1. Preamble: HPS and the troubled marriage between philosophy and the sciences

On 11^th October 2007, at the first international conference on Integrated History and Philosophy of Science (&HPS1) hosted by the Center for Philosophy of Science in Pittsburgh, Ernan McMullin (University of Notre Dame) portrayed a rather gloomy scenario concerning the current relationship between history and philosophy of science (HPS), on the one hand, and mainstream philosophy, on the other hand, as testified by a significant drop in the presence of HPS papers at various meetings of the American Philosophical Association (APA).

Since my research activity falls primarily into the category of history and philosophy of science, I am delighted to be able to contribute to this volume on Conceptions of Philosophy, by discussing what I see as the very important role that history and philosophy of science plays, or ought to play within philosophy. And the aforementioned gloomy depiction of the current relationship between HPS and philosophy invites some preliminary reflections. There is no doubt, I think, that recent years have witnessed an increasing gap between the sort of topics and themes pursued by HPS scholars, and those pursued by their colleagues in mainstream philosophy. HPS scholars are interested in practicing philosophy by looking at science and history of science in the first place, and by exploring the specific ways in which new scientific ideas and concepts historically originated and evolved. They think that good philosophy has to be historically and scientifically informed. Analytic philosophers pursue philosophy as a perfectly independent discipline, which not only does not need to resort to the sciences or to history of science, but it ought not to, if philosophy has to remain a logically rigorous and methodologically autonomous discipline (independent of any historical and scientific contingency). This gap concerns methodologies, systems of values, and intellectual priorities: there could hardly be a more profound gulf. Speciation within a population is per se a positive, healthy sign of adaptation to the environment. But I think that the type of speciation that we are witnessing in history and philosophy of science within philosophy should not be regarded as a happy parting of the ways. I want to begin this paper by briefly reminding what is at stake in this parting of the ways and what both parties risk losing, or, sadly, have already lost sight of.

Without denying the methodological autonomy of philosophy as a discipline, we should not forget at the same time that philosophy began – in the words of Aristotle – with the sense of wonder that men experience in front of nature. Philosophy flourished for centuries as the highest expression of men's strive to understand nature and the world they lived in. For centuries, philosophy has gone hand in hand with the sciences. Nor can the sciences dispense with philosophy. In Newton's time, the name for physics was natural philosophy, and scientific discussions on the nature of space, time and gravitation were entangled with metaphysical debates on nature. Still in twentieth-century physics, the reception of relativity theory and quantum mechanics in the works of Einstein, Bohr, Reichenbach, Weyl and others was entangled with epistemological debates about a priori knowledge and the nature of physical reality, whereas some of the most beautiful pages in history of science were written in the first half of the last century by people such as Alexander Koyré, who came from Edmund Husserl's phenomenology, or Émile Meyerson, who studied Descartes and Kant as well as being a historian of chemistry.

These are just a few scattered examples of how fruitful the interaction among philosophy, the sciences and, I would add, the history of science (which seems to me an important ‘third man’ in this binary relation between philosophy and the sciences), has been for long time. Speciation is a recent phenomenon of our time.

In this paper I want to go back to what I take to be an important turning point in the relationship between philosophy and the sciences, namely to Immanuel Kant. Kant's critical philosophy marks probably the highest point in the happy long marriage between philosophy and the sciences. At the same time, it marks also a watershed: after Kant, the marriage became increasingly rocky. The aim of this paper is to offer a historical reconstruction and a possible (tentative and surely not exhaustive) diagnosis of why such a happy long marriage between philosophy and the sciences went eventually wrong after Kant.

In section 2, I focus on Kant's view on philosophy and the sciences, from his early scientific writings to the development of critical philosophy and the pressing epistemological problems he felt the need to address in response to the sciences of his time. In section 3, I take a look at the relationship between philosophy and the sciences after Kant in the early nineteenth century: despite the fruitful Kantian legacy in some of the greatest achievements of nineteenth century physical sciences, post-Kantian German philosophy began to signal an increasing divide between philosophy and the sciences. In section 4, I turn to the relationship between philosophy and the sciences in the twentieth century. In particular, I pay attention to three main episodes in twentieth-century philosophy. The first episode is the revival of neo-Kantianism with the Marburg school of Hermann Cohen and Ernst Cassirer (section 4.1); the second is the emergence of logical positivism, especially of Rudolf Carnap's philosophy of science with its debt and, at the same time, departure from the neo-Kantian tradition (section 4.2). The third significant episode is Thomas Kuhn's establishment of HPS as a new field or sub-field of philosophy, and the consequences that it still has for HPS as is practised today. I conclude the paper (section 5) by foreshadowing what I hope to be a better future for the philosophy and the sciences of the twenty-first century (and for HPS itself as a subject area that investigates the relationship between philosophy and the sciences) by recovering what I take to be the most important Kantian insight in this respect. Namely, that epistemology should be informed by the scientific preoccupations of our time, as much as philosophy of science should rediscover the Kantian epistemological soul that it has long lost.

