This essay examines the relationship between monads and space in Kant’s early pre-critical work, with special attention devoted to the question of ubeity, a Scholastic doctrine that Leibniz describes as “ways of being somewhere”. By focusing attention on this concept, evidence will be put forward that supports the claim, held by various scholars, that the monad-space relationship in Kant is closer to Leibniz’ original conception than the hypotheses typically offered by the later Leibniz-Wolff school. In addition, Kant’s monadology, in conjunction (...) with God’s role, also helps to shed light on further aspects of his system that are broadly Leibnizian, such as monadic activity and the unity of space. (shrink)

In his argument for the possibility of knowledge of spatial objects, in the Transcendental Deduction of the B-version of the Critique of Pure Reason, Kant makes a crucial distinction between space as “form of intuition” and space as “formal intuition.” The traditional interpretation regards the distinction between the two notions as reflecting a distinction between indeterminate space and determinations of space by the understanding, respectively. By contrast, a recent influential reading has argued that the two notions can be fused into (...) one and that space as such is first generated by the understanding through an act of synthesis of the imagination. Against this reading, this article argues that a key characteristic of space as a form of intuition is its nonconceptual unity, which defines the properties of space and is as such necessarily independent of determination by the understanding through the transcendental synthesis of the imagination. The conceptual unity that the understanding prescribes to the manifold in intuition, by means of the categories, defines the formal intuition. Furthermore, this article argues that it is the sui generis, nonconceptual unity of space, when takenas a unity for the understanding by means of conceptual determination, that first enables geometric knowledge and knowledge of spatially located particulars. (shrink)

The aim of this paper is to situate Kant in the debate on free will. Whereas Kantians often assume that Kant's views on free will cannot be brought under any of the headings of this debate, contemporary free will theorists commonly assume that Kant is an incompatibilist of the libertarian type. I argue against both assumptions: Kant can and should be characterized as a compatibilist and more specifically as a soft determinist. After removing some persistent misconceptions about Kant's position in (...) the free will debate, I contend that Kant affirms the truth of determinism, that he rejects the possibility of libertarian free will and that he considers the sort of freedom required for moral responsibility to be compatible with determinism. (shrink)

It is widely accepted that the notion of an inertial frame is central to Newtonian mechanics and that the correct space-time structure underlying Newton’s methods in Principia is neo-Newtonian or Galilean space-time. I argue to the contrary that inertial frames are not needed in Newton’s theory of motion, and that the right space-time structure for Newton’s Principia requires the notion of parallelism of spatial directions at different times and nothing more. Only relative motions are definable in this framework, never absolute (...) ones. (shrink)

This is a survey of the concept of continuity. Efforts to explicate continuity have produced a plurality of philosophical conceptions of continuity that have provably distinct expressions within contemporary mathematics. I claim that there is a divide between the conceptions that treat the whole continuum as prior to its parts, and those conceptions that treat the parts of the continuum as prior to the whole. Along this divide, a tension emerges between those conceptions that favor philosophical idealizations of continuity and (...) those that are more readily available for mathematico-scientific use. (shrink)

The paper critically scrutinizes the widespread idea that Russell subscribes to a "Universalist Conception of Logic." Various glosses on this somewhat under-explained slogan are considered, and their fit with Russell's texts and logical practice examined. The results of this investigation are, for the most part, unfavorable to the Universalist interpretation.

Kantian philosophy of space, time and gravity is significantly affected in three ways by particle physics. First, particle physics deflects Schlick’s General Relativity-based critique of synthetic a priori knowledge. Schlick argued that since geometry was not synthetic a priori, nothing was—a key step toward logical empiricism. Particle physics suggests a Kant-friendlier theory of space-time and gravity presumably approximating General Relativity arbitrarily well, massive spin-2 gravity, while retaining a flat space-time geometry that is indirectly observable at large distances. The theory’s roots (...) include Seeliger and Neumann in the 1890s and Einstein in 1917 as well as 1920s–1930s physics. Such theories have seen renewed scientific attention since 2000 and especially since 2010 due to breakthroughs addressing early 1970s technical difficulties. Second, particle physics casts additional doubt on Friedman’s constitutive a priori role for the principle of equivalence. Massive spin-2 gravity presumably should have nearly the same empirical content as General Relativity while differing radically on foundational issues. Empirical content even in General Relativity resides in partial differential equations, not in an additional principle identifying gravity and inertia. Third, Kant’s apparent claim that Newton’s results could be known a priori is undermined by an alternate gravitational equation. The modified theory has a smaller symmetry group than does Newton’s. What Kant wanted from Newton’s gravity is impossible due its large symmetry group, but is closer to achievable given the alternative theory. (shrink)

