It is commonly thought that the distinction between subjectively valid judgements of perception and objectively valid judgements of experience in the Prolegomena is not consistent with the account of judgement Kant offers in the B Deduction, according to which a judgement is ‘nothing other than the way to bring given cognitions to the objective unity of apperception’. Contrary to this view, I argue that the Prolegomena distinction maps closely onto that drawn between the mathematical and dynamical principles in the System (...) of Principles: Kant’s account of the Prolegomena distinction strongly suggests that it is the Analogies of Experience that make it possible for judgements of perception to give rise to judgements of experience. This means that judgements of perception are objectively valid with regard to the quantity and quality of objects, and subjectively valid with regard to the relation they posit between objects. If that is the case, then the notion of a judgement of perception is consistent with the B Deduction account of judgement. (shrink)

This paper aims to show that Frege’s and Hilbert’s mutual disagreement results from different notions of Anschauung and their relation to axioms. In the first section of the paper, evidence is provided to support that Frege and Hilbert were influenced by the same developments of 19th-century geometry, in particular the work of Gauss, Plücker, and von Staudt. The second section of the paper shows that Frege and Hilbert take different approaches to deal with the problems that the developments in 19th-century (...) geometry posed for the traditional Kantian philosophy of mathematics. Frege maintains that Anschauung is a source of knowledge by which we acknowledge geometrical axioms as true. For Hilbert, in contrast, axioms provide one of several correct “pictures” of reality. Hilbert’s position is thereby deeply influenced by epistemological ideas from Hertz and Helmholtz, and, in turn, influenced the neo-Kantian Cassirer. (shrink)

Abstract: This essay addresses three specific moments in the history of the role played by intuition in Kant's system. Part one develops Kant's attitude toward intuition in order to understand how ‘sensible intuition’ becomes the first step in his development of transcendental idealism and how this in turn requires him to reject the possibility of an ‘intellectual intuition’ for human cognition. Part two considers the role of Jacobi when it came to interpreting both Kant's epistemic achievement and what were taken (...) to be the outstanding problems of freedom's relation to nature; problems interpreted to be resolvable only via an appeal to ‘intellectual intuition’. Part three begins with Kant's subsequent return to the question of freedom and nature in his Critique of Judgment. With Goethe's contemporaneous Metamorphoses of Plants as a contrast case, it becomes clear that whereas Goethe can embrace the role of an intuitive understanding in his account of nature and within the logic of polarity in particular, Kant could never allow an intuition of nature that in his system would spell the very impossibility of freedom itself. (shrink)

This paper analyzes the historical context and systematic importance of Kant's hypothetical use of reason. It does so by investigating the role of hypotheses in Kant's philosophy of science. We first situate Kant’s account of hypotheses in the context of eighteenth-century German philosophy of science, focusing on the works of Wolff, Meier, and Crusius. We contrast different conceptions of hypotheses of these authors and elucidate the different theories of probability informing them. We then adopt a more systematic perspective to discuss (...) Kant's idea that scientific hypotheses must articulate real possibilities. We argue that Kant's views on the intelligibility of scientific hypotheses constitute a valuable perspective on scientific understanding and the constraints it imposes on scientific rationality. (shrink)

A volume of papers inspired by the work of George E. Smith on confirmation and evidence in advanced science—from Newton's gravitation theory to the physics of molecules.

It is widely held that, in his pre-Critical works, Kant endorsed a necessitation account of laws of nature, where laws are grounded in essences or causal powers. Against this, I argue that the early Kant endorsed the priority of laws in explaining and unifying the natural world, as well as their irreducible role in in grounding natural necessity. Laws are a key constituent of Kant’s explanatory naturalism, rather than undermining it. By laying out neglected distinctions Kant draws among types of (...) natural law, grounding relations, and ontological levels, I show that his early works present a coherent and sophisticated laws-first account of the natural order. (shrink)

The Berlin Group was an equal partner with the Vienna Circle as a school of scientific philosophy, albeit one that pursued an itinerary of its own. But while the latter presented its defining projects in readily discernible terms and became immediately popular, the Berlin Group, whose project was at least as sig-nificant as that of its Austrian counterpart, remained largely unrecognized. The task of this chapter is to distinguish the Berliners’ work from that of the Vienna Circle and to bring (...) to light its impact in the history of scientific philosophy. (shrink)

