I examine how Kant argues for the transcendental ideality of space. I defend a reading on which Kant accepts the ideality of space because it explains our (actual) knowledge that mathematical judgments are necessarily true. I argue that this reading is preferable over the alternative suggestion that Kant can infer the ideality of space directly from the fact that we have an a priori intuition of space. Moreover, I argue that the reading I propose does not commit Kant to incoherent (...) modal views. If we carefully distinguish between different senses of modality, the fact that our spatial form of intuition is (in some sense) contingent does not undermine the claim that this form can explain how our mathematical judgments are (in some sense) necessary. (shrink)

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)

Despite the importance of Kant's claims about mathematical cognition for his philosophy as a whole and for subsequent philosophy of mathematics, there is still no consensus on his philosophy of arithmetic, and in particular the role he assigns intuition in it. This inquiry sets aside the role of intuition for the nonce to investigate Kant's conception of natural number. Although Kant himself doesn't distinguish between a cardinal and an ordinal conception of number, some of the properties Kant attributes to number (...) can be characterized as cardinal or ordinal. This essay argues that Kant's conception of number includes both cardinal and ordinal elements; it suggests that the cardinal elements provide the basis of a conception of number in general, while the ordinal elements contribute to specifying the exact size of particular collections. In considering these elements, roles for intuition begin to emerge, setting the stage for a reevaluation of the role of intuition in Kant's arithmetic. (shrink)

In this paper, I argue, first, that Hegel defended a version of the analytic/synthetic distinction—that, indeed, his version of the distinction deserves to be called Kantian. For both Kant and Hegel, the analytic/synthetic distinction can be explained in terms of the discursive character of cognition: insofar as our cognition is discursive, its most basic form can be articulated in terms of a genus/species tree. The structure of that tree elucidates the distinction between analytic and synthetic judgments. Second, I argue that (...) Hegel has an interesting and so far unexplored argument for the analytic/synthetic distinction: Hegel argues that the systematic relationship between concepts expressed in a genus/species tree can only be expressed through synthetic judgments. Third and finally, I explore some of the implications that the arguments in the first two parts of the essay have for understanding the way in which Hegel differs from Kant. I argue that Hegel accepts Kant's point that discursive cognition cannot be used to cognize the absolute. However, Hegel thinks that we can, nevertheless, cognize the absolute. I explore the character of this non-discursive cognition and argue that we can understand Hegel's glosses on this form of cognition—as simultaneously analytic and synthetic and as having a circular structure—through contrasting it with his account of discursive cognition. As a consequence, I argue that we must give up on attempts to understand ‘the dialectical method’ and ‘speculative cognition’ on the model of discursive cognition. (shrink)

This thesis aims to throw an illuminating light on the as yet neglected concept of nothing in Kant’s system, a concept which is taken into consideration, by Kant, in accordance with the guiding thread of the categories of the understanding. My main argument is that Kant has a fourfold division of nothing and each has a transcendental function in his system. This function is basically a limiting one; setting up negative determinations without which Kant’s system would have never been constituted (...) as it is now. It is shown in the thesis that the concept of nothing is divided basically into four: first, nothing as ens rationis that limits and thereby protects knowledge, secondly nothing as nihil privativum that defines the boundaries of phenomenal reality, thirdly nothing as ens imaginarium that makes possible the unity of experience and finally, nothing as nihil negativum that draws the lines of logical thinking. All make, in the last resort and by being the concepts of the opposite, experience possible. The thesis consists of four chapters. The first chapter is an exposition of all four divisions of nothing, the second is the display specifically of the concepts of ens rationis and nihil negativum, and the third is of the concepts of ens imaginarium and nihil privativum. The auxiliary argument of the thesis is that while Hegel makes a strong charge of externality against and thereby severely criticizes the Kantian concept of the thing-in-itself, - the concept of which I propose to be contained under the concept of ens rationis- Kant has equally convincing arguments against such a charge. This is the topic of the fourth and final chapter which has an implicit aim of creating the image of a powerful critical Hegel but on the other hand an equally enduring and war-like Kant. Kant is presented as a philosopher who has powerful responses to institute a balance between himself and his opponent. When Kant’s differing concepts of nothing are taken into account, Hegel’s attack of externality, it is maintained, appears not to have taken into account the full measure of the resources of the Kantian position. Even when it is said that the attack is against one specific concept of the thing-in-itself alone, Kant still seems to have enough resources for toleration and defence indeed. (shrink)

In the chapter of the Critique of Pure Reason entitled ‘The Discipline of Pure Reason in Dogmatic Use’, Kant contrasts mathematical and philosophical knowledge in order to show that pure reason does not (and, indeed, cannot) pursue philosophical truth according to the same method that it uses to pursue and attain the apodictically certain truths of mathematics. In the process of this comparison, Kant gives the most explicit statement of his critical philosophy of mathematics; accordingly, scholars have typically focused their (...) interpretations and criticisms of Kant’s conception of mathematics on this small section of the Critique. (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)

