Initially trained as a physicist, Kuhn became a leading and extraordinarily influential figure in the history of science. He saw his work in the history of science as contributing to a novel philosophical conception of the nature of science. At the outset of Structure, for example, Kuhn announces his intention to replace the “development-by-accumulation” model he associates with the philosophical tradition before him—including, in particular, what he calls “early logical positivism”—with a new model of radical conceptual discontinuity or incommensurability.Footnote ¹Structure was written during Kuhn's tenure teaching philosophy and history of science at Berkeley, and, shortly after its publication, he took up a new post as professor of philosophy and history of science at Princeton. From 1983 until his death in 1996 Kuhn was professor of philosophy at MIT, where he attempted further to articulate his conception of incommensurability, taking account of developments in linguistics and philosophy of language.

We can distinguish several stages in Kuhn's relationship with philosophy as a discipline after the publication of Structure. At first his work was severely criticized and rejected within Anglo-American philosophy of science, which had been greatly influenced by logical positivism and empiricism after the war.Footnote ² In the 1970s and 1980s, however, there was a turn away from this influence throughout the Anglo-American world, and Kuhn's work (among others) was widely credited with being an important factor in this turn.Footnote ³ Beginning in the 1990s, in the context of renewed interest in the history of logical positivism and empiricism, a number of scholars (including myself) then called attention to striking similarities between Kuhn's views and those of the “early logical positivists”—in so far as they, many years before Kuhn, had already emphasized the deeply revolutionary character, from a conceptual point of view, of Einstein's theory of relativity (compare note 1 above).Footnote ⁴ This historical work highlighted Kantian and neo-Kantian aspects of the philosophy of logical positivism, and Kuhn, very late in his career, also underscored such influences on his own view, characterizing it, appropriately, as a version of “Kantianism with moveable categories.”Footnote ⁵ After reconsidering the relationship between Kuhn and logical positivism, together with the neo-Kantian aspects of this philosophy, I shall devote the rest of my discussion to the roots of both Kuhn's philosophy and his historiography in the neo-Kantian tradition.

George Reisch first called attention to the striking parallels between Kuhn and logical positivism in a paper provocatively entitled “Did Kuhn Kill Logical Empiricism?”.Footnote ⁶ Beginning with the fact that Structure first appeared as a volume of the International Encyclopedia of Unified Science (the official monograph series of the logical empiricist movement in exile), Reisch presents two previously unpublished letters written to Kuhn by Rudolf Carnap in the latter's capacity as editor. There Carnap expresses enthusiastic approval of Kuhn's ideas and states that he especially “liked your emphasis on the new conceptual frameworks which are proposed in revolutions in science, and, on their basis, the posing of new questions, not only answers to old problems.”Footnote ⁷ This is by no means surprising, as Reisch also explains, because of the deep affinities between Carnap's underlying philosophical perspective and Kuhn's ideas. Natural science, for Carnap, is to be conceived as represented within a particular formal language or linguistic framework. And perhaps Carnap's most fundamental thought is that there are a plurality of essentially different and non-intertranslatable such frameworks. For Carnap, moreover, there is no sense in which one such framework can be correct while another is incorrect. Rather, all standards of logical correctness are relative or internal to a particular choice of linguistic framework. External questions concerning which linguistic framework to adopt are not similarly adjudicable by already established logical rules but rather require a conventional or pragmatic choice based on suitability or adaptedness for one or another given purpose.Footnote ⁸ Such an external question, involving a change from one linguistic framework to a different one, is precisely what is at issue, for Carnap, in a scientific revolution.Footnote ⁹

