Studies in History and Philosophy of Modern Physics 43 (2012) 105–111

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Studies in History and Philosophyof Modern Physics

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Essay Review

Constituting objectivity: Transcendental perspectives on modern physics

Jonathan Everett

University College London, Department of Science and Technology Studies, Gower Street, London WC1E 6BT, United Kingdom

a r t i c l e i n f o

Article history:

Received 2 January 2012

Accepted 24 January 2012Available online 19 April 2012

When citing this paper, please use the full journal title Studies in History and Philosophy of Modern Physics

1. Transcendental approaches in physics

There is increasing interest in exploring Kantian approaches inthe study of the history and philosophy of physics. The most well-known examples of this trend—Friedman’s (2001), Ryckman’s(2005) and DiSalle’s (2006)—focus on Kantianism in the contextof the development of the general theory of relativity. The editedcollection Constituting Objectivity seeks to develop key Kantianinsights—in the most part—in the context of later developmentsin physics: as well as discussing relativity the volume also providesKantian interpretations of Bohr’s development of quantum theoryand continues to provide Kantian insight from later interpretationsof quantum mechanics all the way through to considering non-commutative geometry and loop quantum gravity. The volumecontains papers on a wide variety of subjects and offers an essentialintroduction to the breadth of Kantian trends in modern physics.

The central focus is on the role of mathematics in physics. Indeed,in their Introduction, the Editors stress that the transcendentalquestion arises as soon as one realises that the key epistemologicalquestions of physics concern mathematical physics (p. 3).The particular problem that they identify is as to how it is possiblethat the fundamental equations of physics—appealing only togeneral concepts and universal principles—generate a series ofmathematical models that seem to accurately capture aspects ofthe world. They describe this as a ‘‘computational synthesis’’, whichis taken to be the modern analogue of Kant’s mathematical con-struction. The contributions of the volume, then, are intended toexplore different aspects of the development of mathematical

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physics and show how successive formalisms enable the construc-tion of models of observable phenomena. One particularly interestingphilosophical consequence, which I will highlight in this review, is asto how we should understand the principles that form the founda-tions of the fundamental equations of physics.

The book consists of three parts. First there is a historicalsurvey of transcendental readings of physics: this contains sixvery strong essays that together provide an excellent introductorysurvey of Kant’s philosophy of science and how it was developedby Cassirer and the early logical-positivists in response to thetheory of relativity and quantum physics. The second part is thelargest, consisting of 19 essays relating to transcendental epis-temologies of modern physics. This section begins by looking atmodern physics generally and investigating how Kantian insightsmay shed light on our modern understanding of, e.g., laws of natureand objects. The attention then shifts to look at more specific issues.There is a small section on transcendental approaches in relativityand cosmology, but the focus is really on issues in quantum physics.There is a particularly strong section on the history of quantumphysics, which explores Kantian elements in Bohr’s thought aswell as an interesting article on the little-known attempt ofHenry-Hermann to unify quantum physics and transcendentalphilosophy. In the two remaining sections that deal with quantumphysics more recent developments are considered. The first of thesesections is broadly concerned with the nature of quantum objects,how they should be understood and how they relate to our everydayperception of the world. The second of these sections considerstranscendental attempts to unify relativistic and quantum theories.The final, and shortest, section of the book contains four essays thatsuggest alternative epistemological approaches as more appropriateways to understand modern physics. I will not discuss this final

J. Everett / Studies in History and Philosophy of Modern Physics 43 (2012) 105–111106

section in this review as I intend to focus on how successful thevolume is in making a case for pursuing a form of Kantianism inmodern physics.

Given the scope of the present review, it is not possible tofollow the intricate details of too many of the fascinating con-tributions to the volume, so I will select just a few articles that Ifeel provide the most promising starting points for understandingmodern physics in a transcendental fashion. An important part ofthe project of this book is to chart the development of mathema-tical physics, and in clarifying the role of key principles at variousstages of the development of the mathematical formalism: thevolume as a whole is incredibly informative in this respect. In thisreview, I focus on drawing out two different Kantian accounts ofthese principles that are present in the volume. On what I refer toas the strongly Kantian account these principles seem to beunderstood as replacing the Kantian categories so as to providegeneral conditions for the possibility of experience in general(though not necessarily as deriving directly from human cognitivefaculties). Alternatively, some papers adopt a more modest Kan-tian account, according to which the principles are taken only tobe preconditions for the possibility of a given scientific theory.Finally, some contributions take the Kantian problem to be anepistemic one as to our knowledge of the unobservables.