2. Kant on philosophy and the sciences

For centuries, philosophy and natural sciences went hand in hand. Newton called his masterpiece Philosophiae naturalis principia mathematica to indicate that his aim was to investigate the mathematical principles of what at the time was still called natural philosophy. It is within this Galilean–Newtonian tradition that we can find some paradigmatic examples of the fruitful two-way relationship between philosophy and the sciences. Immanuel Kant is one of those paradigmatic examples. Kant was educated within this Galilean–Newtonian tradition, and in all his writings there is a constant reference to Newton's natural philosophy as the highest example of the secure foundations achieved by the physical sciences of his time. Kant's intense and life-long engagement with the sciences of his time which I am going to briefly summarise in what follows – from his pre-critical writings to his critical period up to his last and incomplete work published in the Opus postumum – testifies to what is probably one of the highest points in the troubled marriage between philosophy and the sciences.

In the pre-critical period,Footnote ¹ Kant composed twenty-five works, of which several on physics and astronomy. Most of these pre-critical works focussed on the then ongoing lively debates concerning physical sciences. For instance, Kant's very first work back in 1747 entitled Thoughts on the true estimation of Living Forces (Reference Kant and Watkins1747) addressed one of the most debated topics at the time: namely, the physical concept of vis viva (the ancestor of the current concept of kinetic energy), which Leibniz defined as the product of mass times squared velocity, by correcting Descartes's definition in terms of mass times velocity. Eight years later, in 1755, Kant wrote another scientific essay entitled Universal Natural History and Theory of the Heavens, which was bound to have a long-lasting impact in the history of astronomy because of the introduction of the so-called ‘nebular hypothesis’.Footnote ² The key idea, later expanded by Laplace in Reference Kant, Förster and Rosen1796 and now known as the Kant–Laplace hypothesis, was that the universe and the galaxies in it originated from a nebula (a rotating cloud of gases that expanded and gradually cooled down) according to the fundamental laws of physics, in particular Newton's laws as the expression of God's divine providence, Although kant legged to differ from Newton on the exact role of God in the constitution of the universe.

Even more interesting for the relationship between philosophy and the sciences of his time was the theme of Physical Monadology (1756).Footnote ³ With this work Kant intervened in the then heated debate – triggered by the Berlin Academy of Sciences Prize Question for 1745–7-between the Leibnizians–Wolffians, on the one hand, and the Newtonian Pierre Maupertuis, on the other hand, on the specific theme as to whether Leibniz's monadology was compatible with the Newtonian idea of infinite divisibility of space and time. Kant's original proposal was to try to reconcile the Newtonian idea of the infinite divisibility of space with a physical monadology that regarded monads as physical point-like centers of attractive and repulsive forces filling a space, rather than as Leibnizian metaphysical substances occupying a finitely divisible space.Footnote ⁴ If the theme of this early writing is per se already symptomatic of Kant's engagement both with mainstream (Leibnizian–Wolffian) metaphysics and with the physics of his time, on the other hand, the far-reaching consequences of Kant's original attempt to reconcile the two are even more extraordinary. Indeed, Kant's take on physical monads anticipated the dynamical theory of matter that he developed later in Reference Kant and Friedman1786 in the Metaphysical Foundations of Natural Science, and that was bound to have a huge impact in the development of the physical sciences of nineteenth century from Oersted to Faraday, as we shall see in the next section.

With the Inaugural Dissertation of 1770, entitled Concerning the Form and Principles of the Sensible and the Intelligible World, which marks a watershed in Kant's philosophy, Leibnizian metaphysics and Newtonian science are finally disentangled. Against both the Newtonian and the Leibnizian tradition and their respective attempts to reconcile physics with a metaphysics of space, time, and physical substances, Kant's critical philosophy for the very first time introduced a distinction between the faculty of sensible cognition and the faculty of intellectual cognition, and relegated the monadic realm to the second, and space and time as autonomous forms of sensible intuition to the former.

With the beginning of Kant's critical period, the relationship between philosophy and the sciences was completely reconsidered. The task for Kant was no longer to reconcile physical discoveries with metaphysical debates on the nature of space, time, and physical substances. Instead, the main task for Kant's critical philosophy became that of explaining and justifying how the very successful mathematical-physical sciences of his time were possible, by looking at the conditions of possibility of our scientific knowledge of nature. The answer that Kant gave to this question is well-known: our scientific knowledge of nature is the serendipitous result of applying pure concepts of the faculty of understanding to ‘appearances’, intended as the conceptually still undetermined spatio-temporal objects as given to the mind in empirical intuition. If the task of critical philosophy was to explain why we have achieved such secure foundations in the mathematics and natural sciences of the time, the answer that critical philosophy gave to this epistemological question relied on the way in which our mind contributes to our scientific knowledge, by projecting onto nature a priori forms of sensibility such as space and time as well as a priori principles of the understanding, such as for instance causality.

It is not my aim in this paper to enter into the details of Kant's critical philosophy. Instead, since the topic of this paper is to analyse the relationship between philosophy and the sciences after Kant, I simply want to highlight some points which I deem relevant to this topic. First, as the above short remarks about Kant's pre-critical writings show, we can legitimately regard Kant's critical philosophy as the final outcome of Kant's life-long commitment to both the philosophy and the sciences of his time (namely, to Leibniz–Wolff metaphysics on the one hand, and Newtonian physics, on the other hand). Second, the original solution that Kant gave to the problem of how to reconcile the two, consisted in relegating traditional metaphysical debates to the noumenal realm and redefining the role of philosophy as mainly centred around the epistemological questions of ‘how is pure mathematics possible?’ and ‘how is pure natural science possible?’. Kant's transcendental method starts from the fact of science and traces it back to the conditions of possibility of our scientific knowledge. Indeed, the exact sciences continued to play a key role in Kant's critical philosophy as the very source of inspiration and motivation for his entire epistemological project.