German supporters of the Kantian philosophy in the late 19th century took one of two forks in the road: the fork leading to Baden, and the Southwest School of neo-Kantian philosophy, and the fork leading to Marburg, and the Marburg School, founded by Hermann Cohen. Between 1876, when Cohen came to Marburg, and 1918, the year of Cohen's death, Cohen, with his Marburg School, had a profound influence on German academia.

The article proposes an interpretation of Kant’s notions of form of, and formal intuition of space to explain and justify the claim that representing space as object requires a synthesis. This involves identifying the transcendental conditions of the analytic unity of consciousness of this formal intuition and distinguishing between it and its content. On this reading which builds upon recent proposals, footnote B160–1n. involves no revision of the Transcendental Aesthetic: space is essentially characterized by non-conceptual features. The article also addresses (...) worries about the infinite magnitude and the unicity of space, by considering the characteristics and requirements of geometric constructions. (shrink)

Kant claims that we cannot cognize the mutual interaction of substances without their being in space; he also claims that we cannot cognize a ‘spatial community’ among substances without their being in mutual interaction. I situate these theses in their historical context and consider Kant’s reasons for accepting them. I argue that they rest on commitments regarding the metaphysical grounding of, first, the possibility of mutual interaction among substances-as-appearances and, second, the actuality of specific distance-relations among such substances. By illuminating (...) these commitments, I shed light on Kant’s metaphysics of space and its relation to Newton and Leibniz’s views. (shrink)

Prolegomena §38 is intended to elucidate the claim that the understanding legislates a priori laws to nature. Kant cites various laws of geometry as examples and discusses a derivation of the inverse-square law from such laws. I address 4 key interpretive questions about this cryptic text that have not yet received satisfying answers: How exactly are Kant's examples of laws supposed to elucidate the Legislation Thesis? What is Kant's view of the epistemic status of the inverse-square law and, relatedly, of (...) the legitimacy of the geometric derivation of that law? Whose account of laws, the understanding, and space is Kant critiquing in the passage? What positive account of the relationship between laws, the understanding, and space is Kant offering in the passage? My answer to depends crucially on my answers to –. As I interpret Kant, he holds that a wide range of a priori laws—including geometric laws, the inverse-square law, and the universal laws discussed in the Analytic of Principles—are ‘grounded’ in categorial syntheses rather than the intrinsic nature of the space given to us in pure intuition. (shrink)

Since his Metaphysische Anfangsgründe der Naturwissenschaft was first published in 1786, controversy has surrounded Immanuel Kant’s conception of matter. In particular, the justification for both his dynamical theory of matter and the related dismissal of mechanical philosophy are obscure. In this paper, I address these longstanding issues and establish that Kant’s dynamism rests upon Leibnizian, metaphysical commitments held by Kant from his early pre-Critical texts on natural philosophy to his major critical works. I demonstrate that, throughout his corpus and inspired (...) by Leibniz, Kant endorses the a priori law of continuity of alteration as a truth of metaphysics, according to which all alterations in experience must occur gradually through all intervening degrees. The principle thus legislates against mechanical philosophy’s absolutely impenetrable atoms, as they would would involve instantaneous changes of velocity in impact. This reveals the metaphysical incoherencies in mechanical philosophy and leaves Kant’s own dynamical theory of matter, grounded on material forces, as the only viable approach to physical explanation. Subsequently, I demonstrate that Kant nevertheless made conceptual space in his system for the theoretical consideration of mechanical explanations, which makes manifest one of the positive roles that the faculty of reason can play with respect to natural science. (shrink)