In their Introduction to the volume, the editors Bitbol,Kerszberg and Petitot themselves suggest that there are a numberof different ways to develop Kantian accounts of modern physics:they are clear that their intention is to relativise the a priori. Bitbolet al. (2009) understand this as ‘‘making the a priori relative to acertain situation of science that can change from one step toanother of its history’’. The difference between the strongly andweakly Kantian accounts lies in how different authors interpretthis methodological demand. The stronger reading seems to takemathematical science as being a means to learn something of thecategories that govern the understanding: as science changes sodoes our knowledge of these categories. The weaker reading takesthis to be a requirement to look for scientific principles that area priori constraints on a particular scientific theory (and this in turncan be understood, as we will see, constitutively or regulatively).

In this review I discuss the historical basis for these differingapproaches: Kerszberg’s contribution explains the thinking behindthe strongly Kantian approach while some motivation for the weakapproach can be found in Schmitz-Rigal’s and Cei and French’sdiffering accounts of Cassirer. I then provide a brief overview of themost important part of the book—Transcendental Epistemologies and

Modern Physics—to capture something of the variety to be found inthe volume. Finally I select five papers from this section to discuss inmore depth. I look at the contributions of Friedman, Ryckman,Pringe, Bitbol and Petitot. Friedman, Ryckman and Pringe areconcerned to explain the conditions of the possibility of scientifictheories; Bitbol and Petitot seek to provide a novel version oftranscendentalism by laying out the conditions for the possibilityof our applying mathematical formalism to experience, in this sensethey are more concerned with the conditions of the possibility ofexperience in general. I suggest that, while the arguments of Bitboland Petitot are impressive, the former—more modest—brand ofKantianism has more promising prospects.

2. Historical transcendental readings of physics

The volume begins with a historical survey of transcendentalreadings of physics. Contributions from Friedman and Kerszbergprovide insightful treatments of Kant’s account of Newtonianphysics: Friedman discusses Kant’s regulative understanding ofNewton’s absolute space, while Kerszberg focuses on Kant’streatment of kinematics in the Metaphysical Foundations of Natural

Science and the Opus Postumum. In the Introduction the editorsmake it clear that they consider relativizing the a priori to be themost promising approach for preserving key Kantian intuitions inmodern physics: the historical precedent for this strategy isdeveloped in the second part of this section. Contributions bySchmitz-Rigal and Cei and French consider Cassirer’s neo-Kan-tianism, Bonnet and de Calan examine the Kantian roots ofSchlick’s conventionalism and Parrini provides a compelling casefor the enduring validity and relevance of Carnap’s conceptionof the relativized a priori, in spite of Quine’s renowned objectionsto it.

Kerszberg’s analysis of Kant’s transcendental account ofNewtonian mechanics is a useful starting point. This contributionoffers a helpful summary of Kant’s philosophy of science, whichshould enable those without too much background in Kantianphilosophy to grasp some of the Kantian arguments that follow.Kerszberg’s contribution is also a very useful one for clarifyinghow the strongly Kantian approach is meant to proceed.Kerszberg shows how the principles of pure understanding findexpression in Newtonian physics: the central idea is that incoming into contact with natural science, the pure concepts ofthe understanding ‘‘open themselves up to an outer representa-tion of what they are as pure ideas’’ (Kerszberg, p. 72). The ideaseems to be that in carrying a scientific theory through themoments of the categories, we may reveal something of how tooutwardly represent the principles of pure understanding. This,we will see in Section 4.2, seems to be precisely Petitot’smethodology in his contribution.

In the two articles on Cassirer, the historical foundation for aslightly different version of Kantianism begins to emerge.Schmitz-Rigal emphasises Cassirer’s concern with the possibilityof the historical development of scientific concepts; Cei andFrench focus on Cassirer’s philosophy of quantum mechanics toa structuralist reading of Cassirer, according to which the struc-ture of the laws of the theory constitute quantum objects.Both Schmitz-Rigal and Cei and French emphasise Cassirer’srejection of the Kantian distinction between the faculty of theunderstanding and the faculty of sensibility, which necessitatesreconsidering the Kantian notion of constitutivity. As suchboth articles provide an account of how Cassirer sought to re-store constitutivity without reference to Kant’s transcendentalfaculties. Schmitz-Rigal does so by emphasising the constitutiverole of symbols; Cei and French do so by emphasising theconstitutive role of the structure of scientific laws in the quantumcontext.

