Embed Size (px)
Citation preview
This article was downloaded by: [University of Sussex Library]On: 18 August 2014, At: 07:33Publisher: RoutledgeInforma Ltd Registered in England and Wales Registered Number: 1072954 Registeredoffice: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK
International Studies in the Philosophyof SciencePublication details, including instructions for authors andsubscription information:http://www.tandfonline.com/loi/cisp20
Pragmatism, Bohr, and the CopenhagenInterpretation of Quantum MechanicsReza Maleeh & Parisa AmaniPublished online: 23 Apr 2014.
To cite this article: Reza Maleeh & Parisa Amani (2013) Pragmatism, Bohr, and the CopenhagenInterpretation of Quantum Mechanics, International Studies in the Philosophy of Science, 27:4,353-367, DOI: 10.1080/02698595.2013.868182
To link to this article: http://dx.doi.org/10.1080/02698595.2013.868182
PLEASE SCROLL DOWN FOR ARTICLE
Taylor & Francis makes every effort to ensure the accuracy of all the information (the“Content”) contained in the publications on our platform. However, Taylor & Francis,our agents, and our licensors make no representations or warranties whatsoever as tothe accuracy, completeness, or suitability for any purpose of the Content. Any opinionsand views expressed in this publication are the opinions and views of the authors,and are not the views of or endorsed by Taylor & Francis. The accuracy of the Contentshould not be relied upon and should be independently verified with primary sourcesof information. Taylor and Francis shall not be liable for any losses, actions, claims,proceedings, demands, costs, expenses, damages, and other liabilities whatsoever orhowsoever caused arising directly or indirectly in connection with, in relation to or arisingout of the use of the Content.
This article may be used for research, teaching, and private study purposes. Anysubstantial or systematic reproduction, redistribution, reselling, loan, sub-licensing,systematic supply, or distribution in any form to anyone is expressly forbidden. Terms &Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions
Pragmatism, Bohr, and theCopenhagen Interpretationof Quantum MechanicsReza Maleeh and Parisa Amani
In this article, we argue that although Bohr’s version of the Copenhagen interpretation is
in line with several key elements of logical positivism, pragmatism is the closest approxi-
mation to a classification of the Copenhagen interpretation, whether or not pragmatists
directly influenced the key figures of the interpretation. Pragmatism already encompasses
important elements of operationalism and logical positivism, especially the liberalized
Carnapian reading of logical positivism. We suggest that some elements of the Copenha-
gen interpretation, which are in line with logical positivism, are also supported by prag-
matism. Some of these elements are empirical realism, fallibilism, holism, and
instrumentalism. However, pragmatism goes beyond logical positivism in espousing
some other key elements of the Copenhagen interpretation, though imperfectly, such as
the correspondence principle, complementarity, and indeterminism.
1. Introduction
Mostly, Niels Bohr, Werner Heisenberg, and Max Born are considered the initiators of
the Copenhagen interpretation, though they never used the term as a name for their
shared ideas. Like logical positivism and pragmatism, the Copenhagen interpretation
is not a unified idea and the views of the initiators changed over time. This article is
concerned with Bohr’s ideas on the Copenhagen interpretation subsequent to the Ein-
stein–Podolski–Rosen (EPR) article.
Bohr thought of quantum mechanics as a generalization of classical physics, even
though quantum mechanics violates some of the fundamental ontological principles
Reza Maleeh is at the School of History, Philosophy, Religion and Classics, University of Queensland. Correspon-
dence to: School of History, Philosophy, Religion and Classics, University of Queensland, St Lucia, QLD 4072,
Australia. E-mail: [email protected]. Parisa Amani is at the Department of Physical Chemistry, Khajeh Nasir
Toosi University of Technology. Correspondence to: Department of Physical Chemistry, Khajeh Nasir Toosi
University of Technology, P.O. Box 16315-1618, Tehran, Iran. E-mail: [email protected]
International Studies in the Philosophy of Science, 2013Vol. 27, No. 4, 353–367, http://dx.doi.org/10.1080/02698595.2013.868182
© 2014 Open Society Foundation
Dow
nloa
ded
by [
Uni
vers
ity o
f Su
ssex
Lib
rary
] at
07:
33 1
8 A
ugus
t 201
4
on which classical physics rested. Bohr’s semi-classical atomic model, presented in
1913, violated the principles of continuity and determinism. The principle of continu-
ity holds that there are necessarily intervening states between every distinguished
initial and final states, through which all processes have to go. According to Bohr’s
semi-classical model, by contrast, there is no definite intermediate place through
which the electron passes in its transition from one orbit to another. In classical
physics, the principle of determinism claims that the earlier state of a system uniquely
determines the later state of that system. In Bohr’s model, however, transition between
orbits (between the ground state and an exited state) takes place based on intrinsic
chance, making it impossible to predict when the transition occurs.
Between 1913 and 1925, the above atomic model was subject to some improvement.
However, it ran into problems when one tried to apply it to spectra other than that of
hydrogen. By 1925, Heisenberg had formulated a consistent quantum mechanics,
replacing Bohr’s model by a non-classical model with the aid of principles of
quantum mechanics. However, Bohr and Heisenberg never totally agreed on how to
interpret and understand the mathematical formalism of quantum mechanics as
well as certain atomic phenomena. This is why there is no homogenous Copenhagen
interpretation. In this article, by the term ‘Copenhagen interpretation’ we refer to
Bohr’s post-EPR ideas on indeterminism, his correspondence principle, his comple-
mentarity interpretation of certain atomic phenomena, and Born’s statistical interpret-
ation of the wave function.
