it is only
the totality of the elements that possesses empirical content.
Much the same point could be made, and was made by Duhem himself (see
Duhem 1906, part 2, ch. 6, sects. 8 and 9), against those who would
insulate certain statements against empirical refutation by claiming
for them the status of conventional definitions. Edouard Le Roy (1901)
had argued thus about the law of free fall. It could not be refuted by
experiment because it functioned as a definition of “free
fall.” And Henri Poincaré (1901) said much the same about
the principles of mechanics more generally. As Einstein answered the
neo-Kantians, so Duhem answered this species of conventionalist: Yes,
experiment cannot refute, say, the law of free fall by itself, but
only because it is part of a larger theoretical whole that has
empirical content only as a whole, and various other elements of that
whole could as well be said to be, alone, immune to refutation.
That Einstein should deploy against the neo-Kantians in the early
1920s the argument that Duhem used against the conventionalism of
Poincaré and Le Roy is interesting from the point of view of
Einstein’s relationships with those who were leading the
development of logical empiricism and scientific philosophy in the
1920s, especially Schlick and Reichenbach. Einstein shared with
Schlick and Reichenbach the goal of crafting a new form of empiricism
that would be adequate to the task of defending general relativity
against neo-Kantian critiques (see Schlick 1917 and 1921, and
Reichenbach 1920, 1924, and 1928; for more detail, see Howard 1994a).
But while they all agreed that what Kant regarded as the a priori
element in scientific cognition was better understood as a
conventional moment in science, they were growing to disagree
dramatically over the nature and place of conventions in science. The
classic logical empiricist view that the moment of convention was
restricted to conventional coordinating definitions that endow
individual primitive terms, worked well, but did not comport well with
the holism about theories
It was this argument over the nature and place of conventions in
science that underlies Einstein’s gradual philosophical
estrangement from Schlick and Reichenbach in the 1920s. Serious in its
own right, the argument over conventions was entangled with two other
issues as well, namely, realism and Einstein’s famous view of
theories as the “free creations of the human spirit” (see,
for example, Einstein 1921). In both instances what troubled Einstein
was that a verificationist semantics made the link between theory and
experience too strong, leaving too small a role for theory, itself,
and the creative theorizing that produces it.
If theory choice is empirically determinate, especially if theoretical
concepts are explicitly constructed from empirical primitives, as in
Carnap’s program in the
Aufbau
(Carnap 1928), then it
is hard to see how theory gives us a story about anything other than
experience. As noted, Einstein was not what we would today call a
scientific realist, but he still believed that there was content in
theory beyond mere empirical content (on the relations between
Einstein’s realism and constructism see Ryckman 2017, ch. 8 and
9). He believed that theoretical science gave us a window on nature
itself, even if, in principle, there will be no one uniquely correct
story at the level of deep ontology (see below, section 5). And if the
only choice in theory choice is one among conventional coordinating
definitions, then that is no choice at all, a point stressed by
Reichenbach, especially, as an important positive implication of his
position. Reichenbach argued that if empirical content is the only
content, then empirically equivalent theories have the same content,
the difference resulting from their different choices of coordinating
definitions being like in kind to the difference between “es
regnet” and “il pleut,” or the difference between
expressing the result of a measurement in English or metric units,
just two different ways of saying the same thing. But then, Einstein
would ask, where is there any role for the creative intelligence of
the theoretical physicist if there is no room for genuine choice in
science, if experience somehow dictates theory construction?
The argument over the nature and role of conventions in science
continued to the very end of Einstein’s life, reaching its
highest level of sophistication in the exchange between Reichenbach
and Einstein the Library of Living Philosopher’s volume,
Albert Einstein: Philosopher-Physicist
(Schilpp 1949). The
question is, again, whether the choice of a geometry is empirical,
conventional, or a priori. In his contribution, Reichenbach reasserted
his old view that once an appropriate coordinating definition is
established, equating some “practically rigid rod” with
the geometer’s “rigid body,” then the geometry of
physical space is wholly determined by empirical evidence:
The choice of a geometry is arbitrary only so long as no definition of
congruence is specified. Once this definition is set up, it becomes an
empirical question
which
geometry holds for physical
space.… The conventionalist overlooks the fact that only the
incomplete statement of a geometry, in which a reference to the
definition of congruence is omitted, is arbitrary. (Reichenbach 1949,
297)
Einstein’s clever reply includes a dialogue between two
characters, “Reichenbach” and
“Poincaré,” in which “Reichenbach”
concedes to “Poincaré” that there are no perfectly
rigid bodies in nature and that physics must be used to correct for
such things as thermal deformations, from which it follows that what
we actually test is geometry plus physics, not geometry alone. Here an
“anonymous non-positivist” takes
“Poincaré’s” place, out of respect, says
Einstein, “for Poincaré’s superiority as thinker
and author” (Einstein 1949, 677), but also, perhaps, because he
realized that the point of view that follows was more Duhem than
Poincaré. The “non-positivist” then argues that
one’s granting that geometry and physics are tested together
contravenes the positivist identification of meaning with
verifiability:
Non-Positivist:
If, under the stated circumstances, you hold
distance to be a legitimate concept, how then is it with your basic
principle (meaning = verifiability)? Must you not come to the point
where you deny the meaning of geometrical statements and concede
meaning only to the completely developed theory of relativity (which
still does not exist at all as a finished product)? Must you not grant
that no “meaning” whatsoever, in your sense, belongs to
the individual concepts and statements of a physical theory, such
meaning belonging instead to the whole system insofar as it makes
“intelligible” what is given in experience? Why do the
individual concepts that occur in a theory require any separate
justification after all, if they are indispensable only within the
framework of the logical structure of the theory, and if it is the
theory as a whole that stands the test? (Einstein 1949, 678).