Schmitz-Rigal focuses on Cassirer’s claim that progress in eventhe most basic terms of a theory is an essential characteristic ofscience. That is, whereas Kant had taken the possibility of New-tonian science to be the important scientific fact that requiredtranscendental analysis, Cassirer understood this historical fact ofthe progress of knowledge (scientific or otherwise) to be the keyfact that stands in need of transcendental analysis. Knowledge,then, should not be treated as something fixed, instead it moreclosely resembles an operator whose functions and presupposi-tions Cassirer strove to discover.

In her contribution, Schmitz-Rigal nicely explores and clarifiesthe role that symbols played in Cassirer’s dynamic account ofknowledge. It is somewhat difficult to precisely pin down the rolesymbols in Cassirer’s philosophy, the most helpful way to initiallyunderstand them is as playing something like the role ofthe categories in Cassirer’s version of neo-Kantianism. Symbolicreference, then, is what allows us to refer ‘‘some-thing’’ as a definiteobject, they are ‘‘objectifying organisations’’ within a givendomain (whether this be physics, language, art, religion or mythetc.): each symbolic form provides rules within its field ofapplication. In the case of physics, these rules enable the physicist

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to constitute such properties of phenomena as stability, identifia-bility and re-identifiability, which permits the identification ofphysical phenomena as phenomena that can be a subject ofknowledge.

According to Schmitz-Rigal’s account, Cassirer’s main concernwas to explain a historical process of objectification. The emphasisis slightly different on Cei and French’s account: on this readingCassirer is concerned to explain the constitution of quantumobjects by way of the structure of scientific laws. Cei and Frenchargue that the core concept to this end is functional coordination,which is a fundamental, primitive, notion expressing a relation ofmutual coordination between two things. Cei and French suggestthat the purpose of this is to mimic Kant’s Schematism, butwithout the commitment to pure intuition by providing a ‘‘fixedlawful ordering of phenomena [to enable us] to speak of itsobjective significance’’ (Cassirer, 1907, quoted in Cei and French,p. 97). For Cei and French this is important because they arguethat Cassirer interprets causality as a general principle that grantsthe possibility of applying the idea of functional coordinationaccording to a law universally (p. 105).

The idea of laws is therefore central to Cei and French’s readingof Cassirer. Now, Cassirer understood a law as consisting of alogico-mathematical part and an empirical part arising fromexperience. Cei and French attempt to show that once thisunderstanding of law is combined with the idea of functionalcoordination, relations become conceptually prior to objects. Ifthis is so, they argue, the laws—in a sense—constitute theobjectivity of quantum objects.

In presenting Cassirer as a precursor to structuralism, Cei andFrench break somewhat with the received understanding ofCassirer’s work. Their argument is a novel one that deserves someattention. However, the point of these discussions of Cassirer is tohighlight that there is a different approach to Kantianism than theone advocated in the Introduction by the editors. On this versionof Kantianism, one carefully examines either a given scientifictheory or the development of a scientific theory to assess the roleof certain principles in respect to constituting the objectivity of

the theory: that is, it is not intended to generalise to apply eitherto experience as a whole or to permit anything resembling areconfiguring of the pure principles of the understanding in themanner that Kerszberg suggests.

3. An overview of proposed transcendental epistemologies

The next part of the book—Transcendental Epistemologies and

Modern Physics—is very much the heart of this rich editedcollection: we are presented with 19 different articles thatattempt to find a place for broadly Kantian intuitions in modernphysics. Some of these articles appeal to Kantian intuitions in onlythe very broadest sense. On occasion, it can seem as if the Kantianelement is not actually doing that much work in the paper andseems to appear as a rather ancillary consideration; whereas inother articles the Kantian motivation is set at centre-stage. Evenwithin the articles that offer a more determined attempt toexplain the constitutivity of objectivity, there is rich variety inthe sense in which this project is understood, depending on whatis meant by ‘‘objectivity’’. Some papers understand this in thestrongest sense, where what is to be explained is just how it isthat humans perceive objects; some papers understand theproject to be accounting for the intersubjectivity of scientifictheories. Some papers, I would suggest, pursue a quite differentproject where Kantian philosophy is not used to motivate a searchfor constitutive principles, but instead—through regulativeprinciples—is used to understand the historical development ofnew scientific theories.

Taken together the papers in this section provide a rich introduc-tion to a wide-range of methods for salvaging key Kantian intuitionsin modern physics: it is best used as a means of orientation withinthis growing discipline to see which paths seem most promising. It isimpossible to do full justice to all the papers, so instead of attemptingto do so I offer here a brief overview before turning my attention toexamining the two types of Kantianism that I take to have the bestprospect of success.