As the seventeenth century progressed, there was a growing realization among those who reflected on the kind of knowledge the new sciences could afford (among them Kepler, Bacon, Descartes, Boyle, Huygens) that hypothesis would have to be conceded a much more significant place in natural philosophy than the earlier ideal of demonstration allowed. Then came the mechanics of Newton's Principia, which seemed to manage quite well without appealing to hypothesis (though much would depend on how exactly terms like "force" and (...) "attraction" were construed). If the science of motion could dispense with causal hypothesis and the attendant uncertainty, why should this not serve as the goal of natural philosophy generally? The apparent absence of causal hypothesis from the highly successful new science of motion went far towards shaping, in different ways, the account of scientific knowledge given by many of the philosophers of the century following, notable among them Berkeley, Hume, Reid, and Kant. This "Newtonian" interlude in the history of the philosophy of science would today be accounted on the whole a byway. The Principia, despite its enormous achievement in shaping subsequent work in mechanics, was from the beginning too idiosyncratic from an epistemic standpoint to serve as model for the natural sciences generally. (shrink)

One of the central debates in contemporary Kant scholarship concerns whether Kant endorses a “conceptualist” account of the nature of sensory experience. Understanding the debate is crucial for getting a full grasp of Kant's theory of mind, cognition, perception, and epistemology. This paper situates the debate in the context of Kant's broader theory of cognition and surveys some of the major arguments for conceptualist and non-conceptualist interpretations of his critical philosophy.

In this essay I analyse Kant’s view on the regulative role of reason, and in particular on what he describes as the ‘indispensably necessary’ role of ideas qua foci imaginarii in the Appendix. I review two influential readings of what has become known as the ‘transcendental illusion’ and I offer a novel reading that builds on some of the insights of these earlier readings. I argue that ideas of reason act as imaginary standpoints, which are indispensably necessary for scientific knowledge (...) by making inter-conversational agreement possible. Thus, I characterise scientific knowledge as a distinctive kind of perspectival knowledge. This novel reading can illuminate the role of reason in complementing the faculty of understanding and sheds light on the apparent dichotomy between the first and the second part of the Appendix. More to the point, this novel reading takes us right to the heart of what scientific knowledge is, according to Kant, and how it differs from bogus knowledge and opinion. (shrink)

On 11thOctober 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).

This paper explores the scientific sources behind Kant’s early dynamic theory of matter in 1755, with a focus on two main Kant’s writings: Universal Natural History and Theory of the Heavens and On Fire. The year 1755 has often been portrayed by Kantian scholars as a turning point in the intellectual career of the young Kant, with his much debated conversion to Newton. Via a careful analysis of some salient themes in the two aforementioned works, and a reconstruction of the (...) scientific sources behind them, this paper shows Kant’s debt to an often overlooked scientific tradition, i.e. speculative Newtonian experimentalism. The paper argues that more than the Principia, it was the speculative experimentalism that goes from Newton’s Opticks to Herman Boerhaave’s Elementa chemiae via Stephen Hales’ Vegetable Staticks that played a central role in the elaboration of Kant’s early dynamic theory of matter in 1755. (shrink)

It is well known that Kant claims that causal judgments, including judgments about forces, must have an a priori basis. It is less well known that Kant claims that we can perceive the repulsive force of bodies through the sense of touch. Together, these claims present an interpretive puzzle, since they appear to commit Kant to both affirming and denying that we can have perceptions of force. My first aim is to show that both sides of the puzzle have deep (...) roots in Kant's philosophy. My second aim is to present three potential solutions to the puzzle and show that each faces problems. (shrink)

Logic is usually thought to concern itself only with features that sentences and arguments possess in virtue of their logical structures or forms. The logical form of a sentence or argument is determined by its syntactic or semantic structure and by the placement of certain expressions called “logical constants.”[1] Thus, for example, the sentences Every boy loves some girl. and Some boy loves every girl. are thought to differ in logical form, even though they share a common syntactic and semantic (...) structure, because they differ in the placement of the logical constants “every” and “some”. By contrast, the sentences Every girl loves some boy. and Every boy loves some girl. are thought to have the same logical form, because “girl” and “boy” are not logical constants. Thus, in order to settle questions about logical form, and ultimately about which arguments are logically valid and which sentences logically true, we must distinguish the “logical constants” of a language from its nonlogical expressions. (shrink)

Let me start with a well-known story. Kant held that logic and conceptual analysis alone cannot account for our knowledge of arithmetic: “however we might turn and twist our concepts, we could never, by the mere analysis of them, and without the aid of intuition, discover what is the sum [7+5]” (KrV, B16). Frege took himself to have shown that Kant was wrong about this. According to Frege’s logicist thesis, every arithmetical concept can be defined in purely logical terms, and (...) every theorem of arithmetic can be proved using only the basic laws of logic. Hence, Kant was wrong to think that our grasp of arithmetical concepts and our knowledge of arithmetical truth depend on an extralogical source—the pure intuition of time (Frege 1884, §89, §109). Arithmetic, properly understood, is just a part of logic. (shrink)