Two years before the Quine’s publication of “Two Dogmas of
Empiricism” (1951), Einstein here makes explicit the semantic
implications of a thoroughgoing holism.
If theory choice is empirically underdetermined, then an obvious
question is why we are so little aware of the underdetermination in
the day-to-day conduct of science. In a 1918 address celebrating Max
Planck’s sixtieth birthday, Einstein approached this question
via a distinction between practice and principle:
The supreme task of the physicist is … the search for those
most general, elementary laws from which the world picture is to be
obtained through pure deduction. No logical path leads to these
elementary laws; it is instead just the intuition that rests on an
empathic understanding of experience. In this state of methodological
uncertainty one can think that arbitrarily many, in themselves equally
justified systems of theoretical principles were possible; and this
opinion is,
in principle
, certainly correct. But the
development of physics has shown that of all the conceivable
theoretical constructions a single one has, at any given time, proved
itself unconditionally superior to all others. No one who has really
gone deeply into the subject will deny that, in practice, the world of
perceptions determines the theoretical system unambiguously, even
though no logical path leads from the perceptions to the basic
principles of the theory. (Einstein 1918, 31; Howard’s
translation)
But why is theory choice, in practice, seemingly empirically
determined? Einstein hinted at an answer the year before in a letter
to Schlick, where he commended Schlick’s argument that the deep
elements of a theoretical ontology have as much claim to the status of
the real as do Mach’s elements of sensation (Schlick 1917), but
suggested that we are nonetheless speaking of two different kinds of
reality. How do they differ?
It appears to me that the word “real” is taken in
different senses, according to whether impressions or events, that is
to say, states of affairs in the physical sense, are spoken of.
If two different peoples pursue physics independently of one another,
they will create systems that certainly agree as regards the
impressions (“elements” in Mach’s sense). The mental
constructions that the two devise for connecting these
“elements” can be vastly different. And the two
constructions need not agree as regards the “events”; for
these surely belong to the conceptual constructions. Certainly on the
“elements,” but not the “events,” are real in
the sense of being “given unavoidably in experience.”
But if we designate as “real” that which we arrange in the
space-time-schema, as you have done in the theory of knowledge, then
without doubt the “events,” above all, are real.…
I would like to recommend a clean conceptual distinction
here
. (Einstein to Schlick, 21 May 1917, CPAE, Vol. 8, Doc.
343)
Why, in practice, are physicists unaware of underdetermination? It is
because ours is not the situation of “two different peoples
pursu[ing] physics independently of one another.” Though
Einstein does not say it explicitly, the implication seems to be that
apparent determination in theory choice is mainly a consequence of our
all being similarly socialized as we become members of a common
scientific community. Part of what it means to be a member of a such a
community is that we have been taught to make our theoretical choices
in accord with criteria or values that we hold in common.
3. Simplicity and Theory Choice
For Einstein, as for many others, simplicity is the criterion that
mainly steers theory choice in domains where experiment and
observation no longer provide an unambiguous guide. This, too, is a
theme sounded early and late in Einstein’s philosophical
reflections (for more detail, see Howard 1998, Norton 2000, van Dongen
2002, 2010, 2017 Giovanelli 2018). For example, the just-quoted remark
from 1918 about the apparent determination of theory choice in
practice, contrasted with in-principle underdetermination
continues:
Furthermore this conceptual system that is univocally coordinated with
the world of experience is reducible to a few basic laws from which
the whole system can be developed logically. With every new important
advance the researcher here sees his expectations surpassed, in that
those basic laws are more and more simplified under the press of
experience. With astonishment he sees apparent chaos resolved into a
sublime order that is to be attributed not to the rule of the
individual mind, but to the constitution of the world of experience;
this is what Leibniz so happily characterized as
“pre-established harmony.” Physicists strenuously reproach
many epistemologists for their insufficient appreciation of this
circumstance. Herein, it seems to me, lie the roots of the controversy
carried on some years ago between Mach and Planck. (Einstein 1918, p.
