Hermeneutic strategies in Gerd Buchdahl’s Kantian philosophy of science

Gerd Buchdahl’s international reputation rests on his masterly writings on Kant. In them he showed how Kant transformed the philosophical problems of his predecessors and he minutely investigated the ways in which Kant related his critical philosophy to the contents and methods of natural science. Less well known, if only because in large part unpublished, are the writings in which Buchdahl elaborated his own views on the methods and status of the sciences. In this paper I examine the roles of hermeneutics in Buchdahl’s reconstruction of Kant’s philosophical system and in his own ‘transcendental methodological’ approach to the philosophy of science. The first section looks at Buchdahl’s views on the theory and practice of historical interpretation and at the Husserlian hermeneutic scheme of reduction and realisation that he used in his later accounts of the philosophies of science of Kant and himself. The second section concentrates on Buchdahl’s treatment of the grounds of science in Kant; and the third on the hermeneutic strategies Buchdahl employed in articulating and justifying his own views. The paper closes with reflections on the impact and importance of Buchdahl’s interpretation of Kant’s critical philosophy in relation to the sciences and of his own hermeneutically based philosophy of science.     

The metaphor of epigenesis: Kant,Blumenbach and Herder

Over the last few decades, the meaning of the scientific theory of epigenesis and its significance for Kant's critical philosophy have become increasingly central questions. Most recently, scholars have argued that epigenesis is a key factor in the development of Kant's understanding of reason as self-grounding and self-generating. Building on this work, our claim is that Kant appealed to not just any epigenetic theory, but specifically Johann Friedrich Blumenbach's account of generation, and that this appeal must be understood not only in terms of self-organization, but also in terms of the demarcation of a specific domain of inquiry: for Blumenbach, the study of life; for Kant, the study of reason. We argue that Kant adopted this specific epigenetic model as a result of his dispute with Herder regarding the independence of reason from nature. Blumenbach's conception of epigenesis and his separation of a domain of the living from the non-living lent Kant the tools to demarcate metaphysics, and to guard reason against Herder's attempts to naturalize it.     

Ernst Cassirer's transcendental account of mathematical reasoning

Cassirer's philosophical agenda revolved around what appears to be a paradoxical goal, that is, to reconcile the Kantian explanation of the possibility of knowledge with the conceptual changes of nineteenth and early twentieth-century science. This paper offers a new discussion of one way in which this paradox manifests itself in Cassirer's philosophy of mathematics. Cassirer articulated a unitary perspective on mathematics as an investigation of structures independently of the nature of individual objects making up those structures. However, this posed the problem of how to account for the applicability of abstract mathematical concepts to empirical reality. My suggestion is that Cassirer was able to address this problem by giving a transcendental account of mathematical reasoning, according to which the very formation of mathematical concepts provides an explanation of the extensibility of mathematical knowledge. In order to spell out what this argument entails, the first part of the paper considers how Cassirer positioned himself within the Marburg neo-Kantian debate over intellectual and sensible conditions of knowledge in 1902–1910. The second part compares what Cassirer says about mathematics in 1910 with some relevant examples of how structural procedures developed in nineteenth-century mathematics.     

Why history matters to philosophy of physics

Naturalized metaphysics remains the default presupposition of much contemporary philosophy of physics. As metaphysics is supposed to concern the general structure of reality, so scientific naturalism draws upon our best physical theories to attempt to answer the foundational question “par excellence ” viz., “how could the world possibly be the way this theory says it is?” A particular case study, Hilbert's attempt to analyze and explain a seeming “pre-established harmony” between mind and nature, is offered as a salutary reminder that naturalism's ready inference from physical theory to ontology may be too quick.     

Symmetries and the philosophy of language

In this paper, I consider the role of exact symmetries in theories of physics, working throughout with the example of gravitation set in Newtonian spacetime. First, I spend some time setting up a means of thinking about symmetries in this context; second, I consider arguments from the seeming undetectability of absolute velocities to an anti-realism about velocities; and finally, I claim that the structure of the theory licences (and perhaps requires) us to interpret models which differ only with regards to the absolute velocities of objects as depicting the same physical state of affairs. In defending this last claim, I consider how ideas and resources from the philosophy of language may usefully be brought to bear on this topic.     

Cartesian echoes in Kant’s philosophy of nature

In this paper, we take the cue from a recent observation of Dan Warren about pre-Newtonian elements in Kant’s philosophy of nature to argue that there are two puzzles concerning Kant’s claim that mechanical laws presuppose dynamical laws in Chapter Three of Metaphysical Foundations of Natural Science. We offer responses on Kant’s behalf to these puzzles. These responses take us through a journey via Kant’s first pre-Critical work, True Estimation of Living Forces, and the then lively debate between Cartesians and Leibnizians. We show how some important Cartesian echoes, clearly evident in True Estimation, have played a role in shaping some seminal ideas of Kant on dynamical forces.     