According to Kant, pure intuition is an indispensable ingredient of mathematical proofs. Kant‘s thesis has been considered as obsolete since the advent of modern relational logic at the end of 19th century. Against this logicist orthodoxy Cassirer’s “critical idealism” insisted that formal logic alone could not make sense of the conceptual co-evolution of mathematical and scientific concepts. For Cassirer, idealizations, or, more precisely, idealizing completions, played a fundamental role in the formation of the mathematical and empirical concepts. The aim of (...) this paper is to outline the basics of Cassirer’s idealizational account, and to point at some interesting similarities it has with Kant’s and Peirce’s philosophies of mathematics based on the key notions of pure intuition and theorematic reasoning, respectively. (shrink)

Arguably no concept is more fundamental to science than that of causality, for investigations into cases of existence, persistence, and change in the natural world are largely investigations into the causes of these phenomena. Yet the metaphysics and epistemology of causality remain unclear. For example, the ontological categories of the causal relata have been taken to be objects (Hume 1739), events (Davidson 1967), properties (Armstrong 1978), processes (Salmon 1984), variables (Hitchcock 1993), and facts (Mellor 1995). (For convenience, causes and effects (...) will usually be understood as events in what follows.) Complicating matters, causal relations may be singular (Socrates’s drinking hemlock caused Socrates’s death) or general (Drinking hemlock causes death); hence the relata might be tokens (e.g., instances of properties) or types (e.g., types of events) of the category in question. Other questions up for grabs are: Are singular causes metaphysically and/or epistemologically prior to general causes or vice versa (or neither)? What grounds the intuitive asymmetry of the causal relation? Are macro-causal relations reducible to micro-causal relations? And perhaps most importantly: Are causal facts (e.g., the holding of causal relations) reducible to non-causal facts (e.g., the holding of certain spatiotemporal relations)? (shrink)

This paper focuses on Kant's account of physical geography and his theory of the Earth. In spelling out the epistemological foundations of Kant's physical geography, the paper examines 1) their connection to the mode of holding-to-be-true, mathematical construction and empirical certainty and 2) their implications for Kant's view of cosmopolitan right. Moreover, by showing the role played by the mathematical model of the Earth for the foundations of Kant's Doctrine of Right, the exact relationship between the latter and physical geography (...) is highlighted. Finally, this paper shows how, in Kant's view, the progress of physical geography can be assured if and only if the free circulation of human beings is established and regulated by law. Therefore, examining the mutual relationship between the theory of Earth and the foundations of right opens new perspectives on the relationship between epistemology and practical philosophy within Kant's system. (shrink)

Abstract: This article contends that the relation of early logical empiricism to Kant was more complex than is often assumed. It argues that Reichenbach's early work on Kant and Einstein, entitled The Theory of Relativity and A Priori Knowledge (1920) aimed to transform rather than to oppose Kant's Critique of Pure Reason. One the one hand, I argue that Reichenbach's conception of coordinating principles, derived from Kant's conception of synthetic a priori principles, offers a valuable way of accounting for the (...) historicity of scientific paradigms. On the other hand, I show that even Reichenbach, in line with Neo-Kantianism, associated Kant's view of synthetic a priori principles too closely with Newtonian physics and, consequently, overestimated the difference between Kant's philosophy and his own. This is even more so, I point out, in the retrospective account logical empiricism presented of its own history. Whereas contemporary reconstructions of this history, including Michael Friedman's, tend to endorse this account, I offer an interpretation of Kant's conception of a priori principles that contrasts with the one put forward by both Neo-Kantianism and logical empiricism. On this basis, I re-examine the early Reichenbach's effort to accommodate these principles to the paradigm forged by Einstein. (shrink)

