1. Introduction
Recently, Michael Friedman has argued that his new Kantian account of the structure of scientific theories, primarily developed as a rival to holistic accounts, has the virtue of resolving the problem of incommensurability. The notion of incommensurability first appeared in Thomas Kuhn's The Structure of Scientific Revolutions (Reference Kuhn1962), which has had a great impact on the philosophy of science since it was published. The central thesis of the book is that rival revolutionary scientific theories are not commensurable. What substantiates this thesis is Kunh's twofold claim that perceptual experience is theory dependent and rival revolutionary theories have radically different conceptual frameworks (or in Kuhn's term, paradigms) within which even the seemingly common notions of these theories possess different meaning. This implies that what counts as empirical evidence from the perspective of one theory cannot be recognized as empirical evidence from the perspective of a rival one. It then follows that empirical evidence cannot decide between two rival revolutionary theories.Footnote 1
The thesis of incommensurability was widely interpreted to imply scientific relativism and even irrational theory choice. In his later writings, Kuhn rejected the radical implications of his account. Nevertheless, the incommensurability thesis, even in its moderate form, undermines the possibility of theory choice based on a genuine empirical test. That is why it is still considered to be a central problem in the contemporary philosophy of science.
In his recent works, Friedman addresses precisely this problem and claims that his neo-Kantian philosophy has the resources to explain how theory choice based on a genuine empirical test is still possible. Friedman basically argues that the problem of incommensurability can finally be resolved through a crucial experiment designed from a retrospective view of revolutionary scientific transitions given by his new synthesis of Ernst Cassirer's insight into the constitutive role of mathematical structures in physics and Hans Reichenbach's insight into the necessity of coordinating principles for establishing a connection between mathematical structures and empirical phenomena.Footnote 2
The attractiveness of Friedman's project cannot be denied. Nevertheless, a closer look at his program reveals that it is far from accomplishing its promise. On the contrary, his philosophy, primarily developed in Dynamics of Reason, understood correctly, not only leads to the problem of incommensurability but actually substantiates the thesis itself. From Friedman's perspective, this, if true, would undermine the credibility of his account. Seen from another perspective, however, if Friedman's central neo-Kantian claims are true (and my argument in this article is sound), we then have an elegant philosophical account of the incommensurability thesis that substantiates Kuhn's historical analysis. In a word, I argue that the virtue of Friedman's neo-Kantian philosophy of science is not that it resolves the problem of incommensurability, as Friedman believes it to be, but that it gives philosophical substance to the thesis of incommensurability.
I will reach this conclusion in three stages. To prepare the ground, I will first give a summary of Friedman's philosophical account. Next, I will discuss his conception of crucial experiment, which, according to Friedman, not only distinguishes his account from holistic ones but also shows how the problem of incommensurability can be resolved. Particularly, I will explain his exemplary crucial experiment designed to compare Newtonian physics and Einstein's theory of relativity. I will then highlight the inconsistency between the requirements of Friedman's conception of crucial experiment and his account of the role of constitutive principles in a scientific theory. In the final section, I will argue that this inconsistency implies either the implausibility of Friedman's philosophical account of scientific theories (more precisely, his conception of the role of constitutive principles) or the impossibility of designing a crucial experiment compatible with his account of scientific theories. An adequate understanding of this inconsistency, as I will argue, suggests that Friedman's overall account is not merely committed to the incommensurability thesis but has actually given us much needed philosophical arguments for why and how the incommensurability thesis can be substantiated from a certain neo-Kantian point of view.Footnote 3
2. The Dynamics of Friedman's Philosophy of Science
According to Friedman's dynamic but differentiated account of knowledge, theories in mathematical 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. The mechanical part is composed of coordinating principles, which connect the mathematical part to the concrete empirical phenomena. Finally, the empirical part contains the empirical laws. Friedman calls the principles of the first two (mathematical and mechanical) parts, constitutive (or relativized a priori) principles. Following Hans Reichenbach's account, Friedman drops the apodictic character of a priori, for he believes that constitutively a priori principles can be redefined relative to the theories in question. Still, for him, the role of constitutive principles “is to provide the necessary framework within which the testing of properly empirical laws is then possible” (Reference Friedman2001, 83). In a word, “constitutive principles are necessary conditions of the possibility of properly empirical laws” (74).