It is especially noteworthy, therefore, that Kuhn, towards the end of his career, explicitly acknowledges these affinities between his views and Carnap's. Kuhn expresses embarrassment, to begin with, that “[w]hen I received the kind letter in which Carnap told me of his pleasure in the manuscript [one of the letters concerning the initial publication of Structure cited by Reisch], I interpreted it as mere politeness, not as an indication that we might usefully talk.”Footnote ¹⁰ But Kuhn then goes on to explain the “correspondingly deep difference” between Carnap and himself—which, he thinks, survives the acknowledged parallels. This does not consist, as one might first expect, in the circumstance that Carnap's linguistic rules must always be explicitly formulated whereas the rules and standards governing a Kuhnian paradigm are largely tacit. Kuhn rather emphasizes that he, unlike Carnap, is concerned from the start with historical development, so that, in particular, language change “is cognitively significant for me as it was not for Carnap.”Footnote ¹¹ Kuhn's point, as I understand it, is that a change of language, for Carnap, is not cognitive or epistemic in the only sense of “epistemology” Carnap recognizes. For, although Carnap, as Reisch emphasizes, does connect his notion of change of language with scientific revolutions, he never discusses such revolutions in any serious way. Such a historical investigation could never be a part of what Carnap himself preserves of epistemology, namely the logic of science (Wissenschaftslogik)—the formulation and examination of a variety of possible linguistic frameworks within which the results of the special sciences may be represented. What is crucial, for Carnap, is that the only remaining properly philosophical problems are purely formal and belong to the application of logic to the language of the special sciences.Footnote ¹² For Kuhn, by contrast, as the very first chapter of Structure makes clear, the point is precisely that historical examination of scientific change can, above all, be genuinely philosophical.

We can deepen our appreciation of the affinities between Carnap and Kuhn—and also their important differences—by looking more closely into the backgrounds and intellectual contexts of both views. I suggested above that early logical positivism took its starting point from an explicit recognition of the profoundly revolutionary character of Einstein's theory of relativity. Carnap attempted philosophically to come to terms with this theory in his doctoral dissertation, written under the direction of the neo-Kantian philosopher Bruno Bauch at Jena.Footnote ¹³ One cannot, Carnap argues, still maintain Kant's original conception of the fixed synthetic a priori status of specifically Euclidean geometry. So Carnap instead defends a generalization of Kant's conception of spatial intuition according to which only the infinitesimally Euclidean character of physical space is thereby determined a priori.

This conception has significant points in common with that developed by the neo-Kantian philosopher Ernst Cassirer slightly earlier.Footnote ¹⁴ And Carnap's colleague Hans Reichenbach developed a related neo-Kantian approach around the same time.Footnote ¹⁵ Reichenbach draws a distinction between two meanings of the Kantian a priori: necessary and unrevisable, fixed for all time, on the one hand, and “constitutive of the concept of the object of [scientific] knowledge,” on the other.Footnote ¹⁶ Reichenbach argues, on this basis, that the lesson of the theory of relativity is that the former meaning must be dropped while the latter should be retained. Relativity theory involves a priori constitutive principles as necessary presuppositions of its properly empirical claims just as much as did Newtonian physics, but these principles have changed in the transition from the latter theory to the former. Whereas Euclidean geometry is indeed constitutively a priori in the context of Newtonian physics, for example, only infinitesimally Euclidean geometry is constitutively a priori in the context of general relativity. The result is thus a relativized conception of a priori constitutive principles that change and develop along with the development of the sciences themselves.

The influence of neo-Kantian philosophy—and Cassirer in particular—is seen most clearly, however, in Carnap's first major work, the Aufbau.Footnote ¹⁷ Carnap focuses especially on the “genetic” (erzeugende) conception of knowledge characteristic of the Marburg School of neo-Kantianism founded by Cassirer's teacher Hermann Cohen. Empirical science, on this conception, proceeds by progressively embedding natural phenomena in an ordered sequence of abstract relational structures as we successively articulate and refine mathematical representations of these phenomena in the actual historical development of our theories. This procedure results in an infinite, never-ending sequence of relational structures, but one which is nonetheless converging on a limit-structure or limit-theory representing the ideal completion of scientific progress. The object of scientific knowledge is never completely given: it is only successively approximated in the limit as the ideal X towards which our mathematical representations of nature are converging.Footnote ¹⁸