Circularity,indispensability, and mathematical explanation in science

In this paper I consider the objection that the Enhanced Indispensability Argument (EIA) is circular and hence fails to support mathematical platonism. The objection is that the explanandum in any mathematical explanation of a physical phenomenon is itself identified using mathematical concepts. Hence the explanandum is only genuine if the truth of some mathematical theory is already presupposed. I argue that this objection deserves to be taken seriously, that it does sometimes undermine support for EIA, but that there is no reason to think that circularity is an unavoidable feature of mathematical explanation in science.     

Maimon's criticism of Kant's doctrine of mathematical cognition and the possibility of metaphysics as a science

The aim of this paper is to discuss Maimon's criticism of Kant's doctrine of mathematical cognition. In particular, we will focus on the consequences of this criticism for the problem of the possibility of metaphysics as a science. Maimon criticizes Kant's explanation of the synthetic a priori character of mathematics and develops a philosophical interpretation of differential calculus according to which mathematics and metaphysics become deeply interwoven. Maimon establishes a parallelism between two relationships: on the one hand, the mathematical relationship between the integral and the differential and on the other, the metaphysical relationship between the sensible and the supersensible. Such a parallelism will be the clue to the Maimonian solution to the Kantian problem of the possibility of metaphysics as a science.     

Trans-Planckian philosophy of cosmology

I provide some philosophical groundwork for the recently proposed ‘trans-Planckian censorship’ conjecture in theoretical physics. In particular, I argue that structure formation in early universe cosmology is, at least as we typically understand it, autonomous with regards to quantum gravity, the high energy physics that governs the Planck regime in our universe. Trans-Planckian censorship is then seen as a means of rendering this autonomy an empirical constraint within ongoing quantum gravity research.     

Distinctively mathematical explanation and the problem of directionality: A quasi-erotetic solution

The increasing preponderance of opinion that some natural phenomena can be explained mathematically has inspired a search for a viable account of distinctively mathematical explanation. Among the desiderata for an adequate account is that it should solve the problem of directionality —the reversals of distinctively mathematical explanations should not count as members among the explanatory fold but any solution must also avoid the exclusion of genuine explanations. In what follows, I introduce and defend what I refer to as a quasi-erotetic solution which provides a remedy to the problem in the form of an additional necessary condition on explanation.     

John Wheeler’s Desert Island: The conservatism of non-empirical physics

This paper argues that non-empirical physics, as paradigmatically embodied by string theory, is a conservative research program, in spite of appearances. John Wheeler's 1950s research program of "daring conservatism" is identified as another non-empirical research program that checks all the same boxes as string theory. This case study is used to further analyze the connection between conservatism and a non-empirical approach. It is concluded that the prime difficulty of non-empirical physics is not that it involves unbridled speculation, but that the lack of empirical input prevents it from achieving revolutionary progress.     

Gauss’ quadratic reciprocity theorem and mathematical fruitfulness

This paper presents an account of the fruitfulness of new mathematical calculi in terms of their relationship to existing mathematical methods which is suggested by Carl Friedrich Gauss. This is done by considering some remarks that Gauss made explaining the fruitfulness of new calculi. These can be clarified in the context of his own (very fruitful) theory of congruences, which is considered as a case study for this alternative account. Such an account has the benefit of not being dependent on a particular metaphysical view in the philosophy of mathematics.     

Mathematical method and Newtonian science in the philosophy of Christian Wolff

This paper aims to illuminate Christian Wolff’s view of mathematical reasoning, and its use in metaphysics, by comparing his and Leibniz’s responses to Newton’s work. Both Wolff and Leibniz object that Newton’s metaphysics is based on ideas of sense and imagination that are suitable only for mathematics. Yet Wolff expresses more regard (than Leibniz) for Newton’s scientific achievement. Wolff’s approval of the use of imaginative ideas in Newtonian mathematical science seems to commit him to an inconsistent triad. For he rejects their use in metaphysics, and also holds that every scientific discipline must follow mathematics’ method. A facile resolution would be to suppose Wolff identifies the method of mathematics with the order in which propositions are deduced, or with “analysis” that reveals the structure of concepts. This would be to assimilate Wolff’s view to Leibniz’s (on which all mathematical propositions are ultimately derived from definitions, and definitions are justified by conceptual analysis). On this construal, mathematical reasoning involves only the understanding. But Wolff conceives mathematics’ method more broadly, to include processes of concept-formation which involve perception and imagination. Thus my way of resolving the tension is to find roles for perception and imagination in the formation of metaphysical concepts.     

