ERNST CASSIRER AND THOMAS KUHN: THE NEO‐KANTIAN TRADITION IN HISTORY AND PHILOSOPHY OF SCIENCE
2008; Wiley; Volume: 39; Issue: 2 Linguagem: Inglês
10.1111/j.1467-9191.2008.00293.x
ISSN1467-9191
Autores Tópico(s)Classical Philosophy and Thought
ResumoA central problem facing contemporary history and philosophy of science derives from the publication of Thomas Kuhn's The Structure of Scientific Revolutions in 1962. In particular, Kuhn applied lessons initially learned from early 20th-century work in the history of science to develop a strikingly new philosophical picture of the nature of science. Directly confronting what he called the development-by-accumulation model of scientific progress, Kuhn presented an alternative conception according to which the development of science is frequently punctuated by essentially discontinuous revolutionary transitions where the dominant paradigm governing a particular stage of what Kuhn calls normal science experiences a revolutionary transformation resulting in a succeeding paradigm fundamentally incommensurable with the earlier one. Moreover, since the two succeeding paradigms—the transition from Newtonian physics to Einstein's theory of relativity was one of Kuhn's central illustrations—are incommensurable (i.e., non-intertranslatable) with one another, the choice between them appears not to be straightforwardly rational. Since the concepts and principles of the two paradigms have radically different meanings, it is no longer clear that empirical evidence can straightforwardly decide between them. Indeed, the very terms in which the two paradigms describe the empirical phenomena may themselves have radically different meanings. One conclusion Kuhn drew from this picture is that there is no real sense in which the evolution of science can be seen as a process of convergence to an ultimate single truth about reality, where succeeding theories or paradigms appear as ever better approximations to such a final truth.1 And this conclusion, in turn, can easily be radicalized, resulting in a relativist and historicist conception according to which there is no sense of scientific progress at all: Succeeding theories or paradigms are simply different historically conditioned moments in a completely directionless temporal process, and the only notion of truth then available is an essentially relativized and historicized one. Kuhn himself strenuously resisted these particular implications of his views, hoping to replace the development-by-accumulation model and the ideal of intertheoretic convergence with an evolutionary model of scientific progress whereby succeeding theories become continually better adapted problem-solving tools without converging to a final endpoint (cf. footnote 1). Nevertheless, this suggestion of Kuhn's has not won many adherents, and the problem dominating much of the post-Kuhnian work in the history, philosophy, and sociology of science has been precisely the relativist and historicist predicament just sketched: If succeeding paradigms, as Kuhn taught, are really incommensurable, how can we possibly escape the conclusion, in currently fashionable parlance, that "all knowledge is local"? At the end of the 19th and beginning of the 20th century, the Marburg School of Neo-Kantianism founded by Hermann Cohen, and later developed by Paul Natorp and Ernst Cassirer, articulated a historicized version of Kantianism aimed at adapting the critical philosophy to the deep revolutionary changes affecting mathematics and the mathematical sciences throughout this period.2 In particular, the development of non-Euclidean geometries appeared decisively to undermine Kant's original conception of the synthetic a priori character of our cognition of space, and 19th-century developments in mathematical physics suggested that Newtonian physics, in particular, may not be the final word. In response to these developments, the Marburg School replaced Kant's original "static" or timeless version of the synthetic a priori with what they conceived as an essentially developmental or "genetic [erzeugende]" conception of scientific knowledge. Since Kuhn, very late in his career, characterized himself as "a Kantian with moveable categories,"3 one might naturally wonder about the relationship between Kuhn's own view and that of the Marburg School. The answer, as we shall see, is both interesting and complicated. In Cassirer's version of the genetic conception of knowledge, most fully articulated in Substanzbegriff und Funktionsbegriff, appearing in 1910, we begin with the progression of theories produced by modern mathematical natural science in its actual historical development. This progression takes its starting point, to be sure, with Euclidean geometry and Newtonian physics, but we now know, as Kant himself did not, that this is only a starting point, not a rigidly fixed and forever unrevisable a priori structure. Subsequent to the Euclidean-Newtonian paradigm, in particular, there has been a developmental sequence of abstract mathematical structures ("systems of order"), which is itself ordered by the abstract mathematical relation of approximate backward-directed inclusion—as, for example, the new non-Euclidean geometries contain the older geometry of Euclid as a