The question of the dimensionality of space has informed the development of physics since the beginning of the twentieth century in the quest for a unified picture of quantum processes and gravitation. Scientists have worked within various approaches to explain why the universe appears to have a certain number of spatial dimensions. The question of why space has three dimensions has a genuinely philosophical nature that can be shaped as a problem of justifying a contingent necessity of the world. In (...) contrast to explanations of three-dimensionality based on anthropic arguments, we support the search for a theory that provides a justification for the dimensionality of space based on a combination of deductive and inductive reasoning applied to science. In doing so, we argue that Kant correctly approached the question in “Thoughts on the true estimation of living forces” by connecting space dimensionality and the inverse square law. In expounding the strategy of Kant’s argument, we describe the main features of a general Kantian explanation of the dimensionality of space and discuss them with respect to current accounts of explanation in the philosophy of science, such as inference to the best explanation and the deductive-nomological model. (shrink)

The relativistic revolution led to varieties of neo-Kantianism in which constitutive principles define the object of scientific knowledge in a domain-dependent and historically mutable manner. These principles are a priori insofar as they are necessary premises for the formulation of empirical laws in a given domain, but they lack the self-evidence of Kant’s a priori and they cannot be identified without prior knowledge of the theory they purport to frame. In contrast, the rationalist endeavors of a few masters of theoretical (...) physics have led to comprehensibility conditions that are easily admitted in a given domain and yet suffice to generate the theory of this domain. The purpose of this essay is to compare these two kinds of relativized a priori, to discuss the nature of the comprehensibility conditions, and to demonstrate their effectiveness in a modular conception of physical theories. (shrink)

In this paper I extend the case for a necessitation account of particular laws in Kant's philosophy of science by examining the relation between reason's hypothetical use in the Appendix to the Transcendental Dialectic and the legitimate hypotheses identified in the Doctrine of Method. Building on normative accounts of reason's ideas, I argue that reason's hypothetical use does not describe the connections between objects and their grounds, which lie beyond the reach of the understanding, but merely prescribes the relations between (...) appearances and their conditions, for which the understanding must seek. A legitimate hypothesis, I suggest, is a proposition we hold to be true that fills in one or several of those relations. The problematic character of hypotheses requires that we evaluate our reasons for holding them to be true. While natural modality is grounded in the nature of things, which cannot be fully known, our reasons for assent can and must be grounded on features of objects that are epistemically available to us. (shrink)

This article is an investigation of parallel themes in Heinrich Hertz's philosophy science and Kant's theory of schemata, symbols and regulative ideas. It is argued that Hertz's "pictures" bears close similarities to Kantian "schemata", that is, they are rules linking concepts to intuitions and provide them with their meaning. Kant's distinction between symbols and schemata is discussed and related to Hertz's three pictures of mechanics. It is argued that Hertz considered his own picture of mechanics (the "hidden mass" picture) as (...) symbolic in a different way than the force and energy pictures. In the final part of the article it is described how Harald Høffding soon after the publication of Hertz's Principles of Mechanics developed a general theory of analogical reasoning, relying on the ideas of Hertz and Kant. (shrink)

This article is an investigation of parallel themes in Heinrich Hertz's philosophy science and Kant's theory of schemata, symbols and regulative ideas. It is argued that Hertz's "pictures" bears close similarities to Kantian "schemata", that is, they are rules linking concepts to intuitions and provide them with their meaning. Kant's distinction between symbols and schemata is discussed and related to Hertz's three pictures of mechanics. It is argued that Hertz considered his own picture of mechanics as symbolic in a different (...) way than the force and energy pictures. In the final part of the article it is described how Harald Høffding soon after the publication of Hertz's Principles of Mechanics developed a general theory of analogical reasoning, relying on the ideas of Hertz and Kant. (shrink)

A murder of an Afro-American detainee by a policeman at the end of May 2020 caused a public outrage in the United States, which led to a campaign against the monuments to historical figures whose reputation, according to the protesters, was marred by racism. Some German publicists, impressed by the campaign, initiated an analogous search for racists among the national thinkers and politicians of the past. Suddenly Kant emerged as a ‘scapegoat’. This statement is an attempt to assess such reactions (...) from the perspective of Russia’s experience. (shrink)