31)
There is more than a little autobiography here, for as Einstein
stressed repeatedly in later years, he understood the success of his
own quest for a general theory of relativity as a result of his
seeking the simplest set of field equations satisfying a given set of
constraints.
Einstein’s celebration of simplicity as a guide to theory choice
comes clearly to the fore in the early 1930s, when he was immersed his
project of a unified field theory (see, van Dongen 2010 for a
reconstruction of the philosophical underpinning of Einstein’s
search of a unified field theory). Witness what he wrote in his 1933
Herbert Spencer lecture:
If, then, it is true that the axiomatic foundation of theoretical
physics cannot be extracted from experience but must be freely
invented, may we ever hope to find the right way? Furthermore, does
this right way exist anywhere other than in our illusions? May we hope
to be guided safely by experience at all, if there exist theories
(such as classical mechanics) which to a large extent do justice to
experience, without comprehending the matter in a deep way?
To these questions, I answer with complete confidence, that, in my
opinion, the right way exists, and that we are capable of finding it.
Our experience hitherto justifies us in trusting that nature is the
realization of the simplest that is mathematically conceivable. I am
convinced that purely mathematical construction enables us to find
those concepts and those lawlike connections between them that provide
the key to the understanding of natural phenomena. Useful mathematical
concepts may well be suggested by experience, but in no way can they
be derived from it. Experience naturally remains the sole criterion of
the usefulness of a mathematical construction for physics. But the
actual creative principle lies in mathematics. Thus, in a certain
sense, I take it to be true that pure thought can grasp the real, as
the ancients had dreamed. (Einstein 1933, p. 183; Howard’s
translation)
Einstein’s conviction that the theoretical physicist must trust
simplicity is that his work was moving steadily into domains ever
further removed from direct contact with observation and experiment.
Einstein started to routinely claim that this was the lesson he had
drawn from the way in which he had found general relativity (Norton
2000). There are, however, good reasons to think that Einstein’s
selective recollections (Jannsen and Renn 2007) were instrumental to
his defense of relying on a purely mathematical strategy in the search
for a unified field theory (van Dongen 2010):
The theory of relativity is a beautiful example of the basic character
of the modern development of theory. That is to say, the hypotheses
from which one starts become ever more abstract and more remote from
experience. But in return one comes closer to the preeminent goal of
science, that of encompassing a maximum of empirical contents through
logical deduction with a minimum of hypotheses or axioms. The
intellectual path from the axioms to the empirical contents or to the
testable consequences becomes, thereby, ever longer and more subtle.
The theoretician is forced, ever more, to allow himself to be directed
by purely mathematical, formal points of view in the search for
theories, because the physical experience of the experimenter is not
capable of leading us up to the regions of the highest abstraction.
Tentative deduction takes the place of the predominantly inductive
methods appropriate to the youthful state of science. Such a
theoretical structure must be quite thoroughly elaborated in order for
it to lead to consequences that can be compared with experience. It is
certainly the case that here, as well, the empirical fact is the
all-powerful judge. But its judgment can be handed down only on the
basis of great and difficult intellectual effort that first bridges
the wide space between the axioms and the testable consequences. The
theorist must accomplish this Herculean task with the clear
understanding that this effort may only be destined to prepare the way
for a death sentence for his theory. One should not reproach the
theorist who undertakes such a task by calling him a fantast; instead,
one must allow him his fantasizing, since for him there is no other
way to his goal whatsoever. Indeed, it is no planless fantasizing, but
rather a search for the logically simplest possibilities and their
consequences. (Einstein 1954, 238–239; Howard’s
translation)
What warrant is there for thus trusting in simplicity? At best one can
do a kind of meta-induction. That “the totality of all sensory
experience can be ‘comprehended’ on the basis of a
conceptual system built on premises of great simplicity” will be
derided by skeptics as a “miracle creed,” but, Einstein
adds, “it is a miracle creed which has been borne out to an
amazing extent by the development of science” (Einstein 1950, p.