When Carnap, in the Aufbau, first introduces the question of the basic or fundamental relations on which his “constitutional system of reality” is to be erected, he cites Cassirer's Substance and Function as showing the necessity of formally defined relational concepts for ordering the “undigested experiential given” favored by “positivism.”Footnote ¹⁹ Carnap thus hopes to achieve a synthesis of empiricism and Kantianism—a synthesis that emphasizes, as does Cassirer, the indispensability of logico-mathematical formal structures for underwriting the clarity, precision, and intersubjective communicability of empirical scientific knowledge. Carnap also follows Cassirer in representing empirical knowledge by a serial or step-wise sequence of abstract formal structures, depicting, in an idealized fashion, how our scientific methods for acquiring knowledge actually play out in practice. For Carnap, however, this is not a temporal series of successor theories in the historical progress of mathematical natural science, but rather a sequence of levels or ranks in the hierarchy of logical types of Whitehead's and Russell's Principia Mathematica.Footnote ²⁰

The historically oriented epistemology of the Marburg tradition—which proceeds largely by the methods of intellectual history—is here transformed into a purely logical exercise: the project of formally presenting the logical definitions of all objects of (current) scientific knowledge subsisting at the various levels of Carnap's constitutional system. And, in the course of this formal exercise, Carnap is able, by means of the theory of types, to transcend the Marburg doctrine of the essentially incomplete character of the object of scientific knowledge—its character, that is, as a never-to-be-completed X. For Carnap, all objects whatsoever are defined or “constituted” at definite finite ranks within the hierarchy of logical types, and it is only the further empirical specification of these objects that remains essentially incomplete. As a result, Carnap is also able to reject the Kantian conception of synthetic a priori principles. Objects are defined or constituted by stipulation and then further investigated by experience: “According to the conception of constitutional theory there are no other components in cognition than these two—the conventional and the empirical—and thus no synthetic a priori [components].”Footnote ²¹

In a direct engagement with neo-Kantian epistemology, Carnap thereby arrives at the same point that was reached in the context of the logical positivists’ earlier engagement with Einsteinian relativity theory. Kant's synthetic a priori principles governing our empirical scientific knowledge are no longer necessarily fixed, but become subject to choice, and are relativized to a specific scientific context. Thus Carnap here stands on the brink of his mature philosophy of linguistic frameworks, which, as explained above, has striking affinities with the Kuhnian theory of scientific revolutions.Footnote ²² This philosophy can thus be viewed as a kind of generalization and “logicization” of the conception of relativized a priori principles developed by Reichenbach, resulting from Carnap's simultaneous engagement with both the details of neo-Kantian epistemology and the most recent developments in modern mathematical logic.

I began by noting that Kuhn, towards the end of his career, explicitly acknowledges the Kantian and neo-Kantian background to the development of logical empiricism and the resulting parallels with his own views. Commenting, in particular, on Reichenbach's distinction between two meanings of the a priori (fixed and unrevisable versus constitutive relative to a theory), Kuhn remarks that both meanings “make the world in some sense mind-dependent, but the first disarms the apparent threat to objectivity by insisting on the absolute fixity of the categories, while the second relativizes the categories (and the experienced world with them) to time, place, and culture.”Footnote ²³ Kuhn, like the early logical positivists, has thus adopted a relativized conception of Kantian a priori principles. Yet Kuhn's perspective, unlike theirs, is essentially historical: their a priori is relativized to a theory or linguistic framework, not to a “time, place, or culture.” And this point, too, can be further illuminated against the background and context of Kuhn's historiography.