The aim of this research is to explore what relations self-affection bears to the intuitions of inner sense. I propose that self-affection makes some contribution to formal intuitions and empirical consciousness by arguing that the functions of self-affection consist respectively in conceptualising and conscious-making. I begin by examining Kant’s concept of inner sense and point out that inner sense as a receptive faculty depends on self-affection. In so doing, I emphasise that self-affection includes both a pure and an empirical aspect (...) which corresponds to Kant’s distinction between the transcendental synthesis of imagination and the empirical synthesis of apprehension. Then, I focus on the pure aspect and argue that the conceptualising function involved in the pure self-affection is decisive for the generation of formal intuition. In particular, I explain why the formal intuition of time depends on the intuition of space and how it is constituted by drawing a line. After that, I turn to analysing the empirical aspect of self-affection and show that by virtue of the empirical synthesis of apprehension one is aware of both the empirical contents of representations and the mental actions performed on them, whereby I suggest that this empirical conscious-making function can be understood as an act of distinguishing from a mereological point of view. (shrink)

Kant’s dissertation for the Master’s degree Succinct Exposition of Some Meditations on Fire was written in Latin in 1755 as a sample (specimen) preceding a Master’s exam, but its first printing did not appear until 1838. What is the relevance of this Master’s dissertation for historical and philosophical studies? To answer this question I analyse the structure and give a brief summary of the dissertation, look at the history of its writing and try to identify the place of this work (...) among Kant’s other papers on natural philosophy. I then demonstrate that Kant’s concept of ether as an elastic matter of fire, heat and light containing the forces of attraction and repulsion originates in the dissertation On Fire. I identify the provisions in Kant’s early works which he later develops in the Master’s dissertation and establish continuity between the text of On Fire and the so-called Physical Monadology, draw parallels between the ideas enunciated by Kant in his first dissertation and the interpretation of ether in the printed works that followed. Finally, I put forward the hypothesis of the heuristic potential of the On Fire treatise for the analysis of Kant’s manuscript legacy. Perhaps this dissertation will enable researchers to clear up some tangled propositions in Kant’s Opus Postumum. However, a series of further studies is needed to verify the hypothesis. (shrink)

This paper examines Du Châtelet’s and Kant’s responses to the famous vis viva controversy – Du Châtelet in her Institutions Physiques (1742) and Kant in his debut, the Thoughts on the True Estimation of Living Forces (1746–49). The Institutions was not only a highly influential contribution to the vis viva controversy, but also a pioneering attempt to integrate Leibnizian metaphysics and Newtonian physics. The young Kant’s evident knowledge of this work has led some to speculate about his indebtedness to her (...) philosophy. My study corrects such speculations as well as misunderstandings of the Living Forces. This corrective result has implications for how to investigate Kant’s relation to the ever-evolving landscape of Leibniz exegeses. (shrink)

This paper tries to make sense of Kant's scattered remarks about conic sections to see what light they shed on his philosophy of mathematics. It proceeds by confronting his remarks with the source that seems to have informed his thinking about conic sections: the Conica of Apollonius. The paper raises questions about Kant's attitude towards mathematics and the way he understood the cognitive resources available to us to do mathematics.

The aim of this paper is to show that attention to Kant's philosophy of mathematics sheds light on the doctrine that there are two stems of the cognitive capacity, which are distinct, but equally necessary for cognition. Specifically, I argue for the following four claims: The distinctive structure of outer sensible intuitions must be understood in terms of the concept of magnitude. The act of sensibly representing a magnitude involves a special act of spontaneity Kant ascribes to a capacity he (...) calls the productive imagination. Contrary to what is assumed by many commentators, it is not the case that the Two Stems Doctrine implies that a representation is either sensible or spontaneity-dependent, but not both. Outer sensible intuitions are both sensible and spontaneity-dependent – they are sensible because they exhibit the kind of structure Kant takes to be distinctive of outer sensible intuitions, and they depend on spontaneity because they are cases of sensibly representing a magnitude. (shrink)