The first sub-section is intended to address general Kantianissues. This part of the book begins with Harre’s The Transcen-

dental Domain of Physics, which, while interesting in itself, doesnot really constitute an attempt to develop a transcendentalapproach in any substantial sense. Harre attempts to reconstructKant’s distinction between noumena and phenomena in terms oflevels of reality, some of which can be perceived and some ofwhich cannot. Harre’s contribution is, then, Kantian only in theloosest sense. Brittan’s article follows Harre’s and offers even lesscheer for the reader seeking to salvage some Kantian intuitions.Brittan suggests that the Kantian notion of causality should nowbe understood as entangled with the principle of separability,which the Bell result requires us to reject; we are left with a starkcontradiction between Kantian intuitions and quantum physics. Ifwe take the Bell theorem seriously and wish to remain Kantian,Brittan concludes, we must seek a new metaphysics of experi-ence. Mittelstaedt, in his contribution, discusses the constitutionof objects in classical and quantum physics: he argues that muchof the Kant’s transcendental strategy can be applied to thequantum realm as long as we abandon the requirement thatobjects be individuals and content ourselves with securing classes

of object.There is a slight change of pace in the next four articles, with

much more focus on the details of Kant’s philosophy. Boniolo’sarticle is centred around an account of the role of the laws ofnature in Kant’s critical works: he identifies three levels ofempirical law in Kant’s critical system and suggests that thisprovides a way to discriminate between nomological andaccidental universals. Kauark-Leite, inspired by the Marburgtradition, takes the Anticipations of Perception to contain theessence of Kant’s transcendental methodology. Having explainedhow this methodology works in the classical context, Kauark-Leite argues that the same methodology can be seen to shed lighton quantum physics. Stoltzner provides a detailed discussion of theprinciple of least action, arguing that it cannot be understood as aconstitutive principle and is, therefore, better understood as servinga regulative function. Falkenburg’s contribution ends the sub-sectionby summarising the major principles of Kant’s philosophy, andarguing that these may help us to develop an alternative to realistand empiricist accounts of subatomic reality.

There follows a brief a section on Kantian approaches torelativity and cosmology. Here Friedman and Ryckman attemptto develop nuanced historical accounts, according to which keyKantian intuitions played a role in the development of the theoryof relativity (these contributions will be discussed in more depthin Section 4). The third article in this section is Balashov’s accountof the role of transcendental arguments in physical cosmology.This is another paper that does not really live up to the promise ofproviding an account of the constitutivity of objectivity (or of howwe constitute the notion of objectivity). Balashov focuses on weak‘‘anthropic arguments’’, that is, arguments about our localuniverse being structured in such a way as to permit the existenceof beings capable of cognizing it. Balashov then provides acompelling argument for the historical relevance of this form ofargument in the development of cosmology. However, while thisresembles transcendental arguments—broadly construed—theKantian aspect of the paper is very much tangential to Balashov’soverall goal.

J. Everett / Studies in History and Philosophy of Modern Physics 43 (2012) 105–111108

Having dealt with general issues and space–time, attentionturns to quantum physics. The discussion of quantum physicsbegins with a section looking at the history of the development ofthe theory and its relationship with Kantianism. Brock and Pringeboth contribute papers that examine Kantian elements in Bohr’sthought. Brock attempts to unify certain aspects of Cassirer’s andBohr’s understanding of quantum physics and Pringe argues thatthe role of the principles of correspondence and complementarityin the development of Bohr’s theory is best understood as regulativein a Kantian sense. The historical section closes with Soler’sdiscussion of Grete Henry-Harmann’s 1935 attempt to renderKantianism and quantum physics consistent. Henry-Harmann is alittle-known figure in this field of study, and Soler’s article serves asa stimulating introduction to her work.

After the historical discussion of quantum mechanics, thefocus of the volume shifts to discussing Kantian approaches tomore recent developments in quantum physics. For example,Bitbol argues for a transcendental understanding of decoherence,according to which this phenomenon is part of a two-step processthat constitutes the outcomes of particular measurement events.Osnaghi’s paper comes next and covers what is, by now, somefamiliar ground: he argues, along similar lines to Cei and French,that if we are to constitute the objectivity of quantum objects wemust dispense with discussion of individual quantum objects and,like Bitbol, argues for a transcendental understanding of deco-herence. This part of the volume then concludes with Catrenproposing a novel definition of physical objects, with the aim ofarguing that quantum mechanical objects fit this definition morenaturally than classical objects. This is another contribution that isnot overtly Kantian in its approach, and, indeed, it is not entirelyclear how we should understand this paper as contributing to theoverall project.