continuously approximated limiting case. We can thereby conceive all the theories in our sequence as continuously converging, as it were, on a final or limit theory, such that all previous theories in the sequence are approximate special cases of this final theory. This final theory is only a regulative ideal in the Kantian sense—it is only progressively approximated but never in fact actually realized.4 Nevertheless, the idea of such a continuous progression toward an ideal limit constitutes the characteristic "general serial form" of our mathematical-physical theorizing, and, at the same time, it bestows on this theorizing its characteristic form of objectivity. For, despite all historical variation and contingency, there is, nonetheless, a continuously converging progression of abstract mathematical structures framing, and making possible, all of our empirical knowledge. However, in full agreement with Kant's original "critical" theory of knowledge, convergence, on this new view, does not take place toward a mind- or theory-independent "reality" of ultimate "substantial things" or "things-in-themselves." Rather, the convergence in question occurs entirely within the series of historically developed mathematical structures: "Reality," on this view, is simply the purely ideal limit or endpoint toward which the sequence of such structures is mathematically converging—or, to put it another way, it is simply the series itself, taken as a whole.5 It is not clear, at first sight, whether and how this conception of intertheoretic convergence relates to Kuhn's view of the matter. As we have said, Kuhn rejects all talk of convergence to a final truth about a mind-independent reality, but so, as we have just seen, does the Marburg genetic conception of knowledge. Moreover, the situation becomes especially interesting (and complicated) when we observe that Cassirer's work in the history of science and philosophy—work which is directly informed by the Marburg genetic conception of knowledge—is an important part of the background to Kuhn's own historiography. Cassirer began his career as an intellectual historian, one of the very greatest of the 20th century. His first major work, Das Erkenntnisproblem in der Philosophie und Wissenschaft der neueren Zeit, published (in two volumes) in 1906–07, is a magisterial and deeply original contribution to both the history of philosophy and the history of science. It is the first work, in fact, to develop a detailed reading of the scientific revolution as a whole in terms of the "Platonic" idea that the thoroughgoing application of mathematics to nature (the so-called mathematization of nature) is the central and overarching achievement of this revolution. And Cassirer's work is acknowledged as such by such seminal historians as Edwin Burtt, Alexandre Koyré, and E. J. Dijksterhuis, who developed this theme later in the century in the course of establishing the discipline of history of science as we know it today.6 Cassirer, for his part, simultaneously articulated an interpretation of the history of modern philosophy as the development and eventual triumph of what he calls "modern philosophical idealism." This tradition takes its inspiration, according to Cassirer, from idealism in the Platonic sense, from an appreciation of the "ideal" formal structures paradigmatically studied in mathematics, and it is distinctively modern in recognizing the fundamental importance of the systematic application of such structures to empirically given nature in modern mathematical physics—a progressive and synthetic process wherein mathematical models of nature are successively refined and corrected without limit. For Cassirer, it is Galileo, above all, in opposition to both sterile Aristotelian-Scholastic formal logic and sterile Aristotelian-Scholastic empirical induction, who first grasped the essential structure of this synthetic process, and the development of "modern philosophical idealism" in the work of Descartes, Spinoza, Gassendi, Hobbes, Leibniz, and finally Kant then consists in its increasingly self-conscious philosophical articulation and elaboration. Thus, the main philosophical lesson of Cassirer's historical narrative (not at all surprisingly) is that the nature and character of modern mathematical physics as a whole is best represented by the Marburg genetic conception of knowledge. Das Erkenntnisproblem exerted a decisive influence on early 20th-century history of science, especially in its more philosophically oriented guises. It was especially important for such writers as Emile Meyerson, Léon Brunschvicg, Hélène Metzger, Anneliese Maier, and Alexandre Koyré—and Koyré, in turn, exerted an especially important influence on Kuhn.7 It is no wonder, then, that Kuhn, in an Afterword (first published in 1984)8 appended to his book on Planck and black-body radiation, states:9"The concept of historical reconstruction that underlies [this book] has from the start been fundamental to both my historical and my philosophical work. It is by no means original: I owe it primarily to Alexandre Koyré; its ultimate sources lie in Neo-Kantian philosophy." Thus, Kuhn, toward the end of his career, not only characterized his distinctive philosophical conception as a dynamical and