Friedman explains that his notion of possibility should not be understood in terms of merely logical possibility. The notion of possibility, for Friedman, has two distinguishable aspects, namely, logical possibility and empirical (or real) possibility. Logical possibility is given by the mathematical 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 constitutive framework. In this way, a constitutive framework “secures the empirical content of the theory” (Reference Friedman2001, 83), for it “defines a space of empirical possibilities (statements that can be empirically true or false)” (84). And an empirical test against the background of such a framework indicates “which empirical possibilities are actualized,” that is, which empirical statements are true or false (84).
According to Friedman, then, constitutive principles are necessary conditions 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” (Reference Friedman2001, 83). He explains this further in the following statement: “We have said that constitutive principles are necessary conditions of the possibility of properly empirical laws. But this does not mean that they are necessary conditions in the standard sense, where A is a necessary condition of B simply if B implies A. To say that A is a constitutive condition of B rather means that A is a necessary condition, not simply of the truth of B, but of B's meaningfulness or possession of a truth value. It means, in now relatively familiar terminology, that A is a presupposition of B” (74). Friedman restricts the relevance of his notion of presupposition mainly to the area of mathematical physics. Still, he considers that constitutive principles of mathematical physics also function as presuppositions of all empirical truths, at least, in the natural sciences, as he claims: “We want to reserve this characterization for particularly fundamental presuppositions lying at the basis of mathematical physics—principles which, accordingly, can plausibly be taken as fundamental presuppositions of all empirical truth (at least in the natural sciences)” (74). In brief, for Friedman, constitutive principles are presuppositions of empirical truths (i.e., necessary conditions of the meaningfulness of empirical claims), particularly in the area of mathematical physics and, accordingly, in the natural sciences in general.
Friedman also provides us with examples of constitutive principles for two revolutionary theories of physics, namely, Newtonian physics and Einstein's general theory of relativity. In Newtonian physics, viewed retrospectively, says Friedman, the constitutive framework is given by Euclidean geometry and the laws of motion; while the former belongs to the mathematical part, the latter belongs to the mechanical part and functions as coordinating principles (Reference Friedman2001, 76–77). In Einstein's general theory of relativity, the constitutive principles consist of the four-dimensional (semi-) Riemannian manifold of variable curvature, as the mathematical part and the two coordinating principles, the light principle and the principle of equivalence. As Friedman explains, the light principle, “the law of constancy and source-independence of the velocity of light coordinates concrete physical phenomena with the Lorentzian (or infinitesimally Minkowskian) character of the new four dimensional space-time metric,” and the principle of equivalence, “the law that freely falling ‘test particles’ in a gravitational field follow four dimensional geodesic paths of this metric then completes the coordination” (79).
3. Friedman's Crucial Experiment Reveals the Crucial Problem
In order to overcome the problem of incommensurability, Friedman aims to give a conception of an empirical test stronger than both a pragmatic and a hypothetico-deductive view of empirical evidence. According to Friedman, a pragmatic approach considers scientific theories merely as instruments of prediction and, therefore, takes empirical evidence as a matter of accurate prediction, and the hypothetico-deductive account appeals only to inferential relationships among the statements, and hence, from the perspective of this approach, empirical confirmation can only be viewed as a test of the logical conjunction of statements as a whole, which amounts to a holistic conception of confirmation that supports Quinean philosophy of science (Reference Friedman2001, 83–85). Friedman argues that his account of a constitutive framework has the resources to substantiate a stronger notion of empirical evidence that can overcome the shortcomings of both a pragmatic and a holistic conception.
