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Explaining the splendour of science
Stud. Hist. Phil. Sci., Vol. 29, No. 1, pp. 155-165, 1998 0 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0039-3681/98 $19.00+0.00
Pergamon
ESSAYREVIEW Explaining the Splendour of Science Henk W. de Regt*
James W. McAllister, Beauty and Revolution in Science (Ithaca and London: Cornell University Press, 1996), xiv + 232 pp. ISBN o-8014-3240-5, Cloth, s29.95lE23.50. Why do scientists
regard certain theories as more beautiful
than others? How do
aesthetic evaluations affect scientific development? James McAllister has set himself the task of answering such questions by providing a general, systematic analysis of the aesthetic aspects of science. The result is Beauty and Revolution in Science, a sophisticated and insightful, yet highly readable book. McAllister endorses a ‘rationalist image of science’ (p. 7), asserting the existence of certain universal, rational rules for practising science. His aim is to reconcile this rationalist image with two recalcitrant features of actual science: the fact that scientists evaluate theories on their aesthetic merits, and the occurrence of revolutions in scientific development. To this end he introduces a division of criteria for theory choice
into ‘logico-empirical
criteria’
and ‘aesthetic
criteria’.
Prime
examples of the former are ‘consistency with extant empirical data’ and ‘internal consistency’, while the latter may include such diverse items as ‘symmetry’, ‘visualizability’
and ‘consistency
ter contends
that both sorts of criteria can have a rational justification,
with an accepted metaphysical
worldview’.
McAlliscontrary to
the accepted opinion that aesthetic criteria introduce a subjective and therefore irrational element into theory choice. This justification proceeds, however, in two essentially different ways. Logico-empirical criteria are warranted through ‘goal analysis’: from the goal of science we can derive these criteria as being necessary
* Department of History and Foundations of Mathematics and Science, University Box 80.000, 3508 TA, Utrecht, The Netherlands (email: [email protected]).
PII: SOO39-3681(97)00026-5 155
of Utrecht, P.O.
156
Studies in History and Philosophy of Science
presuppositions ‘formulating adequacy,
for its achievement theories
that possess
(McAllister
specifies the goal of science
the highest
possible
or truth’ p. 76). Rational justification
can be attained through ‘inductive projection’: choice has been conducive
degrees
as
of empirical
of aesthetic criteria, by contrast,
when a particular criterion for theory
to the goal of science so far, we may inductively
con-
clude that it will remain so when applied in future cases. This leads to the central thesis of McAllister’s book, to wit that scientists’ aesthetic preferences are formed and updated by the ‘aesthetic induction’: ‘A community compiles its aesthetic canon at a certain date by attaching to each property a weighting
proportional
to the degree of empirical
adequacy then attributed to the
set of current and recent theories that have exhibited that property’ (p. 78). This implies that there exists a correlation between empirical and aesthetic values, albeit in a rather indirect way. Thus, when scientists appraise a theory, they evaluate it both on its empirical
and on its aesthetic merits. The latter evaluation
reflects the
empirical performance of earlier theories with the same aesthetic properties. A clear example of this process, cited by McAllister (pp. 56-58) is the rise and fall of Cartesian corpuscularism.
A central metaphysical
principle
of corpuscularism
was
the rejection of all ‘occult’ properties such as active powers and action at a distance; only contact action was admitted as an explanatory principle. The great empirical successes of this approach, compared with the earlier theories of alchemists and astrologers,
lead to the firm establishment
of its aesthetic canon. When Newton
formulated his law of gravitation, his inductively formed aesthetic sense told him that the law needed a corpuscularist explanation of the apparent action at a distance. As is well known, extremely
successful
he did not succeed. at the empirical
His theory, however,
turned out to be
level. This caused a change in the aesthetic
canon, which was updated by aesthetic induction: tance was not regarded as ugly and unintelligible
after some time action at a disanymore. Indeed, Newton himself
later did not hesitate to speak of active powers of matter. In the eighteenth century, action at a distance became an accepted property of matter and Newton’s law of gravitation
a paradigmatic
form of explanation.
As a kind of corollary to his thesis of the aesthetic induction, a new model of scientific revolutions.
McAllister
Aesthetic canons are essentially
presents
conservative,
since they reflect the properties of past theories. They can be updated by aesthetic induction, but this is always a gradual change. However, in some situations of theory choice, when it appears quite difficult to find a theory which conforms to the extant aesthetic canon, one may witness a scientific revolution. According to McAllister, a revolution always consists in an ‘aesthetic rupture’ (p. 125). That is to say, the scientific community decides to adopt a theory which is empirically successful but aesthetically displeasing, and accordingly it decides to abandon the established aesthetic canon. After some time, of course, the aesthetic induction will operate again and a new canon will be formed. McAllister presents case studies to support this model of science, particularly
of scientific
revolutions.
Analysing
Explaining the Splendour of Science
four (allegedly)
revolutionary
157
episodes
only two of them are real revolutions two are not (Copernicus,
relativity
in the history of science, (Kepler, quantum
theory).
In this review I will focus on two aspects of McAllister’s critically
discuss his analysis
he argues that
theory), while the other
of scientific
revolutions,
book. First, I will
comparing
its merits with
those of Kuhn’s well known account. Secondly, I will attempt to apply McAllister’s model to the issue of intelligibility in science: if we demand that scientific theories provide understanding, and if we specify (necessary) criteria for intelligibility, should these be regarded as aesthetic criteria, and would they comply with McAllister’s analysis? 1. Aesthetic Canons and Scientific Revolutions Aesthetic
canons
induce scientists
to tread known paths, to formulate
theories
with familiar features. Only when a problem or an unexpected discovery stubbornly resists explanation along aesthetically pleasing lines, this conservatism may give way to a scientific revolution. McAllister accepts the occurrence of revolutions in science as a historical fact, and he claims that his account of scientific revolutions provides the best explanation of them. In particular, he contrasts his view of revolutions as ‘aesthetic ruptures’ with the classic account of Thomas Kuhn (1970). There appear to be two major differences between McAllister’s model of revolutions and Kuhn’s, First, McAllister holds that his model, in contrast to Kuhn’s, explains both the continuity and the radical changes exhibited by scientific development. Secondly, the role of aesthetic values is precisely opposite in the two models: in Kuhn’s view they induce revolutions, whereas in McAllister’s view they inhibit revolutions. detail. McAllister
Let us consider
McAllister’s
claims that a great advantage
arguments
on these two points in more
of his model is that it can account for
the radical breaks which scientific revolutions are, while still allowing for some continuity in such processes. His distinction between two sets of criteria for theory choice makes this possible: in a revolution
the set of aesthetic criteria is abandoned,
whereas the set of empirical criteria remains unchanged. Kuhn is allegedly unable to account for this aspect of scientific development, because he treats all criteria on a par. I believe, however, that McAllister is attacking a straw man here. Kuhn’s actual views are more sophisticated and do allow for continuity and rupture as well. According to McAllister (p. 126), the fact that revolutions occur, compels any model of science to meet four obligations, among which are: (a) it ‘must acknowledge that a scientific revolution constitutes a radical transformation in a community’s criteria for theory choice’; and (b) ‘revolutions should not be portrayed as being so deep that they leave no element of scientific practice unchanged’. Subsequently, he claims that Kuhn’s writings can be interpreted in two different ways, where under one interpretation only obligation (a) is fulfilled, while under the other only (b) is met. The first is the familiar radical interpretation of Kuhn’s
Studies in History and Philosophy of Science
158
original
1962 text, asserting that a paradigm-shift
introduces
a completely
new set
of criteria. This would imply that, to quote a famous phrase, ‘the proponents competing
paradigms
practice
150), and that, accordingly, of ‘incommensurability’.
their trades in different
communication
Obviously,
between
worlds’
(Kuhn,
them is impossible
this radical interpretation
of
1970, p. because
conflicts with obli-
gation (b). In later writings, however, Kuhn has attempted to mitigate such radical conclusions. Particularly in his ‘Objectivity, Value Judgment, and Theory Choice’ (1977), he emphasises that ‘trans-paradigmatic’ exist. He mentions five: accuracy, consistency,
criteria for theory evaluation also scope, simplicity, and fruitfulness.