historicized version of Kantianism (footnote 3), but also explicitly acknowledged the background to his own historiography in Neo-Kantian philosophy. Nevertheless, there were (at least) two different strands in this early 20th-century historiographical tradition: a more Kantian strand associated with Brunschvicg and Maier and what we might call a more "Cartesian" strand associated with Meyerson and his student Metzger. Moreover, Meyerson is the most important philosophical influence on Koyré's historiography—Kuhn also cites Meyerson as an influence, along with Brunschvicg, Metzger, Maier, and, indeed, Cassirer himself10—and the philosophical perspective shared by both Meyerson and Koyré is diametrically opposed, in most essential respects, to that originally articulated by Cassirer.11 In the work of Cassirer and Meyerson, in particular, we find two sharply diverging visions of the philosophical history of modern science. For Cassirer, this history is seen as a process of evolving rational purification of our view of nature, as we progress from naively realistic "substantialistic" conceptions, focusing on underlying substances, causes, and mechanisms subsisting behind the observable phenomena, to increasingly abstract purely "functional" conceptions, where we finally abandon the search for underlying ontology in favor of ever more precise mathematical representations of phenomena in terms of exactly formulated universal laws. For Meyerson, by contrast, this same history is seen as a necessarily dialectical progression (in something like the Hegelian sense), wherein reason perpetually seeks to enforce precisely the "substantialistic" impulse, and nature continually offers her resistance in the ultimate irrationality of temporal succession. Thus, the triumph of the scientific revolution, for Meyerson, is represented by the rise of mechanistic atomism, wherein elementary corpuscles preserve their sizes, shapes, and masses while merely changing their mutual positions in uniform and homogeneous space via motion, and this same demand for transtemporal substantial identity is also represented, in more recent times, both by Lavoisier's use of the principle of the conservation of matter in his new chemistry and by the discovery of the conservation of energy. Yet, in the even more recent discovery of what we now know as the second law of thermodynamics ("Carnot's principle"), which governs the temporally irreversible process of "degradation" or "dissipation" of energy, we encounter nature's complementary and unavoidable resistance to our a priori logical demands. It is by no means surprising, therefore, that Meyerson, in the course of considering, and rejecting, what he calls "anti-substantialistic conceptions of science," explicitly takes issue with Cassirer's central claim, in Das Erkenntnisproblem, that "[m]athematical physics turns aside from the essence of things and their inner substantiality in order to turn towards their numerical order and connection, their functional and mathematical structure."12 And it is also no wonder that Cassirer, in the course of a discussion of "identity and difference, constancy and change," explicitly takes issue with Meyerson's views: "The identity towards which thought progressively strives is not the identity of ultimate substantial things but the identity of functional orders and coordinations."13 Thus, in direct and explicit opposition to the Meyersonian view, Cassirer's whole point is that thought does not require a "substantialistic" or "ontological" identity over time of permanent "things" but merely a purely mathematical continuity over time formulated in successively articulated mathematical structures.14 If I am not mistaken, this deep philosophical opposition between Meyerson and Cassirer receives a very clear echo in Kuhn's theory of scientific revolutions, particularly with regard to the question of continuity and convergence over time. Here Kuhn shows himself, in this respect, to be a faithful follower of the Meyersonian viewpoint, for he consistently gives the question an ontological ("substantialistic") rather than a mathematical ("functional") interpretation.15 Thus, for example, when Kuhn famously considers the relationship between relativistic and Newtonian mechanics, he rejects the notion of a fundamental continuity between the two theories on the grounds that the "physical referents" of their terms are essentially different, and he nowhere considers the contrasting idea, characteristic of Cassirer's work, that continuity of purely mathematical structures is sufficient. Moreover, Kuhn consistently gives an ontological rather than a mathematical interpretation to the question of theoretical convergence over time: The question is always whether our theories can be said to converge to an independently existing "truth" about reality, to a theory-independent external world.16 It follows, then, that Kuhn's rejection of intertheoretic convergence cannot be taken as a straightforward confutation of Cassirer's position. For Kuhn simply assumes, in harmony with the Meyersonian viewpoint, that there is rational continuity over time only if there is also substantial identity. Since, as Kuhn argues, the "physical referents" of Newtonian and relativistic