342). The success of previous physical theories justifies our trusting
that nature is the realization of the simplest that is mathematically
conceivable
But for all that Einstein’s faith in simplicity was strong, he
despaired of giving a precise, formal characterization of how we
assess the simplicity of a theory. In 1946 he wrote about the
perspective of simplicity (here termed the “inner
perfection” of a theory):
This point of view, whose exact formulation meets with great
difficulties, has played an important role in the selection and
evaluation of theories from time immemorial. The problem here is not
simply one of a kind of enumeration of the logically independent
premises (if anything like this were at all possible without
ambiguity), but one of a kind of reciprocal weighing of
incommensurable qualities.… I shall not attempt to excuse the
lack of precision of [these] assertions … on the grounds of
insufficient space at my disposal; I must confess herewith that I
cannot at this point, and perhaps not at all, replace these hints by
more precise definitions. I believe, however, that a sharper
formulation would be possible. In any case it turns out that among the
“oracles” there usually is agreement in judging the
“inner perfection” of the theories and even more so
concerning the degree of “external confirmation.”
(Einstein 1946, pp. 21, 23).
As in 1918, so in 1946 and beyond, Einstein continues to be impressed
that the “oracles,” presumably the leaders of the relevant
scientific community, tend to agree in their judgments of simplicity.
That is why, in practice, simplicity seems to determine theory choice
univocally.
4. Univocalness in the Theoretical Representation of Nature
In the physics and philosophy of science literature of the late
nineteenth and early twentieth centuries, the principle according to
which scientific theorizing should strive for a univocal
representation of nature was widely and well known under the name that
it was given in the title of a widely-cited essay by Joseph Petzoldt,
“The Law of Univocalness” [“Das Gesetz der
Eindeutigkeit”] (Petzoldt 1895). An indication that the map of
philosophical positions was drawn then in a manner very different from
today is to found in the fact that this principle found favor among
both anti-metaphysical logical empiricists, such as Carnap, and
neo-Kantians, such as Cassirer. It played a major role in debates over
the ontology of general relativity and was an important part of the
background to the development of the modern concept of categoricity in
formal semantics (for more on the history, influence, and demise of
the principle of univocalness, see Howard 1992 and 1996). One can find
no more ardent and consistent champion of the principle than
Einstein.
The principle of univocalness should not be mistaken for a denial of
the underdetermination thesis. The latter asserts that a multiplicity
of theories can equally well account for a given body of empirical
evidence, perhaps even the infinity of all possible evidence in the
extreme, Quinean version of the thesis. The principle of univocalness
asserts (in a somewhat anachronistic formulation) that any one theory,
even any one among a set of empirically equivalent theories, should
provide a univocal representation of nature by determining for itself
an isomorphic set of models. The unambiguous determination of theory
choice by evidence is not the same thing as the univocal determination
of a class of models by a theory.
The principle of univocalness played a central role in
Einstein’s struggles to formulate the general theory of
relativity. When, in 1913, Einstein wrongly rejected a fully generally
covariant theory of gravitation, he did so in part because he thought,
wrongly, that generally covariant field equations failed the test of
univocalness. More specifically, he reasoned wrongly that for a region
of spacetime devoid of matter and energy—a
“hole”—generally covariant field equations permit
the construction of two different solutions, different in the sense
that, in general, for spacetime points inside the hole, they assign
different values of the metric tensor to one and the same point (for
more on the history of this episode, see Stachel 1980 and Norton
1984). But Einstein’s “hole argument” is wrong, and
his own diagnosis of the error in 1915 rests again, ironically, on a
deployment of the principle of univocalness. What Einstein realized in
1915 was that, in 1913, he was wrongly assuming that a coordinate
chart sufficed to fix the identity of spacetime manifold points. The
application of a coordinate chart cannot suffice to individuate
manifold points precisely because a coordinate chart is not an
invariant labeling scheme, whereas univocalness in the representation
of nature requires such invariance (see Howard and Norton 1993 and
Howard 1999 for further discussion).
Here is how Einstein explained his change of perspective in a letter
to Paul Ehrenfest of 26 December 1915, just a few weeks after the
publication of the final, generally covariant formulation of the
general theory of relativity:
In §12 of my work of last year, everything is correct (in the
first three paragraphs) up to that which is printed with emphasis at
the end of the third paragraph. From the fact that the two systems
\(G(x)\) and \(G'(x)\), referred to the same reference system, satisfy
the conditions of the grav. field, no contradiction follows with the
univocalness of events. That which was apparently compelling in these
reflections founders immediately, if one considers that
the reference system signifies nothing real
that the (simultaneous) realization of two different \(g\)-systems
(or better, two different grav. fields) in the same region of the
continuum is impossible according to the nature of the theory.
