Although Kant envisaged a prominent role for logic in the argumentative structure of his Critique of pure reason, logicians and philosophers have generally judged Kant's logic negatively. What Kant called `general' or `formal' logic has been dismissed as a fairly arbitrary subsystem of first order logic, and what he called `transcendental logic' is considered to be not a logic at all: no syntax, no semantics, no definition of validity. Against this, we argue that Kant's `transcendental logic' 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 Kant's Table of Judgements in §9 of the Critique of pure reason, is indeed, as Kant claimed, complete for the kind of semantics he had in mind. This result implies that Kant's 'general' logic is after all a distinguished subsystem of first order logic, namely what is known as geometric logic. (shrink)

This article examines the Kantian thesis of the a priori nature of our knowledge of space. Because it makes the representation of objects possible as external to us and all others, and consequently, as distinct and individualized, space (whatever its structure may be) claims the status as necessary condition and as apriori possibility of all knowledge. However, in the light of various physical, psychological and philosophical considerations, it seems that the particular structure allocated by Kant to space (i.e. uniqueness, infinity, (...) continuity, homogeneity, isotropy, Euclidean character and three-dimensional character) is neither necessary nor a priori but is rather contingent and dependent on experience. For this reason a pragmatist relativization of the transcendental approach appears to be necessary: the structure of space which makes knowledge possible is not apriori in an absolute sense, but rather, it is determined within the context of a certain practice, which is characterized by a certain mode of interaction with the environment and reveals particular empirical constraints to which this spatial structure must fit. (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)

Philological background information is presented on the origin and composition of the text generally known as Kant's Logic. The text, which was not in the strict sense of the word written by Kant himself, but rather assembled by another writer whom Kant had authorized to do so on his behalf, is a mixture of materials, not all of which originate directly from Kant, and cannot claim full authenticity.

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)

Kant criticizes the so-called hypothesis at the end of the B-Deduction on the ground that it entails scepticism. I examine the historical context of Kant's criticism, and identify the targets as both Crusius and Leibniz. There are two claims argued for in this paper: first, that attending to the context of the opposition to certain forms of nativism affords a way of understanding Kant's commitment to the so-called , by contrasting the possession conditions for the categories with those for innate (...) ideas; secondly, it provides an insight with regard to Kant's understanding of the dialectic with scepticism. Kant's claim is that a certain explanatory lacuna that attaches to Humean empiricism can be seen to apply equally to any nativist theory. The lacuna concerns the explanation of the modal purport of a priori necessity, i.e. how it is that our consciousness can even distinguish contents that are represented as necessary features of objects. (shrink)

Must space be a unity? This question, which exercised Aristotle, Descartes and Kant, is a specific instance of a more general one; namely, can the topology of physical space change with time? In this paper we show how the discussion of the unity of space has been altered but survives in contemporary research in theoretical physics. With a pedagogical review of the role played by the Euler characteristic in the mathematics of relativistic spacetimes, we explain how classical general relativity (modulo (...) considerations about energy conditions) allows virtually unrestrained spatial topology change in four dimensions. We also survey the situation in many other dimensions of interest. However, topology change comes with a cost: a famous theorem by Robert Geroch shows that, for many interesting types of such change, transitions of spatial topology imply the existence of closed timelike curves or temporal non-orientability. Ways of living with this theorem and of evading it are discussed. (shrink)

In this paper, I argue that Heisenberg's mature philosophy of quantum mechanics must be understood in the context of his epistemological project to reinterpret and redefine Kant's notion of the a priori. After discussions with Weizsäcker and Hermann in Leipzig in the 1930s, Heisenberg attempted to ground his interpretation of quantum mechanics on what might be termed a 'practical' transformation of Kantian philosophy. Taking as his starting point, Bohr's doctrine of the indispensability of classical concepts, Heisenberg argued that concepts such (...) as space, time and causality can be regarded as 'practically a priori', in so far as they remain the conditions for the possibility of experience and even of 'objective reality', though they are not universal and necessary in a strictly Kantian sense. We cannot avoid using classical concepts in the description of experiments in quantum theory, despite the fact that there are limits to their applicability. Such concepts are, for Heisenberg, historically contingent, yet indispensable in our time, because we have no other language through which we can describe and conceive of the interaction between 'object' and 'measuring device'. (shrink)