During the last few decades, much has been written on Bohr’s interpretation of
quantum mechanics. Some philosophers and scientists have depicted it as a positiv-
istic, subjectivistic, or operationalist philosophy. As Jan Faye (2008) puts it, today phi-
losophers have reached a consensus that Bohr’s philosophy is neither positivistic nor
subjectivistic, although it may contain some elements of these two schools. In this
article, we compare the elements shared between the Copenhagen interpretation
and logical positivism on the one hand and the Copenhagen interpretation and prag-
matism on the other. Then we will conclude that while there are positivistic and oper-
ationalist components in pragmatism, pragmatism goes beyond other schools in
supporting the Copenhagen interpretation, especially when it comes to ‘complemen-
tarity’ as the core of Bohr’s version of the Copenhagen interpretation.1
Like the Copenhagen interpretation, logical positivism and pragmatism are not
unified ideas. Within each school, apart from the change of thinkers’ views over
time, thinkers differed from one another, often sharply. By ‘logical positivism’, we
mostly mean the ideas shared among the left wing of the Vienna Circle, which
included Otto Neurath, Hans Hahn, Phillip Frank, and Rudolf Carnap. What the thin-
kers in the left wing shared was the rejection of radical verificationism, initiated by
Carnap in the mid-1930s. Such a significant change in the left wing’s position is
known as the ‘liberalization of empiricism’, the core of which is what Carnap (1937)
dubbed the principle of tolerance.
For Charles Sanders Peirce and William James, the core of pragmatism is the prag-
matic maxim, according to which the contents of hypotheses are clarified by their
‘practical consequences’. Christopher Hookway (2008) distinguishes two senses of
354 R. Maleeh and P. Amani
Dow
nloa
ded
by [
Uni
vers
ity o
f Su
ssex
Lib
rary
] at
07:
33 1
8 A
ugus
t 201
4
pragmatism: a narrow sense and a wide sense. The narrow sense refers to Peirce’s prag-
matic maxim (or Peirce’s principle) and to those who embrace such a principle. Peirce
and James count as pragmatists in the narrow sense. However, pragmatism can be
thought of as a tradition embracing thinkers somewhat sceptical of the maxim and
its application while holding a set of philosophical views and approaches that are
characteristic of pragmatism. Such thinkers are pragmatists in the wider sense.
In this article, we will deal with certain key elements of the thought of Peirce and
with aspects of James’s thought that are in line with those elements, that is, the prag-
matic maxim, instrumentalism, and tychism, according to which there is an objective
feature of spontaneous chance activity in nature free from the exact and necessary dic-
tates of mechanical laws. By the term ‘pragmatists’, then, we refer to those who endorse
such elements.
Section 2 deals with the shared elements between the three schools, that is, the
Copenhagen interpretation, logical positivism, and pragmatism. As stated above,
pragmatism goes beyond logical positivism in supporting the Copenhagen interpret-
ation philosophically, having more elements in common with the Copenhagen
interpretation. In section 3, we discuss such an idea. In section 4, then, we conclude
that pragmatism is the closest approximation to a philosophical classification of the
Copenhagen interpretation.
2. Shared Concepts
In what follows, we try to pin down the shared ideas between the three schools: ideas
on empirical reality and weak objectivity, fallibilism, holism, and instrumentalism.
2.1. Empirical Reality and Weak Objectivity
One of the key elements of the Copenhagen interpretation is its commitment to the
notion of ‘weak objectivity’. Weak objectivity holds that, when faced by a specified
experimental set-up, scientists can unambiguously agree on what can and what
cannot happen (Lindley 1996, 159–160). The view advocates an empirical reality
that is not independent of the observer, but is the same for all observers. In other
words, empirical reality is the reality that cannot be separated from experience and
depends on subjects in order to have the weak objectivity characterized by intersubjec-
tivity. Empirical reality rejects the concept of ‘thing in itself ’ as meaningless. For Bohr,
‘objective’ means ‘intersubjectively valid’ as distinct from the object’s pre-existing
properties (Murdoch 1987, 105). According to Bohr, the
description of atomic phenomena has in these respects a perfectly objective charac-ter, in the sense that no explicit reference is made to any individual observer and thattherefore, with proper regard to relativistic exigencies, no ambiguity is involved inthe communication of information. (Bohr 1963, 3)
According to Aage Petersen, Bohr holds that ‘there is no quantum world. There is only
an abstract quantum physical description. It is wrong to think that the task of physics
International Studies in the Philosophy of Science 355
Dow
nloa
ded
by [
Uni
vers
ity o
f Su
ssex
Lib
rary
] at
07:
33 1
8 A
ugus
t 201
4
is to find out how nature is. Physics concerns what we can say about nature’ (Petersen
1963, 9). We will come back to the notion of empirical reality in section 2.3.
Logical positivism takes a similar attitude. The most distinguishing doctrine of the
members of the Vienna Circle was the ‘verifiability principle’ as a criterion for the
meaningfulness of statements. Logical positivists divided all meaningful statements
into two classes: analytic a priori and synthetic a posteriori. The former are true or
false in virtue of their logical forms or their meaning, whereas the truth or falsity of
the latter is ascertained only by means of experience. Thus, the synthetic statements
of the empirical sciences are cognitively meaningful if they are testable in some
sense. This way construed, statements whose truth or falsity is not in their logical
forms or meaning and which are not experimentally testable are considered
meaningless.