In place of §12, the following reflections must appear. The
physically real in the universe of events (in contrast to that which
is dependent upon the choice of a reference system) consists in
spatiotemporal coincidences
.* [Footnote *: and in nothing
else!] Real are, e.g., the intersections of two different world lines,
or the statement that they
do not
intersect. Those statements
that refer to the physically real therefore do not founder on any
univocal coordinate transformation. If two systems of the \(g_{\mu
v}\) (or in general the variables employed in the description of the
world) are so created that one can obtain the second from the first
through mere spacetime transformation, then they are completely
equivalent. For they have all spatiotemporal point coincidences in
common, i.e., everything that is observable.
These reflections show at the same time how natural the demand for
general covariance is. (CPAE, Vol. 8, Doc. 173)
Einstein’s new point of view, according to which the physically
real consists exclusively in that which can be constructed on the
basis of spacetime coincidences, spacetime points, for example, being
regarded as intersections of world lines, is now known as the
“point-coincidence argument.” (Giovanelli 2021). Einstein
might have been inspired by a paper by the young mathematician Erich
Kretschmann (Howard and Norton 1993; cf. Giovanelli 2013) or possibly
by a conversation with Schlick (Engler and Renn, 2017). Spacetime
coincidences play this privileged ontic role because they are
invariant and, thus, univocally determined. Spacetime
coordinates
lack such invariance, a circumstance that
Einstein thereafter repeatedly formulated as the claim that space and
time “thereby lose the last vestige of physical reality”
(see, for example, Einstein to Ehrenfest, 5 January 1916, CPAE, Vol.
8, Doc. 180).
One telling measure of the philosophical importance of
Einstein’s new perspective on the ontology of spacetime is the
fact that Schlick devoted his first book,
Raum und Zeit in den
gegenwärtigen Physik
(1917), a book for which Einstein had
high praise (see Howard 1984 and 1999). But what most interested
Einstein was Schlick’s discussion of the reality concept.
Schlick argued that Mach was wrong to regard only the elements of
sensation as real. Spacetime events, individuated invariantly as
spacetime coincidences, have as much or more right to be taken as
real, precisely because of the univocal manner of their determination.
Einstein wholeheartedly agreed, though he ventured the above-quoted
suggestion that one should distinguish the two kinds of
reality—that of the elements and that of the spacetime
events—on the ground that if “two different peoples”
pursued physics independently of one another they were fated to agree
about the elements but would almost surely produce different
theoretical constructions at the level of the spacetime event
ontology. Note, again, that underdetermination is not a failure of
univocalness. Different though they will be, each people’s
theoretical construction of an event ontology would be expected to be
univocal.
Schlick, of course, went on to become the founder of the Vienna
Circle, a leading figure in the development of logical empiricism, a
champion of verificationism. That being so, an important question
arises about Schlick’s interpretation of Einstein on the
univocal determination of spacetime events as spacetime coincidences.
The question is this: Do such univocal coincidences play such a
privileged role because of their reality or because of their
observability. Clearly the former—the reality of that which is
univocally determined—is important. But are univocal spacetime
coincidences real because, thanks to their invariance, they are
observable? Or is their observability consequent upon their invariant
reality? Einstein, himself, repeatedly stressed the observable
character of spacetime coincidences, as in the 26 December 1915 letter
to Ehrenfest quoted above (for additional references and a fuller
discussion, see Howard
1999).
Schlick, still a self-described realist in 1917, was clear about the
relationship between observability and reality. He distinguished
macroscopic coincidences in the field of our sense experience, to
which he does accord a privileged and foundational epistemic status,
from the microscopic point coincidences that define an ontology of
spacetime manifold points. Mapping the former onto the latter is, for
Schlick, an important part of the business of confirmation, but the
reality of the spacetime manifold points is in no way consequent upon
their observability. Indeed, how, strictly speaking, can one even talk
of the observation of
infinitesimal
spacetime coincidences of
the kind encountered in the intersection of two world lines? In fact,
the order of implication goes the other way: Spacetime events
individuated as spacetime coincidences are real because they are
invariant, and such observability as they might possess is consequent
upon their status as invariant bits of physical reality. For Einstein,
and for Schlick in 1917, understanding the latter—physical
reality—is the goal of physical theory.
5. Realism and Separability
As we have seen, Schlick’s
Raum und Zeit in den
gegenwärtigen Physik
promoted a realistic interpretation of
the ontology of general relativity. After reading the manuscript early
in 1917, Einstein wrote to Schlick on 21 May that “the last
section ‘Relations to Philosophy’ seems to me
excellent” (CPAE, Vol. 8, Doc. 343), just the sort of praise one
would expect from a fellow realist. Three years earlier, the Bonn
mathematician, Eduard Study, had written another well-known, indeed
very well-known defense of realism,
Die realistische Weltansicht
und die Lehre vom Raume
(1914). Einstein read it in September of
1918. Much of it he liked, especially the droll style, as he said to
Study in a letter of 17 September (CPAE, Vol. 8, Doc. 618). Pressed by
Study to say more about the points where he disagreed, Einstein
replied on 25 September in a rather surprising way:
I am supposed to explain to you my doubts? By laying stress on these
it will appear that I want to pick holes in you everywhere. But things
are not so bad, because I do not feel comfortable and at home in any
of the “isms.” It always seems to me as though such an ism
were strong only so long as it nourishes itself on the weakness of it
counter-ism; but if the latter is struck dead, and it is alone on an
open field, then it also turns out to be unsteady on its feet.