Friedman first sets his standard of empirical confirmation in the following way:
In our present conception, by contrast, physical coordinating principles are just as much essential parts of the network of empirical evidential relationships as are the principles of logic and mathematics. An empirical test of Einstein's field equations by the advance of the perihelion of Mercury therefore counts as an empirical reason, in the present sense, for accepting these field equations as empirically true, but it does not count, in the same sense, as an empirical reason for accepting the principle of equivalence. Indeed, as we have seen, if the principle of equivalence is not already accepted prior to this procedure, it cannot generate empirical evidence for Einstein's equations at all—which rather, without the principle of equivalence, revert to being merely logically possible. (Reference Friedman2001, 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 a constitutive framework (such as the principle of equivalence in Einstein's theory) cannot yet be regarded as empirically tested. He claims that empirical evidence for such principles within different frameworks can only be empirical motivation for our decision of fixing them as coordinating principles for a new framework but not a genuine empirical test of those principles (87–91).
According to Friedman, the Michelson-Morley and Lorand von Eötvös experiments, which are framed within an essentially classical spatio-temporal structure, can provide only empirical motivation for Einstein to choose the light principle and the principle of equivalence as the coordinating principles of the general theory of relativity. These experiments, according to Friedman's standard, cannot count as empirical tests of general relativity because the two coordinating principles, the light principle and the principle of equivalence, are essential for providing the new space-time structure with a “determinate empirical meaning,” and their elevation to the status of coordinating principles (to accomplish this task) involves a “non-empirical element of decision” (Reference Friedman2001, 88). In a word, Friedman argues that the results of these experiments do not count as genuine empirical evidence for general relativity because coordinating principles are not empirically tested in these experiments. To resolve the problem of incommensurability, then, “the crucial question,” for Friedman, is how coordinating principles can be “empirically tested and confirmed (or disconfirmed) in the same sense as those principles I am [he is] here characterizing as properly empirical laws” (87).
For a better understanding, we shall focus on a specific coordinating principle to see what is considered to be an empirical motivation for preferring 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 of the velocity of light. Friedman rightly argues that the Michelson-Morley experiment does not show that light has the same invariant velocity in all inertial frames. At most, it just shows the invariance for the presupposed inertial frame of the experiment. More important, “the Michelson-Morley experiment, can in no way be viewed as an empirical test or ‘crucial experiment’ of special relativity with respect to its theoretical alternatives; and it is not a test, for precisely this reason, of the relativistic light principle” (Reference Friedman2001, 87). For Friedman, the crucial point is that in this experiment the light principle is tested within a constitutive framework—based on “essentially classical spatio-temporal structure”—in which there is no place for relativity theory (87). That is why the experiment cannot be viewed as a crucial experiment of relativity theory with respect to the Newtonian theory, and for this reason, it cannot be seen as an empirical test of the relativistic light principle.
According to Friedman, to confirm a theory empirically, one should make a crucial experiment designed within a common constitutive framework under which two rival theories can be placed. Such an experiment is central to Friedman's account of an empirical test for distinguishing his view from holistic accounts and, more crucially, for resolving the problem of incommensurability. In order to show how this kind of genuine empirical test is possible, Friedman designs a crucial experiment for comparing the Newtonian theory and general relativity. He argues that we can give an alternative formulation to the Newtonian theory of gravitation based on freely falling trajectories in a gravitational field—a new formulation that is still empirically equivalent to the traditional Newtonian theory. Such an alternative formulation, according to Friedman, places the Newtonian 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 (Reference Friedman2001, 92).