The paper attempts to summarize the debate on Kant’s philosophy of geometry and to offer a restricted area of mathematical practice for which Kant’s philosophy would be a reasonable account. Geometrical theories can be characterized using Wittgenstein’s notion of pictorial form . Kant’s philosophy of geometry can be interpreted as a reconstruction of geometry based on one of these forms — the projective form . If this is correct, Kant’s philosophy is a reasonable reconstruction of such theories as projective geometry; (...) and not only as they were practiced in Kant’s time, but also as architects use them today. (shrink)

Consider the laws of nature—the laws of physics, for example. One familiar philosophical question about laws is this: what is it to be a law of nature? More specifically, is a law of nature a regularity, or a generalization stating a regularity? Or is it something else? Another philosophical question is: how, and to what extent, can we have knowledge of the laws of nature? I am interested here in Kant's answers to these questions, and their place within his broader (...) theoretical philosophy during the period spanning from the first to the third Critique. (shrink)

The abstract status of Kant's account of his ‘general logic’ is explained in comparison with Gödel's general definition of a formal logical system and reflections on ‘abstract’ (‘absolute’) concepts. Thereafter, an informal reconstruction of Kant's general logic is given from the aspect of the principles of contradiction, of sufficient reason, and of excluded middle. It is shown that Kant's composition of logic consists in a gradual strengthening of logical principles, starting from a weak principle of contradiction that tolerates a sort (...) of contradictions in predication, and then proceeding to the (constructive) principle of sufficient reason, and to a classical-like logic, which includes the principle of excluded middle. A first-order formalisation is applied to this reconstruction, which reveals implicit modalities in Kant's account of logic, and confirms the implementability of Kant's logic into a sound and complete formal system. (shrink)

Gödel's philosophical views were to a significant extent influenced by the study not only of Leibniz or Husserl, but also of Kant. Both Gödel and Kant aimed at the secure foundation of philosophy, the certainty of knowledge and the solvability of all meaningful problems in philosophy. In this paper, parallelisms between the foundational crisis of metaphysics in Kant's view and the foundational crisis of mathematics in Gödel's view are elaborated, especially regarding the problem of finding the “secure path of a (...) science” for both mathematics and philosophy. Gödel's temporal subjectivism and metaphysical conceptual objectivism are presented as positively or negatively motivated by Kant's viewpoints. A remark on Gödel's collapse of modalities (in accordance with the collapse of objective time) is added. (shrink)

In this paper I argue that constructivism in mathematics faces a dilemma. In particular, I maintain that constructivism is unable to explain (i) the application of mathematics to nature and (ii) the intersubjectivity of mathematics unless (iii) it is conjoined with two theses that reduce it to a form of mathematical Platonism. The paper is divided into five sections. In the first section of the paper, I explain the difference between mathematical constructivism and mathematical Platonism and I outline my argument. (...) In the second, I argue that the best explanation of how mathematics applies to nature for a constructivist is a thesis I call Copernicanism. In the third, I argue that the best explanation of how mathematics can be intersubjective for a constructivist is a thesis I call Ideality. In the fourth, I argue that once constructivism is conjoined with these two theses, it collapses into a form of mathematical Platonism. In the fifth, I confront some objections. (shrink)

In this introductory article we reconstruct several broad developments in the scholarship on Kant’s theory of natural science with a particular focus on the Anglophone context over the past half-century. Our goal is to illuminate the co-development of Kant scholarship and the philosophy of science during this period and to identify points of influence in both directions. In section 2 we present an overview of the scholarship on Kant’s account of natural laws. In section 3 we survey the diverse interpretations (...) of Kant’s views on biology and consider recent appeals to Kant by philosophers of biology. In section 4 we explore several recent developments in philosophy of science that have potential synergies with Kant scholarship. Our aim is not simply to establish that Kant’s philosophy can have relevance for philosophy of science but also to point out where it has been and continues to be relevant. Appreciating this relevance, we suggest, can help identify productive lines of inquiry for Kant studies. (shrink)