I attempt a reconstruction of Kant's version of the causal theory of time that makes it appear coherent. Two problems are at issue. The first concerns Kant's reference to reciprocal causal influence for characterizing simultaneity. This approach is criticized by pointing out that Kant's procedure involves simultaneous counterdirected processes-which seems to run into circularity. The problem can be defused by drawing on instantaneous processes such as the propagation of gravitation in Newtonian mechanics. Another charge of circularity against Kant's causal theory (...) was leveled by Schopenhauer. His objection was that Kant's approach is invalidated by the failure to deliver non-temporal criteria for distinguishing between causes and effects. I try to show that the modern causal account has made important progress toward a successful resolution of this difficulty. The fork asymmetry, as based on Reichenbach's principle of the common cause, provides a means for the distinction between cause and effect that is not based on temporal order (if some preconditions are realized). (shrink)

By way of these investigations, we hope to understand better the rationale behind Kant's theory of intuition, as well as to grasp many facets of the relations ...

My title, of course, is an exaggeration. The world no more became mathematical in the seventeenth century than it became ironic in the nineteenth. Either it was mathematical all along, and seventeenth-century philosophers discovered it was, or, if it wasn’t, it could not have been made so by a few books. What became mathematical was physics, and whether that has any bearing on the furniture of the universe is one topic of this paper. Garber says, and I agree, that for (...) Descartes bodies are the things of geometry made real ( Ref). That is a claim about the world: what God created, and what we know in physics, is nothing other than res extensa and its modes. Others, including Marion, hold that in modern science, here represented at its origins by Descartes, representation displaces beings: the knower no longer confronts Being or beings but rather a system of signs, a “code” as Marion calls it, to which the knower stands in the relation of subject to object. The Meditations, or perhaps even the Regulæ, are the first step toward the transcendental idealism of Kant. Most of this paper will be devoted to a more concrete question. Physics in the seventeenth century increasingly became a matter of applying mathematical knowledge to the solution of physical problems. The “mixed sciences” of astronomy, optics, and music, sciences then distinct from physics, became models of understanding for all of natural philosophy. My interest here is in one aspect of that development: how particular physical situations are transformed into mathematical. I will look at the work of Descartes and Isaac Beeckman, contrasting their visions of “physico-mathematics”. (shrink)

Perspectives on Kant's teachings on geography and how they relate his understanding of the world.

(A) Books: (3) Kant, Science, and Human Nature (Oxford: OUP, forthcoming). (2) Rationality and Logic (Cambridge: MIT Press, forthcoming). (1) Kant and the Foundations of Analytic Philosophy (Oxford: Clarendon/OUP, 2001 [pbk., 2004]). (B) Articles: (30) "Kant, Wittgenstein, and the Fate of Analysis," in M. Beaney (ed.), The Analytic Turn (London: Routledge, forthcoming.) (29) "Kant and the Analytic Tradition," in C. Boundas (ed.), A Companion to the Twentieth-Century Philosophies (Edinburgh: Univ. of Edinburgh Press, forthcoming).