Explicitly endorsing the traditional view in this respect, Kuhn (1977, p. 322) deems these criteria as belonging to ‘the shared basis for theory choice’. McAllister classifies these moderate remarks as a second interpretation of Kuhn, which is opposed to the radical Kuhn. This moderate interpretation then fails to meet obligation (a), according to McAllister
(p. 127): ‘Unless Kuhn can identify some further category
of criteria for theory choice that are paradigm specific, it remains unclear how any deep transformations
in scientific practice can occur’.
It seems to me that this conclusion all, Kuhn’s mitigations account,
is drawn far too hastily, however.
should clearly be regarded as supplementary
not as replacing
it. Nowhere
First of
to his earlier
does Kuhn suggest that he withdraws
all
earlier claims concerning the deep changes that paradigm-shifts bring about. It is only the radical view that nothing remains the same across a paradigm change that he wishes to deny. While admitting
that scientific
development
is continuous
in
some respects, one can still hold that revolutions
cause serious changes in criteria
for theory choice. For example, the metaphysical
presuppositions
basis of a paradigm may change completely
which lie at the
(as, for instance, in the transition
from
the particle theory of light to the wave theory). This is clearly a paradigm-specific criterion
of the kind that McAllister
it is a criterion
which McAllister
asked for in the quotation
above. Moreover,
himself would classify as an aesthetic criterion.
Thus it seems that Kuhn would agree that it is the aesthetic criteria which change in revolutions.
Nevertheless,
he does not draw an explicit
and sharp distinction
between two sets of criteria. The reason for this will become clear from the following. There is an important
feature of the above-mentioned
‘trans-paradigmatic’
criteria, which is overlooked by McAllister and which provides additional evidence against his second, ‘moderate’ interpretation of Kuhn. Kuhn emphasises that these criteria do not function as rules but as values, for two reasons: they are not very precise and they may conflict with each other. Therefore, though criteria such as accuracy and consistency always play an important part in theory choice, the way in which they are applied may vary from one situation to another, and thus also from one paradigm to another. This implies that their status is not essentially different from that of paradigm-specific criteria: as regards permanence and immutability they differ merely in degree.
Explaining the Splendour of Science
This sophisticated the history McAllister
159
reading of Kuhn does explain both continuity
of science,
as does McAllister’s
model.
Indeed,
and rupture in
contrary
to what
wants us to believe, Kuhn’s view is not very different from his own in
this respect. A striking incommensurability
illustration
is provided
by McAllister’s
discussion
thesis. He criticizes Kuhn for holding untenable
of the
views on com-
munication between scientists in different paradigms, and he suggests that his own model entails only ‘partial incomprehension’ in such cases (p. 134). However, this latter view is similar to Kuhn’s account of ‘partial communication’ (1977, pp. 33% 339). I conclude that McAllister’s claim that his model is superior to Kuhn’s with respect to the issue of continuity
and rupture is unfounded.
Let us turn to the second major difference
between Kuhn’s model and McAllis-
ter’s, which is the impact of aesthetic values in revolutionary there exists
a real disagreement
McAllister
maintains
between
the authors.
periods. At this point As already
that aesthetic criteria have an essentially
mentioned,
conservative
func-
tion: they lead to theories which are similar to earlier ones. A scientific revolution occurs despite the existence of an aesthetic canon, and consists in its abandonment in favour of considerations despite empirical their claims
of mere empirical
considerations.
against
historical
one needs an independent
evidence,
criterion
of revolutions
McAllister
175-176) completely
for determining
precludes
apparently
in opposition
Unfortunately,
McAllister
is.
that either Kuhn or while McAllister
(pp.
proposal of a heliocentric
he claims that-precisely
for that reason-
to Kuhn’s view. criterion
does not explicitly
for identifying
scientific
provide such a criterion;
above. He introduces
revol-
on which ‘scientists adopt theories that differ radically
predecessors’
criterion because of its vagueness revolutionary?).
(p.
of testing. For example, in
apparent:
he is not aware of the problem mentioned
utions simply as occasions
himself
what a ‘real’ revolution
agrees with Kuhn that Copernicus’
we need a clear and independent
from their immediate
by McAllister
the possibility
theory was induced by aesthetic concerns,
revolutions.
and in a sense
arises: if one wants to conduct this test,
this problem is manifestly
it was not a revolution, Therefore,
as suggested
by means of the characteristics
suggest, obviously
the case of Copernicus
concerns,
Here one can assess the two models by testing
138). However, one difficulty immediately Identification
adequacy. By contrast, Kuhn’s model
only happen thanks to aesthetic
asserts that revolutions
(p. 125). Obviously,
this will not suffice as a
(Which difference is radical enough to be labelled
It seems, however,
that in his case studies McAllister
implicitly
employs a more specific criterion, namely the way in which the new theory was received by contemporary scientists. Thus, he argues that Copernicus’ theory was welcomed by mid-sixteenth century astronomers (see pp. 171-174) because of its aesthetic virtues. By contrast, Kepler’s model of the solar system at first met with severe resistance because of its ‘ugly’ ellipses. Only after some time, when its great empirical success had become clear, did the scientific community accept it
Studies in History and Philosophy of Science
160
(pp. 178-181).
The reception of the theory by the scientific community
to serve as a criterion to identify it as a revolution:
thus appears
a truly revolutionary
not easily accepted by contemporary scientists. Although I doubt whether this criterion is really adequate,
theory is
I contend that even
if one employs
it, some of McAllister’s own examples fail to support his model of revolutions. The examples I have in mind are his case studies in the history of modern physics: relativity theory and quantum theory. With respect to relativity theory, McAllister advances the unorthodox view that its development by Albert Einstein was not a scientific revolution. It is well known that Einstein’s motives for constructing relativity theory were not based on empirical problems but on aesthetic considerations. McAllister adds that Einstein derived these motives from an extant ‘classical’ aesthetic canon. He claims that both special and general relativity theory were therefore welcomed by the community (pp. 186 and 188) and concludes that they were not revolutionary. However, historian Lewis Pyenson has provided a detailed description of the reception of relativity in Germany which shows that the theory was not so easily accepted. Instead, the community of physicists was divided into advocates and opponents, engaging in heated debates, precisely as McAllister (pp. 13&l 3 1) predicts for revolutions. Around 19 11, its adversaries called relativity theory a ‘jest’ and both parties testified to the revolutionary character of Einstein’s theory (see Pyenson, 1987, pp. 78 and 66-68). Further evidence against McAllister’s thesis can be found in Paul Ehrenfest’s I9 12 inaugural lecture. Ehrenfest observed a ‘peculiar revolutionary atmosphere dominating theoretical physics at this moment’ (Ehrenfest, 1913, p. 3, my translation). In his analysis, the main problem was that experimental evidence provided by A. A. Michelson
contradicted
existing
theories of the ether, while the
ether hypothesis served as a basic presupposition of contemporary physics. In 1904, H. A. Lorentz had proposed a theory of molecular forces which reconciled the experiments with the ether-hypothesis. Einstein’s 1905 theory of special relativity, however, constituted a much more radical solution of the problem: Einstein simply rejected the ether hypothesis, replacing it by the revolutionary postulate of the constancy of the velocity of light, which Ehrenfest found difficult to grasp and to accept. It should be concluded, in my opinion, that even on McAllister’s own implicit criterion relativity theory did constitute a revolution. Since Einstein’s revolutionary proposal was inspired not by empirical but by aesthetic considerations (indeed, from the empirical point of view, Lorentz’s 1904 theory was equally acceptable), it is therefore a counter-example to McAllister’s model. Moreover, this example reveals that actual situations may be less straightforward than McAllister suggests. McAllister seems to hold that a theory is either aesthetically pleasing or not, and that appraisal of aesthetic merit is always conservative. But Einstein’s theory was aesthetically innovative in one respect, since it abandoned the ether hypothesis and the notion of absolute time, but conservative in another, as it was an attempt to enhance the symmetry of classical physics.