No wonder Kant opened the Preface to the second edition of the Critique of Pure Reason (1787) by programmatically linking his Copernican turn to the work of scientists such as Galileo, Torricelli and Stahl:

Galileo is here portrayed as the scientist who paradigmatically accomplished the revolutionary shift that Kant was urging for in epistemology: namely, the shift from the view that our scientific knowledge proceeds from nature itself (i.e. that what we believe there is proceeds from what there is, which is the very source of the problem of knowledge) to the opposite Kantian view, according to which ‘we can cognize of things a priori only what we ourselves have put into them’.Footnote ⁶ The certainty and secure foundation achieved by natural science from the time of Galileo onwards is – to Kant's eyes – the paradigmatic expression of this shift. Reason must approach nature with its principles on the one hand, and with experiments thought out in accordance with these principles, on the other hand.Footnote ⁷ And the task of transcendental philosophy is to clarify what are the principles that make our scientific knowledge of nature possible.

Thus, by asking how pure natural science is possible, Kant was trying to justify why we do in fact have a science of nature from the time of Galileo onwards. It is from this particular perspective – I want to suggest – that we can read Kant's entire philosophical enterprise from the Metaphysical Foundations of Natural Science (Reference Kant and Friedman1786) until his last incomplete work ‘Transition from the Metaphysical Foundations of Natural Science to Physics’ published in the Opus postumum.

In the Metaphysical Foundations of Natural Science (1786) Kant expressly tried to latch the transcendental apparatus developed in the Critique of Pure Reason onto the physical sciences of his time, namely Galilean–Newtonian physics, so as to provide a justification for its secure foundations.Footnote ⁸ The task of this fundamental work is to show how the empirical concept of matter can be schematised according to the table of categories developed in the Transcendental Analytic of the Critique of Pure Reason, i.e. namely according to the four categories of quantity, quality, relation and modality. Hence, four corresponding chapters entitled respectively Metaphysical Foundations of Phoronomy, Dynamics, Mechanics and Phenomenology. And while the chapter on Phoronomy investigates matter as a mathematical point-like movable in space endowed exclusively with a certain ‘quantity of motion’ (namely, speed and direction), in the following chapter ‘Metaphysical Foundations of Dynamics’, Kant defined the empirical concept of matter according to the category of quality as the movable that fills a space through a particular moving force. More precisely, he introduced a priori attractive and repulsive forces (which featured already in the 1756 Physical Monadology) as two fundamental moving forces, through which matter can fill a space by either causing other bodies to approach it or to be removed from it. Kant derived these two fundamental moving forces a priori from two basic properties of matter, namely its impenetrability and its ability to strive to enlarge the space that it fills so as to counteract the opposite tendency expressed by the repulsive force.

The a priori introduction of these two fundamental moving forces paves the way to the chapter on Mechanics, where Kant reformulated Newton's three laws of motion, including Newton's second law, which is regarded as instantiating the category of causality (whereby the impressed force is the cause of change in the inertial state of the system). Finally, in the fourth chapter on Phenomenology, the empirical concept of matter as the movable in space is defined according to the category of modality. Kant's aim was to show how to transform appearance (Erscheinung) into experience (Erfahrung); more precisely, how to transform apparent motions into true motions. According to Friedman,Footnote ⁹ since Kant rejected Newton's view on absolute space and time, he needed to find a way of explaining true or absolute motions without resorting to absolute space as a privileged reference frame. Kant's strategy consisted in identifying the centre of mass of our solar system as a privileged reference frame. To this purpose, he needed to derive Newton's law of gravitation, responsible for the planetary motions in the solar system, as a necessary and universal feature of matter as the movable in space.

Without going any further into this discussion, the point I want to stress is that following Friedman's reading, in the Metaphysical Foundations of Natural Science Kant was trying to give an answer to the epistemological question ‘how is pure natural science possible?’ by looking at the specific way in which Newton's three laws of motion and the law of gravitation could be justified within the conceptual apparatus of Kant's transcendental philosophy.

In this respect, the Metaphysical Foundations of Natural Science occupies a central role in the history of epistemological naturalism, namely in the view according to which answers to the problem of knowledge can be found by drawing on natural sciences (especially, the physical sciences as historically developed from the time of Galileo and Newton onwards). Kant's epistemological naturalismFootnote ¹⁰ starts with the questions ‘what is knowledge?’, ‘how is scientific knowledge of nature possible?’. The pursuit of these epistemological questions led him naturally to the sciences and to philosophy of science in the attempt to understand the growth of scientific knowledge from the time of Galileo onwards.