In this common constitutive framework, it is then possible to compare the two rival theories, the Newtonian theory and general relativity, “using a common notion of real [empirical] possibility and a common notion of empirical evidence” (Reference Friedman2001, 92). Hence, for Friedman, the advance of the perihelion of Mercury now counts as genuine empirical evidence for general relativity. More specifically, what is regarded to be confirmed by experience is the special relativistic light principle, as Friedman explains:
In this framework we can now compare both the Newtonian theory and general relativity using a common notion of real possibility and a common notion of empirical evidence; and, of course, general relativity now comes out as confirmed by the evidence (such as the advance of the perihelion of Mercury) in preference to the Newtonian theory. … In other words, what is here preferentially confirmed by the evidence is exactly the special relativistic light principle. That which is characterized as non-empirical constitutive principle, entirely beyond the reach of standard empirical testing, at one stage of scientific progress can be subject to precisely such testing at a later stage. But this is just as it should be on a truly dynamical conception of the a priori. (Reference Friedman2001, 92)
First, it is crucial to be clear about the status of the light principle and also to specify the constitutive principles of this common constitutive framework. Friedman rightly does not count the light principle among the constitutive principles of this framework. The light principle appears as an empirical statement within this common framework. Otherwise, it would not be possible to argue that the light principle is confirmed empirically.
Friedman says that this common constitutive framework is “given, essentially, by the Riemannian theory of manifolds and the principle of equivalence” (Reference Friedman2001, 92). Let us recall that, according to Friedman, the constitutive framework of general relativity is composed of a mathematical part (i.e., the Riemannian theory of manifolds) and the two coordinating principles, the principle of equivalence and the light principle. In the common framework, however, the light principle is no longer counted as a coordinating principle; rather, it is considered to be an empirical statement under test. But, if the light principle is now an empirical statement, do we not need another coordinating principle for the common framework that can play the role of the light principle, that is, that can provide the coordination between the mathematical part of the common framework and the empirical phenomena? Indeed, we do, as Friedman also explains in a note: “Indeed, in imagining carrying out the above empirical test of the light principle we are tacitly supposing the availability of an alternative empirical coordination for spatio-temporal structure—such as one based (at least infinitesimally) on rigid bodies and physical clocks. This leads to subtle problems which cannot be discussed here” (92 n. 29).
Let us leave aside for a moment the possible problems involved in finding the required coordinating principles and simply assume that there are such principles that provide us with an alternative empirical coordination for the common framework. We also assumed that the light principle is an empirical statement within this common framework since it is empirically confirmable. But does the light principle still count as a constitutive principle in general relativity? Friedman explicitly says that it does: “The light principle still counts as constitutive in general relativity, however, for we can still use it to define the infinitesimally Minkowskian metrical structure” (Reference Friedman2001, 92 n. 29). But does ‘the light principle’ characterized as an empirical statement in the common constitutive framework of the imaginary crucial experiment share the same empirical content with ‘the light principle’ counted as a constitutive principle in the particular framework of general relativity?
If Friedman gives a negative answer (i.e., that the light principle does not have the same empirical content within these two different constitutive frameworks), then how can he count this experiment as an empirical test of “the relativistic light principle”? In other words, it is then unclear how Friedman can consider the advance of the perihelion of Mercury as genuine empirical evidence for the light principle in particular and for the general theory of relativity in general. For Friedman, this crucial experiment exemplifies how an empirical comparison of two rival theories is genuinely possible. It follows that if Friedman still wants to consider this experiment as crucial, he is compelled to give a positive answer; namely, the light principle in this imaginary common framework has the same empirical content as the light principle of general relativity.
But a positive answer has its own problems. The coordinating principles of the common constitutive framework, like any other coordinating principle, define what Friedman calls empirical possibility. Friedman has already informed us that without coordinating principles the empirical claims (in mathematical physics) would have no empirical content. We assumed that the light principle is an empirical statement within this common framework since it is empirically confirmable. It then follows that without the coordinating principles of the common framework, the availability of which Friedman tacitly supposes, the light principle would have no empirical content in this crucial experiment. In other words, the coordinating principles of the common framework are the necessary conditions of the meaningfulness of the light principle, for it is an empirical statement within this framework. However, the genuine constitutive framework of general relativity does not include those specific coordinating principles of the common framework among its coordinating principles. If the coordinating principles of the common framework are necessary conditions of the empirical meaningfulness of the light principle, then it is not clear how the light principle can possess the same empirical content within general relativity, which does not include those specific coordinating principles.