Explaining the Splendour of Science McAllister’s
second case study in the history of modem
genesis of quantum was a genuinely of revolutions
161
theory. He maintains,
revolutionary
science concerns
as does indeed everybody
episode, and he argues that it confirms
because it saw the abandonment
the
else, that this his model
of an aesthetic canon and the accept-
ance of a new theory purely on empirical grounds. Determinism and visualizability are presented as examples of aesthetic criteria which were repudiated in the quantum revolution.
Although
the actual situation
this is a plausible
was more complex
account
to some extent, I think that
and that aesthetic factors also contributed
positively to the development of quantum theory. For example, in 1923 Louis de Broglie advanced the hypothesis of matter waves on purely aesthetic grounds; empirical evidence for it came only in 1927 (McAllister cites this example on p. 43). De Broglie’s idea had a strong impact upon Niels Bohr and Erwin Schrodinger, and thus played a crucial role in the history of quantum Another
example
is Wolfgang
Pauli, a physicist
mechanics.
with a highly developed
aes-
thetic sense who made decisive contributions to the construction of quantum mechanics. Daniel Serwer has observed that Pauli valued ‘legitimacy’ and consistency of a scientific theory above its empirical definable,
adequacy. Though legitimacy
it clearly is an aesthetic feature: while unifying
is not easily
power and a prohibition
of ad hoc hypotheses were important conditions for it, Pauli emphasised that judgment of legitimacy was ultimately a matter of ‘physical intuition’ (Serwer, 1977, p. 245). In addition,
Pauli endorsed
operationalism,
contain only concepts that are completely observational operations. Operationalism theory choice because it is not warranted
by goal analysis.
classified
as an aesthetic
demand.
important
for his discovery
of the exclusion
senberg during his discovery 132). The quantum-mechanical considerations
Pauli’s
aesthetic principle,
of matrix mechanics revolution
the view that a theory should
definable in terms of experimental and/or is not a logico-empirical criterion for It should therefore be
preferences
were directly
and influenced
was thus induced by more than empirical
alone.
The case of Pauli reveals a more general problem with McAllister’s confuses
Werner Hei-
(see De Regt, 1993, pp. 112-
positivist
approaches
and empirical
concerns.
Positivist
account: it
views, such as
Pauli’s operationalism,
must be sharply distinguished
from the bare demand
theories be empirically
adequate, since they constrain
theory choice in a way that
transcends therefore
that demand. be regarded
In McAllister’s as an aesthetic
model, a penchant predilection.
for positivism
Nevertheless,
McAllister
that
should also
tends to associate the attitude of revolutionary scientists with positivism (see for instance, p. 200). This causes confusion, since in his view revolutionaries do not have aesthetic ideals but care only about empirical adequacy. A better term for McAllister’s revolutionaries would be ‘opportunists’, because for them any theory is acceptable as long as it complies with the logico-empirical criteria. I believe, however, that such opportunism is relatively rare. During the quantum revolution only Heisenberg was at times such an opportunist (see Serwer, p. 255); Pauli and
162
Studies in History and Philosophy of Science
Bohr certainly were not. Although revolutionary
scientists may often be positivists,
this does not imply that they refrain from aesthetic judgment, are committed
to a particular
As an illustration,
but rather that they
aesthetics.
consider the issue of visualizability.
classical physics are straightforwardly
visualizable,
Whereas the theories of
quantum theory resists visualiz-
ation in important respects. For some physicists, such as Schrodinger, this was a severe obstacle for accepting it as a definitive theory of atomic structure (see De Regt, 1997). Bohr, Heisenberg and Pauli, however, had fewer problems with a non-visualizable quantum theory. Why? Either they preferred abstract theories to visualizable ones, or they did not care at all about this aspect of theories. In the former case they had alternative aesthetic ideals; in the latter case they were utionary scientists in McAllister’s sense. It appears that McAllister decides second option: he presents Bohr and Heisenberg as opportunists who merely doned the classical aesthetic demand of visualizability (pp. 193-94). Earlier
revolon the abanin the
book (p. 50), however, the preference for abstract theories was classified as an aesthetic criterion, which is connected with positivism. I maintain that during the quantum revolution this alternative aesthetics was also present, contrary to McAllister’s claims. It is reflected in favourable attitudes towards the non-visualizable matrix mechanics. For example, Pauli’s operationalism led him to reject explicitly visualizable models of the atom, because the path of an electron cannot be defined operationally (see De Regt, 1993, pp. 115-l 16). This is clearly an aesthetic judgment, which was independent of the empirical adequacy of the models in question. Considerations of this sort reveal the existence of a positivist aesthetics which positively contributed to the quantum-mechanical revolution. 2. Intelligibility and Aesthetics These criticisms notwithstanding, I am of the opinion that McAllister’s book contains many valuable ideas. In the remaining part of this review I will illustrate this by employing McAllister’s model in a discussion of a specific question, which is beyond the scope of his book: the question of whether universal intelligibility
of scientific
criteria for the
theories exist. This issue has become particularly
acute
in modern physics, as many properties of classical theories which seem to guarantee intelligibility are wanting in quantum theory. Not wishing to give up the demand that science provides understanding of natural phenomena (besides description and prediction), the question arises on what conditions understanding is achieved. Are such conditions universally valid or historically varying constraints on theory choice? Applying McAllister’s terminology: are intelligibility criteria examples of aesthetic criteria? An example of a classical.criterion for intelligibility is visualizability. As mentioned above, for Erwin Schrodinger visualizability was a desirable aesthetic virtue, but it was more than that: he regarded it as a necessary condition for understanding. The fact that in German the two notions almost coincide in the term Anschaulich-
Explaining the Splendour of Science keit illustrates
the naturalness
theories must be visualizable our manner of thinking it we cannot understand
of this connection.
