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The Real Virtue of Friedman's Neo-Kantian Philosophy of Science*Bket

Michael Friedman has recently developed a neo-Kantian conception of science as arival to holistic accounts. According to Friedman, the main virtue of his neo-Kantianphilosophy is that it resolves the problem of incommensurability. A close reading ofFriedman's work, however, indicates that his account surprisingly accomplishes theopposite of what he believes to have defended. This article will argue that the realvirtue of Friedman's neo-Kantian account of scientific theories is not that it resolvesthe problem of incommensurability but that it provides an elegant philosophical ac-count much needed to substantiate Thomas Kuhn's historical thesis of incommensura-bility.

1. Introduction. Recently, Michael Friedman has argued that his newKantian account of the structure of scientific theories, primarily developedas a rival to holistic accounts, has the virtue of resolving the problem ofincommensurabihty. The notion of incommensurability first appeared inThomas Kuhn's The Structure of Scientific Revolutions (1962), which hashad a great impact on the philosophy of science since it was published.The central thesis of the book is that rival revolutionary scientific theoriesare not commensurable. What substantiates this thesis is Kunh's twofoldclaim that perceptual experience is theory dependent and rival revolu-* Received December 2009; revised March 2010.tTo contact the author, please write to: Departm ent of Philosophy, University of NotreDame, 100 Malloy Hall, Notre Dame, IN 46556; e-mail: bkorkut@nd.edu.JMy gratitude goes to Don Howard for his positive comments on the earliest versionof this article and to the participants of the History and Philosophy of Science dis-cussion group at the University of Notre Dame for their feedback on a presentation

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2 BKET KORKUTtionary theories have radically different conceptual frameworks (or inKuhn's term, paradigms) within which even the seemingly common no-tions of these theories possess different meaning. This implies that whatcounts as empirical evidence from the perspective of one theory cannotbe recognized as empirical evidence from the perspective of a rival one.It then follows that empirical evidence cannot decide between two rivalrevolutionary theories.'The thesis of incommensurability was widely interpreted to imply sci-entific relativism and even irrational theory choice. In his later writings,Kuhn rejected the radical implications of his account. Nevertheless, theincommensurability thesis, even in its moderate form, undermines thepossibility of theory choice based on a genuine empirical test. That is whyit is still considered to be a central problem in the contemporary philos-ophy of science.In his recent works, Friedman addresses precisely this problem andclaims that his neo-Kantian philosophy has the resources to explain howtheory choice based on a genuine empirical test is still possible. Friedmanbasically argues that the problem of incommensurability can finally beresolved through a crucial experiment designed from a retrospective viewof revolutionary scientific transitions given by his new synthesis of ErnstCassirer's insight into the constitutive role of mathematical structures inphysics and Hans Reichenbach's insight into the necessity of coordinatingprinciples for establishing a connection between mathematical structuresand empirical phenomena.^The attractiveness of Friedman's project cannot be denied. Neverthe-less, a closer look at his program reveals that it is far from accomplishingits promise. On the contrary, his philosophy, primarily developed in Dy-namics of Reason, understood correctly, not only leads to the problem ofincommensurability but actually substantiates the thesis itself. From1. In the philosophical literature, Kuhn's thesis is considered to involve three types ofincommensurability: (1) perceptual (perceptual experience cannot provide a commonground for theory comparison), (2) semantic (the languages of two rival revolutionarytheories are not intertranslatable, and intertranslatability is required for the possibilityof theory comparison), and (3) methodological (there is no common measure of com-parison because the methods of evaluation are different). According to my interpre-tation here, 3 is a natural outcome of 1 and 2 because even if empirical confirmationcan reasonably be counted as a common method of evaluation, 1 and 2 together implythat there can be no common empirical measure of comparison, for what is perceivedto be empirical evidence depends on the theory in view and cannot be translated into

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Friedman's perspective, this, if true, would undermine the credibility ofhis account. Seen from another perspective, however, if Friedman's centralneo-Kantian claims are true (and my argument in this article is sound),we then have an elegant philosophical account of the incommensurabilitythesis that substantiates Kuhn's historical analysis. In a word, I arguethat the virtue of Friedman's neo-Kantian philosophy of science is notthat it resolves the problem of incommensurability, as Friedman believesit to be, but that it gives philosophical substance to the thesis of incom-mensurability.