If physical sciences, in particular the Galilean–Newtonian tradition, is Kant's main concern in the Metaphysical Foundations of Natural Science, on the other hand in the final period of his career and life Kant somehow went back to a series of problems that occupied him already in his early (mid-1750s) works, in particular new discovery in experimental physics and chemistry about combustion, cohesion of solids, and changes of physical state. And if back in Reference Kant and Friedman1786, he had dismissed chemistry as a ‘systematic art’ rather than a proper science, now Kant's awareness of Lavoisier's chemical revolution at the turn of the century, and of the then fashionable theories of caloric and ether as the substances for heat and light, features clearly in his last and never completed work entitled ‘Transition from the Metaphysical Foundations of Natural Science to Physics’, published as part of the Opus postumum.Footnote ¹¹

In this last work, which in Kant's intention was meant to fill a gap he felt was still open in his transcendental philosophy after the Critique of Judgment, Kant claimed that in order to complete the transition from the metaphysical foundations of natural science to physics, it was not enough to establish a priori attraction and repulsion as two fundamental moving forces in nature. It was not enough because there remains a gap between postulating these two fundamental moving forces in nature from a metaphysical point of view, on the one hand, and accounting for the wide range of specific empirical properties of matter discovered by the chemical revolution by the end of eighteenth century, on the other hand. Hence the necessity to bridge the gap between the all-encompassing metaphysical framework canvassed in the Metaphysical Foundations on the one hand, and the multifarious range of more specific empirical properties of matter that natural scientists were discovering, on the other hand.

This is the specific task that Kant aimed to accomplish with the ‘Transition to Physics’, where by physics Kant meant ‘the systematic investigation of nature as to empirically given forces of matter, insofar as they are combined among one another in one system’ (22: 298). The main concern of the ‘Transition’ was then to justify and ground bottom-up a system of empirically given forces in nature. The problem is that in nature we may observe objects moving in space and time, changing physical state (from solid to liquid to gaseous) or displaying some properties (e.g. being elastic). But these are only appearances [Erscheinungen]. Only when we introduce moving forces as the underlying causes that make the objects move in space, or change their physical state or displaying some physical or chemical properties, do we have a conceptually determined appearance or phenomenon as the proper object of scientific knowledge. Once again, the category of causality was regarded as crucial in our scientific understanding of a variety of physical phenomena involving moving forces (e.g. forces responsible for the solidification, liquefaction, elasticity, and cohesion of objects).Footnote ¹² Thus, still in this last and incomplete work, Kant was striving to implement and extend his transcendental apparatus well beyond Newtonian physics to include pneumatic chemistry, theories of heat and light, and even biological theories of his time.Footnote ¹³

To sum up, with Immanuel Kant epistemology, or better what became later known as Erkenntnistheorie Footnote ¹⁴ acquired a central role in philosophy: analyses of the transcendental conditions for human knowledge replaced time-honoured metaphysical discussions about the nature of time and space triggered by Newtonian science and the Leibniz–Clarke debate. But the normative role of epistemology in tackling the problem of knowledge is – in Kant's view-intrinsically related to the role of the sciences as exemplars of human knowledge. Kant's epistemological naturalism is entangled with and ultimately leads into philosophy of science: the latter is necessary to accomplish the normative task of the former.

I take this as the greatest Kantian insight that unfortunately both current epistemologists and philosophers of science in the Anglo-American world seem to have lost sight of. From the 1930s onwards, in the Anglo-American world, knowledge was identified with justified true belief, and the task of epistemology was no longer to investigate the ‘fact of science’ so as to find the transcendental conditions for human knowledge, but rather to investigate the logical structure and syntax of language so as to find the sufficient conditions for beliefs to count as knowledge. In the rest of this paper, I attempt a diagnosis of how we got to this stage of detaching epistemology from philosophy of science and hence from science itself. I believe that despite the revival of naturalized epistemology in the second half of twentieth-century, there remains a gap between the philosophy and the sciences that has never been bridged since the time of Kant. And the first signs of this increasing gap became soon evident in the Kant aftermath, at the beginning of the nineteenth century.

3. Philosophy and the sciences after Kant. The nineteenth century

In this section, I take a brief look at some salient aspects of the relationship between philosophy and the sciences after Kant, with a focus on two main aspects of the Kantian legacy for the nineteenth century. The first concerns the impact that Kant's philosophy of science had for the developments of the nineteenth-century physical sciences. The second is more directly related to the end of Kant's epistemological naturalism, i.e. his project of tackling the problem of knowledge by taking the sciences as exemplars of human knowledge, in the post-Kantian German tradition. Let us take a look at the first of these two aspects.