According to Kant in the Prolegomena, the natural kind proposition (GYM) "Gold is a yellow metal" is analytically true, necessary, and a priori. Saul Kripke and Hilary Putnam have argued that on the contrary propositions such as (GYM) are neither analytic, nor necessary, nor a priori. The Kripke-Putnam view is based on the doctrine of "scientific essentialism" (SE). It is a direct consequence of SE that propositions such as (GE) "Gold is the element with atomic number number 79" are metaphysically (...) necessary and a posteriori. Were Kant to travel by time-machine to the present and to consider (GE), however, he would regard it as metaphysically contingent; and even if he were able to admit it as necessary, it would be synthetic a priori, and not a posteriori. In these ways, the conflict between Kant and the scientific essentialists is a sharply-defined one: if the essentialists are right, then the Kantian theory of meaning, necessity, and a priori knowledge is wrong; but if Kant is right, then SE is wrong. As a prolegomenon to the development and defense of Kant's positive theory of natural kind propositions, this paper undertakes a Kantian critique of SE. Following the Introduction, the paper has three sections. The first section spells out the main theses and assumptions of SE. The second section, setting aside the semantic and logical components of SE, focuses on its epistemic and metaphysical components and offers four Kantian arguments against them. The final section offers Kantian "diagnoses" of the flaws in SE exposed by the four critical arguments. (shrink)

Key words: <span class='Hi'>Kant</span>, Moses Mendelssohn, Christian Wolff, Christian Crusius, transcendental psychology, possibility of scientific psychology.

I argue that we need not accept Quine's holistic conception of mathematics and empirical science. Specifically, I argue that we should reject Quine's holism for two reasons. One, his argument for this position fails to appreciate that the revision of the mathematics employed in scientific theories is often related to an expansion of the possibilities of describing the empirical world, and that this reveals that mathematics serves as a kind of rational framework for empirical theorizing. Two, this holistic conception does (...) not clearly demarcate pure mathematics from applied mathematics. In arguing against Quine, I present a formal account of applied mathematics in which the mathematics employed in an empirical theory plays a role that is analogous to the epistemological role Kant assigned synthetic a priori propositions. According to this account, it is possible to insulate pure mathematics from empirical falsification, and there is a sense in which applied mathematics can also be labeled as a priori. (shrink)

This article notes six advances in recent analytic Kant research: (1) Strawson's interpretation, which, together with work by Bennett, Sellars, and others, brought renewed attention to Kant through its account of space, time, objects, and the Transcendental Deduction and its sharp criticisms of Kant on causality and idealism; (2) the subsequent investigations of Kantian topics ranging from cognitive science and philosophy of science to mathematics; (3) the detailed work, by a number of scholars, on the Transcendental Deduction; (4) the clearer (...) understanding of transcendental idealism sparked by reactions to Allison's epistemic account; (5) the resulting need—prompted also by new studies of the thing in itself—to face up to the old question of the philosophical defensibility of such idealism; and (6) the active engagement with Kant's ethics and political philosophy that derives from Rawls's and others' work. (shrink)

This accessible and practical edition of Kant's best introduction to his own work is designed especially for students. Assuming no prior knowledge of the Prolegomena to Any Future Metaphysics, esteemed scholar Gunter Zoller provides an extensive introduction that covers Kant's life, the origin and reception of the Prolegomena, the organization of the work, its principal arguments, and its philosophical significance. Detailed notes, a chronology, a glossary, an annotated bibliography, and two reviews of the Critique of Pure Reason--which establishes the specific (...) intellectual background of the Prolegomena--are also included. (shrink)

This new, revised edition of Kant's Prolegomena, the best introduction to the theoretical side of his philosophy, presents his thought clearly through careful attention to his original language. Also included are selections from the Critique of Pure Reason, which fill out and explicate some of Kant's central arguments (including famous sections of the Schematism and Analogies), and in which Kant himself explains his special terminology. The first reviews of the Critique, to which Kant responded in the Prolegomena, are included in (...) this revised edition. First Edition Hb (1997): 0-521-57345-9 First Edition Pb (1997): 0-521-57542-7. (shrink)

We are republishing these classic works in affordable, high quality, modern editions, using the original text and artwork.