163 Schrodinger
in space and time, because
argued that scientific ‘we cannot really alter
in space and time, and what we cannot comprehend at all’ (Schrodinger,
within
1928, p. 27). In contrast, Wolfgang
Pauli held that intelligibility did not have to be equated with visualizability. As explained above, he came to reject visualizability on aesthetic grounds. Pauli reasoned that after a while quantum mechanics would ‘automatically’ lead to a new conception of intelligibility: Even though the demand [. . .] for Anschaulichkeit is partly a legitimate and a healthy one, still this demand should never count in physics as an argument for the retention of fixed conceptual systems. Once the new conceptual systems are settled, then these will also be anschdich (quoted in Sewer, 1977, p. 234; translation slightly revised). This..historical controversy seems to fit nicely into McAllister’s model. While Schrodinger clung to the extant aesthetic canon of classical physics, Pauli anticipated a new quantum-mechanical aesthetics. Furthermore, Pauli’s argument suggests that we simply have to get used to this new canon and that what counts as intelligible is determined by it. This appears a plausible position. The intelligibility of a theory credibly depends on its aesthetic features such as visualizability, simplicity, and consistency with accepted metaphysical worldviews (e.g. determinism). From this one might draw the conclusion that the notion of intelligibility is an inductively constructed aesthetic requirement, which does not have a necessary or privileged interpretation. But is that really the case? In order to find out whether intelligibility criteria are indeed subject to aesthetic induction, let us see how the case of quantum theory has developed. Have Pauli’s anticipations come true? Have quantum-mechanical conceptions ‘settled’, and is the theory nowadays regarded as anschaulich, that is to say: intelligible? Conceptions have indeed settled in the sense that physicists have grown accustomed to manipulating the mathematical formalism. They have, moreover, settled in the sense that physicists now see beauty in the structure of quantum mechanics (see McAllister, pp. 65, 195, 201). However, it is as yet far from clear in what sense quantum mechanics provides us with understanding, over and above its predictive power. When Pauli envisaged a new form of Anschaulichkeit, I suspect that he had no idea of what precisely it would look like. Today we are still in the dark. The ongoing debates on the conceptual problems of the theory and the existence of many rival interpretations prove that there is as yet no consensus regarding the way quantum theory provides us with understanding of nature. Of the various interpretations which try to sketch an intelligible world-picture behind quantum-mechanical formalism, some employ classical ideals of intelligibility, such as visualizability or causality. Although these ideals retain their attractiveness (as exemplified by the popularity of Feynman-diagrams in quantum electrodynamics), the prospects of such approaches seem questionable. However, as yet, no convincing, generally accepted alternative ideal of intelligibility has emerged, contrary to Pauli’s expectations. It has to be concluded that, while aesthetic induction has perhaps led us to a better appreciation of the beauty of quantum theory, it has failed to provide us with a view of its intelligibility.
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Studies
in History and Philosophy of Science
Where does this observation lead us? There seem to be three possible responses. First, one might be tempted to jump to the conclusion that aesthetic induction is not at all applicable to intelligibility criteria. However, this answer is too radical, because there are in fact many cases in which inductive adaptation of such criteria can be observed. One only has to think of the example, mentioned earlier, of Newtonian actio in distans versus Cartesian contact action. Whereas the former was at first considered unintelligible, some decades later this had changed completely. There is an evident historical dimension to intelligibility criteria, of which McAllister’s model provides a plausible account. A second response might be that we have not yet waited long enough for a new intelligibility criterion to emerge. Seventy years is a long time, but perhaps still more time is needed to adapt to such radical changes as were brought about by the quantum revolution. In the light of the above considerations, however, it seems to me that we should not rely too strongly on this possibility. For it was noticed that in all other respects we have become used to quantum theory (manipulating it; appraising its beauty). Why should its intelligibility be so much more resistant? Moreover, a whole new generation of physicists has grown up with the theory, and many of them keep wrestling with its conceptual problems. To wait for another generation to come will probably make no difference. A further objection to the second response is that it suggests that a theory automatically and necessarily brings with it a unique interpretation which embodies its intelligibility. However, in general, and particularly in the case of quantum theory, this does not happen. In his book McAllister does not distinguish sharply between theories and their interpretations. It seems that he takes interpretations to be part of theories: of the aesthetic properties of theories he lists in Chapter 3, some properties can be virtues of mathematical formalism (e.g. symmetry), others pertain only to interpretations of formalism (e.g. visualizability), and still others simply are interpretations (e.g. invocation of a model). It is legitimate to employ such a broad conception of ‘theory’ (including interpretation), but then McAllister’s model fails to account for situations in which several ‘theories’ are empirically equivalent. An example is the competition between various ‘quantum theories’ (being the quantum-mechanical formalism together with a particular interpretation). Here one cannot decide on a particular theory merely on its empirical virtues and then wait for an aesthetic canon to emerge. Rather, we should actively search for intelligible interpretations, and thus we need a criterion for intelligibility beforehand. This brings us to the third and last response. One might assume that there are inherent limitations to human understanding. This would imply that intelligibility criteria, though they may vary in history due to changing aesthetic canons, are subject to a universal constraint. If this is true, the question arises: what is this constraint and what determines it? In contrast to what one might suspect at first sight, the constraint cannot belong to the set of logico-empirical criteria. Although these are indeed universal constraints on theory choice, they are derived from the aim of science (which McAllister specified as formulating empirically adequate theories), and that aim does not entail any constraint on the intelligibility of theories. A more plausible assumption is that limitations on human understandingand thus intelligibility criteria-are determined by the structure of the mind or the
Explaining the Splendour of Science
165
brain, and can perhaps be revealed and explained by cognitive science. An alternative view of the suggested universal constraints on theorizing is that they are historically contingent, but much stronger and far more resistant to change than the aesthetic criteria considered by McAllister. They could be of the same sort as A. C. Crombie’s ‘styles of scientific thinking’ or Gerald Holton’s ‘themata’. Admittedly, my discussion of the question of the nature and the status of intelligibility criteria for scientific theories has not led to definite conclusions. This important topic demands further investigation. Whereas McAllister’s model can usefully be applied to the issue, it is clearly not the final word. 3. Conclusion Beauty and Revolution in Science sheds new light on the aesthetics
of science.
It differs from many earlier studies of this topic in offering a clearly stated theory instead of vague speculations. Because of this, McAllister’s views are open to criticism and testing. In this review, I have accepted the invitation by criticizing his model of scientific revolutions, which I believe to be not completely adequate. However, this criticism should not be taken as disputing the value of the book. It is a stimulating study, that relates to a broad spectrum of subjects. McAllister’s theses invite further elaboration and application, as I have attempted to show for the case of ‘intelligibility’. Although it is obviously impossible to discuss every aspect of the book in a review, I finally want to mention the chapter in which McAllister draws an arresting analogy between the development of applied art (specifically nineteenth-century architecture) and that of science. Such thoughtprovoking
ideas are typical of the book, and make it a pleasure to read.
Acknowledgements--I wish to thank Tim Budden, Dennis Dieks, and Janneke van Dis for comments on earlier versions. This work was supported by the Foundation for Research in the Field of Philosophy and Theology which is subsidized by the Netherlands Organisation for Scientific Research (NWO).