Logical positivism holds that all metaphysical and normative moral claims would
count as meaningless as well as statements about a ‘thing in itself ’, as there is no
way to test them experimentally in principle. In this regard, A. J. Ayer states that
the ‘originality of the logical positivists lay in their making the impossibility of meta-
physics depend not upon the nature of what could be known but upon the nature of
what could be said’ (Ayer 1959, 11). This is very close to Bohr’s attitude quoted earlier.
With regard to the meaningfulness of statements, Ayer proposes that
a sentence is factually significant to any given person, if, and only if, he knows howto verify the proposition which it purports to express, that is, if he knows whatobservations would lead him, under certain conditions, to accept the propositionas being true, or reject it as being false. (Ayer 1952, 35)
Then Ayer proceeds with more clarifications about factual propositions. According to
him, the mark of a genuine factual proposition is that, in conjunction with certain
other premises, some experiential propositions can be deduced from it, the experien-
tial propositions being not in principle deducible from those other premises alone
(Ayer 1952, 38–39). The proponents of such a view are regarded as the advocates of
‘experimental reality’, meaning that repeating an experimental procedure leads to
observing the same phenomena. As stated above, this is the view that logical positivism
advocates.
Later, logical positivism faced serious criticism regarding the impossibility of exact
verifiability of a statement. Carnap was one of the key figures of the Vienna Circle who
first noticed the impotence of verifiability. Through his ‘liberalization of empiricism’,
he substituted ‘verification’ for ‘degrees of confirmation’.2
Pragmatism also espouses the ideas of empirical reality and weak objectivity. For
Peirce and James, the core of pragmatism is the ‘pragmatic maxim’, according to
which the contents of a hypothesis can be clarified by means of tracing its practical
consequences. For a perfect clarification of our ideas about any subject, we just
need to know what imaginary practical consequences it can have and what effects
we can expect from it. In other words, for extending a mental conception, we just
need to determine to what behaviour such a conception is supposed to apply. That
behaviour, then, is the unique meaning of that conception for us. In his opinion,
356 R. Maleeh and P. Amani
Dow
nloa
ded
by [
Uni
vers
ity o
f Su
ssex
Lib
rary
] at
07:
33 1
8 A
ugus
t 201
4
‘our idea of anything is our idea of its sensible effects’ (Peirce [1878] 1992, sec. 2). In
Peirce’s view, we have no conception of any quality of objects, unless through the con-
ceived effects; for example, there would be a difference between a hard thing and a soft
thing only if they were brought to a test.
According to Peirce, we have to ‘consider what effects, which might conceivably
have practical bearings, we conceive the object of our conception to have. Then, our
conception of these effects is the whole of our conception of the object’ (Peirce
[1878] 1992, sec. 2). Peirce, like James, embraced the idea of absurdity of a priori onto-
logical metaphysics as well as the absurdity of the concept of the ‘thing in itself ’. He
holds that the application of some conceptions can serve as a barrier to effective inves-
tigation. The pragmatic maxim
will serve to show that almost every proposition of ontological metaphysics is eithermeaningless gibberish—one word being defined by other words, and they by stillothers, without any real conception ever being reached—or else is downrightabsurd. . . . All such rubbish being swept away, what will remain of philosophywill be a series of problems capable of investigation by the observational methodsof the true sciences. . . . So, instead of merely jeering at metaphysics, . . . the pragma-ticist extracts from it a precious essence, which will serve to give life and light to cos-mology and physics. (Peirce 1931–1935, vol. 5, para. 523)
2.2. Fallibilism
Pragmatists advocate ‘fallibilism’, the view that in principle all beliefs and methods
could turn out to be flawed. This doctrine completely dominates Peirce’s thoughts
according to which knowledge is never certain, but is always hypothetical and suscep-
tible to correction. Fallibilism is the acceptance of the idea that since our experimental
knowledge can be altered and reconsidered by later observations, it may be that all our
current knowledge is false.
Regarding the reconsideration of our experimental knowledge, Peirce proposes that
nothing is vital for science; nothing can be. Its accepted propositions, therefore, arebut opinions at most; and the whole list is provisional. The scientific man is not inthe least wedded to his conclusions. He risks nothing upon them. He stands ready toabandon one or all as soon as experience opposes them. (Peirce 1931–1935, vol. 1,para. 635)
Bohr and logical positivists both conceded fallibilism, though they never used the
term. The Copenhagen interpretation regards theories as tools that are subject to
alteration or replacement with more practical theories with respect to the investigation
purposes and goals.3
In a similar manner, Carnap believed in the openness of scientific statements. In
1937, he remarked that there was no statement (even mathematical) immune to altera-
tion and modification:
No rule of the physical language is definitive; all rules are laid down with the reser-vation that they may be altered as soon as it seems expedient to do so. This appliesnot only to the P-rules but also to the L-rules, including those of mathematics. In
International Studies in the Philosophy of Science 357
Dow
nloa
ded
by [
Uni
vers
ity o
f Su
ssex
Lib
rary
] at
07:
33 1
8 A
ugus
t 201
4
this respect, there are only differences in degree; certain rules are more difficult torenounce than others. (Carnap 1937, 318)
‘L-rules’ and ‘P-rules’ refer to ‘logical rules’ and ‘empirical rules’, respectively.