The final part of this large section of Constituting Objectivity isconcerned with developments that go beyond quantum mechanics.The first paper—contributed by Stomatescu and Dosch, Muller andSieroka—attempts to grapple in thoroughly Cassirerian fashionswith the symbolic structure of modern physics, while the finalpaper is Petitot’s impressive attempt to develop a Kantian account ofnoncommutative geometry with not even a passing mention ofCassirer. Petitot’s paper is of greatest interest in this section: in itPetitot offers a truly impressive attempt to reconstruct the steps ofKant’s analysis of classical mechanics in line with the demands ofnoncommutative geometry.

From this brief overview of the articles in this section it is clearthat there are a number of different types of article found here.Some are careful historical pieces that clarify how Kantian philoso-phers have dealt with the challenge posed by modern physics; someapproach Kantianism only tangentially; some others are concernedto uncover the a priori basis for certain scientific theories; and someseek to fully re-evaluate the sense in which the objectivity ofperception is constituted. In the following, final section, I look atsome of the contributions that pursue the latter two approachesmost successfully in my view, and to give an indication of thedifferences in approach.

4. Strong and modest Kantianism

In Section 2, I emphasised that there seem to be two broadways in which philosophers have sought to apply Kantianphilosophy to modern physics. Firstly, we saw Kerszberg indicatea potential way forward by taking the development of modernscience to bear on our consideration of the Kantian categories.Secondly, we have seen Cassirer seek to move away from thetranscendental faculty of psychology and to focus on the role ofcertain principles within science itself. In this section I explore

how these alternative approaches manifest themselves in thecentral part of this edited collection.

4.1. A priori scientific principles

Let us begin by looking at some of the papers that advocate theweaker Kantian approach: I will focus on the contributions ofFriedman, Ryckman and Pringe. Each of these papers proceed byconsidering the role of certain key principles in the historicaldevelopment of a scientific theory: Friedman considers the role ofthe light postulate and equivalence principle in the developmentof general relativity; Ryckman examines the role of the require-ment of gauge invariance in the development of general relativ-ity; and Pringe argues that the principles of correspondence andcomplementarity play a regulative role in the development ofquantum physics. What these papers, and the others that advo-cate this approach, have in common is that they take particularscientific principles to be a priori requirements for the develop-ment of a particular theory, but do not take any additional stepsto suggest anything about the nature of the faculty of the under-standing. Rather, all can broadly be seen to advocate a regulativeunderstanding of the role of these principles.

Friedman’s paper ‘Einstein, Kant, and the Relativized A Priori’,represents a further development of the main line of argument inhis Dynamics of Reason (2001). Friedman clarifies (p. 254) that heintended the main argument in this work to be a historicalaccount of how theories of space–time developed from Newtonto Einstein as mediated by concurrent developments in thephilosophy of science, particularly those of Helmholtz, Machand Poincare. Friedman tackles the issue as to how an essentiallyhistorical argument should be understood within the context oftranscendental philosophy. That is, how, when the historicaldetails are entirely contingent can the argument be compre-hended within the context of transcendental philosophy (which,Friedman says, is intended to provide necessary preconditions ofknowledge).

Friedman solves this problem by arguing that at each stage ofthe development of space–time theories, given the intellectualtools available at the time, each successive transformation of theconception of space–time was necessary. So, prior to Kant’sintervention in the debate as to the nature of space the possibleapproaches were exhausted by Newton’s conception of absolutespace and Leibniz’s relationalism. However, given both Kant’sunique account of the human intellect and the fact that explana-tions of phenomena in terms of human cognitive faculties weredeemed acceptable in the late eighteenth century, the third waythat Kant found between Newton and Leibniz was the only

possible one. In that sense, though the tools and possibilities thatKant had to work with were quite contingent, the conclusion thathe came to (given these tools) was necessary.

Friedman goes on to claim that Kant’s particular means ofconnecting the foundations of geometry to the relativity of motionwere then successively transformed by Helmholtz and Poincare,and as such ultimately played a crucial role the development ofgeneral relativity. Helmholtz’s geometry is taken to be the mini-mal extension of Kant’s geometry once Lobachevskii, Bolyai andRiemann have firmly established their non-Euclidean geometries.Friedman treats Poincare’s conventionalist methodology as thenatural extension of Helmholtz’s work in light of Lie’s moresophisticated group-theoretic account of geometry and the devel-opment of the concept of an inertial frame. Einstein, Friedmanclaims, situates his understanding of geometry between Helm-hotz’s and Poincare’s. The crucial thought experiment, for Fried-man, is the relativistically rotating disc. According to the theory ofrelativity—crucially involving the light postulate—if you have arotating disc then measuring rods placed along the axis do not

J. Everett / Studies in History and Philosophy of Modern Physics 43 (2012) 105–111 109

contract whereas rods placed along the circumference do contract.This means that more unit measuring rods fit along the circum-ference than one would expect in Euclidean geometry and that,therefore, the circumference is measured as greater than pd.Einstein suggests that while Poincare is correct sub specie aeterni,we should provisionally rely on Helmholtz’s conception of practi-cally rigid bodies to conclude that space–time geometry isempirically determined as non-Euclidean (this step is permittedby Einstein’s equivalence principle which unites gravitational andinertial effects).