References De Regt, H. W. (1993) Philosophy and the Art of Scientijic Discovery (Ph.D. dissertation, Vrije Universiteit Amsterdam). ., De Regt, H.W. (1997) ‘Erwin Schrodinger, Anschaulichkeit and Quantum Theory’, Studies in History and Philosophy of ModernJ’hysics 288, 461-481. Ehrenfest, P. (1913) Zur Krise der Lichtather-Hypothese (Berlin: Springer). Pyenson, L. (1987) ‘The Relativity Revolution in Germany’, in T. F. Glick (ed.), The Comparative Reception of Relativio (Dordrecht: Reidel), pp. 59-l 11. Kuhn, T. S. (1970) The Structure of Scientljic Revolutions, 2nd Edn (Chicago: Chicago University Press). Kuhn, T. S. (1977) ‘Objectivity, Value Judgment, and Theory Choice’, in The Essential Tension (Chicago: Chicago University Press), pp. 320-339. Schrodinger, E. (1928) Collected Papers on Wave Mechanics (London: Blackie). Serwer, D. (1977) ‘Unmechanischer Zwang: Pauli, Heisenberg, and the Rejection of the Mechanical Atom, 1923-1925’, Historical Studies in the Physical Sciences 8, 189-256.
Pergamon
ESSAYREVIEW Explaining the Splendour of Science Henk W. de Regt*
James W. McAllister, Beauty and Revolution in Science (Ithaca and London: Cornell University Press, 1996), xiv + 232 pp. ISBN o-8014-3240-5, Cloth, s29.95lE23.50. Why do scientists
regard certain theories as more beautiful
than others? How do
aesthetic evaluations affect scientific development? James McAllister has set himself the task of answering such questions by providing a general, systematic analysis of the aesthetic aspects of science. The result is Beauty and Revolution in Science, a sophisticated and insightful, yet highly readable book. McAllister endorses a ‘rationalist image of science’ (p. 7), asserting the existence of certain universal, rational rules for practising science. His aim is to reconcile this rationalist image with two recalcitrant features of actual science: the fact that scientists evaluate theories on their aesthetic merits, and the occurrence of revolutions in scientific development. To this end he introduces a division of criteria for theory choice
into ‘logico-empirical
criteria’
and ‘aesthetic
criteria’.
Prime
examples of the former are ‘consistency with extant empirical data’ and ‘internal consistency’, while the latter may include such diverse items as ‘symmetry’, ‘visualizability’
and ‘consistency
ter contends
that both sorts of criteria can have a rational justification,
with an accepted metaphysical
worldview’.
McAlliscontrary to
the accepted opinion that aesthetic criteria introduce a subjective and therefore irrational element into theory choice. This justification proceeds, however, in two essentially different ways. Logico-empirical criteria are warranted through ‘goal analysis’: from the goal of science we can derive these criteria as being necessary
* Department of History and Foundations of Mathematics and Science, University Box 80.000, 3508 TA, Utrecht, The Netherlands (email: [email protected]).
PII: SOO39-3681(97)00026-5 155
of Utrecht, P.O.
156
Studies in History and Philosophy of Science
presuppositions ‘formulating adequacy,
for its achievement theories
that possess
(McAllister
specifies the goal of science
the highest
possible
or truth’ p. 76). Rational justification
can be attained through ‘inductive projection’: choice has been conducive
degrees
as
of empirical
of aesthetic criteria, by contrast,
when a particular criterion for theory
to the goal of science so far, we may inductively
con-
clude that it will remain so when applied in future cases. This leads to the central thesis of McAllister’s book, to wit that scientists’ aesthetic preferences are formed and updated by the ‘aesthetic induction’: ‘A community compiles its aesthetic canon at a certain date by attaching to each property a weighting
proportional
to the degree of empirical
adequacy then attributed to the
set of current and recent theories that have exhibited that property’ (p. 78). This implies that there exists a correlation between empirical and aesthetic values, albeit in a rather indirect way. Thus, when scientists appraise a theory, they evaluate it both on its empirical
and on its aesthetic merits. The latter evaluation
reflects the
empirical performance of earlier theories with the same aesthetic properties. A clear example of this process, cited by McAllister (pp. 56-58) is the rise and fall of Cartesian corpuscularism.
A central metaphysical
principle
of corpuscularism
was
the rejection of all ‘occult’ properties such as active powers and action at a distance; only contact action was admitted as an explanatory principle. The great empirical successes of this approach, compared with the earlier theories of alchemists and astrologers,
lead to the firm establishment
of its aesthetic canon. When Newton
formulated his law of gravitation, his inductively formed aesthetic sense told him that the law needed a corpuscularist explanation of the apparent action at a distance. As is well known, extremely
successful
he did not succeed. at the empirical
His theory, however,
turned out to be
level. This caused a change in the aesthetic
canon, which was updated by aesthetic induction: tance was not regarded as ugly and unintelligible
after some time action at a disanymore. Indeed, Newton himself
later did not hesitate to speak of active powers of matter. In the eighteenth century, action at a distance became an accepted property of matter and Newton’s law of gravitation
a paradigmatic
form of explanation.
As a kind of corollary to his thesis of the aesthetic induction, a new model of scientific revolutions.
McAllister
Aesthetic canons are essentially
presents
conservative,
since they reflect the properties of past theories. They can be updated by aesthetic induction, but this is always a gradual change. However, in some situations of theory choice, when it appears quite difficult to find a theory which conforms to the extant aesthetic canon, one may witness a scientific revolution. According to McAllister, a revolution always consists in an ‘aesthetic rupture’ (p. 125). That is to say, the scientific community decides to adopt a theory which is empirically successful but aesthetically displeasing, and accordingly it decides to abandon the established aesthetic canon. After some time, of course, the aesthetic induction will operate again and a new canon will be formed. McAllister presents case studies to support this model of science, particularly
of scientific
revolutions.
Analysing
Explaining the Splendour of Science
four (allegedly)
revolutionary
157
episodes
only two of them are real revolutions two are not (Copernicus,
relativity
in the history of science, (Kepler, quantum
theory).
In this review I will focus on two aspects of McAllister’s critically
discuss his analysis
he argues that
theory), while the other
of scientific
revolutions,
book. First, I will
comparing
its merits with
those of Kuhn’s well known account. Secondly, I will attempt to apply McAllister’s model to the issue of intelligibility in science: if we demand that scientific theories provide understanding, and if we specify (necessary) criteria for intelligibility, should these be regarded as aesthetic criteria, and would they comply with McAllister’s analysis? 1. Aesthetic Canons and Scientific Revolutions Aesthetic
canons
induce scientists
to tread known paths, to formulate
theories
with familiar features. Only when a problem or an unexpected discovery stubbornly resists explanation along aesthetically pleasing lines, this conservatism may give way to a scientific revolution. McAllister accepts the occurrence of revolutions in science as a historical fact, and he claims that his account of scientific revolutions provides the best explanation of them. In particular, he contrasts his view of revolutions as ‘aesthetic ruptures’ with the classic account of Thomas Kuhn (1970). There appear to be two major differences between McAllister’s model of revolutions and Kuhn’s, First, McAllister holds that his model, in contrast to Kuhn’s, explains both the continuity and the radical changes exhibited by scientific development. Secondly, the role of aesthetic values is precisely opposite in the two models: in Kuhn’s view they induce revolutions, whereas in McAllister’s view they inhibit revolutions. detail. McAllister
Let us consider
McAllister’s
claims that a great advantage
arguments
on these two points in more
of his model is that it can account for
the radical breaks which scientific revolutions are, while still allowing for some continuity in such processes. His distinction between two sets of criteria for theory choice makes this possible: in a revolution
the set of aesthetic criteria is abandoned,
whereas the set of empirical criteria remains unchanged. Kuhn is allegedly unable to account for this aspect of scientific development, because he treats all criteria on a par. I believe, however, that McAllister is attacking a straw man here. Kuhn’s actual views are more sophisticated and do allow for continuity and rupture as well. According to McAllister (p. 126), the fact that revolutions occur, compels any model of science to meet four obligations, among which are: (a) it ‘must acknowledge that a scientific revolution constitutes a radical transformation in a community’s criteria for theory choice’; and (b) ‘revolutions should not be portrayed as being so deep that they leave no element of scientific practice unchanged’. Subsequently, he claims that Kuhn’s writings can be interpreted in two different ways, where under one interpretation only obligation (a) is fulfilled, while under the other only (b) is met. The first is the familiar radical interpretation of Kuhn’s
Studies in History and Philosophy of Science
158
original
1962 text, asserting that a paradigm-shift
introduces
a completely
new set
of criteria. This would imply that, to quote a famous phrase, ‘the proponents competing
paradigms
practice
150), and that, accordingly, of ‘incommensurability’.