So,
away we go
“The physical world is real.” That is supposed to be the
fundamental hypothesis. What does “hypothesis” mean here?
For me, a hypothesis is a statement, whose
truth
must be
assumed for the moment,
but whose meaning must be raised above all
ambiguity
. The above statement appears to me, however, to be, in
itself, meaningless, as if one said: “The physical world is
cock-a-doodle-doo.” It appears to me that the “real”
is an intrinsically empty, meaningless category (pigeon hole), whose
monstrous importance lies only in the fact that I can do certain
things in it and not certain others. This division is, to be sure, not
an
arbitrary
one, but instead ….
I concede that the natural sciences concern the “real,”
but I am still not a realist. (CPAE, Vol. 8, Doc. 624)
Lest there be any doubt that Einstein has little sympathy for the
other side, he adds:
The positivist or pragmatist is strong as long as he battles against
the opinion that there [are] concepts that are anchored in the
“A priori.” When, in his enthusiasm, [he] forgets that all
knowledge consists [in] concepts and judgments, then that is a
weakness that lies not in the nature of things but in his personal
disposition just as with the senseless battle against hypotheses, cf.
the clear book by Duhem. In any case, the railing against atoms rests
upon this weakness. Oh, how hard things are for man in this world; the
path to originality leads through unreason (in the sciences), through
ugliness (in the arts)-at least the path that many find passable.
(CPAE, Vol. 8, Doc. 624)
What could Einstein mean by saying that he concedes that the natural
sciences concern the “real,” but that he is “still
not a realist” and that the “real” in the statement,
“the physical world is real,” is an “intrinsically
empty, meaningless category”?
The answer might be that realism, for Einstein, is not a philosophical
doctrine about the interpretation of scientific theories or the
semantics of theoretical
terms.
For Einstein, realism is a physical postulate, one of a most
interesting kind, as he explained on 18 March 1948 in a long note at
the end of the manuscript of Max Born’s Waynflete Lectures,
Natural Philosophy of Cause and Chance
(1949), which Born had
sent to Einstein for commentary:
I just want to explain what I mean when I say that we should try to
hold on to physical reality. We are, to be sure, all of us aware of
the situation regarding what will turn out to be the basic
foundational concepts in physics: the point-mass or the particle is
surely not among them; the field, in the Faraday/Maxwell sense,
might be, but not with certainty. But that which we conceive as
existing (’actual’) should somehow be localized in time
and space. That is, the real in one part of space, A, should (in
theory) somehow ‘exist’ independently of that which is
thought of as real in another part of space, B. If a physical system
stretches over the parts of space A
and
B, then what is
present in B should somehow have an existence independent of what is
present in A. What is actually present in B should thus not depend
upon the type of measurement carried out in the part of space, A; it
should also be independent of whether or not, after all, a measurement
is made in A.
If one adheres to this program, then one can hardly view the
quantum-theoretical description as a
complete
representation
of the physically real. If one attempts, nevertheless, so to view it,
then one must assume that the physically real in B undergoes a sudden
change because of a measurement in A. My physical instincts bristle at
that suggestion.
However, if one renounces the assumption that what is present in
different parts of space has an independent, real existence, then I do
not at all see what physics is supposed to describe. For what is
thought to by a ‘system’ is, after all, just conventional,
and I do not see how one is supposed to divide up the world
objectively so that one can make statements about the parts. (Born
1969, 223–224; Howard’s translation)
Realism is thus the thesis of spatial separability, the claim that
spatial separation is a sufficient condition for the individuation of
physical systems, and its assumption is here made into almost a
necessary condition for the possibility of an intelligible science of
physics.
The postulate of spatial separability as that which undergirds the
ontic independence and, hence, individual identities of the systems
that physics describes was an important part of Einstein’s
thinking about the foundations of physics since at least the time of
his very first paper on the quantum hypothesis in 1905 (Einstein
1905a; for more detail on the early history of this idea in
Einstein’s thinking, see Howard 1990b and Bacciagaluppi and
Crull 2024). But the true significance of the separability principle
emerged most clearly in 1935, when (as hinted in the just-quoted
remark) Einstein made it one of the central premises of his argument
for the incompleteness of quantum mechanics (see Howard 1985 and
1989). It is not so clearly deployed in the published version of the
Einstein, Podolsky, Rosen paper (1935), but Einstein did not write
that paper and did not like the way the argument appeared there.