There seem to be some very good reasons for a philosopher of science to be a deductivist about scientific reasoning. Deductivism is apparently connected with a demand for clarity and definiteness in the reconstruction of scientists' reasonings. And some philosophers even think that deductivism is the way around the problem of induction. But the deductivist image is challenged by cases of actual scientific reasoning, in which hard-to-state and thus discursively ill-defined elements of thought nonetheless significantly condition what practitioners accept as (...) cogent argument. And arguably, these problem cases abound. For example, even geometry--for most of its history--was such a problem case, despite its exactness and rigor. It took a tremendous effort on the part of Hilbert and others, to make geometry fit the deductivist image. Looking to the empirical sciences, the problems seem worse. Even the most exact and rigorous of empirical sciences--mechanics--is still the kind of problem case which geometry once was. In order for the deductivist image to fit mechanics, Hilbert's sixth problem (for mechanics) would need to be solved. This is a difficult, and perhaps ultimately impossible task, in which the success so far achieved is very limited. I shall explore some consequences of this for realism as well as for deductivism. Through discussing links between non-monotonicity, skills, meaning, globality in cognition, models, scientific understanding, and the ideal of rational unification, I argue that deductivists can defend their image of scientific reasoning only by trivializing it, and that for the adequate illumination of science, insights from anti-deductivism are needed as much as those which come from deductivism. (shrink)

This book is a welcome contribution to the literature on Kant's philosophy of mathematics in two particular respects. First, the author systematically traces the development of Kant's thought on mathematics from the very early pre-Critical writings through to the Critical philosophy. Secondly, it puts forward a challenge to contemporary Anglo-Saxon commentators on Kant's philosophy of mathematics which merits consideration.A central theme of the book is that an adequate understanding of Kant's pronouncements on mathematics must begin with the recognition that mathematics (...) in Kant's time was poised at the beginning of what Pierobon calls the ‘algebraic revolution’ of the nineteenth century. For Kant, Euclidean geometry, with its heavy reliance on the geometric image, was the paradigm of certainty. The algebraic revolution of the nineteenth century replaced that paradigm with an algebraic formalism, thereby freeing mathematics from any connection to the geometric image, and also severing the link to intuition. Pierobon describes this as the ‘divergence between the image and writing [l'écriture]’. So great was the shift, Pierobon suggests, that, after the developments of the nineteenth century, it became difficult to find any sense in Kant's conception of mathematics as sensible knowledge. This, certainly, was the view of Russell, who notoriously claimed in Mysticism and Logic that modern developments in logic dealt a ‘fatal blow to the Kantian philosophy’ and that ‘the whole doctrine of a priori intuitions, by which Kant explained the possibility of pure mathematics, is wholly inapplicable to mathematics in its present form’.1 Pierobon claims, though, that much of Anglo-Saxon commentary on Kant's philosophy of mathematics begins from this ‘rationalist and logicist’ position, reading Kant's philosophy of mathematics from a post-algebraic-revolution perspective. This book attempts to offer a corrective to that position by offering a Kantian conception of mathematics …. (shrink)

The role of analogy appears in surprisingly different areas of the first Critique. On the one hand, Kant considered the concept to have a specific enough meaning to entitle the principle concerned with causation an analogy; on the other hand we can find Kant referring to analogy in various parts of the Transcendental Dialectic in a seemingly different manner. Whereas in the Transcendental Analytic, Kant takes some time to provide a detailed (if not clear) account of the meaning of the (...) term ‘analogy’ and his reasons for his employment of it, in the Transcendental Dialectic on the other hand, Kant’s employment of the term seems far less technical. It would seem on the face of it, that Kant has two senses of ‘analogy’: one technical sense reserved for those constitutive principles of the understanding as laid out in the Analytic, and another casual and commonplace use of the term. This picture, although it contains elements of truth, is ultimately misleading. I argue for three claims in this paper. Firstly, I suggest that there can be found in the first Critique a unified conception of analogy. Secondly, I argue that Kant self-consciously differentiated his employment of analogy from the employment that can be found in many early modern philosophers, e.g. Locke. Thirdly, I will tentatively suggest that this interpretation of analogy can aid us in addressing certain contentious areas of transcendental idealism, most notably the account of causation. (shrink)

It is often maintained that one insight of Kant's Critical philosophy is its recognition of the need to distinguish accounts of knowledge acquisition from knowledge justification. In particular, it is claimed that Kant held that the detailing of a concept's acquisition conditions is insufficient to determine its legitimacy. I argue that this is not the case at least with regard to geometrical concepts. Considered in the light of his pre-Critical writings on the mathematical method, construction in the Critique can be (...) seen to be a form of concept acquisition, one that is related to the modal phenomenology of geometrical judgement. (shrink)