In this interesting and engaging book, Shabel offers an interpretation of Kant's philosophy of mathematics as expressed in his critical writings. Shabel's analysis is based on the insight that Kant's philosophical standpoint on mathematics cannot be understood without an investigation into his perception of mathematical practice in the seventeenth and eighteenth centuries. She aims to illuminate Kant's theory of the construction of concepts in pure intuition—the basis for his conclusion that mathematical knowledge is synthetic a priori. She does this through (...) a contextualized interpretation of his notion of mathematical construction, which she argues can be approached by looking at Euclid's Elements and Christian Wolff's mathematical textbooks. The importance of the former for her interpretation is justified by the fact that nearly all of Kant's mathematical examples in the Critique are Euclidean propositions. The importance of the latter is revealed through the fact that Wolff's textbooks were not only widely read and representative of the state of elementary mathematics during Kant's time; Kant was also intimately familiar with them. During the thirty years prior to the publication of the Critique, he used the textbooks in the college-level introductory courses in mathematics and physics that he taught.In the introduction to her book, Shabel helpfully distinguishes her approach to Kant's philosophy of mathematics from that of previous commentators. She points out that most commentators assessed Kant's thoughts on mathematics in terms of the ‘supposedly devastating effects of the discovery of non-Euclidean geometry on his theory of space’ .1 Bertrand Russell, for example, criticized Kant for his lack of a proper …. (shrink)

This paper gives a contextualized reading of Kant's theory of real definitions in geometry. Though Leibniz, Wolff, Lambert and Kant all believe that definitions in geometry must be ‘real’, they disagree about what a real definition is. These disagreements are made vivid by looking at two of Euclid's definitions. I argue that Kant accepted Euclid's definition of circle and rejected his definition of parallel lines because his conception of mathematics placed uniquely stringent requirements on real definitions in geometry. Leibniz, Wolff (...) and Lambert thus accept definitions that Kant rejects because they assign weaker roles to real definitions. (shrink)

The trick, of course, is to pick your targets carefully: they should be central to the mainstream of contemporary philosophy, not marginal. Watkins has certainly done that. The target he has chosen is the problem of causation. His three-part aim is, first, to embed Kant’s theory of causation in its 18th century pre-Critical and especially Leibnizian setting; second, to argue that Kant’s Critical theory of causation is not in fact a reply to Hume, and that Kant’s metaphysics of causation depends (...) as much on the Third Analogy of Experience and the Third Antinomy of Pure Reason as it does on the Second Analogy; and third, that reconsidering Kant’s Critical metaphysics of causation from a pre-Critical and rationalist point of view can contribute to a serious reconsideration of the theory of agent causation in the contemporary debate about free will. (shrink)

It is occasionally claimed that the important work of philosophers, physicists, and mathematicians in the nineteenth and in the early twentieth centuries made Kant’s critical philosophy of geometry look somewhat unattractive. Indeed, from the wider perspective of the discovery of non-Euclidean geometries, the replacement of Newtonian physics with Einstein’s theories of relativity, and the rise of quantificational logic, Kant’s philosophy seems “quaint at best and silly at worst”.1 While there is no doubt that Kant’s transcendental project involves his own conceptions (...) of Newtonian physics, Euclidean geometry and Aristotelian logic, the issue at stake is whether the replacement of these conceptions collapses Kant’s philosophy into an unfortunate embarrassment.2 Thus, in evaluating the debate over the contemporary relevance of Kant’s philosophical project one is faced with the following two questions: (1) Are there any contradictions between the scientific developments of our era and Kant’s philosophy? (2) What is left from the Kantian legacy in light of our modern conceptions of logic, geometry and physics? Within this broad context, this paper aims to evaluate the Kantian project vis à vis the discovery and application of non-Euclidean geometries. Many important philosophers have evaluated Kant’s philosophy of geometry throughout the last century,3 but opinions with regard to the impact of non-Euclidean geometries on it diverge. In the beginning of the century there was a consensus that the Euclidean character of space should be considered as a consequence of the Kantian project, i.e., of the metaphysical view of space and of the synthetic a priori character of geometry. The impact of non-Euclidean geometries was then thought as undermining the Kantian project since it implied, according to positivists such.. (shrink)

Kant’s natural philosophy in the Metaphysical Foundations of Natural Science is heavily influenced by Newton’s Principia. However, a closer look makes it clear that Kant’s project has also been influenced by other thinkers. One of these thinkers is Leonard Euler. His work was of great influence for Kant, not only with regards to his view on space and inertia but on the relation between metaphysics and natural science in general. Even though Euler’s Physics built on Newton’s work, he differs from (...) him in fundamental regards, leading to crucial developments inside classical mechanics. Here I will discuss the influence of Euler on the work of Kant and focus on Euler’s view on the two entangled problems of inertia and space. It will become clear that both Euler and Kant went through a development concerning these fundamental notions. After shortly highlighting the differences between Kant and Newton, I shall go through the development of important parts of Euler’s natural philosophy concerning the above mentioned themes. I intend to demonstrate that he, through his refutation of Wolffianism, became an advocate for the necessity of absolute space but also denied the existence of an internal force of inertia. After that I will show how Kant’s reading of Euler lead to crucial changes of his natural philosophy in particular and his philosophical enterprise in general. I therefore analyze Kant’s revision of his theory of space and inertia in his precritical writings. Building upon that, I will show the influence of these thoughts on his Metaphysical Foundations. (shrink)

The life sciences have been very much in vogue these days in the history of early modern philosophy. In the 1960s, 1970s, and beyond, historians of philosophy c.