Pluralism and anarchism in quantum physics: Paul Feyerabend's writings on quantum physics in relation to his general philosophy of science

This paper aims to show that the development of Feyerabend's philosophical ideas in the 1950s and 1960s largely took place in the context of debates on quantum mechanics.In particular, he developed his influential arguments for pluralism in science in discussions with the quantum physicist David Bohm, who had developed an alternative approach to quantum physics which (in Feyerabend's perception) was met with a dogmatic dismissal by some of the leading quantum physicists. I argue that Feyerabend's arguments for theoretical pluralism and for challenging established theories were connected to his objections to the dogmatism and conservatism he observed in quantum physics.However, as Feyerabend gained insight into the physical details and historical complexities which led to the development of quantum mechanics, he gradually became more modest in his criticisms. His writings on quantum mechanics especially engaged with Niels Bohr; initially, he was critical of Bohr's work in quantum mechanics, but in the late 1960s, he completely withdrew his criticism and even praised Bohr as a model scientist. He became convinced that however puzzling quantum mechanics seemed, it was methodologically unobjectionable – and this was crucial for his move towards ‘anarchism’ in philosophy of science.     

String theory,Einstein, and the identity of physics: Theory assessment in absence of the empirical

String theorists are certain that they are practicing physicists. Yet, some of their recent critics deny this. This paper argues that this conflict is really about who holds authority in making rational judgment in theoretical physics. At bottom, the conflict centers on the question: who is a proper physicist? To illustrate and understand the differing opinions about proper practice and identity, we discuss different appreciations of epistemic virtues and explanation among string theorists and their critics, and how these have been sourced in accounts of Einstein's biography. Just as Einstein is claimed by both sides, historiography offers examples of both successful and unsuccessful non-empirical science. History of science also teaches that times of conflict are often times of innovation, in which novel scholarly identities may come into being. At the same time, since the contributions of Thomas Kuhn historians have developed a critical attitude towards formal attempts and methodological recipes for epistemic demarcation and justification of scientific practice. These are now, however, being considered in the debate on non-empirical physics.     

‘This inscrutable principle of an original organization’: epigenesis and ‘looseness of fit’ in Kant’s philosophy of science

Kant’s philosophy of science takes on sharp contour in terms of his interaction with the practicing life scientists of his day, particularly Johann Blumenbach and the latter’s student, Christoph Girtanner, who in 1796 attempted to synthesize the ideas of Kant and Blumenbach. Indeed, Kant’s engagement with the life sciences played a far more substantial role in his transcendental philosophy than has been recognized hitherto. The theory of epigenesis, especially in light of Kant’s famous analogy in the first Critique (B167), posed crucial questions regarding the ‘looseness of fit’ between the constitutive and the regulative in Kant’s theory of empirical law. A detailed examination of Kant’s struggle with epigenesis between 1784 and 1790 demonstrates his grave reservations about its hylozoist implications, leading to his even stronger insistence on the discrimination of constitutive from regulative uses of reason. The continuing relevance of these issues for Kant’s philosophy of science is clear from the work of Buchdahl and its contemporary reception.     

Physically locating the present: A case of reading physics as a contribution to philosophy

By means of an example, special relativity and presentism, I argue for the importance of reading history of physics as a contribution to philosophy, and for the fruitfulness of this approach to doing integrated history and philosophy of science. Within philosophy of physics, presentism is widely regarded as untenable in the light of special relativity. I argue that reading Newton's Principia as a contribution to philosophy reveals a law-constitutive approach to the unity of what there is, from which an alternative approach to presentism within physics emerges. This view respects the methodological and epistemological commitments of philosophy of physics in “taking special relativity seriously”, but proposes an alternative approach to the status of spacetime (as epistemic) and to the ground of what is real (law-constitution). While this approach to presentism does not preserve all of the contemporary presentist desiderata, it offers the possibility that the spatiotemporal extent of an existing thing is less than its entire history as represented in the block universe. I argue that the approach warrants further philosophical investigation.     

Radical mathematical Thomism: beings of reason and divine decrees in Torricelli’s philosophy of mathematics

Evangelista Torricelli (1608-1647) is perhaps best known for being the most gifted of Galileo’s pupils, and for his works based on indivisibles, especially his stunning cubature of an infinite hyperboloid. Scattered among Torricelli’s writings, we find numerous traces of the philosophy of mathematics underlying his mathematical practice. Though virtually neglected by historians and philosophers alike, these traces reveal that Torricelli’s mathematical practice was informed by an original philosophy of mathematics. The latter was dashed with strains of Thomistic metaphysics and theology. Torricelli’s philosophy of mathematics emphasized mathematical constructs as human-made beings of reason, yet mathematical truths as divine decrees, which upon being discovered by the mathematician ‘appropriate eternity’. In this paper, I reconstruct Torricelli’s philosophy of mathematics—which I label radical mathematical Thomism—placing it in the context of Thomistic patterns of thought.