Historians and philosophers of science have recently begun to pay more attention to the impact of Kant's philosophy of science for nineteenth-century physical sciences.Footnote ¹⁵ One of the most significant implications was the role that Kant's dynamic theory of matter played for the movement known as Naturphilosophie that developed mainly around Friedrich von Schelling's two main works Ideas towards a philosophy of nature (Reference Schelling1797) and First Outline of a System of Philosophy of Nature (Reference Schelling1799). As mentioned in the previous section, following Friedmans analysis, in the Metaphysical Foundations of Natural Science Kant identified two fundamental moving forces in nature: a repulsive force responsible for matter's impenetrability and an attractive force counterbalancing the repulsive force. Kant's aim was to start with these two a priori established moving forces to provide a top-down justification for his three laws of mechanics. Kant saw the three laws of motion as ultimately grounded on the transcendental principles of substance, causality and reciprocity and on the constitutive role these principles play for experience. This top-down procedure finds its natural counterpart in a bottom-up procedure that Kant developed from the Critique of Judgment (Reference Kant, Guyer and Matthews1790) to the ‘Transition from the Metaphysical Foundations of Natural Science to Physics’ in the Opus postumum. According to this alternative bottom-up procedure, we should start instead from empirically given forces of matter and empirical laws, such as those that the chemical revolution was discovering at the end of eighteenth century, and try to subsume them under higher level yet still empirical laws so as to seek after a system of forces in nature. Systematicity or systematic unity in the investigation of nature was presented as an open-ended, regulative (as opposed to constitutive) principle of scientific inquiry. It is precisely this distinction between constitutive versus regulative principles, which in Kant runs parallel to the distinction between the faculty of understanding and the faculty of reason or reflective judgmentFootnote ¹⁶ that the Naturphilosophen dismantled.

The Naturphilosophen rejected the dualism between constitutive and regulative principles, and gave a constitutive twist to the regulative principle of systematicity. While Kant stressed systematicity as a regulative principle that the mind projects upon nature, Schelling saw nature itself as systematic and ordered. The speculative physics championed by Naturphilosophen regarded nature as productivity, i.e. as natura naturans (as opposed to natura naturata). This idea of nature as productivity prompted an investigation of forces in nature as the causes of variety of phenomena.

The Naturphilosophen extended Kant's dynamic theory of matter well beyond what Kant had envisaged: for them, nature as a whole dialectically evolved from the inert/lifeless matter described by Kant into the variety of forms described by contemporary chemistry and biology. Under the influence of the Romantics (from Goethe to Novalis) and influenced by the new electrochemistry, Schelling extended Kant's theory of matter beyond attraction and repulsion and regarded magnetic, electrical and galvanic forces as a dialectical development of these two fundamental forces of matter.Footnote ¹⁷ The search for interconversion processes in the name of the unity and productivity of nature was open, and became a dominant theme of nineteenth-century physical sciences. The interconversion of electrical and magnetic phenomena is one example.

Indeed, Schelling's reinterpretation of Kant in his System of Transcendental Idealism (Reference Schelling1800) had important implications for the history of electromagnetism in the early nineteenth century. Hans Christian Oersted's pioneering discovery in 1820 that the passage of electric current in a wire could twist sideways a magnetic needle marks the beginning of electromagnetic theory. Oersted was deeply influenced by Schelling, who he came to know via Johann W. Ritter, and even more so by Kant's own dynamic theory of matter that was the subject of his doctoral dissertation.Footnote ¹⁸ Moreover, he attended Fichte's lectures in Berlin and Friederich Schlegel's lecture at Jena.

Some historians of science have even stressed the influence that the German Naturphilosophie had in the English-speaking world through Samuel Taylor Coleridge, who was a disciple of Kant in his stay in Germany at the end of eighteenth century, and back in England, allegedly inspired his friend Humphry Davy and via Davy, Michael Faraday, who worked for Davy at the Royal Institution in London.Footnote ¹⁹ It is no surprise then that Faraday's discovery of electromagnetic induction in 1831 was welcomed by Schelling as vindicating the Naturphilosophie manifesto of nature as productivity.

Electromagnetism is not the only example of how Kant's philosophy of science, via Schelling's reformulation, had an impact on the physical sciences of the nineteenth century. The interconversion of heat and mechanical work expressed by the first law of thermodynamics – jointly discovered by Julius Robert Mayer, Hermann von Helmholtz and James Prescott Joule in the 1840s – is another eloquent example. While the link between Mayer and Naturphilosophie has become a debated issue in history of science after Thomas Kuhn's seminal article ‘Energy conservation as an example of simultaneous discovery’ in the late 1950s,Footnote ²⁰ a more robust historical link between Naturphilosophie and Hermann von Helmholtz, whose father was a close friend of Fichte, has generally been recognised.Footnote ²¹

But the Kantian legacy for nineteenth-century science is not confined to the interconversion processes at work in electromagnetism and thermodynamics. It extends also to more theoretical aspects of mathematical physics in the works of Jakob F. Fries' The Mathematical Philosophy of Nature (1822).Footnote ²² In the same aforementioned spirit of rejecting the constitutive/regulative distinction and affirming the priority of the regulative over the constitutive, Fries saw Euler and Lagrange's principles of analytical mechanics as the result of a bottom-up approach for systematizing mechanical experience before any constitutive principle could be found and any forces of matter identified. Even more striking is the impact of Kant's Transcendental Aesthetic for the discovery of non-Euclidean geometries. For Kant, the universal and necessary status of Euclidean geometry could be traced back to the fact that objects are given to the mind in empirical intuition according to space and time as a priori forms of sensibility. Hermann von Helmholtz challenged Kant on the allegedly necessary status of Euclidean geometry by showing that what makes space seem Euclidean is a series of sense-impressions about the free mobility of rigid bodies and paths of light rays, and the very same empirical evidence can acquaint us with the structure of a non-Euclidean space; hence the non-necessary status of Euclid's fifth postulate. In this way, Helmholtz's empiricism paved the way to Poincaré's conventionalism about geometry, and to non-Euclidean geometries in relativity theory in the twentieth century.Footnote ²³