I will reach this conclusion in three stages. To prepare the ground, Iwill first give a summary of Friedman's philosophical account. Next, Iwill discuss his conception of crucial experiment, which, according toFriedman, not only distinguishes his account from holistic ones but alsoshows how the problem of incommensurability can be resolved. Partic-ularly, I will explain his exemplary crucial experiment designed to com pareNewtonian physics and Einstein's theory of relativity. I will then highlightthe inconsistency between the requirements of Friedman's conception ofcrucial experiment and his account of the role of constitutive principles ina scientific theory. In the final section, I will argue that this inconsistencyimplies either the implausibility of Friedman's philosophical account ofscientific theories (more precisely, his conception of the role of constitutiveprinciples) or the impossibility of designing a crucial experiment com-patible with his account of scientific theories. An adequate understandingof this inconsistency, as I will argue, suggests that Friedman's overallaccount is not merely committed to the incommensurability thesis but hasactually given us much needed philosophical arguments for why and howthe incommensurability thesis can be substantiated from a certain neo-Kantian point of view.'2. The Dynamics of Friedman's Philosophy of Science. According toFriedman's dynamic but differentiated account of knowledge, theories inmathematical physics consist of three asymmetrically functioning parts:a mathematical part, a mechanical part, and a properly empirical part.The mathematical part contains the abstract mathematical structures. Themechanical part is composed of coordinating principles, which connectthe mathematical part to the concrete empirical phenomena. Finally, theempirical part contains the empirical laws. Friedman calls the principles

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4 BKET KORKUTof the first two (mathematical and mechanical) parts, constitutive (or re-lativized a priori) principles. Following Hans Reichenbach's account,Friedman drops the apodictic character of a priori, for he believes thatconstitutively a priori principles can be redefined relative to the theoriesin question. Still, for him, the role of constitutive principles "is to providethe necessary framework within which the testing of properly empiricallaws is then possible" (2001, 83). In a word, "constitutive principles arenecessary conditions of the possibility of properly empirical laws" (74).Friedman explains that his notion of possibility should not be under-stood in terms of merely logical possibility. The notion of possibility, forFriedman, has two distinguishable aspects, namely, logical possibilityand empirical (or real) possibility. Logical possibility is given by themathematical part of a constitutive framework. Mere logical possibility,however, does not secure empirical possibility. According to Friedman,empirical possibility is provided by the coordinating principles of a con-stitutive framework. In this way, a constitutive framework "secures theempirical content of the theory" (2001, 83), for it "defines a space ofempirical possibilities (statements that can be empirically true or false)"(84). And an empirical test against the background of such a frameworkindicates "which empirical possibilities are actualized," that is, which em-pirical statements are true or false (84).According to Friedman, then, constitutive principles are necessary con-ditions of not only logical possibility but also empirical possibility (i.e.,possession of empirical content), for "without a constitutive framework,the putatively empirical laws would have no empirical content after all"(2001, 83). He explains this further in the following statement: "We havesaid that constitutive principles are necessary conditions of the possibilityof properly empirical laws. But this does not mean that they are necessaryconditions in the standard sense, where A is a necessary condition of Bsimply if B implies A. To say that A is a constitutive condition of B rathermeans that A is a necessary condition, not simply of the truth of B, butof B's meaningfulness or possession of a truth value. It means, in nowrelatively familiar terminology, that A is a presupposition of B" (74). Fried-man restricts the relevance of his notion o presupposition mainly to thearea of mathematical physics. Still, he considers that constitutive prin-ciples of mathematical physics also function as presuppositions of allempirical truths, at least, in the natural sciences, as he claims: "We wantto reserve this characterization for particularly fundamental presuppo-