2.3. Wholeness and Holism
After the EPR article, Bohr gave up speaking of ‘disturbance’ in relation to the
‘uncertainty principle’, since the notion seemed to indicate that elementary particles
were classical particles with definite inherent kinematic and dynamic properties. The
post-EPR Bohr also gave up using the notion of complementary descriptions in
favour of complementary phenomena or information. ‘Phenomena’ in Bohr’s
mature view refer to experimentally observed effects of quantum objects upon
measuring instruments, not to the physical space–time properties of such objects
themselves or their behaviour. The representations of such interactions between
quantum objects and measuring instruments would then be describable and inter-
subjectively communicable in terms of classical concepts. A ‘phenomenon’ is a
measurement of the values of complementary properties that requires a complete
description of the entire experimental set-up. By using the new concepts, Bohr
emphasizes ‘the impossibility of any sharp separation between the behavior of
atomic objects and the interaction with the measuring instruments which serve to
define the conditions under which the phenomena appear’. Thus, according to
Bohr, phenomena are individual in the sense that ‘any attempt of subdividing the
phenomena will demand a change in the experimental arrangements introducing
new possibilities of interaction between objects and measuring instruments’
(Bohr 1949, 39–40).
Bohr’s notion of individual phenomena in the quantum world indicates his com-
mitment to the notion of ‘wholeness’, according to which, at the quantum level,
quantum objects are inseparable from measuring instruments. It is not possible to sub-
divide Bohr’s individual phenomena. This is the specific characteristic of experimen-
tation in the quantum domain embraced by the Copenhagen interpretation. At a
macrolevel, however, the object under observation and the measuring instrument
can count as separate entities. The notion of wholeness can further be explicated
through the Stern–Gerlach (SG) experiment.
The SG experiment, prepared and carried out by Otto Stern and his junior col-
laborator Walther Gerlach, established experimentally the so-called quantization of
angular momentum and therefore the discreteness of the magnetic moment of
atomic particles. The experiment can also be used to demonstrate the specific
role of measurement in quantum mechanics and the inseparability of quantum
objects from measuring instruments. This is what we are concerned with in this
article.
In the SG experiment, a beam of particles, say electrons, passing through an
inhomogeneous magnetic field is deflected from its initial trajectory. Electrons will
be deflected up or down, showing that they have an intrinsic angular momentum
that takes only certain quantized values, known as their spins.
358 R. Maleeh and P. Amani
Dow
nloa
ded
by [
Uni
vers
ity o
f Su
ssex
Lib
rary
] at
07:
33 1
8 A
ugus
t 201
4
Electrons are spin 212 particles, meaning that there are only two possible spin
angular momentum values measured along any axis, +h̄/2 and 2h̄/2. A detector, as
our observation device, will let us observe one of the two possible values, that is,
spin-up or spin-down. This can be shown by the angular momentum quantum
number j.4
Conducting the experiment along the z-axis, the corresponding angular
momentum operator will be Jz. Mathematically, all this can be formulated as follows:
C| l = c1
∣∣C j=+�h
2l + c2
∣∣C j=−�h
2l
Figure 1(a) shows a beam of electrons passing through an SG apparatus along the
z-axis with the blocked spin-down channel, resulting in spin-up detection. If the
spin-up beam of electrons is passed through a second similar SG device, it will be
observed that all electrons come out again in one beam with spin-up electrons.
Figure 1 The Stern–Gerlach experiment: (a) alignment Z+/Z; (b) alignment Z+/X; and (c) alignment Z+/X+/Z.
International Studies in the Philosophy of Science 359
Dow
nloa
ded
by [
Uni
vers
ity o
f Su
ssex
Lib
rary
] at
07:
33 1
8 A
ugus
t 201
4
Now, as shown in Figure 1(b), if the resulting beam coming out of the first SG appar-
atus is passed through a second SG device with its magnetic field aligned with x, the
outcome will be shocking: two beams of spin-up and spin-down electrons with
equal numbers of electrons are detected as if the first SG apparatus were not present.
In the third scenario, illustrated in Figure 1(c), the spin-down channel of the second
SG device in Figure 1(b) is blocked and the spin-up beam of electrons along the x-axis is
passed through a third SG device with its magnetic field aligned with z. There will again
be a weird outcome: two beams of spin-up and spin-down electrons with equal number
of electrons are detected as if the first and the second SG devices were not present.
The moral of all this is that the behaviour of atomic objects is not separable from the
performance of a well-defined measurement in the presence of a well-defined measur-
ing instrument. In this sense, atomic objects and the measuring instruments are part of
an inseparable whole (wholeness). The notion of wholeness in the Copenhagen
interpretation is not an idea shared with logical positivism and pragmatism.
In a more general manner, however, the notion of wholeness emphasizes the idea of
empirical realism through the notion of (what we call) ‘holism’, the idea that is shared
with logical positivists and pragmatists and will be depicted as follows. Bohr, like
logical positivists and pragmatists, held that physical reality, detached from the
human mind’s perceptual capacities, is not graspable. According to Bohr, we experi-
ence (represent) the real world of external objects through our senses. This reality
exists independently of its being represented. It is the existence of such an objective
real world, common to all experiential subjects, that makes intersubjective communi-
cation possible in an unambiguous way through classical concepts.