If the light principle manages to have the same empirical content in both frameworks (i.e., the framework of general relativity and the common framework of the imaginary crucial experiment), then the only plausible way to explain the situation is that the coordinative principles of the common framework are not necessary conditions for the light principle to have an empirical content. It follows that some proper empirical statements can have an empirical content without any need for the presupposition of the coordinating principles. How do we distinguish them from other empirical truths? More crucially, if there are such empirical statements, then how can coordinating principles genuinely function as presuppositions, that is, necessary conditions of the meaningfulness of empirical statements?
Perhaps the dilemma here partly reveals what Friedman means by the “subtle problems” that arise in our search for an alternative empirical coordination for the common framework, the availability of which he tacitly assumes. But what seems more mysterious is how Friedman, without explicitly providing these alternative coordinating principles of the common framework, could still imagine that the statements in this framework would have an empirical content and even discuss the confirmation of an empirical statement, namely, the light principle.Footnote 4
If my argument above is sound, then either the light principle does not have the same empirical content both in general relativity and in the common framework, which means that the crucial experiment falls short of being “crucial” (i.e., being an empirical test of the relativistic light principle), or the light principle possesses the same empirical content in both of the frameworks, which implies that this crucial experiment can serve Friedman's purposes only at the price of inconsistency with the role of the coordinating principles (as presuppositions of empirical possibility). In general terms, the problem can be formulated in the following way. According to Friedman's standard, for a genuine comparison of two rival revolutionary theories, we need to design a crucial experiment with a shared constitutive framework in order to test a coordinating principle of one of the two rival revolutionary theories, say, the C principle. The problem is that without violating the role of coordinating principles as presuppositions of empirical possibility, one cannot, in principle, provide a 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 principles should both (i) be necessary conditions of the empirical meaningfulness of the C principle as an empirical statement under test and (ii) preserve the same empirical content that this C principle has within the original framework of the theory in which it functions as a coordinating principle, but conditions (i) and (ii) are incompatible, for the satisfaction of (ii) implies the refutation of (i). And without satisfying (ii), the experiment falls short of being crucial. This simply means that if we do not want to abandon Friedman's conception of coordinating principles in particular and his neo-Kantian project in general, then we are obliged to conclude that a crucial 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 with Friedman's conception of constitutive principles reveal? It simply reveals that Friedman's neo-Kantian account constitutes the philosophical groundwork of Kuhn's incommensurability thesis. How do we arrive at this conclusion?
Friedman, like Kuhn, holds that revolutionary scientific theories have radically different conceptual frameworks and explains this conceptual difference essentially by his notion of coordinating principles, that is, revolutionary rival theories have different coordinating principles that connect their mathematical parts to the empirical realm in different ways.Footnote 5 As opposed to Kuhn, however, Friedman argues that the problem of incommensurability can be resolved from a retrospective point of view. He suggests that we need to make a crucial experiment designed to test a coordinating principle (of one of the two theories), and for such an experiment, we shall first establish a common constitutive framework (by way of retrospective reconstruction) that can coordinate these two revolutionary theories to the empirical realm in the same manner. To show how this can be possible, Friedman attempts to design an exemplary crucial experiment. And our analysis has suggested that the real trouble Friedman faces in this attempt is not what he seems to be concerned about, namely, “the subtle problems” involved in finding coordinating principles for the common framework of this exemplary crucial experiment. It is deeper than that. One cannot provide coordinating principles for a common framework without at the same time violating the role of coordinating principles as presuppositions of empirical possibility. If this is the case, then regardless of the principles one suggests, either they can no longer be properly considered as coordinating principles or the experiment falls short of being crucial.