This is a hugely truncated form of a delicate historical analysis,but hopefully it is sufficient to show the sort of move thatFriedman is advocating. The idea is that Kant’s key geometricalinsight—transformed through the work of Poincare andHelmholtz—in addition with the light postulate and the equiva-lence principle, are necessary conditions for the development ofgeneral relativity.

Ryckman, similarly, is concerned with showing that therequirement of gauge invariance in the development of purelyinfinitesimal geometry acts as an a priori ‘‘constraint of reason-ableness’’ (p. 296) based on ideas of finitism and the relations ofcongruence and immediate comparison (especially relating tovectors). Weyl’s account of gravitation is motivated by aperceived inconsistency in Riemann’s geometry whereby themagnitude and orientation of vectors are treated asymmetrically:when one transports, in infinitesimal steps, a vector around aclosed path, when it returns to its starting position its orientationwill have changed, but its length will not have. As a consequence,it is only possible to compare lengths of a vector that areseparated by an arbitrary distance: one cannot so compareorientations. Weyl—influenced by Husserl—took this to be asituation in need of remedy: Weyl solved the problem byconstructing a geometry in which both the length and orientationof vectors can only be immediately compared.

Weyl, therefore, amends Riemannian geometry by insistingthat in both the case of orientation and length the comparisonmust take place by parallel transport of a comparison vector ininfinitesimal steps along the path between the two vectors wewish to compare. With the Riemannian account so-adjusted, Weylshows that it now has a much weaker, conformal structure. Thismeans that the length of a vector at any point is arbitrary: incomparing vectors, then, the meaningful comparisons we canmake are as to the angle between them and as to their relativelengths. This gives rise to a metrically connected manifold,defining a broad set of physically possible geometries from whichthe actual world-geometry must be distinguished. It is at thispoint that Weyl requires the univocal choice of a gauge invariantaction function on the metric and electromagnetic four-potential.This, Ryckman argues, was introduced primarily as an a priori

constraint of reasonableness. This assigns a regulative role togauge freedom: it arises primarily from the requirement of reasonthat the physical interpretation of the mathematical formulationof a theory should be compatible with the mathematics.

I will consider Pringe’s contribution briefly here to give an ideaof how this sort of analysis might be seen to work in the quantumrealm—though Brock’s article would serve as well for thispurpose. Pringe examines Bohr’s development of quantum theoryand argues that the principles of correspondence and comple-mentarity should be understood as playing a regulative role inBohr’s thought. Pringe understands the principle of correspon-dence to just be the methodological demand to seek analogiesbetween quantum and classical physics.1 It is based on the idea

1 There is slight confusion here: while Pringe is correct that this is how Bohr

came to understand the principle, this is not how Bohr initially intended the

that there may be a perfect similarity between two relations inentirely dissimilar things: so, if there is a relation between twoobjects in classical physics we may—by this principle—take thereto be the same relation between two quantum objects. Pringeargues that the principle is chiefly motivated by the idea of thesystematicity of nature and, as such, should be understood as aregulative principle.

Bohr, indeed, goes so far as to suggest that classical objects actas ‘‘symbolic analogies’’ to enable the interpretation of quantumformalism: in particular this is needed to import notions ofspatio-temporal location and causality into the theory (thesebeing necessary for a theory to have objective validity). So incertain situations, we may treat a quantum object either as if itwere either a classical particle or as if it were a wave. Comple-mentarity enters the picture by ensuring systematic unity, in linewith the regulative demands of reason. Because quantum objectsbehave in some situations as if they were a wave and in someothers as if they were a particle, complementarity is introduced asthe claim that only the totality of the phenomena exhausts theinformation about the quantum object. That is, complementarityacts to ensure that both wave-like and particle-like phenomenaare phenomena of the one quantum object.