However, as Dugald Murdoch puts it, for Bohr, while the truth value of an exper-
imental statement is independent of our knowledge and perception,
it is not also independent of our ability to know or means of knowing its truth-value, since our means of knowing are simply the experimental arrangement andthe measurement procedure which defines the preconditions of the meaningfulassertability of the sentence in question; and the truth-value is not independentof what we do. (Murdoch 1987, 215)
According to this view, Bohr is neither a naive realist nor radical empiricist, but what
we earlier called an empirical realist.5
The empirical realist component present in Bohr’s philosophy, as well as in logical
positivism and pragmatism, leads to a notion of ‘holism’, meaning that we do not have
any idea of something, e.g. a physical entity, unless it affects our senses under well-
defined experimental conditions. This requires that the entity under observation,
the measuring instrument, and the observer be parts of a whole. The way nature
appears to us depends on our investigative method and on the way we set up instru-
ments to observe it. Holism is a view common to all three schools.
2.4. Instrumentalism
Bohr holds a non-realist view when it comes to the applicability of a theory of pure
mathematics to the real physical world, seeing the value of such a theory as primarily
360 R. Maleeh and P. Amani
Dow
nloa
ded
by [
Uni
vers
ity o
f Su
ssex
Lib
rary
] at
07:
33 1
8 A
ugus
t 201
4
instrumental. Such a theory would be a useful tool for organizing our observations and
making predictions under well-defined conditions. Bohr is highly sceptical of the view
that the physical world can be uniquely described by some theory of pure mathematics.
By the same token, the mathematical formalism of quantum mechanics, according
to Bohr, does not give us any ‘pictorial’ representation of the world; such a formalism
includes imaginary quantities that do not have any real-world counterparts. While
parts of measuring instruments can be described by means of classical physics, it is
impossible to describe quantum objects in terms of a classical or quantum mechanical
formalism. Quantum formalism is able only to predict the outcome of experiments in
question, but is unable to describe or account for the underlying quantum processes
leading to the observable effects.
The entire formalism is to be considered as a tool for deriving predictions of definiteor statistical character, as regards information obtainable under experimental con-ditions described in classical terms and specified by means of parameters enteringinto the algebraic or differential equations of which the matrices or the wave-func-tions, respectively, are solutions. These symbols themselves, as is indicated alreadyby the use of imaginary numbers, are not susceptible to pictorial interpretation;and even derived real functions like densities and currents are only to be regardedas expressing the probabilities for the occurrence of individual events observableunder well-defined experimental conditions. (Bohr 1948, 144)
Logical positivism has a similar approach to this notion. Logical positivists hold that
scientific theories are just tools for prediction and the knowledge we acquire from
them is limited to what they predict about the observational features of observables.
Scientific theories are instruments that can be replaced by better theories where pre-
ferred. Later Carnap speaks of different language frameworks, suggesting that one
should choose a framework with respect to the specific application and usefulness
of the framework one has in mind. This led to the ‘principle of logical tolerance’,
according to which ‘everyone is free to use the language most suited to his purpose’
(Carnap 1963, 18). Projecting the ‘principle of tolerance’, Carnap emphasizes investi-
gating all practically useful forms, although it is important to distinguish between con-
structive and non-constructive definitions and proofs (Carnap 1963, 49).
Pragmatism endorses a similar idea. James believed that a scientific theory is to be
understood as ‘an instrument: it is designed to achieve a purpose—to facilitate action
or increase understanding’ (James [1907] 1975, 33). Any scientific theory is assessed
based on how well it can be used for the extension of our experiences and it can
reduce those experiences to a judgement and extend and coordinate our experiences.
James criticized the traditional view of early scientists according to which ‘clearness,
beauty, and simplification’ of their theories sufficed to think that they had discovered
the final truth (James [1907] 1975, 31). Indeed, contemporary scientists stress the
practical usefulness of theories.
Thus, no theory is the absolute transcript of reality. Each theory may be useful from
some point of view (James [1907] 1975, 33). For James, this makes concepts and the-
ories instruments whose practical usefulness depends on how well they achieve the
intended goal (Hookway 2008).
International Studies in the Philosophy of Science 361
Dow
nloa
ded
by [
Uni
vers
ity o
f Su
ssex
Lib
rary
] at
07:
33 1
8 A
ugus
t 201
4
It is seen that the mission that Bohr and James assign to science has nothing to do
with the essence of objects. A scientific theory is to be understood as just an instru-
ment. This idea is in line with the idea projected by logical positivists.6
So far we have proposed a selection of key elements, common between the Copen-
hagen interpretation, logical positivism, and pragmatism. In what follows, it is shown
that there are some other key elements of the Copenhagen interpretation shared only
with pragmatism, not supported by logical positivism.
3. Pragmatism Goes Beyond
In this section, we see how pragmatism goes beyond logical positivism in support of
the Copenhagen interpretation. The following elements are common only between
pragmatism and the Copenhagen interpretation.
3.1. Correspondence Rule
The full correspondence rule indicates that the transition between stationary states in
atoms is permitted if and only if there is a corresponding harmonic component in the
classical motion (Bohr 1972–2008, 479). For Bohr, the rule was required for the con-
struction of a theory of quantum mechanics and further development of it in such a
way that in high quantum numbers it predicts values that are a close approximation to
the values of classical physics: ‘The whole apparatus of the quantum mechanics can be
regarded as a precise formulation of the tendencies embodied in the correspondence
principle’ (Bohr 1925, 49). However, the introduction of the non-classical concept of
spin, which did not have any classical counterpart, was a fatal blow to the correspon-
dence principle. It was not possible to reconcile classical periodic motion presumed by
the correspondence principle with the classically non-describable electron spin.