This conclusion is a natural result of the role Friedman assigns to the constitutive 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 natural sciences) turn out to be devoid of empirical content. Defined as such, constitutive principles manage to resist any holistic confirmation. But this also means that an empirical reason for favoring one theory with respect to a rival one, which would be sufficient for empirical confirmation in a holistic account, does not count as genuine empirical evidence for accepting that theory as empirically confirmed from the perspective of Friedman's neo-Kantian approach. Since Friedman feels compelled to raise his standard of empirical confirmation to resist holism and also encounters the problem of incommensurability, he proposes that a genuine empirical confirmation can be provided by a crucial experiment designed to test two rival theories placed under a common constitutive framework.
We have already seen the inconsistency that arises in our attempt to design a crucial experiment in accord with Friedman's overall account. But what does this inconsistency basically imply? It implies that the following two claims cannot be reconciled. (1) Constitutive principles play a distinctive role within a scientific theory; more precisely, they provide the necessary constitutive framework “that secures the empirical content of the theory” and without which “the putatively empirical laws would have no empirical content” (Reference Friedman2001, 83). (2) A crucial experiment designed to test two rival theories placed within a common constitutive framework is possible (and such a crucial experiment is required to overcome the problem of incommensurability since, according to Friedman's standard, empirical evidence in a holistic manner is not sufficient for a genuine empirical confirmation).
In simpler terms, the inconsistency forces us to hold either a holistic account of scientific theories (if we deny the first claim) or the incommensurability thesis (if we deny the second claim). If we remind ourselves that the main goal of Friedman's project is to give a neo-Kantian account of scientific theories against “naturalistic epistemological holism,” which “is entirely incapable of providing an adequate philosophical perspective on these [exact] sciences” (Reference Friedman2001, xii), then it would be a dramatic turn to deny the first claim in order to avoid this inconsistency and suggest that Friedman's view is committed to holism. Therefore, if we still want to approve of Friedman's project, as opposed to a holistic one, then we shall acknowledge that one of the merits of Friedman's refined account is not that it resolves the problem of incommensurability but that it establishes the neo-Kantian philosophical groundwork for Kuhn's historical analysis of incommensurability.
Appendix A Friedman's Recent Articles on the Problem of Incommensurability
In his articles after Dynamics of Reason, Friedman reaffirms the close connection between Kuhn's theory and his neo-Kantian account, for instance, when he says, “in Thomas Kuhn's theory of the nature and character of scientific revolutions we find an informal counterpart of the relativized conception of constitutive a priori principles” (Reference Friedman2002b, 181). He also acknowledges that “this close parallel between the relativized yet still constitutive a priori and Kuhn's scientific revolutions implies … that the former gives rise to the same problems and questions concerning the ultimate rationality of the scientific enterprise” (182). In the same article, Friedman claims that to address these problems, what we need is an “inter-framework notion of communicative rationality … across revolutionary paradigm-shifts” (185), and he adds that there is actually a “type of convergence between successive paradigms,” which “allows us to define a retrospective notion of inter-framework rationality based on the constitutive principles of the latter conceptual framework: since the constitutive principles of the earlier framework are contained in those of the later as an approximate special case, the constitutive principles of the later framework thus define a common rational basis for mutual communication from the point of view of this latter framework” (185–86).
Can this be an indication of Friedman's solution to the problem of incommensurability? This cannot be right, for, in a subsequent article, Friedman himself tells us that “a revolutionary transition … is not characterized only by what we might call retrospective convergent rationality (convergence of abstract mathematical structures, as viewed from the perspective of the later paradigm)” (Reference Friedman2008, 252). In this article, Friedman primarily discusses the views of Cassirer and Kuhn and argues that neither of them can resolve the problem of incommensurability. He expresses his position most clearly when he says: “Like the Marburg School, therefore, I want to confine the discussion to the conceptual realm and avoid ontology; unlike the Marburg School, however, I agree with Kuhn that purely mathematical convergence and continuity is not sufficient” (249 n. 25).