mechanics, for example, cannot be taken to be the same, we are squarely faced with the problem of interparadigmatic incommensurability. Yet Cassirer, as we have seen, is just as opposed to all forms of naïve realism (as well as naïve empiricism) as is Kuhn. He instead proposes a generalized Kantian conception, emblematic of what he himself calls "modern philosophical idealism," according to which scientific rationality and objectivity are secured in virtue of the way in which our empirical knowledge of nature is framed, and thereby made possible, by a continuously evolving sequence of abstract mathematical structures. It is for this reason, in fact, that Einstein's general theory of relativity represents the culmination of "modern philosophical idealism" for Cassirer. In particular, Zur Einsteinschen Relativitätstheorie, published in 1921, is devoted to explaining how this theory—despite first appearances—represents a confirmation rather than a rejection of the Kantian or "critical" theory of knowledge. Cassirer begins by asserting that [t]he reality of the physicist stands opposite the reality of immediate perception as a thoroughly mediated reality: as a totality, not of existing things or properties, but rather of abstract symbols of thought that serve as the expression for determinate relations of magnitude and measure, for determinate functional coordinations and dependencies in the appearances.17 And it then follows that Einstein's theory can be incorporated within the "critical" conception of knowledge "without difficulty, for this theory is characterized from a general epistemological point of view precisely by the circumstance that in it, more consciously and more clearly than ever before, the advance from the copy theory of knowledge to the functional theory is completed."18 Whereas it is true, for example, that Kant himself had envisioned only the use of Euclidean geometry in mathematical physics, the fact that we now employ a non-intuitive, non-Euclidean geometry in the general theory of relativity by no means contradicts the general "critical" point of view. For: Kant also had emphasized decisively [that] this form of dynamical determination does not belong any longer to intuition as such, but rather it is the "rule of the understanding" alone through which the existence of appearances can acquire synthetic unity and be taken together [as a whole] in a determinate concept of experience.19 Hence, the general theory of relativity continues to exemplify the fundamental Kantian insight that the unity of nature as such can only be due to our understanding.20 It is precisely at this point, however, that I find myself in deep disagreement with Cassirer—and with the Marburg School more generally. For I believe that the Marburg tendency to minimize or downplay the role of the Kantian faculty of pure intuition or pure sensibility on behalf of the faculty of pure understanding represents a profound interpretive mistake.21 Kant himself, on the contrary, takes the faculty of pure sensibility to have an independent a priori structure of its own—given by the Euclidean structure of space and the Newtonian structure of time (more precisely, space-time)—and this is the reason, for Kant, that all our sensible or perceptual experience must necessarily be in accordance with these forms (and it is not merely the case, for example, that we must always think or conceive nature in this way). From this point of view, therefore, it is by no means true that the general theory of relativity can be incorporated within the Kantian or "critical" conception "without difficulty." Further, and this is still not as well known as it should be, the logical empiricists basically agreed with Kuhn about the profoundly revolutionary character—from a philosophical point of view—of the general theory of relativity. The most important of their works, from our present point of view, was Hans Reichenbach's Relativitätstheorie und Erkenntnis Apriori, which appeared one year beforeCassirer's book. According to Reichenbach (and the logical empiricists more generally), Einstein's new theory is so radically incommensurable with Newtonian theory that the Kantian critical philosophy itself needs also to be radically revised: A new revolutionary form of scientific philosophy (logical empiricism) is now required in the wake of Einstein's revolutionary theory.22 I agree with Kuhn—and with the logical empiricists—that Einstein's general theory of relativity is in an important sense incommensurable or non-intertranslatable with the Newtonian theory of universal gravitation it replaced. Whereas Newtonian theory represents the action of gravity as an external "impressed force" causing gravitationally affected bodies to deviate from straight inertial trajectories (moving with uniform or constant speed), Einstein's theory depicts gravitation as a curving or bending of the underlying fabric of space-time itself. In this new framework, in particular, there are no inertial trajectories in the sense of the geometry of Euclid and the mechanics of Newton, and gravity is not an "impressed force" causing deviations from such trajectories. Gravitationally affected bodies instead follow the straightest possible paths or geodesics that exist in the