their trades in different
communication
Obviously,
between
worlds’
(Kuhn,
them is impossible
this radical interpretation
of
1970, p. because
conflicts with obli-
gation (b). In later writings, however, Kuhn has attempted to mitigate such radical conclusions. Particularly in his ‘Objectivity, Value Judgment, and Theory Choice’ (1977), he emphasises that ‘trans-paradigmatic’ exist. He mentions five: accuracy, consistency,
criteria for theory evaluation also scope, simplicity, and fruitfulness.
Explicitly endorsing the traditional view in this respect, Kuhn (1977, p. 322) deems these criteria as belonging to ‘the shared basis for theory choice’. McAllister classifies these moderate remarks as a second interpretation of Kuhn, which is opposed to the radical Kuhn. This moderate interpretation then fails to meet obligation (a), according to McAllister
(p. 127): ‘Unless Kuhn can identify some further category
of criteria for theory choice that are paradigm specific, it remains unclear how any deep transformations
in scientific practice can occur’.
It seems to me that this conclusion all, Kuhn’s mitigations account,
is drawn far too hastily, however.
should clearly be regarded as supplementary
not as replacing
it. Nowhere
First of
to his earlier
does Kuhn suggest that he withdraws
all
earlier claims concerning the deep changes that paradigm-shifts bring about. It is only the radical view that nothing remains the same across a paradigm change that he wishes to deny. While admitting
that scientific
development
is continuous
in
some respects, one can still hold that revolutions
cause serious changes in criteria
for theory choice. For example, the metaphysical
presuppositions
basis of a paradigm may change completely
which lie at the
(as, for instance, in the transition
from
the particle theory of light to the wave theory). This is clearly a paradigm-specific criterion
of the kind that McAllister
it is a criterion
which McAllister
asked for in the quotation
above. Moreover,
himself would classify as an aesthetic criterion.
Thus it seems that Kuhn would agree that it is the aesthetic criteria which change in revolutions.
Nevertheless,
he does not draw an explicit
and sharp distinction
between two sets of criteria. The reason for this will become clear from the following. There is an important
feature of the above-mentioned
‘trans-paradigmatic’
criteria, which is overlooked by McAllister and which provides additional evidence against his second, ‘moderate’ interpretation of Kuhn. Kuhn emphasises that these criteria do not function as rules but as values, for two reasons: they are not very precise and they may conflict with each other. Therefore, though criteria such as accuracy and consistency always play an important part in theory choice, the way in which they are applied may vary from one situation to another, and thus also from one paradigm to another. This implies that their status is not essentially different from that of paradigm-specific criteria: as regards permanence and immutability they differ merely in degree.
Explaining the Splendour of Science
This sophisticated the history McAllister
159
reading of Kuhn does explain both continuity
of science,
as does McAllister’s
model.
Indeed,
and rupture in
contrary
to what
wants us to believe, Kuhn’s view is not very different from his own in
this respect. A striking incommensurability
illustration
is provided
by McAllister’s
discussion
thesis. He criticizes Kuhn for holding untenable
of the
views on com-
munication between scientists in different paradigms, and he suggests that his own model entails only ‘partial incomprehension’ in such cases (p. 134). However, this latter view is similar to Kuhn’s account of ‘partial communication’ (1977, pp. 33% 339). I conclude that McAllister’s claim that his model is superior to Kuhn’s with respect to the issue of continuity
and rupture is unfounded.
Let us turn to the second major difference
between Kuhn’s model and McAllis-
ter’s, which is the impact of aesthetic values in revolutionary there exists
a real disagreement
McAllister
maintains
between
the authors.
periods. At this point As already
that aesthetic criteria have an essentially
mentioned,
conservative
func-
tion: they lead to theories which are similar to earlier ones. A scientific revolution occurs despite the existence of an aesthetic canon, and consists in its abandonment in favour of considerations despite empirical their claims
of mere empirical
considerations.
against
historical
one needs an independent
evidence,
criterion
of revolutions
McAllister
175-176) completely
for determining
precludes
apparently
in opposition
Unfortunately,
McAllister
is.
that either Kuhn or while McAllister
(pp.
proposal of a heliocentric
he claims that-precisely
for that reason-
to Kuhn’s view. criterion
does not explicitly
for identifying
scientific
provide such a criterion;
above. He introduces
revol-
on which ‘scientists adopt theories that differ radically
predecessors’
criterion because of its vagueness revolutionary?).
(p.
of testing. For example, in
apparent:
he is not aware of the problem mentioned
utions simply as occasions
himself
what a ‘real’ revolution
agrees with Kuhn that Copernicus’
we need a clear and independent
from their immediate
by McAllister
the possibility
theory was induced by aesthetic concerns,
revolutions.
and in a sense
arises: if one wants to conduct this test,
this problem is manifestly
it was not a revolution, Therefore,
as suggested
by means of the characteristics
suggest, obviously
the case of Copernicus
concerns,
Here one can assess the two models by testing
138). However, one difficulty immediately Identification
adequacy. By contrast, Kuhn’s model
only happen thanks to aesthetic
asserts that revolutions
(p. 125). Obviously,
this will not suffice as a
(Which difference is radical enough to be labelled
It seems, however,
that in his case studies McAllister
implicitly
employs a more specific criterion, namely the way in which the new theory was received by contemporary scientists. Thus, he argues that Copernicus’ theory was welcomed by mid-sixteenth century astronomers (see pp. 171-174) because of its aesthetic virtues. By contrast, Kepler’s model of the solar system at first met with severe resistance because of its ‘ugly’ ellipses. Only after some time, when its great empirical success had become clear, did the scientific community accept it
Studies in History and Philosophy of Science
160
(pp. 178-181).