Separability is, however, an explicit premise in all of
Einstein’s later presentations of the argument for the
incompleteness of quantum mechanics, both in correspondence and in
print (see Howard 1985 for a detailed list of references).
In brief, the argument is this. Separability implies that spacelike
separated systems have associated with them independent real states of
affairs. A second postulate, locality, implies that the events in one
region of spacetime cannot physically influence physical reality in a
region of spacetime separated from the first by a spacelike interval.
Consider now an experiment in which two systems, A and B, interact and
separate, subsequent measurements on each corresponding to spacelike
separated events. Separability implies that A and B have separate real
physical states, and locality implies that the measurement performed
on A cannot influence B’s real physical state. But quantum
mechanics ascribes different theoretical states, different wave
functions, to B depending upon that parameter that is measured on A.
Therefore, quantum mechanics ascribes different theoretical states to
B, when B possesses, in fact, one real physical state. Hence quantum
mechanics is incomplete.
One wants to ask many questions. First, what notion of completeness is
being invoked here? It is not deductive completeness. It is closer in
kind to what is termed “categoricity” in formal semantics,
a categorical theory being one whose models are all isomorphic to one
another. It is closer still to the principle discussed above—and
cited as a precursor of the concept of categoricity—namely, the
principle of univocalness, which we found doing such important work in
Einstein’s quest for a general theory of relativity, where it
was the premise forcing the adoption of an invariant and thus univocal
scheme for the individuation of spacetime manifold points.
The next question is why separability is viewed by Einstein as
virtually an a priori necessary condition for the possibility of a
science of physics. One reason is because a field theory like general
relativity, which was Einstein’s model for a future unified
foundation for physics, is an extreme embodiment of the principle of
separability: “Field theory has carried out this principle to
the extreme, in that it localizes within infinitely small
(four-dimensional) space-elements the elementary things existing
independently of the one another that it takes as basic, as well as
the elementary laws it postulates for them” (Einstein 1948,
321–322). And a field theory like general relativity can do this
because the infinitesimal metric interval—the careful way to
think about separation in general relativistic spacetime—is
invariant (hence univocally determined) under all continuous
coordinate transformations.
Another reason why Einstein would be inclined to view separability as
an a priori necessity is that, in thus invoking separability to ground
individuation, Einstein places himself in a tradition of so viewing
spatial separability with very strong Kantian roots (and, before Kant,
Newtonian roots), a tradition in which spatial separability was known
by the name that Arthur Schopenhauer famously gave to it, the
principium individuationis
(for a fuller discussion of this
historical context, see Howard 1997).
A final question one wants to ask is: “What does any of this
have to do with realism?” One might grant Einstein’s point
that a real ontology requires a principle of individuation without
agreeing that separability provides the only conceivable such
principle. Separability together with the invariance of the
infinitesimal metric interval implies that, in a general relativistic
spacetime, there are joints everywhere, meaning that we can carve up
the universe in any way we choose and still have ontically independent
parts. But quantum entanglement can be read as implying that this
libertarian scheme of individuation does not work. Can quantum
mechanics not be given a realistic interpretation? Many would say,
“yes.” Einstein said, “no.”
6. The Principle Theories—Constructive Theories Distinction
There is much that is original in Einstein’s philosophy of
science as described thus far. At the very least, he rearranged the
bits and pieces of doctrine that he learned from others—Kant,
Mach, Duhem, Poincaré, Schlick, and others—in a
strikingly novel way. But Einstein’s most original contribution
to twentieth-century philosophy of science lies elsewhere, in his
distinction between what he termed “principle theories”
and “constructive theories.” (Giovanelli 2020, 2023)
This idea first found its way into print in a brief 1919 article in
the
Times
of London (Einstein 1919). A constructive theory,
as the name implies, provides a constructive model for the phenomena
of interest. An example would be kinetic theory. A principle theory
consists of a set of individually well-confirmed, high-level empirical
generalizations, “which permit of precise formulation”
(Einstein 1914, 749). Examples include the first and second laws of
thermodynamics. Ultimate understanding requires a constructive theory,
but often, says Einstein, progress in theory is impeded by premature
attempts at developing constructive theories in the absence of
sufficient constraints by means of which to narrow the range of
possible constructive theories. It is the function of principle
theories to provide such constraint, and progress is often best
achieved by focusing first on the establishment of such principles.
According to Einstein, that is how he achieved his breakthrough with
the theory of relativity, which, he says, is a principle theory, its
two principles being the relativity principle and the light
principle.