According to Friedman, to solve the problem of incommensurability, one should show that convergence between successive scientific theories is not merely mathematical but also conceptual. This is precisely why Reichenbach is significant for Friedman because “Reichenbach, unlike Cassirer, emphasizes not only the abstract mathematical structures … but also the need to have some account of how such mathematical structures are linked with or coordinated to concrete empirical phenomena … thereby puts us in a position … to do more justice … to Kuhn's conception” (Reference Friedman2005, 124).
Friedman is right; mathematical convergence (or “retrospective convergent rationality”) is not sufficient for resolving the problem of incommensurability, more precisely, for designing a crucial experiment. To design a crucial experiment, we need to establish a shared constitutive framework, and such a constitutive framework is supposed to secure not merely shared logical possibility but also shared empirical possibility through common coordinating principles. And the question of my article has just been, how is this possible? In Dynamics of Reason, Friedman seems to be aware of the possible problems involved in designing a crucial experiment, but he has not yet clarified the nature and implications of these problems in any of his works. And this is precisely what my article has aimed to do.
Appendix B On the Problems Involved in Designing a Crucial Experiment
In Dynamics of Reason, Friedman (Reference Friedman2001, 92 n. 29) directs us to another article by him for relevant discussion on the problems involved in designing a crucial experiment to test the light principle. In that article (Reference Friedman and Malament2002a), he gives an excellent analysis of the historical background of relativity theory, but, unfortunately, he does not explicitly discuss the problems involved in designing a crucial experiment. Nonetheless, two of his remarks are worth mentioning here, for they seem to support the argument of my article. Friedman informs us that in the context of Helmholtz's studies (on the link between Newtonian physics and non-Euclidean geometries), the condition of rigid bodies and their free mobility is singled out as the coordinating principle of the Newtonian theory (Reference Friedman and Malament2002a, 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 we primarily need is an alternative constitutive framework within which we can place both general relativity and the Newtonian theory so as to test the light principle empirically. For such a common constitutive framework, “given, essentially, by the Riemannian theory of manifolds and the principle of equivalence” (Reference Friedman2001, 92), we also need an alternative coordinating principle (that can replace the light principle, which is now an empirical statement under test). This new coordinating principle, however, should not only play the role of the light principle in relativity theory but also provide an empirical coordination for a new formulation of the Newtonian theory that would still have the same empirical content as the traditional Newtonian theory. More precisely, if, in relativity theory, the light principle serves as “fundamental coordinating principle for the infinitesimally Minkowskian character of the space-time metric” (Reference Friedman and Malament2002a, 217) and the coordinating principle of Newtonian theory is considered to be based on “rigid bodies and free mobility” (218), then it follows that in order to test the light principle within a shared constitutive framework, we need to find a new coordinating principle that can provide an “alternative empirical coordination for spatio-temporal structure—such as one based (at least infinitesimally) on rigid bodies and physical clocks” (Reference Friedman2001, 91 n. 29). The question here is whether this is possible at all, for Friedman has also informed us that the structure of general relativity, “strictly speaking, is quite incompatible with rigid bodies and free mobility” (Reference Friedman and Malament2002a, 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 possible problems involved in designing a particular crucial experiment (to test the light principle) but concerns the impossibility of designing a crucial experiment in accord with the two crucial aspects of Friedman's philosophical system, namely, both his model of crucial experiment as an empirical test of a coordinating principle and his conception of constitutive principles as presuppositions of empirical possibility. If the argument of my article is sound, then it is also no mystery why we cannot overcome the subtle problems involved in designing a crucial experiment within Friedman's philosophical system to test the light principle.