I argue that, by the time of his essay "Concerning the Ultimate Ground of the Differentiation of Directions in Space" (1768), Kant had come to question the status of the Principle of Sufficient Reason as a result, at least in part, of his recognition of the existence of incongruent counterparts. Though Kant's argument against absolute space based on the existence of incongruent counterparts has been much discussed in recent years, its importance as a useful benchmark by which to judge the (...) direction of Kant’s thinking during this period has gone unnoticed. This paper is a modest attempt to remedy this deficiency. (shrink)

The paper addresses the question of the nature and limits of philosophical thought experiments. On the one hand, experimental philosophers are right to claim that we need much more laboratory work in order to have more reliable thought experiments, but on the other hand a naturalism that is too radical is incapable of clarifying the peculiarity of thought experiments in philosophy. Starting from a historico-critical reconstruction of Kant’s concept of the “experiments of pure reason”, this paper outlines an account of (...) thought experiments in philosophy that tries to reconcile the thesis of a principled difference between scientific and philosophical TEs with the position of a methodological naturalism that does not admit any difference in kind between the methods of science and of philosophy. (shrink)

Elsewhere I have tried to provide the justification of both the irreducible distinction of science and philosophy and their inevitable complementarity. Unlike empirical science, philosophy has no limit whatever as far as its possible objects are concerned. To say that there is no limit whatever to the possible objects of philosophy is to say that, strictly speaking, it has no object at all and must find its object outside itself, that is, in common sense knowledge and the natural and human (...) sciences. Against the background of this conception, the paper argues that philosophy of science, as a critical reflection on common sense knowledge and the natural or human sciences, inherits from philosophy in general this two-faced Janus nature, which in the philosophy of science shapes the epistemological status of the discipline in an even more prominent way. To show this in detail, the paper enunciates eleven theses that derive from the intimate connection of unity and distinction that exists between philosophy of science on the one hand and the particular and specialized scientific knowledge on the other. (shrink)

It is a common thought that mathematics can be not only true but also beautiful, and many of the greatest mathematicians have attached central importance to the aesthetic merit of their theorems, proofs and theories. But how, exactly, should we conceive of the character of beauty in mathematics? In this paper I suggest that Kant's philosophy provides the resources for a compelling answer to this question. Focusing on §62 of the ‘Critique of Aesthetic Judgment’, I argue against the common view (...) that Kant's aesthetics leaves no room for beauty in mathematics. More specifically, I show that on the Kantian account beauty in mathematics is a non-conceptual response felt in light of our own creative activities involved in the process of mathematical reasoning. The Kantian proposal I thus develop provides a promising alternative to Platonist accounts of beauty widespread among mathematicians. While on the Platonist conception the experience of mathematical beauty consists in an intellectual insight into the fundamental structures of the universe, according to the Kantian proposal the experience of beauty in mathematics is grounded in our felt awareness of the imaginative processes that lead to mathematical knowledge. The Kantian account I develop thus offers to elucidate the connection between aesthetic reflection, creative imagination and mathematical cognition. (shrink)

According to Kant, the axioms of intuition, i.e. space and time, must provide an organization of the sensory experience. However, this first orderliness of empirical sensations seems to depend on a kind of faculty pertaining to subjectivity, rather than to the encounter of these same intuitions with the real properties of phenomena. Starting from an analysis of some very significant developments in mathematical and theoretical physics in the last decades, in which intuition played an important role, we argue that nevertheless (...) intuition comes into play in a fundamentally different way to that which Kant had foreseen: in the form of a formal or “categorical” yet not sensible intuition. We show further that the statement that our space is mathematically three-dimensional and locally Euclidean by no means follows from a supposed a priori nature of the sensible or subjective space as Kant claimed. In fact, the three-dimensional space can bear many different geometrical and topological structures, as particularly the mathematical results of Milnor, Smale, Thurston and Donaldson demonstrated. On the other hand, it has been stressed that even the phenomenological or perceptual space, and especially the visual system, carries a very rich geometrical organization whose structure is essentially non-Euclidean. Finally, we argue that in order to grasp the meaning of abstract geometric objects, as n-dimensional spaces, connections on a manifold, fiber spaces, module spaces, knotted spaces and so forth, where sensible intuition is essentially lacking and where therefore another type of mathematical idealization intervenes, we need to develop a new form of intuition. (shrink)