Pringe, then, presents a picture according to which thecorrespondence principle guides the reflective judgement oncesymbolic analogies are established and complementarity enablesthe treatment of various symbols as belonging to the onequantum object. This analysis, then, has much in common withthe sort of understanding of the progress of science suggested byCassirer: in particular, the category of causation plays a regulativerole in the development of science while—with the addition ofclassical symbols—constitutes the objectivity of the developingtheory.

The sort of approach exemplified in these articles provides aKantian account of the development of scientific theories that doesnot seek to constitute the objectivity of experience in general butinstead focuses on the objectivity of individual theories. In the nextsection I will consider how the stronger form of Kantianism ispursued.

4.2. Constituting the objects of perception

In contrast with the papers that advocate a more modestversion of Kantianism, some contributions seek to develop amuch stronger version of Kantianism. The stronger Kantianproject seeks to explain the constitution not just of scientificobjects but also the objects of perception. I shall first look atBitbol’s argument that decoherence can be understood in atranscendental fashion, whereby it acts as part of a two-stepprocess to constitute experience: that is, it is a necessaryprecondition for the experience of observing the particular out-comes of measurements. I also examine Petitot’s transcendentalanalysis of noncommutative geometry (NCG) in which it is arguedthat NCG permits the mathematical construction of the physicalcontent of the category of substance.

Bitbol, in his contribution to the volume, argues that deco-herence should be understood as playing a constitutive role inquantum physics. He construes his approach as a third waybetween realist and empiricist understandings of decoherence.The realist understanding of decoherence portrays it as a meansto solve the measurement problem and explain the distinctionbetween the classical and quantum realms. Decoherence, on

(footnote continued)

principle in 1916 when the principle stated that the laws of classical electro-

dynamics should still apply in the quantum domain for high quantum numbers.

J. Everett / Studies in History and Philosophy of Modern Physics 43 (2012) 105–111110

the realist interpretation, is a result of spontaneous interac-tions between a system and its environment that results in thesuppression of interference terms, effectively selecting one termof a superposition. That is, decoherence is taken to be themechanism that ultimately explains why a universe that isfundamentally governed by quantum laws appears to be macro-scopically classical.

The empiricist understanding of quantum mechanics is just asa set of rules that allow the calculation of the probabilities of theexperimental outcomes. So, as Bitbol (p. 351) explains, theempiricist understands a quantum system in terms of an equiva-lence class of specified experimental preparations and a quantumstate only as the probabilities of the various outcomes of con-ceivable experiments. Quantum systems and states should not, onthis view, be understood as implying anything about underlyingreality: they are purely instrumental in predicting certain obser-vable outcomes. Decoherence on this view clearly is not needed toexplain the emergence of classical reality—that is the only realityan empiricist accepts—instead its role is to explain how standardKolmogorovian probabilities emerge from quantum probabilities.That is, it operates at the level of recovering classical probabilitiesfrom quantum probabilities.

Bitbol’s transcendental understanding of decoherence aims tostrike a middle-ground between these realist and empiricistextremes: rather than treating formal universals or factual parti-culars as real, Bitbol argues that what is fundamental is theprocess by which we define formal universals and factual parti-culars in terms of one another. Therefore, for Bitbol the formalismis understood as going beyond empiricism because it is not seenas a mere tool for predicting the observed results of measure-ments: instead, it is understood as constitutive ‘in the sensethat it endows facts with objective meaning by construing themas aspects of a structural invariant’’ (p. 355). The process bywhich the formalism constitutes objectivity is, on Bitbol’saccount, composed of two steps: decoherence is the second ofthese steps.

The first step is concerned with the quantum formalism as awhole, which Bitbol takes to prescribe a statistical order to micro-events. The state-vectors that appear in the formalism aredecontextualised probabilistic invariants whose evolution isgoverned by deterministic equations. Bitbol suggests that simplyby virtue of their being decontextualised—that is detached fromparticular circumstances—these state vectors are constitutive inthe sense that they can be applied generally to any circumstanceto allow us to anticipate a given outcome. Decoherence isinvolved in the second step of the constitutive process: its roleis to show how recognisably classical invariants can be madecompatible with the new invariants of the quantum formalism.Decoherence is a necessary part of the constitutive process ofquantum theory because it enables us to see how the world of theexperimentalists emerges from the formalism by demanding thatif the formalism is to apply to the classical world then it must beinterference-free. Therefore, this constitutive step amounts to ademand placed on the formalism to render it compatible withobservation.