While the principle theories-constructive theories distinction first
made its way into print in 1919, there is considerable evidence that
it played an explicit role in Einstein’s thinking much earlier
(Einstein 1907, Einstein to Sommerfeld 14 January 1908, CPAE, vol. 5,
Doc. 73, Einstein 1914). Nor was it only the relativity and light
principles that served Einstein as constraints in his theorizing.
Thus, he explicitly mentions also the Boltzmann principle, \(S = k
\log W\), as another such:
This equation connects thermodynamics with the molecular theory. It
yields, as well, the statistical probabilities of the states of
systems for which we are not in a position to construct a
molecular-theoretical model. To that extent, Boltzmann’s
magnificent idea is of significance for theoretical physics …
because it provides a heuristic principle whose range extends beyond
the domain of validity of molecular mechanics. (Einstein 1915, p.
262).
Einstein is here alluding the famous entropic analogy whereby, in his
1905 photon hypothesis paper, he reasoned from the fact that black
body radiation in the Wien regime satisfied the Boltzmann principle to
the conclusion that, in that regime, radiation behaved as if it
consisted of mutually independent, corpuscle-like quanta of
electromagnetic energy. The quantum hypothesis is a constructive model
of radiation; the Boltzmann principle is the constraint that first
suggested that model.
There are anticipations of the principle theories-constructive
theories distinction in the nineteenth-century electrodynamics
literature, James Clerk Maxwell, in particular, being a source from
which Einstein might well have drawn (see Harman 1998). At the turn of
the century, the “physics of principles” was a subject
under wide discussion. At the turn of 1900, Hendrik A. Lorentz
(Lorentz 1900, 1905; see Frisch 2005) and Henri Poincaré (for
example, Poincaré 1904; see, Giedymin 1982, Darrigol 1995)
presented the opposition between the “physics of
principles” and the “physics of models” as
commonplace. In a similar vein, Arnold Sommerfeld opposed a
“physics of problems”, a style of doing physics based on
concrete puzzle solving, to the “practice of principles”
defended by Max Planck (Seth 2010). Philipp Frank (1908, relying on
Rey 1909) defined relativity theory as a “ conceptual
theory” based on abstract, but empirically well confirmed
principles rather than on intuitive models. Probably many other
examples could be find. . But however extensive his borrowings (no
explicit debt was ever acknowledged), in Einstein’s hands the
distinction becomes a methodological tool of impressive scope and
fertility. What is puzzling, and even a bit sad, is that this most
original methodological insight of Einstein’s had comparatively
little impact on later philosophy of science or practice in physics.
Only in recent decades, Einstein constructive-principle distinction
has attracted interest in the philosophical literature, originating a
still living philosophical debate on the foundation of spacetime
theories (Brown 2005, Janssen 2009, Lange
2014).
7. Conclusion: Albert Einstein: Philosopher-Physicist
Einstein’s influence on twentieth-century philosophy of science
is comparable to his influence on twentieth-century physics (Howard
2014). What made that possible? One explanation looks to the
institutional and disciplinary history of theoretical physics and the
philosophy of science. Each was, in its own domain, a new mode of
thought in the latter nineteenth century, and each finally began to
secure for itself a solid institutional basis in the early twentieth
century. In a curious way, the two movements helped one another.
Philosophers of science helped to legitimate theoretical physics by
locating the significant cognitive content of science in its theories.
Theoretical physicists helped to legitimate the philosophy of science
by providing for analysis a subject matter that was radically
reshaping our understanding of nature and the place of humankind
within it. In some cases the help was even more direct, as with the
work of Einstein and Max Planck in the mid-1920s to create in the
physics department at the University of Berlin a chair in the
philosophy of science for Reichenbach (see Hecht and Hartmann 1982).
And we should remember the example of the physicists Mach and Ludwig
Boltzmann who were the first two occupants of the new chair for the
philosophy of science at the University of Vienna at the turn of the
century.
Another explanation looks to the education of young physicists in
Einstein’s day. Not only was Einstein’s own youthful
reading heavily focused on philosophy, more generally, and the
philosophy of science, in particular (for an overview, see Einstein
1989, xxiv–xxv; see also Howard 1994b), in which respect he was
not unlike other physicists of his generation, but also his university
physics curriculum included a required course on “The Theory of
Scientific Thought” (see Einstein 1987, Doc. 28). An obvious
question is whether or not the early cultivation of a philosophical
habit of mind made a difference in the way Einstein and his
contemporaries approached physics. As indicated by his November 1944
letter to Robert Thorton quoted at the beginning of this article,
Einstein thought that it did.
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[CPAE]
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1914
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1921
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1923
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1926
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1928
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1930
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1936
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