Immanuel Kant's Metaphysical Foundations of Natural Science (1786) provides metaphysical foundations for the application of mathematics to empirically given nature. The application that Kant primarily has in mind is that achieved in Isaac Newton's Principia (1687). Thus, Kant's first chapter, the Phoronomy, concerns the mathematization of speed or velocity, and his fourth chapter, the Phenomenology, concerns the empirical application of the Newtonian notions of true or absolute space, time, and motion. This paper concentrates on Kant's second and third chapters—the Dynamics (...) and the Mechanics, respectively—and argues that they are best read as providing a transcendental explanation of the conditions for the possibility of applying the (mathematical) concept of quantity of matter to experience. Kant again has in mind the empirical measures of this quantity that Newton fashions in the Principia, and he aims to make clear, in particular, how Newton achieves a universal measure for all bodies whatsoever by projecting the static quantity of terrestrial weight into the heavens by means of the theory of universal gravitation. Kant is not attempting to prove a priori what Newton has established empirically but, rather, to clarify the character of Newton's mathematization by building Newton's empirical measures into the very concept of matter that is articulated in the Metaphysical Foundations. (shrink)

This paper considers the evolution of the problem of scientific rationality from Kant through Carnap to Kuhn. I argue for a relativized and historicized version of the original Kantian conception of scientific a priori principles and examine the way in which these principles change and develop across revolutionary paradigm shifts. The distinctively philosophical enterprise of reflecting upon and contextualizing such principles is then seen to play a key role in making possible rational intersubjective communication between otherwise incommensurable paradigms.

In this opinion piece, the authors offer their personal and idiosyncratic views of the future of the philosophy of science, focusing on its relationship with the history of science and metaphysics, respectively. With regard to the former, they suggest that the Kantian tradition might be drawn upon both to render the history and philosophy of science more relevant to philosophy as a whole and to overcome the challenges posed by naturalism. When it comes to the latter, they suggest both that (...) metaphysics has much to learn from the philosophy of science and that it offers an array of tools that philosophers of science can themselves appropriate. (shrink)

This paper explores Beck’s theory of original representing in order to discuss both its historical and theoretical relevance and its implications concerning Kant’s views on the capacity to judge. My first concern will be to highlight the main points of Beck’s Kant interpretation and to show at which points he misunderstands Kant. My analysis also contains a positive aspect, for I adopt Beck’s claim that there is only one possible standpoint from which critical philosophy ought to be judged. Unlike Beck, (...) I shall argue that this standpoint is that of Judgment’s normativity. I will consider the normative structure of Judgment from three perspectives: the proto-synthetic import of sensibility; the normative character of the pure concepts of the understanding; the lawfulness of the principles of the understanding. My basic idea is that only a normative account of Judgment can prove how and why all experience depends on the possibility of synthetic a priori judgments. On Kant’s account, the capacity to judge applies transcendental rules to establish the laws which make our experience and knowledge both possible and legitimate. Every single object is an object of experience only insofar as it conforms to the normative structure of Judgment. For Kant, to constitute an object means to apply the rules which make something possible as an object of experience and cognition. (shrink)