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)

What are the relationships between philosophy and the history of philosophy, the history of science and the philosophy of science? This selection of essays by Lorenz Krüger (1932-1994) presents exemplary studies on the philosophy of John Locke and Immanuel Kant, on the history of physics and on the scope and limitations of scientific explanation, and a realistic understanding of science and truth. In his treatment of leading currents in 20th century philosophy, Krüger presents new and original arguments for a deeper (...) understanding of the continuity and dynamics of the development of scientific theory. These result in significant consequences for the claim of the sciences that they understand reality in a rational manner. The case studies are complemented by fundamental thoughts on the relationship between philosophy, science, and their common history. (shrink)

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)

Kant maintains that his Critique of Pure Reason follows a “synthetic method” which he distinguishes from the analytic method of the Prolegomena by saying that the Critique “rests on no other science” and “takes nothing as given except reason itself”. The paper presents an account of the synthetic method of the Critique, showing how it is related to Kant’s conception of the Critique as the “science of an a priori judging reason”. Moreover, the author suggests, understanding its synthetic method sheds (...) light on the structure of the Transcendental Deduction, and its function in the work as a whole. (shrink)

Drawing on the original conception of Kant’s synthetic a priori and the relevant related developments in philosophy, this book presents a reconstruction of the intellectual history of the conception of quantity and offers an entirely ...

Recent perspectival interpretations of Kant suggest a way of relating his epistemology to empirical science that makes it plausible to regard Einstein’stheory of relativity as having a Kantian grounding. This first of two articles exploring this topic focuses on how the foregoing hypothesis accounts for variousresonances between Kant’s philosophy and Einstein’s science. The great attention young Einstein paid to Kant in his early intellectual development demonstrates the plausibility of this hypothesis, while certain features of Einstein’s cultural-political context account for his (...) reluctance to acknowledge Kant’s influence, even though contemporary philosophers who regarded themselves as Kantians urged him to do so. The sequel argues that this Kantian grounding probably had a formative influence not only on Einstein’s discovery of the theory of relativity and his view of the nature of science, but also on his quasi-mystical, religious disposition. (shrink)

The existence and nature of the a priori are defining issues for philosophy. A philosopher’s attitude to the a priori is a touchstone for his whole approach to the subject. Sometimes, as in Kant’s critical philosophy, or in Quine’s epistemology, a major new position emerges from reflection on questions that explicitly involve the notions of the a priori or the empirical. But even when no explicit use is made of the notion of the a priori in the questions addressed, a (...) philosopher’s methodology, the range of considerations to which the philosopher is open, his conception of the goals of the subject, his idea of what is involved in justification—all of these cannot fail to involve commitments about the nature and the existence of the a priori. So understanding the a priori is not only of interest in itself. It is also essential for self-understanding, if we are to understand ourselves as philosophers. (shrink)

The seal of the a priori is imprinted on the reception of Kant's philosophy. Piaget's epistemological argumentation seems to ascribe knowledge a more fruitful constructiveness than Kant, seeing the a priori as rooted in unvarying reason. Yet, it seems, he failed to recognize the complexity of Kant's theory, which does not always follow a quid iuris line. Moments of experience, analysis and self-observation played more than a marginal role in his discovery of the a priori. Indeed, Kant himself raises the (...) question of ontogenetic category assimilation in a review which pre-empts Piaget, borrowing the category of `original acquisition' from the doctrine of the laws of natural right. And although Kant should not be elevated to the harbinger of the knowledge on development issues delivered thus far by the history of science and experiments, he did recognize the temporal reference of their categories in principle without resolving their validity in psychogenetic terms. Key Words: a priori • categories • genetic epistemology • Geneva School • neo-Kantianism • original acquisition • Jean Piaget • psychogenesis • self-observation. (shrink)

Some of Catherine Malabou’s recent work has developed her conception of plasticity (originally deployed in a reading of Hegelian Aufhebung ) in relation to neuroscience. This development clarifies and advances her attempt to bring contemporary theory into dialogue with the natural sciences, while indirectly indicating her engagement with the French tradition in philosophy of science and philosophy of medicine, especially the work of Georges Canguilhem. I argue that we can see her development of plasticity as an answer to some specific (...) shortcomings in Canguilhem’s conception of organic or biological normativity as advanced in The Normal and the Pathological . Such a view of plasticity shows its potential to provide the basis for a powerful critical engagement with contemporary conceptions of selfhood, self-transformation, subjectivation, and the general theory of norms. (shrink)