highly non-Euclidean geometry (of variable curvature) of Einsteinian space-time, and the trajectories of so-called "freely falling bodies"—affected by no forces other than gravitation—simply replace the straight inertial trajectories of Newtonian theory (which are straight in the sense of both Euclidean space and Newtonian (space-)time). But why does it follow that Einstein's theory and Newton's theory are incommensurable? After all, once Einstein's theory is in place, we can then derive Newtonian theory from it as an approximate special case (where, for example, we consider relatively small spatial regions that are approximately Euclidean and relatively low velocities in comparison with light), and we can thereby explain, from the point of view of Einstein's theory, why Newton's theory works as well as it does. Kuhn himself is perfectly clear about this, and he responds by insisting that this point of view is post-revolutionary, and, in particular, it uses fundamental mathematical and physical concepts that are simply unavailable from the point of view of the earlier theory: What we derive as an approximate special case from Einstein's theory is therefore not Newton's original theory.23 As a result, the real problem is to show how the fundamental mathematical and physical concepts of the old theory (which are thus not intertranslatable with the new theory) can nonetheless give rise to—can be replaced by—those of the new theory. In my Dynamics of Reason,24 I put the point this way. It is clear, first of all, that Einstein's theory is not even mathematically possible from the point of view of Newton's original theory, for the mathematics required to formulate Einstein's theory—Bernhard Riemann's general theory of geometrical manifolds or "spaces" of any dimension and curvature (Euclidean or non-Euclidean)—did not even exist until the late 19th century. Of course this point, by itself, is perfectly compatible with Cassirer's version of the Marburg conception, for, once the necessary mathematics has been developed, we can then represent the earlier mathematical structure as a special case of the later one, and this is all that Marburg-style convergence requires. However, and in the second place, even after the mathematics required for Einstein's theory was developed, it still remained fundamentally unclear what it could mean actually to apply such a geometry to our sensible experience of nature in a real physical theory. One still needed to show, in other words, that Einstein's new theory is empirically or physically possible as well, and this, in turn, only became clear with Einstein's own work on what he called the principle of equivalence in the years 1907–12. This principle, as we now understand it, says that freely falling bodies follow the straightest possible paths or geodesics in a certain kind of four-dimensional (semi-)Riemannian manifold, and it thereby gives real physical and empirical meaning, for the first time, to this kind of abstract mathematical structure. Einstein's theory thus requires a genuine expansion of our space of intellectual possibilities (both mathematical and empirical), and the problem is then to explain how such an expansion is possible—since the new theory, before the expansion in question, is not even physically possible (in Kant's terminology, it is neither logically nor really possible).25 I cannot develop this in detail here, but my second main point26 is that, in addition to the necessary mathematical developments (the evolution of non-Euclidean geometries, as unified and completed in Riemann's work) and the necessary physical developments (the discovery of the constancy and invariance of the velocity of light, the numerical equality of inertial and gravitational mass underlying the principle of equivalence), we still need a set of parallel developments in contemporaneous scientific philosophy to tie together the relevant innovations in mathematics and physics and thereby effect the necessary expansion in our physical or empirical possibilities. In the case of Einstein's theory, in particular, this process began with Kant's original attempt—in his Metaphysische Anfangsgründe der Naturwissenschaft, and also in the first Critique—to provide philosophical foundations for Newtonian theory.27 In the following 19th century these Kantian foundations for specifically Newtonian theory were then self-consciously successively reconfigured, as scientific philosophers like Ernst Mach (and others) reconsidered the problem of absolute space and motion, and other scientific philosophers—especially Hermann von Helmholtz and Henri Poincaré—reconsidered the empirical and conceptual foundations of geometry in light of the new mathematical discoveries in non-Euclidean geometry. Einstein's initial work on the principle of equivalence—which culminated, as we said, in 1912—then unexpectedly joined these two earlier traditions of scientific thought together and thereby led to the very surprising and entirely new empirical possibility that gravity may, after all, be represented by a non-Euclidean geometry. The crucial breakthrough came when Einstein hit upon the example of the uniformly rotating disk or reference frame—where, in accordance with the principle of equivalence, we are