The reception of the theory by the scientific community
to serve as a criterion to identify it as a revolution:
thus appears
a truly revolutionary
not easily accepted by contemporary scientists. Although I doubt whether this criterion is really adequate,
theory is
I contend that even
if one employs
it, some of McAllister’s own examples fail to support his model of revolutions. The examples I have in mind are his case studies in the history of modern physics: relativity theory and quantum theory. With respect to relativity theory, McAllister advances the unorthodox view that its development by Albert Einstein was not a scientific revolution. It is well known that Einstein’s motives for constructing relativity theory were not based on empirical problems but on aesthetic considerations. McAllister adds that Einstein derived these motives from an extant ‘classical’ aesthetic canon. He claims that both special and general relativity theory were therefore welcomed by the community (pp. 186 and 188) and concludes that they were not revolutionary. However, historian Lewis Pyenson has provided a detailed description of the reception of relativity in Germany which shows that the theory was not so easily accepted. Instead, the community of physicists was divided into advocates and opponents, engaging in heated debates, precisely as McAllister (pp. 13&l 3 1) predicts for revolutions. Around 19 11, its adversaries called relativity theory a ‘jest’ and both parties testified to the revolutionary character of Einstein’s theory (see Pyenson, 1987, pp. 78 and 66-68). Further evidence against McAllister’s thesis can be found in Paul Ehrenfest’s I9 12 inaugural lecture. Ehrenfest observed a ‘peculiar revolutionary atmosphere dominating theoretical physics at this moment’ (Ehrenfest, 1913, p. 3, my translation). In his analysis, the main problem was that experimental evidence provided by A. A. Michelson
contradicted
existing
theories of the ether, while the
ether hypothesis served as a basic presupposition of contemporary physics. In 1904, H. A. Lorentz had proposed a theory of molecular forces which reconciled the experiments with the ether-hypothesis. Einstein’s 1905 theory of special relativity, however, constituted a much more radical solution of the problem: Einstein simply rejected the ether hypothesis, replacing it by the revolutionary postulate of the constancy of the velocity of light, which Ehrenfest found difficult to grasp and to accept. It should be concluded, in my opinion, that even on McAllister’s own implicit criterion relativity theory did constitute a revolution. Since Einstein’s revolutionary proposal was inspired not by empirical but by aesthetic considerations (indeed, from the empirical point of view, Lorentz’s 1904 theory was equally acceptable), it is therefore a counter-example to McAllister’s model. Moreover, this example reveals that actual situations may be less straightforward than McAllister suggests. McAllister seems to hold that a theory is either aesthetically pleasing or not, and that appraisal of aesthetic merit is always conservative. But Einstein’s theory was aesthetically innovative in one respect, since it abandoned the ether hypothesis and the notion of absolute time, but conservative in another, as it was an attempt to enhance the symmetry of classical physics.
Explaining the Splendour of Science McAllister’s
second case study in the history of modem
genesis of quantum was a genuinely of revolutions
161
theory. He maintains,
revolutionary
science concerns
as does indeed everybody
episode, and he argues that it confirms
because it saw the abandonment
the
else, that this his model
of an aesthetic canon and the accept-
ance of a new theory purely on empirical grounds. Determinism and visualizability are presented as examples of aesthetic criteria which were repudiated in the quantum revolution.
Although
the actual situation
this is a plausible
was more complex
account
to some extent, I think that
and that aesthetic factors also contributed
positively to the development of quantum theory. For example, in 1923 Louis de Broglie advanced the hypothesis of matter waves on purely aesthetic grounds; empirical evidence for it came only in 1927 (McAllister cites this example on p. 43). De Broglie’s idea had a strong impact upon Niels Bohr and Erwin Schrodinger, and thus played a crucial role in the history of quantum Another
example
is Wolfgang
Pauli, a physicist
mechanics.
with a highly developed
aes-
thetic sense who made decisive contributions to the construction of quantum mechanics. Daniel Serwer has observed that Pauli valued ‘legitimacy’ and consistency of a scientific theory above its empirical definable,
adequacy. Though legitimacy
it clearly is an aesthetic feature: while unifying
is not easily
power and a prohibition
of ad hoc hypotheses were important conditions for it, Pauli emphasised that judgment of legitimacy was ultimately a matter of ‘physical intuition’ (Serwer, 1977, p. 245). In addition,
Pauli endorsed
operationalism,
contain only concepts that are completely observational operations. Operationalism theory choice because it is not warranted
by goal analysis.
classified
as an aesthetic
demand.
important
for his discovery
of the exclusion
senberg during his discovery 132). The quantum-mechanical considerations
Pauli’s
aesthetic principle,
of matrix mechanics revolution
the view that a theory should
definable in terms of experimental and/or is not a logico-empirical criterion for It should therefore be
preferences
were directly
and influenced
was thus induced by more than empirical
alone.
The case of Pauli reveals a more general problem with McAllister’s confuses
Werner Hei-
(see De Regt, 1993, pp. 112-
positivist
approaches
and empirical
concerns.
Positivist
account: it
views, such as
Pauli’s operationalism,
must be sharply distinguished
from the bare demand
theories be empirically
adequate, since they constrain
theory choice in a way that
transcends therefore
that demand. be regarded
In McAllister’s as an aesthetic
model, a penchant predilection.
for positivism
Nevertheless,
McAllister
that
should also
tends to associate the attitude of revolutionary scientists with positivism (see for instance, p. 200). This causes confusion, since in his view revolutionaries do not have aesthetic ideals but care only about empirical adequacy. A better term for McAllister’s revolutionaries would be ‘opportunists’, because for them any theory is acceptable as long as it complies with the logico-empirical criteria. I believe, however, that such opportunism is relatively rare. During the quantum revolution only Heisenberg was at times such an opportunist (see Serwer, p. 255); Pauli and
162
Studies in History and Philosophy of Science
Bohr certainly were not. Although revolutionary
scientists may often be positivists,
this does not imply that they refrain from aesthetic judgment, are committed
to a particular
As an illustration,
but rather that they
aesthetics.
consider the issue of visualizability.
classical physics are straightforwardly
visualizable,
Whereas the theories of
quantum theory resists visualiz-
ation in important respects. For some physicists, such as Schrodinger, this was a severe obstacle for accepting it as a definitive theory of atomic structure (see De Regt, 1997). Bohr, Heisenberg and Pauli, however, had fewer problems with a non-visualizable quantum theory. Why? Either they preferred abstract theories to visualizable ones, or they did not care at all about this aspect of theories. In the former case they had alternative aesthetic ideals; in the latter case they were utionary scientists in McAllister’s sense. It appears that McAllister decides second option: he presents Bohr and Heisenberg as opportunists who merely doned the classical aesthetic demand of visualizability (pp. 193-94). Earlier
revolon the abanin the
book (p. 50), however, the preference for abstract theories was classified as an aesthetic criterion, which is connected with positivism. I maintain that during the quantum revolution this alternative aesthetics was also present, contrary to McAllister’s claims. It is reflected in favourable attitudes towards the non-visualizable matrix mechanics. For example, Pauli’s operationalism led him to reject explicitly visualizable models of the atom, because the path of an electron cannot be defined operationally (see De Regt, 1993, pp. 115-l 16). This is clearly an aesthetic judgment, which was independent of the empirical adequacy of the models in question. Considerations of this sort reveal the existence of a positivist aesthetics which positively contributed to the quantum-mechanical revolution. 2. Intelligibility and Aesthetics These criticisms notwithstanding, I am of the opinion that McAllister’s book contains many valuable ideas. In the remaining part of this review I will illustrate this by employing McAllister’s model in a discussion of a specific question, which is beyond the scope of his book: the question of whether universal intelligibility
of scientific
criteria for the
theories exist. This issue has become particularly
acute
in modern physics, as many properties of classical theories which seem to guarantee intelligibility are wanting in quantum theory. Not wishing to give up the demand that science provides understanding of natural phenomena (besides description and prediction), the question arises on what conditions understanding is achieved. Are such conditions universally valid or historically varying constraints on theory choice? Applying McAllister’s terminology: are intelligibility criteria examples of aesthetic criteria? An example of a classical.criterion for intelligibility is visualizability. As mentioned above, for Erwin Schrodinger visualizability was a desirable aesthetic virtue, but it was more than that: he regarded it as a necessary condition for understanding. The fact that in German the two notions almost coincide in the term Anschaulich-
Explaining the Splendour of Science keit illustrates
the naturalness
theories must be visualizable our manner of thinking it we cannot understand
of this connection.