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ularly in the area of mathematical physics and, accordingly, in the naturalsciences in general.Friedman also provides us with examples of constitutive principles fortwo revolutionary theories of physics, namely, Newtonian physics andEinstein's general theory of relativity. In Newtonian physics, viewed ret-rospectively, says Friedman, the constitutive framework is given by Eu-clidean geometry and the laws of motion; while the former belongs to themathematical part, the latter belongs to the mechanical part and functionsas coordinating principles (2001, 16-11). In Einstein's general theory ofrelativity, the constitutive principles consist of the four-dimensional (semi-)Riemannian manifold of variable curvature, as the mathematical par t and

the two coordinating principles, the light principle and the principle ofequivalence. As Friedman explains, the light principle, "the law of con-stancy and source-independence of the velocity of light coordinates con-crete physical phenomena with the Lorentzian (or infinitesimally Min-kowskian) character of the new four dimensional space-time metric," andthe principle of equivalence, "the law that freely falling 'test particles' ina gravitational field follow four dimensional geodesic paths of this metricthen completes the coordination" (79).3. Friedman's Crucial Experiment Reveals the Crucial Problem. In orderto overcome the problem of incommensurability, Friedman aims to givea conception of an empirical test stronger than both a pragmatic and ahypothetico-deductive view of empirical evidence. According to Fried-man, a pragmatic approach considers scientific theories merely as instru-ments of prediction and, therefore, takes empirical evidence as a matterof accurate prediction, and the hypothetico-deductive account appeals onlyto inferential relationships among the statements, and hence, from theperspective of this approach, empirical confirmation can only be viewedas a test of the logical conjunction of statements as a whole, whichamounts to a holistic conception of confirmation that supports Quineanphilosophy of science (2001, 83-85). Friedman argues that his account ofa constitutive framework has the resources to substantiate a strongernotion of empirical evidence that can overcome the shortcomings of botha pragmatic and a holistic conception.Friedman first sets his standard of empirical confirmation in the fol-lowing way:

In our present conception, by contrast, physical coordinating prin-

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6 BKET KORKUTpresent sense, for accepting these field equations as empirically true,but it does not count, in the same sense, as an empirical reason foraccepting the principle of equivalence. Indeed, as we have seen, ifthe principle of equivalence is not already accepted prior to thisprocedure, it cannot generate empirical evidence for Einstein's equa-tions a t allwhich rather, without the principle of equivalence, revertto being merely logically possible. (2001, 85-86)

Friedman basically argues that even in the face of empirical evidence (e.g.,the advance of the perihelion of Mercury), coordinative principles of aconstitutive framework (such as the principle of equivalence in E instein'stheory) cannot yet be regarded as empirically tested. He claims that em-pirical evidence for such principles within different frameworks can onlybe empirical motivation for our decision of fixing them as coordinatingprinciples for a new framework but not a genuine empirical test of thoseprinciples (87-91).According to Friedman, the Michelson-Morley and Lorand von Etvsexperiments, which are framed within an essentially classical spatio-temporalstructure, can provide only empirical motivation for Einstein to choosethe light principle and the principle of equivalence as the coordinatingprinciples of the general theory of relativity. These experiments, accordingto Friedman's standard, cannot count as empirical tests of general rela-tivity because the two coordinating principles, the light principle and theprinciple of equivalence, are essential for providing the new space-timestructure with a "determinate empirical meaning," and their elevation tothe status of coordinating principles (to accomplish this task) involves a"non-empirical element of decision" (2001, 88). In a word, Friedmanargues that the results of these experiments do not count as genuineempirical evidence for general relativity because coordinating principlesare not empirically tested in these experiments. To resolve the problemof incomm ensurability, then, "the crucial question," for Friedm an, is howcoordinating principles can be "empirically tested and confirmed (or dis-confirmed) in the same sense as those principles I am [he is] here char-acterizing as properly empirical laws" (87).For a better understanding, we shall focus on a specific coordinatingprinciple to see what is considered to be an empirical motivation forpreferring it to other principles but not yet a genuine empirical test of it;for instance, the light principle, that is, the principle of the invariance ofthe velocity of light. Friedman rightly argues that the Michelson-Morley