Kant is well known for his restrictive conception of proper science. In the present paper I will try to explain why Kant adopted this conception. I will identify three core conditions which Kant thinks a proper science must satisfy: systematicity, objective grounding, and apodictic certainty. These conditions conform to conditions codified in the Classical Model of Science. Kant’s infamous claim that any proper natural science must be mathematical should be understood on the basis of these conditions. In order to substantiate (...) this reading, I will show that only in this way it can be explained why Kant thought (1) that mathematics has a particular foundational function with respect to the natural sciences and (2) as such secures their scientific status. (shrink)

In the Critique of Pure Reason, Kant draws a distinction between appearances and things in themselves, characterizing the latter as uncognizable. While arguing that all we can cognize are appearances, Kant nevertheless maintains that there are thing in themselves. This has struck many as questionable: how can we be in a position to affirm, of things stipulated to be uncognizable, that they exist? In this paper, I take up the challenge of establishing the existence of things in themselves. I begin (...) by making the case that, given Kant’s epistemological strictures, the existence of things in themselves must follow analytically from the existence of appearances. After examining the pitfalls of a recent attempt at establishing the existence of things in themselves, I go on to argue that the feature of appearances in virtue of which their existence analytically entails the existence of themselves is the subjectivity of their form. It is implicit in the notion of something with a subjective form that its matter is provided via affection from without. Moreover, the things providing the matter of appearances can’t be located in space and time, because appearances themselves depend on our sensibility for their formal features. (shrink)

Kant’s three Analogies of Experience, in his Critique of Pure Reason, represent a highly condensed attempt to establish the metaphysical foundations of Newtonian physics. His strategy is to show that the organization of experience in terms of a world of enduring substances undergoing mutual causal interaction is a necessary condition of the temporal ordering even of one’s own subjective states, and thus of coherent experience itself. In his Third Analogy—an examination of the necessary conditions of judgments of simultaneous existence—he argues (...) that certain conceptual presuppositions consistent with Newtonian physics are necessary to time-awareness. His argument, however, appears to be undermined by conventionalism in natural science generally, and by the conventionality of simultaneity in particular. In this paper I discuss Kant’s claims in light of contemporary relativity theory. I suggest that, while his project is obsolete in major respects, there may still be useful insights into time-awareness to be drawn from his work. (shrink)

Extension is probably the most general natural property. Is it a fundamental property? Leibniz claimed the answer was no, and that the structureless intuition of extension concealed more fundamental properties and relations. This paper follows Leibniz's program through Herbart and Riemann to Grassmann and uses Grassmann's algebra of points to build up levels of extensions algebraically. Finally, the connection between extension and measurement is considered.

This article argues that the limited influence of Ludwik Fleck's ideas on philosophy of science is due not only to their indirect dissemination by way of Thomas Kuhn, but also to an incommensurability between the standard conceptual framework of history and philosophy of science and Fleck's own more integratedly historico-social and praxis-oriented approach to understanding the evolution of scientific discovery. What Kuhn named "paradigm" offers a periphrastic rendering or oblique translation of Fleck's Denkstil/Denkkollektiv , a derivation that may also account (...) for the lability of the term "paradigm". This was due not to Kuhn's unwillingness to credit Fleck but rather to the cold war political circumstances surrounding the writing of The Structure of Scientific Revolutions . Following a discussion of Fleck's anatomical allusions, I include a brief discussion of Aristotle (on menstruation and darkened mirrors) and conclude with a reference to the productivity of error in Mach and Nietzsche. (shrink)