163 Schrodinger
in space and time, because
argued that scientific ‘we cannot really alter
in space and time, and what we cannot comprehend at all’ (Schrodinger,
within
1928, p. 27). In contrast, Wolfgang
Pauli held that intelligibility did not have to be equated with visualizability. As explained above, he came to reject visualizability on aesthetic grounds. Pauli reasoned that after a while quantum mechanics would ‘automatically’ lead to a new conception of intelligibility: Even though the demand [. . .] for Anschaulichkeit is partly a legitimate and a healthy one, still this demand should never count in physics as an argument for the retention of fixed conceptual systems. Once the new conceptual systems are settled, then these will also be anschdich (quoted in Sewer, 1977, p. 234; translation slightly revised). This..historical controversy seems to fit nicely into McAllister’s model. While Schrodinger clung to the extant aesthetic canon of classical physics, Pauli anticipated a new quantum-mechanical aesthetics. Furthermore, Pauli’s argument suggests that we simply have to get used to this new canon and that what counts as intelligible is determined by it. This appears a plausible position. The intelligibility of a theory credibly depends on its aesthetic features such as visualizability, simplicity, and consistency with accepted metaphysical worldviews (e.g. determinism). From this one might draw the conclusion that the notion of intelligibility is an inductively constructed aesthetic requirement, which does not have a necessary or privileged interpretation. But is that really the case? In order to find out whether intelligibility criteria are indeed subject to aesthetic induction, let us see how the case of quantum theory has developed. Have Pauli’s anticipations come true? Have quantum-mechanical conceptions ‘settled’, and is the theory nowadays regarded as anschaulich, that is to say: intelligible? Conceptions have indeed settled in the sense that physicists have grown accustomed to manipulating the mathematical formalism. They have, moreover, settled in the sense that physicists now see beauty in the structure of quantum mechanics (see McAllister, pp. 65, 195, 201). However, it is as yet far from clear in what sense quantum mechanics provides us with understanding, over and above its predictive power. When Pauli envisaged a new form of Anschaulichkeit, I suspect that he had no idea of what precisely it would look like. Today we are still in the dark. The ongoing debates on the conceptual problems of the theory and the existence of many rival interpretations prove that there is as yet no consensus regarding the way quantum theory provides us with understanding of nature. Of the various interpretations which try to sketch an intelligible world-picture behind quantum-mechanical formalism, some employ classical ideals of intelligibility, such as visualizability or causality. Although these ideals retain their attractiveness (as exemplified by the popularity of Feynman-diagrams in quantum electrodynamics), the prospects of such approaches seem questionable. However, as yet, no convincing, generally accepted alternative ideal of intelligibility has emerged, contrary to Pauli’s expectations. It has to be concluded that, while aesthetic induction has perhaps led us to a better appreciation of the beauty of quantum theory, it has failed to provide us with a view of its intelligibility.
164
Studies
in History and Philosophy of Science
Where does this observation lead us? There seem to be three possible responses. First, one might be tempted to jump to the conclusion that aesthetic induction is not at all applicable to intelligibility criteria. However, this answer is too radical, because there are in fact many cases in which inductive adaptation of such criteria can be observed. One only has to think of the example, mentioned earlier, of Newtonian actio in distans versus Cartesian contact action. Whereas the former was at first considered unintelligible, some decades later this had changed completely. There is an evident historical dimension to intelligibility criteria, of which McAllister’s model provides a plausible account. A second response might be that we have not yet waited long enough for a new intelligibility criterion to emerge. Seventy years is a long time, but perhaps still more time is needed to adapt to such radical changes as were brought about by the quantum revolution. In the light of the above considerations, however, it seems to me that we should not rely too strongly on this possibility. For it was noticed that in all other respects we have become used to quantum theory (manipulating it; appraising its beauty). Why should its intelligibility be so much more resistant? Moreover, a whole new generation of physicists has grown up with the theory, and many of them keep wrestling with its conceptual problems. To wait for another generation to come will probably make no difference. A further objection to the second response is that it suggests that a theory automatically and necessarily brings with it a unique interpretation which embodies its intelligibility. However, in general, and particularly in the case of quantum theory, this does not happen. In his book McAllister does not distinguish sharply between theories and their interpretations. It seems that he takes interpretations to be part of theories: of the aesthetic properties of theories he lists in Chapter 3, some properties can be virtues of mathematical formalism (e.g. symmetry), others pertain only to interpretations of formalism (e.g. visualizability), and still others simply are interpretations (e.g. invocation of a model). It is legitimate to employ such a broad conception of ‘theory’ (including interpretation), but then McAllister’s model fails to account for situations in which several ‘theories’ are empirically equivalent. An example is the competition between various ‘quantum theories’ (being the quantum-mechanical formalism together with a particular interpretation). Here one cannot decide on a particular theory merely on its empirical virtues and then wait for an aesthetic canon to emerge. Rather, we should actively search for intelligible interpretations, and thus we need a criterion for intelligibility beforehand. This brings us to the third and last response. One might assume that there are inherent limitations to human understanding. This would imply that intelligibility criteria, though they may vary in history due to changing aesthetic canons, are subject to a universal constraint. If this is true, the question arises: what is this constraint and what determines it? In contrast to what one might suspect at first sight, the constraint cannot belong to the set of logico-empirical criteria. Although these are indeed universal constraints on theory choice, they are derived from the aim of science (which McAllister specified as formulating empirically adequate theories), and that aim does not entail any constraint on the intelligibility of theories. A more plausible assumption is that limitations on human understandingand thus intelligibility criteria-are determined by the structure of the mind or the
Explaining the Splendour of Science
165
brain, and can perhaps be revealed and explained by cognitive science. An alternative view of the suggested universal constraints on theorizing is that they are historically contingent, but much stronger and far more resistant to change than the aesthetic criteria considered by McAllister. They could be of the same sort as A. C. Crombie’s ‘styles of scientific thinking’ or Gerald Holton’s ‘themata’. Admittedly, my discussion of the question of the nature and the status of intelligibility criteria for scientific theories has not led to definite conclusions. This important topic demands further investigation. Whereas McAllister’s model can usefully be applied to the issue, it is clearly not the final word. 3. Conclusion Beauty and Revolution in Science sheds new light on the aesthetics
of science.
It differs from many earlier studies of this topic in offering a clearly stated theory instead of vague speculations. Because of this, McAllister’s views are open to criticism and testing. In this review, I have accepted the invitation by criticizing his model of scientific revolutions, which I believe to be not completely adequate. However, this criticism should not be taken as disputing the value of the book. It is a stimulating study, that relates to a broad spectrum of subjects. McAllister’s theses invite further elaboration and application, as I have attempted to show for the case of ‘intelligibility’. Although it is obviously impossible to discuss every aspect of the book in a review, I finally want to mention the chapter in which McAllister draws an arresting analogy between the development of applied art (specifically nineteenth-century architecture) and that of science. Such thoughtprovoking
ideas are typical of the book, and make it a pleasure to read.
Acknowledgements--I wish to thank Tim Budden, Dennis Dieks, and Janneke van Dis for comments on earlier versions. This work was supported by the Foundation for Research in the Field of Philosophy and Theology which is subsidized by the Netherlands Organisation for Scientific Research (NWO).
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