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FRIEDMA N'S NEO-KANTIAN PHILOSOPHY OF SCIENCE 7experiment' of special relativity with respect to its theoretical alternatives;and it is not a test, for precisely this reason, of the relativistic light prin-ciple" (2001, 87). For Friedm an, the crucial point is that in this experimentthe light principle is tested within a constitutive frameworkbased on"essentially classical spatio-temporal structure"in which there is noplace for relativity theory (87). That is why the experiment cannot beviewed as a crucial experiment of relativity theory with respect to theNewtonian theory, and for this reason, it cannot be seen as an empiricaltest of the relativistic light principle.

According to Friedman, to confirm a theory empirically, one shouldmake a crucial experiment designed within a common constitutive frame-work under which two rival theories can be placed. Such an experimentis central to Friedman's account of an empirical test for distinguishinghis view from holistic accounts and, more crucially, for resolving theproblem of incommensurability. In order to show how this kind of genuineempirical test is possible, Friedm an designs a crucial experiment for com-paring the Newtonian theory and general relativity. He argues that wecan give an alternative formulation to the Newtonian theory of gravitationbased on freely falling trajectories in a gravitational fielda new for-mulation that is still empirically equivalent to the traditional Newtoniantheory. Such an alternative formulation, according to Friedman, placesthe New tonian theory in a new constitutive framework, "given, essentially,by the Riemannian theory of manifolds and the principle of equivalence,"in which we can also place the general theory of relativity (2001, 92).

In this common constitutive framework, it is then possible to comparethe two rival theories, the Newtonian theory and general relativity, "usinga common notion of real [empirical] possibility and a common notion ofempirical evidence" (2001, 92). Hence, for Friedman, the advance of theperihelion of Mercury now counts as genuine empirical evidence for gen-eral relativity. More specifically, what is regarded to be confirmed by ex-perience is the special relativistic light principle, as Friedman explains:In this framework we can now compare both the Newtonian theoryand general relativity using a common notion of real possibility anda common notion of empirical evidence; and, of course, general rel-ativity now comes out as confirmed by the evidence (such as theadvance of the perihelion of Mercury) in preference to the N ewtoniantheory. . . . In other words, what is here preferentially confirmed by

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8 BKET KORKUTstage. But this is just as it should be on a truly dynamical conceptionof the a priori. (2001, 92)

First, it is crucial to be clear about the status of the light principle andalso to specify the constitutive principles of this common constitutiveframework. Friedman rightly does not count the light principle amongthe constitutive principles of this framework. The light principle appearsas an empirical statement within this common framework. Otherwise, itwould not be possible to argue that the light principle is confirmed em-pirically.Friedman says that this common constitutive framework is "given, es-sentially, by the Riemannian theory of manifolds and the principle ofequivalence" (2001, 92). Let us recall that, according to Friedman, theconstitutive framework of general relativity is composed of a mathemat-ical part (i.e., the Riemannian theory of manifolds) and the two coor-dinating principles, the principle of equivalence and the light principle.In the common framework, however, the light principle is no longercounted as a coordinating principle; rather, it is considered to be an em-pirical statement under test. But, if the light principle is now an empiricalstatement, do we not need another coordinating principle for the commonframework that can play the role of the light principle, that is, that canprovide the coordination between the mathematical part of the commonframework and the empirical phenomena? Indeed, we do, as Friedmanalso explains in a note: "Indeed, in imagining carrying out the aboveempirical test of the light principle we are tacitly supposing the availabilityof an alternative empirical coordination for spatio-temporal structuresuch as one based (at least infinitesimally) on rigid bodies and physicalclocks. This leads to subtle problems which cannot be discussed here" (92n. 29).Let us leave aside for a moment the possible problems involved infinding the required coordinating principles and simply assume that thereare such principles that provide us with an alternative empirical coordi-nation for the common framework. We also assumed that the light prin-ciple is an empirical statement within this common framework since it isempirically confirmable. But does the light principle still count as a con-stitutive principle in general relativity? Friedman explicitly says that itdoes: "The light principle still counts as constitutive in general relativity,however, for we can still use it to define the infinitesimally Minkowskianmetrical structure" (2001, 92 n. 29). But does 'the light principle' char-