While the Naturphilosophen rejection of the regulative versus constitutive distinction and emphasis on the unity of nature opened undreamt-of avenues for the physical sciences, on the other hand, it also engendered a swirl of new philosophical problems. One of the central tenets of post-Kantian German idealism, from Schelling to Fichte to Hegel, was the rejection of Kant's distinction between the faculty of sensibility and the faculty of understanding. For Kant, the distinction between these two faculties was central to understand how nature as given to us in sensible receptivity could become an object of scientific knowledge. And, for Kant, the answer to the problem of knowledge was to be found in the way in which concepts of the faculty of understanding are ‘schematised’ and applied to spatiotemporal objects of the faculty of sensibility (namely, to ‘appearances’ as given to the mind in empirical intuition according to a priori forms of space and time).

In the hands of post-Kantian German idealists, Kant's interplay of the faculty of sensibility and the faculty of understanding received a new twist, and the contribution of the faculty of sensibility was significantly downplayed. Nature was increasingly regarded as embedded in the conceptual realm, and eventually as the historicized manifestation of the dialectical development of the spirit, according to Hegel. But it is not just the faculty of sensibility that was downplayed to emphasise the conceptual aspect of human knowledge over and above the contribution of sensibility. The same faculty of understanding was in turn downplayed with respect to the faculty of reason. For Kant, there was an important difference between understanding and reason: the former is the realm of constitutive principles that enter in the way we constitute experience by ‘schematizing’ concepts (i.e. by applying them to spatio-temporal appearances); reason, on the other hand, is the realm of regulative principles that provide open-ended and never achievable ideals, towards which we should strive in our scientific knowledge of nature. We have already mentioned that a distinctive feature of Naturphilosophie was the pre-eminence assigned to regulative principles over constitutive ones. A consequence of this shift was precisely the aforementioned development of a new dynamic theory of matter that – in the name of the regulative principle of systematicity – took nature as natura naturans developing dialectically from polar forces. This very same shift, however, had also the effect of opening a gulf between philosophy and the sciences. The historicized, dialectical development of human reason, in conjunction with the downplay of the Kantian faculty of sensibility, meant that knowledge of nature was no longer secured by the Kantian interplay of intuitions and concepts; but rather by the spontaneous activity and dialectical unfolding of human reason itself.

The problem of bridging the gap between what we believe there is and what there is was no longer tackled through Kant's Copernican turn of making appearances conform to our way of representing. Instead, our way of representing became all there is. The very same dichotomy between us as epistemic agents and the external world as an object of knowledge disappeared in post-Kantian German idealism. And with it, the problem of knowledge that had haunted epistemological naturalism from Hume to Kant also disappeared. Or better, in its place now there was a new problem: that of the unbounded autonomy of human reason in its historicised unfolding. The immediate effect of this idealistic twist was of course that the scientific preoccupations that had triggered Kant's Copernican turn were put to rest for some time. The aim of philosophy – for post-Kantian German idealism – was no longer to explain how we can have scientific knowledge of nature. Nor is the aim of science to provide an exemplar of human knowledge: the post-Kantian idealistic tradition rediscovered the importance of the arts and humanities (from music to art) as exemplars of human knowledge alternative to the sciences. Hence the ensuing debate between Naturwissenschaften and Geisteswissenschaften that became so typical of German philosophy.

But it is from within this idealistic tradition that at the end of nineteenth century and beginning of the twentieth century a new movement developed, whose primary aim was to rediscover the problem of knowledge and to return to Kant's epistemological project and to the scientific preoccupations behind it. This movement was the Marburg School of neo-Kantianism with Hermann Cohen, Paul Natorp, and Ernst Cassirer.

4. Philosophy and the sciences after Kant. The twentieth century

5. Conclusion. What future for history and philosophy of science after Kuhn? The Kantian legacy

I want to conclude by urging philosophers of science to go beyond Kuhn. In order to reconcile history and philosophy of science, Kuhn created in fact a new sub-discipline within philosophy of science itself, known as HPS. He set his own philosophical agenda, with his manifesto of scientific revolutions, incommensurability, and theory-choice. He clearly and expressly took his distance from positivistic philosophy of science, and identified new problems and new challenges for philosophers of science to address. By contrast with Kuhn, I think that we do not need to set a separate agenda for a historically informed philosophy of science: we do already have a philosophical agenda with a series of compelling and still open questions (from confirmation to scientific explanation; from underdetermination to laws of nature; from causality to foundational issues in physics and biology, among many others). Those questions have traditionally been regarded as falling in the province of logical analyses dear to positivist philosophy of science. They have been regarded as questions that can be addressed in purely analytical, logical terms without any need to engage with history of science. I think that the future of HPS as an integrated discipline consists in showing that those questions do not belong exclusively to the positivist province and can more profitably be addressed by paying due attention to history of science.