It is worth noting that in his contribution Bitbol is seeking toexplain not just the sense in which quantum objects areconstituted—which, as we saw in Section 3 many of the othercontributors content themselves to doing—but also to explainhow the quantum formalism plays a role in constituting ourexperience of the objects of perception. Petitot’s contribution isengaged in a similar project: he argues that constitutive principleshave a crucial role to play in a given scientific theory in that theyrender both the mathematical formulation and empirical applica-tion of the theory possible in the first place. His focus ison uncovering the constitutive principles of noncommutative

geometry (NCG) and construing them as categories (in somethingvery close to Kant’s sense).

Petitot’s ambition is immediately striking: just as Kant con-strued classical mechanics through the moments of the cate-gories, Petitot intends to construe NCG through the moments ofthe categories and in so doing provide a novel mathematicalinterpretation of the categories of physical objectivity. So, forexample, he shows that the metric of NCG, rather than acting as abackground structure, acts in the same way as the metric ingeneral relativity (as a physical field). Forces, on the other hand,are considered as part of the background structure rather than asa physical field. This is characterised in terms of geometrybelonging to the Mechanical moment of MFNS while force belongsto the Phenomenological moment. This article is by far the longestand most mathematically demanding in the volume, as such it isdifficult to give a more detailed account than this: it remains themost sustained attempt to combine cutting-edge physics with astrong form of Kantianism that I have come across and for thatalone is well worth detailed study.

In these contributions there is a more concerted attempt torecover the objects of perceptual experience than we saw in thepapers we considered in the previous section. The contributionsof the sort considered in the previous section tend to followbroadly Cassirerian intuitions in rejecting the division betweenthe understanding and sensibility and develop Kantian approachesthat are more concerned with the regulative role in the develop-ment of theories. In these papers there is no such clear rejection ofthis distinction and they seem to be engaged in a more purelyKantian project of explaining the relation between perception andthe way in which we come to have knowledge of the objects ofperception.

5. Concluding remarks

Constituting Objectivity is a rich collection of essays thatprovide detailed historical case studies and examine the role oftranscendental methodology in the development of currentscience. My focus in this review has been on trying to draw outand elucidate two different transcendental approaches thatappear throughout the volume: one calls for an integratedapproach to the history and philosophy of science and chartsthe role of regulative principles in guiding the development ofscientific theories; while the other is concerned with providingthe most plausible conditions for the possibility of experience ingeneral, by examining our best current scientific theories. Bothapproaches have their merits and the articles I have highlighted—

as well as some of those that I have not—make convinc-ing cases for understanding certain principles as constitutivein the relevant respect. I tend to find those contributions thatfocus on the historical development of scientific theories moreconvincing.

There is a slight lack of clarity over how far Kerszberg, Bitboland Petitot intend the Kantian project to go. Given Kerszberg’scontribution, in which he seems to provide a groundwork forrevising pure concepts of the understanding in light of thedevelopment of science and Petitot’s very deliberate attempt toconstrue NCG in line with the four moments of the categories, itseems most plausible that the editors intend to provide a meansto re-configure the rules that govern the understanding. This is ahugely ambitious project, worthy of detailed study; howeverI have concerns over the willingness in these papers to takeKant’s transcendental project—in particular the idea that scien-tific theories in some way need to be carried through categoricalmoments—too seriously. Those papers that instead emphasiseKant’s philosophy of science as found in his third Critique, and

J. Everett / Studies in History and Philosophy of Modern Physics 43 (2012) 105–111 111

focus on the regulative role of scientific principles within thecontext of the relevant theory seem, to me, to promise a moreplausible route to a Kantian account of modern physics.

The volume as a whole, then, provides a spectrum of Kantianinsights into how to understand both the development of modernphysics and modern physics itself. Any reader with an interest inKant’s philosophy and the challenge posed to it by subsequentrevolutions in physics will find a great number of stimulatingarticles in this edited collection. The volume may also be ofinterest to philosophers of physics more generally in terms ofintroducing novel ways to consider some persistent foundationalproblems, and works as an exemplary piece of integrated HPS:historical sensitivity is demonstrated in most of the discussions

and clear philosophical lessons are drawn and eventually appliedto contemporary physics.

References

Bitbol, Michel, Kerszberg, Pierre, & Petitot, Jean (Eds.), (2009). Constitutingobjectivity: Transcendental perspectives on modern physics. Berlin: Springer.viiiþ544 pp., ISBN 9781402095092 9 (h169.95 (hardback)).

DiSalle, Robert (2006). Understanding space–time: The philosophical development ofphysics from Newton to Einstein. Cambridge: Cambridge University Press.

Friedman, Michael (2001). Dynamics of reason: The 1999 Kant Lectures atStanford University. CSLI Publications.

Ryckman, Thomas (2005). The reign of relativity: Physics in philosophy 1915–1925.Oxford: Oxford University Press.