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If Friedman gives a negative answer (i.e., that the light principle doesnot have the same empirical content within these two different constitutiveframeworks), then how can he count this experiment as an empirical testof "the relativistic light principle"? In other words, it is then unclear howFriedman can consider the advance of the perihelion of Mercury as gen-uine empirical evidence for the light principle in particular and for thegeneral theory of relativity in general. For Friedman, this crucial exper-iment exemplifies how an empirical comparison of two rival theories isgenuinely possible. It follows that if Friedman still wants to consider thisexperiment as crucial, he is compelled to give a positive answer; namely,the light principle in this imaginary common framework has the sameempirical content as the light principle of general relativity.But a positive answer has its own problems. The coordinating principlesof the common constitutive framework, like any other coordinating prin-ciple, define what Friedman calls empirical possibility. Friedman has al-ready informed us that without coordinating principles the empiricalclaims (in mathematical physics) would have no empirical content. Weassumed that the light principle is an empirical statement within thiscommon framework since it is empirically confirmable. It then followsthat without the coordinating principles of the common framework, theavailability of which Friedman tacitly supposes, the light principle wouldhave no empirical content in this crucial experiment. In other words, thecoordinating principles of the common framework are the necessary con-ditions of the meaningfulness of the light principle, for it is an empiricalstatement within this framework. However, the genuine constitutiveframework of general relativity does not include those specific coordi-nating principles of the common framework among its coordinating prin-ciples. If the coordinating principles of the common framework are nec-essary conditions of the empirical meaningfulness of the light principle,then it is not clear how the light principle can possess the same empiricalcontent within general relativity, which does not include those specificcoordinating principles.

If the light principle manages to have the same empirical content inboth frameworks (i.e., the framework of general relativity and the com-mon framework of the imaginary crucial experiment), then the only plau-sible way to explain the situation is that the coordinative principles ofthe common framework are not necessary conditions for the light principleto have an empirical content. It follows that some proper empirical state-

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10 BKET KORKUTsuppositions, that is, necessary conditions of the meaningfulness of em-pirical statements?

Perhaps the dilemma here partly reveals what Friedman means by the"subtle problems" that arise in our search for an alternative empiricalcoordination for the common framework, the availability of which hetacitly assumes. But what seems more mysterious is how Friedman, with-out explicitly providing these alternative coordinating principles of thecommon framework, could still imagine that the statements in this frame-work would have an empirical content and even discuss the confirmationof an empirical statement, namely, the light principle.**If my argument above is sound, then either the light principle does nothave the same empirical content both in general relativity and in thecommon framework, which means that the crucial experiment falls shortof being "crucial" (i.e., being an empirical test of the relativistic lightprinciple), or the light principle possesses the same empirical content inboth of the frameworks, which implies that this crucial experiment canserve Friedm an's purposes only at the price of inconsistency with the roleof the coordinating principles (as presuppositions of empirical possibility).In general terms, the problem can be formulated in the following way.According to F riedman's standard, for a genuine comparison of two rivalrevolutionary theories, we need to design a crucial experiment with ashared constitutive framework in order to test a coordinating principleof one of the two rival revolutionary theories, say, the C principle. Theproblem is that without violating the role of coordinating principles aspresuppositions of empirical possibility, one cannot, in principle, providea shared constitutive framework under which both theories can be placed:because such a shared framework requires new coordinating principles,and according to Friedman's position, these new coordinating principlesshould both (i) be necessary conditions of the empirical meaningfulnessof the C principle as an empirical statement under test and (ii) preservethe same empirical content that this C principle has within the originalframework of the theory in which it functions as a coordinating principle,but conditions (i) and (ii) are incompatible, for the satisfaction of (ii) impliesthe refutation of (i). And without satisfying (ii), the experiment falls shortof being crucial. This simply means that if we do not want to abandon4. In Dynamics of Reason, Friedman does not explain the nature of these problemsbut directs us to another article by him when he says: "This leads to subtle problems