But I urge to go beyond Kuhn also in another sense. I think we are still under the Carnapian and Kuhnian spell in thinking that philosophy of science should not only be detached from epistemology, but should in fact replace it. My vision of HPS is different. I see history and philosophy of science as integral part of the overarching normative function of epistemology. The practice of history and philosophy of science, as I see it, is inherent the meliorative project of epistemology. That is why I believe that the current risk that HPS runs of being increasingly isolated from philosophy is not just to be blamed on post-Fregean epistemology, but is to be blamed also on Kuhn's radical naturalism that has broken the link between philosophy of science and epistemology intended in the Kantian way. My hope is that HPS will eventually rediscover Kantian epistemological naturalism as the family to which it naturally belongs: we do history and philosophy of science because we are ultimately interested in addressing the problem of how we can and indeed do have scientific knowledge, and why we do have developed such a surprisingly successful science across centuries. In a truly Kantian spirit, I believe that current history and philosophy of science should rediscover its Kantian epistemological soul (to echo a recent paper by Alan Richardson).

Only in this way, can we hope to bridge the gap between philosophy and the sciences that opened wide after Kant. I am not suggesting that like Kant, we should provide a justification for currently accepted scientific theories. Nor am I, of course, suggesting that we have to dust the Kantian apparatus of a priori forms of sensibility and categories of the understanding. I am suggesting instead that any inquiry into the foundations of space-time, or the nature of causation, or living organisms in philosophy of biology, should be addressed and pursued in such a way as to make the question ‘how is scientific knowledge possible?’ at least meaningful (if not answerable). This particular way of reconciling the practice of history and philosophy of science with the Kantian epistemological tradition has been revived in recent times, thanks to the contributions of Gerd Buchdahl, among the first in the 1960s, and more recently Michael Friedman, Robert DiSalle, Thomas Ryckman, Roberto Torretti, Margaret Morrison, among many others.

Gerd Buchdahl was one of the first in the 1960s to voice the necessity of a return to Kant in the treatment of philosophy of science with his marvellous book Metaphysics and the Philosophy of Science (1969a). In more recent years, Michael Friedman has been one of the main advocates of the necessity to rediscover not only Kant's own philosophy of science, but most importantly, Kant's epistemological project and its relevance to twenty-first century history and philosophy of science, despite the widespread prejudice that modern science has proved Kant wrong. In the Kant lectures delivered at Stanford University and published as The dynamics of reason (Reference Friedman2001), Friedman addresses the very delicate and controversial issue of showing how Kant's epistemology can still be fruitfully applied to twentieth-century science. In particular, he set the ambitious task of reconciling Kuhn's view of scientific revolutions with Kant's idea that there are some constitutive a priori elements defining the conditions of possibility of experience as displayed by any scientific theory. By relativising those constitutive a priori elements to different theoretical frameworks, Friedman argues that it is possible to accept the Kuhnian picture of science as a sequence of scientific revolutions and paradigm shifts, while at the same time maintaining the Kantian insight that what makes our scientific knowledge of nature possible is precisely the presence of some constitutively a priori elements within each theory.

The key idea of Friedman's dynamic Kantianism consists then in relativising Kant's notion of a priori. Friedman refers back to Hans Reichenbachs Theory of Relativity and A Priori Knowledge (Reference Reichenbach1920), suggesting that we should distinguish between two possible meanings of the term ‘a priori’ in Kant: namely 1) fixed and unrevisable, and 2) constitutive of the object of experience. According to Reichenbach, modern physics has only proved the first meaning wrong, while the second can be maintained and applied to modern scientific theories such as relativity theory. As such, we can keep on using Kant's notion of a priori even for twentieth-century physics. The a priori becomes relativised: it maintains its constitutive function, while at the same time it is allowed to change with time and to become relative so as to make room for scientific revolutions. This is what Friedman calls the ‘relativised a priori’: it is a significant change compared to Kant, but in a way it allows to reconcile Kant's epistemological project with some modern visions of science.

Accordingly, Friedman claims that we should regard mature theories in science such as Newtonian mechanics or special relativity or general relativity as consisting of two distinct parts: (1) a properly empirical part, containing empirical laws such as Newton's law of gravitation, or Maxwell's equations of electromagnetism in special relativity (SR), or Einstein's equations for the gravitational field in general relativity (GR); and (2) a constitutively a priori part containing both the relevant mathematical principles used in formulating the theory (Euclidean geometry; Minkowski space-time in SR; Riemannian theory of manifolds in GR) and certain fundamental physical principles (Newton's laws of motion in Newtonian mechanics, the light principle of SR, the equivalence principle of GR). The claim is that even if the elements of part (2) (i.e. both mathematical and physical principles) can and typically do change in the history of science through scientific revolutions, nonetheless they still retain their Kantian constitutive a priori character in making possible the empirical part (1) of the theory.