In the Preface to Structure, Kuhn portrays how he shifted his career plans from physics to the history of science, and, in explaining his initial intensive work in the subject, states that he “continued to study the writings of Alexandre Koyré and first encountered those of Emile Meyerson, Hélène Metzger, and Anneliese Maier[; more] clearly than most other recent scholars, this group has shown what it was like to think scientifically in a period when the canons of scientific thought were very different from those current today.”Footnote ²⁴ Then, in the introductory first chapter, Kuhn explains the background to his rejection of the development-by-accumulation model in a recent historiography that is “perhaps best exemplified in the writings of Alexandre Koyré.”Footnote ²⁵ In particular, Kuhn places himself squarely within the historiographical tradition initiated by Koyré in his work on Galileo—a tradition that played a leading role in establishing the history of science as an independent discipline in the immediate postwar period.Footnote ²⁶

In a later survey article on the development of the history of science, Kuhn again explains the initial break with the development-by-accumulation model, which began, according to Kuhn, with “the influence, beginning in the late nineteenth century, of the history of philosophy.” We here learned an “attitude towards past thinkers which came to the history of science from philosophy[;] partly it was learned from men like Lange and Cassirer who dealt historically with people or ideas that were also important for scientific development . . . partly it was learned from a small group of neo-Kantian epistemologists, particularly Brunschvicg and Meyerson.”Footnote ²⁷ And finally, in a “Historiographic/Philosophical Addendum” to his book on Planck and black-body radiation, Kuhn states, “The concept of historical reconstruction that underlies [my 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.”Footnote ²⁸

Virtually all the figures on Kuhn's list of influences are, in one way or another, taking inspiration from, and reacting to, Cassirer's seminal work on the history of modern science and philosophy, Das Erkenntnisproblem.Footnote ²⁹ This is the first work, in particular, to develop a detailed reading of the seventeenth-century scientific revolution 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.Footnote ³⁰ Cassirer simultaneously articulates an interpretation of the history of modern philosophy as the development and eventual triumph of what he calls philosophical idealism. This tradition takes its inspiration from 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. Cassirer thereby interprets the development of modern thought as a whole from the point of view of the philosophical perspective of Marburg neo-Kantianism. And he here anticipates his own later systematic work by interpreting the characteristically modern conception of nature as the triumph of the mathematical-relational concept of function—as expressed in the universal laws of mathematical physics—over the traditional Aristotelian concept of substance.

Yet Meyerson, who is clearly the next-most-seminal figure on Kuhn's list of influences, takes a quite different view. He agrees with Kant and the neo-Kantians concerning the necessity for a priori requirements of the mind to give meaning and structure to the results of empirical science. But he is vehemently opposed to the attempt to assimilate scientific understanding to the formulation of universal laws governing phenomena. Indeed, the central thought of his Identity and Reality (note 26 above) is that genuine scientific knowledge and understanding can never be the result of mere lawfulness (légalité) but must instead answer to the mind's a priori logical demand for identity (identité). And the primary requirement resulting from this demand is precisely that some underlying substance be conserved as absolutely unchanging and self-identical in all sensible alterations of nature. 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 through motion in uniform and homogeneous space. And this same demand for trans-temporal identity is also represented, in more recent times, 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. However, in the even more recent discovery of what we now know as the second law of thermodynamics, 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. In the end, therefore, Meyerson views the development of natural science as progressing via a perpetual dialectical opposition between the mind's a priori demand for substantiality, and thus absolute identity through time, and nature's own irrational a posteriori resistance to this demand.

In the work of Cassirer and Meyerson, then, we find two sharply diverging visions of the 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, in which we 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, where reason perpetually seeks to enforce precisely the substantialistic impulse, and nature continually offers her resistance via the ultimate irrationality of temporal succession. It is by no means surprising, therefore, that Meyerson, in the course of considering, and rejecting, “anti-substantialistic conceptions of science,” explicitly takes issue with Cassirer's characteristic claim that mathematical 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.”Footnote ³¹ And it is also no wonder, similarly, that Cassirer, in the course of his own discussion of “identity and diversity, constancy and change,” explicitly takes issue with Meyerson's views by asserting that the “identity towards which thought progressively strives is not the identity of ultimate substantial things but the identity of functional orders and coordinations.”Footnote ³²