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Friedman's conception of coordinating principles in particular and hisneo-Kantian project in general, then we are obliged to conclude that acrucial experiment (as described by Friedman) is, in principle, not possible(within Friedman's philosophical system).4. Incommensurability: The Problem or the Virtue of Friedman's Account?What does the failure of designing a crucial experiment consistent withFriedman's conception of constitutive principles reveal? It simply revealsthat Friedman's neo-Kantian account constitutes the philosophicalgroundwork of Kuhn's incommensurability thesis. How do we arrive atthis conclusion?

Friedman, like Kuhn, holds that revolutionary scientific theories haveradically different conceptual frameworks and explains this conceptualdifference essentially by his notion of coordinating principles, that is,revolutionary rival theories have different coordinating principles thatconnect their mathematical parts to the empirical realm in different ways.^As opposed to Kuhn, however, Friedman argues that the problem ofincommensurability can be resolved from a retrospective point of view.He suggests that we need to make a crucial experiment designed to testa coordinating principle (of one of the two theories), and for such anexperiment, we shall first establish a common constitutive framework (byway of retrospective reconstruction) that can coordinate these two rev-olutionary theories to the empirical realm in the same manner. To showhow this can be possible, Friedman attempts to design an exemplarycrucial experiment. And our analysis has suggested that the real troubleFriedman faces in this attempt is not what he seems to be concernedabout, namely, "the subtle problems" involved in finding coordinatingprinciples for the common framework of this exemplary crucial experi-ment. It is deeper than that. One cannot provide coordinating principlesfor a common framework without at the same time violating the role ofcoordinating principles as presuppositions of empirical possibility. If thisis the case, then regardless of the principles one suggests, either they can5. For brevity, I have here emphasized the significance of coordinating principles. Ingeneral terms, however, according to Friedman, rival revolutionary theories have dif-ferent constitutive frameworks that are composed of mathematical structures (whichsecure logical possibility) and coordinating principles (which secure empirical possi-bility). And in order to address the problem of incommensurability, Friedman saysthat we must "reckon with real (or empirical) possibility as well as logico-mathematical

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12 BKET KORKUTno longer be properly considered as coordinating principles or the ex-periment falls short of being crucial.

This conclusion is a natural result of the role Friedman assigns to theconstitutive principles. In order to distinguish his account from holism,Friedman strengthens the role of these principles to such an extent that,without presupposing these principles, empirical truths (at least in naturalsciences) turn out to be devoid of empirical content. Defined as such,constitutive principles manage to resist any holistic confirmation. But thisalso means that an empirical reason for favoring one theory with respectto a rival one, which would be sufficient for empirical confirmation in aholistic account, does not count as genuine empirical evidence for ac-cepting that theory as empirically confirmed from the perspective of Fried-man's neo-Kantian approach. Since Friedman feels compelled to raise hisstandard of empirical confirmation to resist holism and also encountersthe problem of incommensurability, he proposes that a genuine empiricalconfirmation can be provided by a crucial experiment designed to testtwo rival theories placed under a common constitutive framework.We have already seen the inconsistency that arises in our attempt todesign a crucial experiment in accord with Friedman's overall account.