Friedman points out that the scientific revolutions of twentieth century have made even more clear the constitutive function of a priori principles in Kantian terms, and have even more emphasised the distinction between those constitutively a priori elements, on the one hand, and the properly empirical part of the theory, on the other hand. The scientific revolution that Einstein brought about with general relativity, for example, has made even more evident the need of finding constitutive principles as coordinating between an increasingly more abstract mathematical framework, on the one hand, and empirical phenomena, on the other hand. Instead of Euclidean three-dimensional space, we now have a four-dimensional Riemannian manifold of variable curvature. In place of inertial trajectories of Newtonian mechanics, we now have the four-dimensional geodesics of the Riemannian metric. In place of Newton's law of gravitation, we now have Einstein's field equations which relate the four dimensional space-time metric with the stress-energy tensor. Hence, there is an increasing need for principles of coordination mediating between the abstract mathematical structures and concrete physical phenomena. In the case of general relativity for instance, the equivalence principle coordinates the four-dimensional Riemannian geodesic paths with the concrete phenomena of free falling particles in a gravitational field. Friedman claims that the equivalence principle in GR and the light principle in SR have exactly the same coordinating function that Newton's laws of motion have in the context of Newtonian mechanics. And like Newton's laws of motion, they too are fundamental mathematical-physical presuppositions without which the properly empirical laws of the new theory (namely, Maxwell's equations for the electromagnetic field in special relativity; and Einstein's equations for the gravitational field in general relativity) have no empirical meaning or application at all.

Against Quine's holism, Friedman then goes on to claim that it is a big mistake to confuse the mathematical-physical part of a theory with the properly empirical part. While we can subject to experiment the latter, we cannot subject to experiment the former. For instance, despite the fact that Riemannian manifolds can be used to formulate both general relativity and a version of classical mechanics, we cannot say that we can test Riemannian manifolds in either of these two different theories, because Riemannian manifolds provide instead the conditions of possibility of either of the two theories and as such cannot be tested in either of them. Riemmanian manifolds together with some fundamental principles such as the equivalence principle in general relativity cannot be subject to experiment or modified because they play a fundamental constitutive function within relativity theory.

In my book Pauli's Exclusion Principle (2005), I have latched onto Friedman's dynamic Kantianism by providing an analysis of a scientific principle, namely Pauli's exclusion principle. Discovered in 1924 by the Austrian Nobel laureate Wolfgang Pauli, the principle excludes the possibility in nature of two electrons, two protons and in general two fermions being in the same dynamic state, and as such it explains a wide array of phenomena such as the stability of matter at the level of galaxies as well as the dynamics of coloured quarks at the subatomic level, among others. I wanted to understand how a scientific principle, such as this one, originates and whether or not it could play a constitutive a priori role like the one that Friedman ascribes it to other scientific principles. I then reconstructed in some historical and physical detail the origins of Pauli's principle in the history of early quantum theory and its evolution with the development of quantum statistics in 1926 and later quantum field theory and quantum chromodynamics in the 1960s. The history of Pauli's principle was in my intention functional to addressing the philosophical question of what a scientific principle is, and more in general the epistemological question of how our scientific knowledge of nature – as displayed by QM (and Pauli's principle in it) – is possible.

In my monograph, I drew attention to a different perspective about scientific principles, one that is still dynamically Kantian in considering them as relative and revisable, and yet is not distinctively Reichenbachian in identifying them with constitutive a priori principles ‘coordinating’ the mathematical with the proper empirical part of a scientific theory. The history of Pauli's exclusion principle lent itself naturally to this alternative perspective, which latches onto Friedman's by highlighting the complementary, regulative Kantian aspect. The upshot of my monograph was to show that an empirical and contingent rule such as Pauli's 1924 exclusion rule attained lawlikeness and necessity because of the systematizing role it played in the quantum mechanics framework, whereby systematicity is not just a desirable feature of scientific knowledge. Rather, in a truly Kantian spirit, systematicity as a regulative principle underpins the possibility itself of identifying empirical regularities as lawlike. It is only the systematizing role that an empirical regularity plays within a body of knowledge that transforms it into a fundamental law of nature. This approach has the advantage of doing justice to the revisable and experimentally testable nature of Pauli's principle as much as it grounds its nomological validity on the degree of empirical support it receives within quantum mechanics.

I have lingered on Friedman's dynamic Kantianism and my own more recent work simply because they represent a possible way (albeit not the only one) of developing history and philosophy of science along the epistemological lines that Kant originally traced. Or better, they represent a possible way of practising history and philosophy of science in such a way that the underlying epistemological question ‘how is scientific knowledge possible?’ remains at least meaningful. But many other ways are possible and need to be explored in future research.

To sum up and conclude, I think we should resist two opposite and similarly dangerous temptations. The first is the temptation to make philosophy of science a branch of science itself, where philosophy risks becoming a footnote at the end of a theorem, be it in decision theory or philosophy of physics. Let us leave the sciences to the scientists and content ourselves as philosophers with the perennial problem of understanding how we could reach scientific knowledge in the first place. The second is the opposite temptation of leaving those epistemological questions to the epistemologists, as if an answer to the problem of knowledge should necessarily pertain to the exclusive domain of epistemology as is practised nowadays in analytic philosophy. If philosophy of science has lost its Kantian epistemological soul, similarly current epistemology seems to have in part lost its scientific soul in trying to pursue those important questions beside and beyond any scientific preoccupation.

Kant opened the path by producing an epistemology that was informed by the scientific preoccupations of his time. The burden now is on us to explore the path further and to venture uncharted territories, even if the path may well be rocky and ultimately open-ended. Or better, it is precisely because the path is probably open-ended that the inquiry into the relationship between philosophy and the sciences can and must go on, after Kant, and despite all the limits of Kant's project.