But Bohr did not give up on the principle, thinking of it as a methodological argu-
ment for establishing a coherent quantum theory. He thought of the principle as a
guideline for Heisenberg’s matrix mechanics:
A fundamental step towards the establishing of a proper quantum mechanics wastaken in 1925 by Heisenberg who showed how to replace the ordinary kinematicalconcepts, in the spirit of the correspondence argument, by symbols referring to theelementary processes and the probability of their occurrence. (Bohr 1937, 48)
Bohr sees the principle as a method whose choice is practically useful as a guide to find
a satisfactory quantum theory. Furthermore, the correspondence principle strengthens
Bohr’s ideas on the significance of classical concepts. Indeed, the rule was based on the
epistemological idea of indispensability of classical concepts in understanding physical
reality. Such an understanding is possible only when classical and quantum phenom-
ena are described in the same classical concepts, so we can practically compare differ-
ent physical experiences.
[T]he necessity of making an extensive use . . . of the classical concepts, upon whichdepends ultimately the interpretation of all experience, gave rise to the formulation
362 R. Maleeh and P. Amani
Dow
nloa
ded
by [
Uni
vers
ity o
f Su
ssex
Lib
rary
] at
07:
33 1
8 A
ugus
t 201
4
of the so-called correspondence principle which expresses our endeavors to utilizeall the classical concepts by giving them a suitable quantum-theoretical re-interpret-ation. (Bohr 1934, 8)
To summarize, Bohr claims that the correspondence rule is a methodology that is prac-
tically useful for symbolizing a quantum theory, as a tool. Applying such a rule allows
us to deal with our experiences within the framework of classical concepts which con-
tains theoretical sentences of quantum mechanics and classical physics. So it is fair to
claim that Bohr kept the rule for pragmatic purposes or, in other words, the rule was
kept on the basis of Peirce’s ‘pragmatic maxim’.
3.2. Complementarity
Bohr’s complementarity holds that the ‘space–time descriptions’ of the atom are
complementary to the ‘claims of causality’, where the latter are interpreted in terms
of physics as the conservation of energy and momentum. In other words, we can attri-
bute kinematic and dynamic properties to the atom only by reference to an exper-
imental outcome.
Quantum objects in Bohr’s eyes are indefinable. That is, Heisenberg’s uncertainty
relations set not only a limit to ‘the extent of the information obtainable by measure-
ments, but . . . also . . . a limit to the meaning which we may attribute to such infor-
mation’ (Bohr 1929, 18). Thus, not only cannot the exact position and momentum
of an object be measured simultaneously, but also the object cannot meaningfully be
said to have exact simultaneous values of these observables. According to Bohr, the
properties of simultaneous exact position and exact momentum cannot be meaning-
fully attributed to one and the same object, since the preconditions for the meaningful
attribution of these properties are mutually exclusive:
Indeed we have in each experimental arrangement suited for the study of properquantum phenomena not merely to do with an ignorance of the value of certainphysical quantities, but with the impossibility of defining these quantities in anunambiguous way. (Bohr 1935, 699)
Such preconditions are determined by the experimental arrangement, i.e. a measuring
instrument as a necessary condition for meaningful applicability of the physical con-
cepts. The sufficient conditions for the meaningful assertability, however, are satisfied
by a phenomenon in Bohr’s technical sense earlier described. A phenomenon is the
performance of well-defined measurement in the presence of a well-defined measuring
instrument.
This shows that Bohr’s theory of meaning includes verificationist or confirmationist
element. However, following Murdoch, we defend the idea that Bohr’s theory of
meaning is based not on logical positivism, but on pragmatism. Simultaneous attribu-
tion of kinematic and dynamic properties to quantum objects is meaningless not prin-
cipally because such properties are simultaneously unobservable, but because such
attribution has no practical consequences. Such an attribution has neither explanatory
nor predictive power. It does not do anything, as a pragmatist would put it.
International Studies in the Philosophy of Science 363
Dow
nloa
ded
by [
Uni
vers
ity o
f Su
ssex
Lib
rary
] at
07:
33 1
8 A
ugus
t 201
4
Unverifiability of simultaneous attribution of kinematic and dynamic properties is
only one factor, among others, which makes it meaningless to assert it:
The meaning of conditions, then, is not primarily epistemic but pragmatic, havingmore to do with what we as agents can do than with what we can know. Nevertheless,for Bohr the verifiability or confirmability of a statement is a necessary condition ofits meaningful assertability; and since experimental statements are verifiable or con-firmable only by means of some physical measurement operation, his theory has anoperationalist component. The operationalist component is already present inPeirce’s theory of meaning. (Murdoch 1987, 225)
Thus, the claim here is that Bohr’s theory of meaning, regarding complementarity, is
on the basis of the pragmatic maxim. The pragmatic maxim is a rational scheme for
rational conduct that should be understood and used within the framework of the
pragmatic theory of meaning.
3.3. Indeterminism
Bohr’s mature philosophy considers Heisenberg’s uncertainty principle as the ontologi-
cal consequence of his complementarity, not as arising from epistemological limit-
ations. In other words, in Bohr’s interpretation of quantum mechanics, the mutual
exclusivity of the position and momentum in the sense of complementarity leads to
the uncertainty relations. In his view, the role of measurement makes indeterminism
a consequence of the non-vanishing value of the quantum of action h. For Bohr, this is
the way nature works in the quantum realm. Such an idea is in line with Peirce’s
tychism, the idea that there is an objective feature of spontaneous chance activity in
nature free from the exact and necessary dictates of mechanical laws. Thus, Bohr’s
way of thinking of indeterminism shares some components with tychism in Peirce’s
philosophy.