The subject of this article is Herder’s unique conception of the soul-body relationship and its divergence from and dependence on Leibniz. Herder’s theory is premised on a rejection of the windowlessness of monads in two important respects: interaction between material bodies (as gleaned from Crusius and Kant) and interaction between the soul and body. Herder’s theory depends on Leibniz insofar as it agrees with the intimate connection Leibniz posits between the soul and the body, as his epistemology demonstrates, with, however, (...) the significant modification that the connection is real. Herder transforms the Leibnizian rehabilitation and use of substantial forms to develop a double-conception of the human soul as both thinking substance and substantial form: the soul, qua thinking substance, needs a body through whose senses it can interact with, and acquire knowledge of, the external world; the soul, qua substantial form, constructs itself this material body by harnessing the forces of attraction and repulsion. Herder’s theory provides an alternative to other contemporary accounts of the soul-body relationship, especially Kant’s, which start from the problem of relating two distinct substances. His unique and original reconciliation of the modern dichotomy of spirit and matter, via his connecting of Leibniz’s realms of final and efficient causes, is of great significance for the rise of German Idealism. (shrink)

Officially, for Kant, judgments are analytic iff the predicate is "contained in" the subject. I defend the containment definition against the common charge of obscurity, and argue that arithmetic cannot be analytic, in the resulting sense. My account deploys two traditional logical notions: logical division and concept hierarchies. Division separates a genus concept into exclusive, exhaustive species. Repeated divisions generate a hierarchy, in which lower species are derived from their genus, by adding differentia(e). Hierarchies afford a straightforward sense of containment: (...) genera are contained in the species formed from them. Kant's thesis then amounts to the claim that no concept hierarchy conforming to division rules can express truths like '7+5=12.' Kant is correct. Operation concepts ( ) bear two relations to number concepts: and are inputs, is output. To capture both relations, hierarchies must posit overlaps between concepts that violate the exclusion rule. Thus, such truths are synthetic. (shrink)

Although Kant (1998) envisaged a prominent role for logic in the argumentative structure of his Critique of Pure Reason, logicians and philosophers have generally judged Kantgeneralformaltranscendental logics is a logic in the strict formal sense, albeit with a semantics and a definition of validity that are vastly more complex than that of first-order logic. The main technical application of the formalism developed here is a formal proof that Kants logic is after all a distinguished subsystem of first-order logic, namely what (...) is known as geometric logic. (shrink)

What is mathematics about? And if it is about some sort of mathematical reality, how can we have access to it? This is the problem raised by Plato, which still today is the subject of lively philosophical disputes. This book traces the history of the problem, from its origins to its contemporary treatment. It discusses the answers given by Aristotle, Proclus and Kant, through Frege's and Russell's versions of logicism, Hilbert's formalism, Gödel's platonism, up to the the current debate on (...) Benacerraf's dilemma and the indispensability argument. Through the considerations of themes in the philosophy of language, ontology, and the philosophy of science, the book aims at offering an historically-informed introduction to the philosophy of mathematics, approached through the lenses of its most fundamental problem. (shrink)

What I call the dynamics of reason is a post-Kuhnian approach to the history and philosophy of science articulating a relativized and historicized version of the Kantian conception of the rationality and objectivity of the modern physical sciences. I here discuss two extensions of this approach. I argue that, although the relativized standards of rationality in question change over time, the particular way in which they do this still preserves the trans-historical rationality of the entire process. I also make a (...) beginning in extending my historical narrative from purely intellectual history (both philosophical and scientific) to the wider cultural context. (shrink)

I demonstrate that the pre-Critical Kant is essentialist and intellectualist about the relational properties of substances. That is to say, God can choose whether or not to create a substance, and whether or not to connect this substance with other substances, so as to create a world: but God cannot choose what the nature of the relational properties is, once the substance is created and connected. The divine will is constrained by the essences of substances. Nonetheless, Kant considers that essences (...) depend upon God, in that they depend upon the divine intellect. I conclude by gesturing towards some possible implications of this interpretation, when considering the role that might be played by God – both historically and conceptually – in relation to the notion of ‘laws of nature’, and when understanding Kant's transcendental idealism and his Critical conception of freedom. (shrink)

This is the most comprehensive book ever published on philosophical methodology. A team of thirty-eight of the world's leading philosophers present original essays on various aspects of how philosophy should be and is done. The first part is devoted to broad traditions and approaches to philosophical methodology. The entries in the second part address topics in philosophical methodology, such as intuitions, conceptual analysis, and transcendental arguments. The third part of the book is devoted to essays about the interconnections between philosophy (...) and neighbouring fields, including those of mathematics, psychology, literature and film, and neuroscience. (shrink)