But what does this inconsistency basically imply? It implies that the fol-lowing two claims cannot be reconciled. (1) Constitutive principles playa distinctive role within a scientific theory; more precisely, they providethe necessary constitutive framework "that secures the empirical contentof the theory" and without which "the putatively empirical laws wouldhave no empirical con tent" (2001, 83). (2) A crucial experiment designedto test two rival theories placed within a common constitutive frameworkis possible (and such a crucial experiment is required to overcome theproblem of incommensurability since, according to Friedman's standard,empirical evidence in a holistic manner is not sufficient for a genuineempirical confirmation).In simpler terms, the inconsistency forces us to hold either a holisticaccount of scientific theories (if we deny the first claim) or the incom-mensurability thesis (if we deny the second claim). If we remind ourselvesthat the main goal of Friedm an's project is to give a neo-Kantian accountof scientific theories against "naturalistic epistemological holism," which"is entirely incapable of providing an adequate philosophical perspectiveon these [exact] sciences" (2001, xii), then it would be a dramatic turn todeny the first claim in order to avoid this inconsistency and suggest that

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the neo-Kantian philosophical groundwork for Kuhn's historical analysisof incommensurability.

Appendix A: Friedman's Recent Articles on the Problemof Incommensurability

In his articles after Dynamics of Reason, Friedman reaffirms the closeconnection between Kuhn's theory and his neo-Kantian account, for in-stance, when he says, "in Thomas Kuhn's theory of the nature and char-acter of scientific revolutions we find an informal counterpart of the re-lativized conception of constitutive a priori principles" (2002b, 181). Healso ackno wledg es th at "this close parallel between the relativized yet stillconstitutive a priori and Kuhn's scientific revolutions implies . . . thatthe former gives rise to the same problems and questions concerning theultimate rationality of the scientific enterprise" (182). In the same article,Friedm an claims tha t to address these problems, wha t we need is an "inter-framework notion of communicative rationality . . . across revolutionaryparadigm-shifts" (185), and he adds that there is actually a "type of con-vergence between successive paradigms," which "allows us to define aretrospective notion of inter-framework rationality based on the consti-tutive principles of the latter conceptual framework: since the constitutiveprincip les of the earlier fram ework are cont ained in tho se of the later asan approximate special case, the constitutive principles of the later frame-work thus define a common rational basis for mutual communicationfrom the point of view of this latter framework" (185-86).

Can this be an indication of Friedman's solution to the problem ofincommensurability? This cannot be right, for, in a subsequent article,Fried ma n himself tells us that "a revolutionary transition . . . is notcharacterized only by what we might call retrospective convergent ratio-nality (convergence of abstract mathematical structures, as viewed fromthe perspective of the later paradigm)" (2008, 252). In this article, Fried-man primarily discusses the views of Cassirer and Kuhn and argues thatneither of them can resolve the problem of incommensurability. He ex-presses his position most clearly when he says: "Like the Marburg School,therefore, I want to confine the discussion to the conceptual realm andavoid ontology; unlike the Marburg School, however, I agree with Kuhnthat purely mathematical convergence and continuity is not sufficient"(249 n. 25).

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14 BKET KORKUTCassirer, emphasizes not only the abstract mathematical structures . . .but also the need to have some account of how such mathematical struc-tures are linked with or coordinated to concrete empirical phenomena. . . thereby puts us in a position . . . to do more justice . . . to K uh n'sconception" (2005, 124).Friedman is right; mathematical convergence (or "retrospective conver-gent rationality") is not sufficient for resolving the problem of incommen-surability, more precisely, for designing a crucial experiment. To design acrucial experiment, we need to establish a shared constitutive framework,and such a cons titutive framew ork is suppo sed to secure not m erely share dlogical possibility but also shared empirical possibility through commoncoord inating principles. An d the question of my article has just been, howis this possible? In Dynamics of Reason, Friedman seems to be aware ofthe possible problems involved in designing a crucial experiment, but hehas not yet clarified the nature and implications of these problems in anyof his works. And this is precisely what my article has aimed to do.