I show one reason why Hegel’s theory of history is an improvement over Kant’s. There is an ambiguity in Kant’s theory of history. He wants, on the one hand, to distinguish empirical history (and, by extension, other empirical sciences which constitute experience) from reason’s a priori regulative role in theory. On the other hand, his view of the nature of sciences and the role of reason precludes such a separation. I trace this problem to different roles assigned the faculties of (...) understanding and reason in our experience. In Hegel’s theory of history, both reason and understanding together constitute the sciences, and thus experience. Hegel argues that history is a unified field employing both understanding and reason. I conclude that the more consistent theory of history for idealists is Hegel’s, and that this consistency partially explains the movement in German Idealism from Kantian to Hegelian thought. (shrink)

The Cambridge Companion to Early Modern Philosophy is a comprehensive introduction to the central topics and changing shape of philosophical inquiry in the seventeenth and eighteenth centuries. It explores one of the most innovative periods in the history of Western philosophy, extending from Montaigne, Bacon and Descartes through Hume and Kant. During this period, philosophers initiated and responded to major intellectual developments in natural science, religion, and politics, transforming in the process concepts and doctrines inherited from ancient and medieval philosophy. (...) In this Companion, leading specialists examine early modern treatments of the methodological and conceptual foundations of natural science, metaphysics, philosophy of mind, logic and language, moral and political philosophy, and theology. A final chapter looks forward to the philosophy of the Enlightenment. This will be an invaluable guide for all who are interested in the philosophical thought of the early modern period. (shrink)

This key collection of essays sheds new light on long-debated controversies surrounding Kant’s doctrine of idealism and is the first book in the English language that is exclusively dedicated to the subject. Well-known Kantians Karl Ameriks and Manfred Baum present their considered views on this most topical aspect of Kant's thought. Several essays by acclaimed Kant scholars broach a vastly neglected problem in discussions of Kant's idealism, namely the relation between his conception of logic and idealism: The standard view that (...) Kant's logic and idealism are wholly separable comes under scrutiny in these essays. A further set of articles addresses multiple facets of the notorious notion of the thing in itself, which continues to hold the attention of Kant scholars. The volume also contains an extensive discussion of the often overlooked chapter in the Critique of Pure Reason on the Transcendental Ideal. Together, the essays provide a whole new outlook on Kantian idealism. No one with a serious interest in Kant's idealism can afford to ignore this important book. Papers by Karl Ameriks, Manfred Baum, Ido Geiger, Lucy Allais, Gary Banham, Steven M. Bayne, Marcel Quarfood, Dennis Schulting, Dietmar Heidemann, Christian Onof and Jacco Verburgt. (shrink)

It has become a standard view in the philosophy of science scholarship (e.g., van Fraassen [1989]) that debates on the problem of laws of nature and/or scientific laws employ pre-Kantian approaches to the subject in question. But what exactly a Kantian approach might look like and, above all, what Kant endorses on this matter are not entirely settled issues. In particular, this regards Kant’s argument on the problem of ’necessity grounding’ with respect to different types of the so-called “empirical laws (...) of nature” (empirische Naturgesetze) in the third Critique. In order to assess the aforementioned problem, in this paper I will address the following questions:1) What is Kant’s main nomological criterion or a combination of criteria, that is, the criterion/criteria according to which we can explicate the distinction between laws of nature and accidentally true statements?2) What exactly is the role of an apriori law of nature, such as the one instantiated by the Second Analogy of Experience, in considering nature as a lawful existence of objects?3) On what grounds can a statement describing a particular causal regularity, for example, the statement “the sun warms the stone” (Prolegomena, N 301), be viewed as an empirical law of nature?4) Is Kant’s systematicity a nomological criterion in the strict and standard sense or, rather, is it a certain kind of transcendental criterion, which not only makes the whole of Kant’s nomological machinery up and running, but also has decisive influence on the final arrangement of nomological criteria? (shrink)