considering a particular kind of non-inertial frame of reference within the framework of special relativity. The result was a non-Euclidean physical geometry as our novel representative of the gravitational field, and Einstein was only able to arrive at this result (as he himself later tells us in his celebrated lecture, Geometrie und Erfahrung, in 1921) by delicately situating himself within the earlier philosophical debate on the empirical and conceptual foundations of geometry between Helmholtz and Poincaré.28 If this is correct, however, we need a more far-reaching revision of Kantian transcendental philosophy than Cassirer has suggested in this case. It is by no means true, in particular, that Einstein's general theory of relativity can be incorporated within transcendental philosophy "without difficulty," since this philosophy, in Kant's original form, is unavoidably committed to the a priori necessary validity of both Euclidean geometry and the fundamental principles of Newtonian mechanics.29 The only way forward, in my view, is to relativize the Kantian a priori to a given scientific theory in a given historical context (following Reichenbach in 1920) and, as a consequence, to historicize the notion of transcendental philosophy itself. Thus, for example, whereas Euclidean geometry and the Newtonian laws of motion were indeed necessary presuppositions for the empirical meaning and application of the Newtonian theory of universal gravitation (and they were therefore constitutively a priori in this context), the radically new mathematical and physical framework consisting of the Riemannian theory of manifolds and the principle of equivalence defines an analogous system of necessary presuppositions in general relativity. Moreover, what makes the latter framework constitutively a priori in this new context is precisely the circumstance that Einstein was only able to arrive at it in the first place by self-consciously situating himself within the earlier tradition of scientific philosophy represented (especially) by Helmholtz and Poincaré—just as this tradition, in turn, had earlier self-consciously situated itself against the background of the original version of transcendental philosophy first articulated by Kant.30 The fundamental idea of the Marburg School was that it is indeed possible to continue the tradition of critical or transcendental philosophy—especially the tradition of critical or transcendental philosophy of science—even in the wake of quite radical revisions of the original Euclidean-Newtonian framework for modern mathematical physics. I believe, as just explained, that this idea is still correct. In order to see this, however, we need to historicize and relativize the notion of transcendental philosophy itself. In particular, Kant's own commitment to the necessary a priori validity of Euclidean geometry and the principles of Newtonian mechanics was an absolutely central part of his own solution to the Newtonian problem of absolute space—and thus it was absolutely central, as well, to Kant's fundamental contention that the structures of mathematical, perceptual, and physical space are necessarily identical. Moreover, it was in precisely this way (as I have argued in detail elsewhere) that Kant was able to replace the Newtonian conception of space—infinite, three-dimensional, Euclidean space—as the sensorium of God with the characteristically Kantian conception of this same space (infinite, three-dimensional, and Euclidean) as the form of our (human) sensibility.31 It was in precisely this way, finally, that Kant was thereby able to create transcendental philosophy in the first place, by fundamentally transforming the earlier metaphysical tradition he inherited in such a way that all consideration of God and divine creation could then be eliminated from natural philosophy on behalf of our human "transcendental subjectivity." The later tradition of scientific philosophy arising in the wake of Kant—including both the more narrowly Neo-Kantian tradition of the Marburg School and the more broadly Kant-inspired work of Helmholtz and Poincaré—simply took this point for granted, and their problem, accordingly, was to reconfigure Kant's original system in the light of later developments in both post-Kantian scientific philosophy and the sciences themselves. This effort, I have argued, can indeed be brought to a successful conclusion, and, when we do so, we also see, further, how the Kuhnian problem of understanding the rationality of revolutionary transitions involving essentially discontinuous or incommensurable scientific paradigms or conceptual frameworks can itself be successfully resolved. We see, in particular, how Kuhn's own favorite example of such a revolutionary transition, the Einsteinian revolution, is characterized not only by what we might call retrospective convergent rationality (convergence of abstract mathematical structures, as viewed from the perspective of the later paradigm) but, more importantly, by prospective convergent rationality as well—from the point of view of the actual historical conceptual evolution, which, in fact, made Einstein's new theory physically or empirically possible in the first place.32
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