Dedekind’s methodology, in his classic booklet on the foundations of arithmetic, has been the topic of some debate. While some authors make it closely analogue to Hilbert’s early axiomatics, others emphasize its idiosyncratic features, most importantly the fact that no axioms are stated and its careful deductive structure apparently rests on definitions alone. In particular, the so-called Dedekind “axioms” of arithmetic are presented by him as “characteristic conditions” in the _definition_ of the complex concept of a _simply infinite_ system. Making (...) sense of Dedekind’s method may be dependent on an analysis of the classical model of deductive science, as presented by authors from the eighteenth and early nineteenth centuries. Studying the modern reconstructions of Euclidean geometry, we show that they did not presuppose deductive independence of the axioms from the definitions. Authors like Wolff elaborated a mathematics _based on definitions_, and the Wolffian model of deductive science shows significant coincidences with Dedekind’s method, despite the great differences in content and approach. Wolff had a conception of definitions as _genetic_, which bears some similarities with Kant’s idea of synthetic definitions: they are understood as positing the content of mathematical concepts and introducing thought objects (_Gedankendinge_) that are the objects of mathematics. The emphasis on the spontaneity of the understanding, which can be found in this philosophical tradition, can also be fruitfully related with Dedekind’s idea of the “free creation” of mathematical objects. (shrink)

The paper presents a detailed interpretation of Edgar Wind’s Experiment and Metaphysics, a unique work on the philosophy of physics which broke with the Neo-Kantian tradition under the influence of American pragmatism. Taking up Cassirer’s interpretation of physics, Wind develops a holistic theory of the experiment and a constructivist account of empirical facts. Based on the concept of embodiment which plays a key role in Wind’s later writings on art history, he argues, however, that the outcomes of measurements are contingent. (...) He then proposes an anti-Kantian conception of a metaphysics of nature. For him, nature is an unknown totality which manifests itself in discrepancies between theories and experiment, and hence the theory formation of physics can increasingly approximate the structure of nature. It is shown that this view is ambiguous between a transcendental, metaphysical realism in Kant’s sense and an internal realism in Putnam’s sense. Wind’s central claim is that twentieth century physics offers new options for resolving Kant’s cosmological antinomies. In particular, he connected quantum indeterminism with the possibility of human freedom, a connection that Cassirer sharply opposed. (shrink)

With the discovery of consistent non-Euclidean geometries, the a priori status of Euclidean proof was radically undermined. In response, philosophers proposed two revisionary interpretations of the practice: some argued that Euclidean proof is a purely formal system of deductive logic; others suggested that Euclidean reasoning is empirical, employing concepts derived from experience. I argue that both interpretations fail to capture the true nature of our geometrical thought. Euclidean proof is not a system of pure logic, but one in which our (...) grasp of the content of geometrical concepts plays a central role; moreover, our grasp of this content is a priori. (shrink)

In attempts to come to grips with Kant’s thought, the influence of the philosophy of Christian Wolff (1679-1754) is often neglected. In this paper, I consider three topics in Kant’s philosophy of mind, broadly construed, where Wolff’s influence is particularly visible: consciousness, self-consciousness, and psychology. I argue that we can better understand Kant’s particular arguments and positions within this context, but also gain a more accurate sense of which aspects of Kant’s accounts derive from the antecedent traditions and which constitute (...) genuine philosophical innovations. (shrink)

In this essay, I call attention to Kant’s and Whewell’s attempt to provide bridging principles between a priori principles and scientific laws. Part of Kant’s aim in the Opus postumum (ca. 1796-1803) was precisely to bridge the gap between the metaphysical foundations of natural science (on the Metaphysical Foundations of Natural Science (1786) see section 1) and physics by establishing intermediary concepts or ‘Mittelbegriffe’ (henceforth this problem is referred to as ‘the bridging-problem’). I argue that the late-Kant attempted to show (...) that the concept of ‘moving force’, an intermediary concept derived from a priori principles, could be given empirical content so that concrete scientific knowledge is arrived at. Thus, the late-Kant wished not only to show that proper scientific laws are necessary a priori (as he had shown in the Metaphysical Foundations of Natural Science) but also that intermediary concepts could be derived from a priori principles which, when interpreted empirically, resulted in the specific forces as established by physics (see section 2). Of course, William Whewell never knew about Kant’s Opus postumum and his attempt to bridge the gap between the metaphysical foundations of science and physics. However, it is striking that Whewell had similar concerns about the Critique of Pure Reason and the Metaphysical Foundations of Natural Science as Kant himself. According to Whewell, the Kantian project was incomplete because it did not show how ‘modifications’ (in the sense of concretizations) of a priori principles could result in empirical laws (section 3). Next, it will be argued, by taking into account several of Whewell’s philosophical notebooks which have scarcely been studied systematically, that Whewell’s doctrine of Fundamental Ideas grew out of his dissatisfaction with the Kantian project with respect to the bridging problem and that his own philosophical position should be seen as an attempt to bypass the bridging-problem. (shrink)