Der Kommentar zur Kritik der reinen Vernunft bietet eine textnahe Erschließung der zentralen Begriffe, Thesen und Argumentationsgänge von Kants Hauptwerk auf aktuellem Forschungsstand. Es ist der erste Kommentar zur KrV, der den gesamten Text in der Fassung der ersten und zweiten Auflage gleichmäßig und lückenlos berücksichtigt. Davon profitieren vor allem die „Transzendentale Dialektik“ und die „Methodenlehre“, die in früheren Gesamtkommentaren meist nicht hinreichend berücksichtigt worden sind. Die Beiträge wurden nach einheitlichen Richtlinien verfasst, wobei unterschiedliche Herangehensweisen und Interpretationsansätze zur Geltung kommen. (...) Um dem Leser dieses Kommentars die Orientierung zu erleichtern, ist jeder Beitrag in drei bzw. vier Teile untergliedert: Der erste Teil behandelt die Stellung und Funktion des kommentierten Textabschnitts in der KrV, der zweite Teil gibt einen Überblick über Inhalt und Aufbau des Abschnitts, der dritte Teil enthält den eigentlichen Textkommentar. Wo dies sinnvoll erschien, wurden in einem vierten Teil wichtige Interpretationsfragen angesprochen. Hinweise auf weiterführende Spezialliteratur am Ende eines jeden Beitrags, eine Auswahlbibliographie zu Kant und zur Kritik der reinen Vernunft sowie ein Namen- und ein Sachregister machen den Band zu einem komfortablen Arbeitsmittel für den Benutzer. Die vorliegende zweite Auflage trägt der Tatsache Rechnung, dass der Band mittlerweile als Standardwerk der Kant-Forschung gilt. Mit Beiträgen von Henry Allison, Karl Ameriksm Reinhard Brandt, Wolfgang Carl, Konrad Cramer, Jean Ferrari Eckart Förster, Volker Gerhardt, Paul Guyer, Otfried Höffe, Hansgeorg Hoppe, Rolf-Peter Horstmann, Heiner F. Klemme, Lothar Kreimendahl, Béatrice Longuenesse, Georg Mohr, Birgit Recki, Alain Renaut, Peter Rohs, Gerhard Seel, Dieter Sturma, Bernhard Thöle, Eric Watkins, Marcus Willaschek. (shrink)

I survey the debate over rationalism and empiricism in science. This chapter contains sections titled: The New Experimental Science as a Challenge to Intuition, Geometry and Intuition, The Mathematical Tradition and Theoretical Science.

In this essay I offer a partial rehabilitation of Cohen’s Kant interpretation. In particular, I will focus on the center of Cohen’s interpretation in KTE, reflected in the title itself: his interpretation of Kant’s concept of experience. “Kant hat einen neuen Begriff der Erfahrung entdeckt,”7 Cohen writes at the opening of the first edition of KTE (henceforth, KTE1), and while the exact nature of that new concept of experience is hard to pin down in the 1871 edition, he states it (...) succinctly in the second edition (henceforth KTE2): experience is Newtonian mathematical natural science.8 While this equation of experience with mathematical natural science has few contemporary defenders, I believe it is substantially correct, with one important qualification. Kant uses the term Erfahrung in a number of different senses in the Kritik der reinen Vernunft (henceforth, KrV). I will argue that a central, and neglected, sense of that key technical term aligns with Cohen’s reading; what Kant sometimes refers to as ‘universal experience’ (sometimes, simply ‘experience’) is, in broad outlines, correctly interpreted by Cohen as mathematical natural science. (shrink)

Theories of epistemology make reference—via the perspective of an observer—to the structure of information transfer, which generates reality, of which the observer himself forms a part. It can be shown that any epistemological approach which implies the participation of tautological structural elements in the information transfer necessarily leads to an antinomy. Nevertheless, since the time of Aristotle the paradigm of mathematics—and thus tautological structure—has always been a hidden ingredient in the various concepts of knowledge acquisition or general theories of information (...) transfer. We hold that Darwin’s Evolutionary Theory is the first scientific theory which consistently presupposes a non-tautological structure for the information transfer and, at the same time, keeps it strictly distinct from the tautological metric of scientific observation. The consequences of this technique—namely the dissociation of information from intentionality—have not yet been fully drawn. (shrink)