However, there are important differences between Peirce’s tychism and indetermi-
nacy in Bohr’s philosophy. Given that Peirce was not alive by the time of the com-
pletion of the quantum formalism by Heisenberg (he died in 1914), his proposal
regarding quantum indeterminacy could at best be that at the microlevel, all physical
properties are indeterminate, not complementary pairs as is in the case of quantum
mechanics.
Another difference between Peirce’s tychistic vision of a world incorporating real
absolute chance and the objective indeterminacy revealed by Bohr’s philosophy of
quantum mechanics is that in the former, laws of nature must be products of evol-
ution.7
However, in Bohr’s philosophy, there is no reason to think that the basic
physical laws, which are of an objectively probabilistic nature, must have an evol-
utionary history of the kind supposed by Peirce. Quantum mechanics predicts, in
a particular statistical way, the outcome of the effects of quantum objects upon the
measuring instruments. In doing so, there is no need to bother to speculate
whether such fundamental laws have changed over time or they have always been
as they are.
364 R. Maleeh and P. Amani
Dow
nloa
ded
by [
Uni
vers
ity o
f Su
ssex
Lib
rary
] at
07:
33 1
8 A
ugus
t 201
4
4. Conclusion
This article claims that, if one were supposed to classify the Copenhagen interpret-
ation, the closest approximation would be to view it as a pragmatist philosophy.
However, identifying Bohr’s reading of the Copenhagen interpretation as pragmatist
is not reductionist. Such identification differs from, for example, Mara Beller’s
(1999) reading of Bohr’s philosophy where she claims that Bohr’s statements are intel-
ligible only if we consider him as a radical operationalist or simple-minded positivist.
The reason is clear: pragmatism already includes operationalist and verificationist
components but the converse of such a claim does not necessarily hold. Such an
inclusion leads pragmatism to share some elements with logical positivism in support-
ing the Copenhagen interpretation. These elements are empirical realism, fallibilism,
holism, and instrumentalism. In supporting the Copenhagen interpretation,
however, pragmatism goes beyond other schools: its pragmatic maxim supports
Bohr’s correspondence rule and complementarity, and Peirce’s notion of tychism
has some commonalities with indeterminism as embraced by the Copenhagen
interpretation.
Acknowledgements
This article would not have been possible without the tolerance and assistance of the
editor of this journal. Also, we wish to express our gratitude to the referees of the
journal for their detailed comments, which helped us to clarify and improve several
aspects of the manuscript. Finally, the first author would like to thank Phil Dowe of
the School of History, Philosophy, Religion and Classics, University of Queensland,
for his support and supervision.
Notes
[1] In doing so, we follow Murdoch’s (1987) reading of Bohr’s notion of complementarity,defending the idea that Bohr’s theory of meaning regarding the ultimate version of comple-mentarity is based on the pragmatic maxim, which itself should be seen within the frameworkof the pragmatic theory of meaning.
[2] The later Carnap’s empiricism has some important commonalities with Bohr’s philosophy.Bohr’s philosophy distinguishes between the symbolic language of the quantum formalism,which counts as a tool for prediction, and observation sentences that are visualizable inspace and time and refer to the so-called individual phenomena. This is similar to the distinc-tion that Carnap draws between the linguistic framework, which lacks empirical content, andobservation sentences within it whose truth or falsity must be verified empirically.
[3] Bohr’s correspondence rule has found another reading among some philosophers of science,referred to as the ‘generalized (or general) correspondence principle’. Post’s (1971) account ofthe principle is as follows: ‘any acceptable new theory L should account for the success of itspredecessor S by “degenerating” into that theory under those conditions under which S hasbeen well confirmed by tests’ (Post 1971, 228). However, there is no consensus among philo-sophers as to whether such a reading can apply to the quantum–classical relation. Forexample, Post himself believes that the generalized correspondence principle does not applyto the quantum–classical relation. He maintains that ‘paradoxically, the only counterexample
International Studies in the Philosophy of Science 365
Dow
nloa
ded
by [
Uni
vers
ity o
f Su
ssex
Lib
rary
] at
07:
33 1
8 A
ugus
t 201
4
we have been able to find to the General Correspondence Principle is the paradigm example ofthe relation of quantum mechanics to classical mechanics’ (Post 1971, 233). Radder (1991,215) rejects this claim, arguing that the generalized correspondence principle does apply tothe case of the quantum–classical relation. He sees Bohr’s correspondence principle as aninstance of the generalized correspondence principle. If Radder is correct, the principle willprovide, at least to the limited extent, a basis for a general account of theory change as arational process through ‘firstly the recognition and rejection of one of the presuppositionsof the old theory, and secondly its replacement by a new hypothesis and a new parameterwhich, when given a limiting value, enables the laws of the new theory’ (Murdoch 1987,243). It is plausible that Bohr, in establishing his correspondence rule, had the above under-standing of the general account of theory change in physics. If this is the case, then it can besaid that Bohr’s philosophy is in line with Peirce’s fallibilism.
[4] If s is the particle’s spin angular momentum and ℓ its orbital angular momentum vector, thenthe total angular momentum j is j ¼ s + ℓ.
[5] Faye (1991, 200) has a more or less similar idea. He calls Bohr’s position on realism ‘objectiveantirealism’, which just as realism operates with a notion of objectivity, and yet, unlike realism,maintains that only decidable statements possess ‘investigation-independent truth values’, notundecidable ones.