It is especially striking, therefore, that Koyré—who is clearly the most direct and important influence for Kuhn—places himself squarely on the side of Meyerson. Indeed, Koyré's Galileo Studies is dedicated to Meyerson, and his allegiance to Meyerson's position in the dispute with Cassirer clearly emerges, if only implicitly, in Koyré's criticism of what he views as Cassirer's excessively Kantian reading of Galileo's “Platonism.”Footnote ³³ That this criticism does not merely concern the interpretation of Galileo, however, is clearly expressed in an earlier paper explaining and defending Meyerson's philosophy to a German audience. Koyré explicitly defends Meyerson's conception against the “anti-substantialistic” pretensions of neo-Kantianism, according to which “science has nothing to do with substantial causes, but is occupied only with constructing functional dependencies, functional interconnections of the phenomena and clothing them in mathematical formulas.”Footnote ³⁴ While science does aim at mathematical laws, of course, this is not the ultimate goal of the rational comprehension of phenomena required by thought. Here Meyerson, following the ancient tradition initiated by Parmenides and Plato, is perfectly correct: the demand for rational comprehension can only be satisfied by absolute unity and self-identity. Yet, as Plato—and, following him, Hegel—clearly saw, the reality with which thought is confronted is essentially irrational. In particular, temporal succession is ultimate and irreducible, and reality itself is a necessary mixture of (rational) sameness and (irrational) otherness. In the end, therefore, despite his well-known emphasis on rationalism and the mathematization of nature, Koyré is a Meyersonian. His “Platonism”—in explicit opposition to the more Kantian version articulated by Cassirer—is clearly and firmly based on a recognition of the limits of mathematical thought.

The historiographical tradition Kuhn attempts to assimilate in his theory of scientific revolutions is thus by no means unitary and uncontentious. On the contrary, it is characterized by a deep philosophical opposition between a mathematical idealist tendency taking its inspiration from Kant and a more realistic and substantialistic tendency taking its inspiration—via the thought of Meyerson—from a mixture of Platonic, Cartesian, and Hegelian ideas. The former tendency, following Kant, renounces the ambition of describing an ontological realm of substantial things subsisting behind the empirical phenomena in favor of a rigorous mathematical description of the lawlike relations among the phenomena themselves. It differs from Kant, however, in recognizing that no particular mathematical structures (such as those of Euclidean geometry and Newtonian physics) are necessarily instantiated in the phenomena. And, accordingly, it portrays the objectivity and universality of scientific progress as a historical evolution marked by a continuous unfolding and generalization of the powers of mathematical thought itself, entirely independently of any concern for the correspondence of such thought to a mind-independent ultimate reality. The latter tendency, by contrast, maintains precisely an ontology of substantial things, and, accordingly, it emphatically rejects the attempt to reduce the task of science to the formulation of precise mathematical laws. It thus ends up with a more pessimistic reading of the history of modern science in which our demand for fundamentally ontological rational intelligibility is met by an inevitable resistance to this demand arising from the irrational essentially temporal character of nature itself.

If I am not mistaken, this deep philosophical tension is clearly echoed in Kuhn's theory of scientific revolutions when he considers the question of theoretical continuity over time. Here Kuhn shows himself, in this respect, to be a follower of the Meyersonian tendency, for he consistently gives the question an ontological rather than a mathematical interpretation. Thus, for example, when Kuhn considers the relationship between relativistic and Newtonian mechanics, in explicit opposition to what he calls “early logical positivism,” he rejects the notion of a fundamental continuity between the two theories on the grounds that the “physical reference” of their terms is essentially different.Footnote ³⁵ And Kuhn nowhere considers the contrasting idea, characteristic of the Marburg School, that continuity of the relevant mathematical structures might be 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 on an independently existing truth about reality, on a theory-independent external world.Footnote ³⁶ By contrast, the Marburg school rejects this realistic reading at the outset. Our theories do not ontologically converge on a mind-independent realm of substantial things. Instead, they mathematically converge within their historical evolution, as they continually approximate, but never actually reach, an ideally complete mathematical representation of the phenomena.