Appendix B: On the Problems Involved in Designing aCrucial Experiment

In Dynamics of Reason, Friedman (2001, 92 n. 29) directs us to anotherarticle by him for relevant discussion on the problems involved in de-signing a crucial experiment to test the light principle. In that article(2002a), he gives an excellent analysis of the historical background ofrelativity theory, but, unfortunately, he does not explicitly discuss theproblems involved in designing a crucial experiment. Nonetheless, two ofhis remarks are worth mentioning here, for they seem to support theargum ent of my article. Fried m an informs us that in the context of Helm-holtz 's studies (on the link between N ew tonian physics and non-E uclideangeom etries), the co nd ition of rigid b odies an d th eir free mo bility is singledout as the coordinating principle of the Newtonian theory (2002a, 218).But he also notes that the structure of relativity theory "strictly speaking,is quite incompatible with rigid bodies and free mobility" (218).Turning back to our concern, to design a crucial experiment what weprimarily need is an alternative constitutive framework within which wecan place both general relativity and the Newtonian theory so as to testthe light principle empirically. For such a common constitutive frame-work, "given, essentially, by the Riemannian theory of manifolds and the

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tonian theory that would still have the same empirical content as thetraditional Newtonian theory. More precisely, if, in relativity theory, thelight principle serves as "fundamental coordinating principle for the in-finitesimally Minkowskian character of the space-time metric" (2002a,217) and the coordinating principle of Newtonian theory is considered tobe based on "rigid bodies and free mobility" (218), then it follows thatin order to test the light principle within a shared constitutive framework,we need to find a new coordinating principle that can provide an "alter-native empirical coordination for spatio-temporal structuresuch as onebased (at least infinitesimally) on rigid bodies and physical clocks" (2001,91 n. 29). The question here is whether this is possible at all, for Friedmanhas also informed us tha t the structure of general relativity, "strictly speak-ing, is quite incompatible with rigid bodies and free mobility" (2002a, 218;emphasis mine).

The argument of my article, however, points out an inconsistency deep-rooted in Friedman's overall account, for it is not restricted to the possibleproblems involved in designing a particular crucial experiment (to testthe light principle) but concerns the impossibility of designing a crucialexperiment in accord with the two crucial aspects of Friedman's philo-sophical system, namely, both his model of crucial experiment as an em-pirical test of a coordinating principle and his conception of constitutiveprinciples as presuppositions of empirical possibility. If the argument ofmy article is sound, then it is also no mystery why we cannot overcomethe subtle problems involved in designing a crucial experiment withinFriedman's philosophical system to test the light principle.REFERENCES

Friedman, Michael. 2001. Dynamics of Reason: The 1999 Kant Lectures at Stanford Uni-versity Standford, CA: CSLI.. 2002a. "Geometry as a Branch of Physics: Background and Context for Einstein's'Geometry and Experience.'" In Reading Natural Philosophy: Essays in the History andPhilosophy of Science and Mathematics, ed. D. B. Malament, 193-229. Chicago: OpenCourt .. 2002b. "Kant, Kuhn, and the Rationality of Science." Philosophy of Science 69 (2):171-90.. 2005. "Ernst Cassirer and Contemporary Philosophy of Science." Angelaki: Journalof the Theoretical Humanities 10 (1): 119-28.-. 2008. "Ernst Cassirer and Thomas Kuhn: The Neo-Kantian Tradition in Historyand Philosophy of Science." Philosophical F orum 39 (2): 239-52.Ku hn, Thom as. 1962. The Structure of Scientific Revolutions. Chicago: University of ChicagoPress.

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