[6] However, instrumentalism as embraced by pragmatists differs from the instrumentalism in Car-napian empiricism in one major sense: whereas pragmatists do not draw any difference betweenanalytic and synthetic sentences with respect to their roles as instruments, for the later Carnaponly linguistic frameworks whose choice is a matter of practical needs are considered as instru-ments. The Carnapian version of instrumentalism does not apply to observation sentenceswhose truth or falseness must be verified empirically. In this respect, Bohr’s instrumentalismis closer to Carnapian empiricism than to pragmatism. For example, Bohr’s acceptance ofBorn’s statistical interpretation of the wave function stems from his belief that the c functionhas only a symbolic meaning and does not refer to anything real in the world.
[7] This is why Peirce’s notion of ‘synechism’ is not in line with Bohr’s philosophy: in synechism,everything is regarded as continuous.
References
Ayer, A. J. 1952. Language, Truth and Logic. New York: Dover.Ayer, A. J., ed. 1959. Logical Positivism. New York: Free Press.Beller, M. 1999. Quantum Dialogue: The Making of a Revolution. Chicago, IL: University of Chicago
Press.Bohr, N. 1925. “Atomic Theory and Mechanics.” In Philosophical Writings of Niels Bohr, edited by J.
Faye and H. J. Folse, vol. 1, 25–51. Woodbridge, CT: Ox Bow Press.Bohr, N. 1929. “Introductory Survey.” In Philosophical Writings of Niels Bohr, edited by J. Faye and H.
J. Folse, vol. 1, 1–24. Woodbridge, CT: Ox Bow Press.Bohr, N. 1934. “Atomic Theory and the Description of Nature.” In Philosophical Writings of Niels
Bohr, edited by J. Faye and H. J. Folse, vol. 1, 92–101. Woodbridge, CT: Ox Bow Press.Bohr, N. 1935. “Can Quantum-mechanical Description of Physical Reality Be Considered Com-
plete?” Physical Review 48: 696–702.Bohr, N. 1937. “Causality and Complementarity.” In Philosophical Writings of Niels Bohr, edited by J.
Faye and H. J. Folse, vol. 4, 83–91. Woodbridge, CT: Ox Bow Press.Bohr, N. 1948. “On the Notions of Causality and Complementarity.” In Philosophical Writings of
Niels Bohr, edited by J. Faye and H. J. Folse, vol. 4, 141–148. Woodbridge, CT: Ox Bow Press.Bohr, N. 1949. “Discussion with Einstein on Epistemological Problems in Atomic Physics.” In Phi-
losophical Writings of Niels Bohr, edited by J. Faye and H. J. Folse, vol. 2, 32–66. Woodbridge,CT: Ox Bow Press.
366 R. Maleeh and P. Amani
Dow
nloa
ded
by [
Uni
vers
ity o
f Su
ssex
Lib
rary
] at
07:
33 1
8 A
ugus
t 201
4
Bohr, N. 1963. Essays 1958–1962 on Atomic Physics and Human Knowledge. New York: Interscience.Bohr, N. 1972–2008. Collected Works. 13 vols. Amsterdam: Elsevier.Carnap, R. 1937. Logical Syntax of Language. Translated by A. Smeaton. London: Kegan, Paul,
Trench, Teubner & Co.Carnap, R. 1963. “Intellectual Autobiography.” In The Philosophy of Rudolf Carnap, edited by P. A.
Schilpp, 3–84. LaSalle: Open Court.Faye, J. 1991. Niels Bohr: His Heritage and Legacy. An Anti-realist View of Quantum Mechanics. Dor-
drecht: Kluwer.Faye, J. 2008. “Copenhagen Interpretation of Quantum Mechanics.” In Stanford Encyclopedia of Phil-
osophy, edited by E. N. Zalta. http://plato.stanford.edu/entries/qm-copenhagen. Accessed 15February 2013.
Hookway, C. 2008. “Pragmatism.” In Stanford Encyclopedia of Philosophy, edited by E. N. Zalta.http://plato.stanford.edu/entries/pragmatism. Accessed 15 February 2013.
James, W. [1907] 1975. Pragmatism: A New Name for Some Old Ways of Thinking. Cambridge, MA:Harvard University Press.
Lindley, D. 1996. Where Does the Weirdness Go? Why Quantum Mechanics Is Strange, But Not AsStrange As You Think. New York: Basic Books.
Murdoch, D. 1987. Niels Bohr’s Philosophy of Physics. Cambridge: Cambridge University Press.Peirce, C. S. [1878] 1992. “How to Make Our Ideas Clear.” In The Essential Peirce, edited by N.
Houser and C. Kloesel, vol. 1, 124–141. Bloomington: Indiana University Press.Peirce, C. S. 1931–1935. Collected Papers, edited by C. Hartshorne, P. Weiss, and A. W. Burks. 8 vols.
Cambridge, MA: Harvard University Press.Petersen, A. 1963. “The Philosophy of Niels Bohr.” Bulletin of the Atomic Scientists 19 (7): 8–14.Post, H. R. 1971. “Correspondence, Invariance and Heuristics: In Praise of Conservative Induction.”
Studies in History and Philosophy of Science 2: 213–255.Radder, H. 1991. “Heuristics and the Generalized Correspondence Principle.” British Journal for the
Philosophy of Science 42: 195–226.
International Studies in the Philosophy of Science 367
Dow
nloa
ded
by [
Uni
vers
ity o
f Su
ssex
Lib
rary
] at
07:
33 1
8 A
ugus
t 201
4
Dow
nloa
ded
by [
Uni
vers
ity o
f Su
ssex
Lib
rary
] at
07:
33 1
8 A
ugus
t 201
4