We argue that a conflict between two conceptions of “quantity of matter” employed in a corollary to proposition 6 of Book III of the Principia illustrates a deeper conflict between Newton’s view of the nature of extended bodies and the concept of mass appropriate for the theoretical framework of the Principia. We trace Newton’s failure to recognize the conflict to the fact that he allowed for the justification of natural philosophical claims by two types of a posteriori, empiricist methodologies. Newton's (...) thoughts on these methodologies demonstrate that his natural philosophy continued to develop after the publication of the first edition of Principia and that De Grav should be understood as an early, and not necessarily representative, text. (shrink)

I advance a novel interpretation of Kant's argument that our original representation of space must be intuitive, according to which the intuitive status of spatial representation is secured by its infinitary structure. I defend a conception of intuitive representation as what must be given to the mind in order to be thought at all. Discursive representation, as modelled on the specific division of a highest genus into species, cannot account for infinite complexity. Because we represent space as infinitely complex, the (...) spatial manifold cannot be generated discursively and must therefore be given to the mind, i.e. represented in intuition. (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)

In my dissertation, I present Hermann Cohen's foundation for the history and philosophy of science. My investigation begins with Cohen's formulation of a neo-Kantian epistemology. I analyze Cohen's early work, especially his contributions to 19th century debates about the theory of knowledge. I conclude by examining Cohen's mature theory of science in two works, The Principle of the Infinitesimal Method and its History of 1883, and Cohen's extensive 1914 Introduction to Friedrich Lange's History of Materialism. In the former, Cohen gives (...) an historical and philosophical analysis of the foundations of the infinitesimal method in mathematics. In the latter, Cohen presents a detailed account of Heinrich Hertz's Principles of Mechanics of 1894. Hertz considers a series of possible foundations for mechanics, in the interest of finding a secure conceptual basis for mechanical theories. Cohen argues that Hertz's analysis can be completed, and his goal achieved, by means of a philosophical examination of the role of mathematical principles and fundamental concepts in scientific theories. (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)

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)

Continental philosophies of science tend to exemplify holistic themes connecting order and contingency, questions and answers, writers and readers, speakers and hearers. Such philosophies of science also tend to feature a fundamental emphasis on the historical and cultural situatedness of discourse as significant; relevance of mutual attunement of speaker and hearer; necessity of pre-linguistic cognition based in human engagement with a common socio-cultural historical world; role of narrative and metaphor as explanatory; sustained emphasis on understanding questioning; truth seen as horizonal, (...) aletheic, or perspectival; and a tolerance for paradoxical and complex forms of expression. Continental philosophy of science is thus more comprehensive than philosophy of science in the analytic tradition, including (and as analytic philosophy of science does not tend to include) perspectives on the history of science as well as the social and practical dimensions of scientific discovery. Where analytic philosophy is about reducing or, indeed, eliminating the perennial problems of philosophy, Continental philosophy is all about thinking and that will mean, as both Heidegger and Nietzsche emphasize, making such problems more not less problematic. (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)

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)

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)

The aggregate EIRP of an N-element antenna array is proportional to N 2. This observation illustrates an effective approach for providing deep space networks with very powerful uplinks. The increased aggregate EIRP can be employed in a number of ways, including improved emergency communications, reaching farther into deep space, increased uplink data rates, and the flexibility of simultaneously providing more than one uplink beam with the array. Furthermore, potential for cost savings also exists since the array can be formed using (...) small apertures. (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.

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.

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)

Hegel seeks to overturn Kant's conclusion that our knowledge is restricted, or that we cannot have knowledge of things as they are in themselves. Understanding this Hegelian ambition requires distinguishing two Kantian characterizations of our epistemic limits: First, we can have knowledge only within the "bounds of experience". Second, we cannot have knowledge of objects that would be accessible only to a divine intellectual intuition, even though the faculty of reason requires us to conceive of such objects. Hegel aims to (...) drive a wedge between these two characterizations, showing that we can have knowledge beyond Kant's bounds of experience, yet without need of divine intuition. And attention to such knowledge is supposed to show that we have no legitimate need to even conceive of divine intuition and its objects - and no need to conclude that our own knowledge is restricted by comparison, or that we cannot know things as they are in themselves. I focus here on the initial case Hegel uses to introduce this extended argument strategy: we can have more knowledge of natural kinds and laws than would be allowed by Kant's bounds of experience. (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)

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)

According to Minkoswki, Einstein's special theory of relativity reveals that ‘space by itself, and time by itself are doomed to fade away into mere shadows’. But perceptual experience represents objects as instantiating shapes like squareness — properties of ‘space by itself’. Thus, STR seems to threaten the veridicality of shape experience. In response to this worry, some have argued that we should analyze the contents of our spatial experiences on the model of traditional secondary qualities. On this picture—defended in recent (...) work by Chalmers —an experience of squareness just represents whatever property usually causes such experiences. This view salvages the veridicality of shape experience, but leaves the nature of the properties we perceive outside our ken. I argue that such a move is unwarranted: STR is compatible with the idea that shape experience acquaints us with the spatial character of our world. In defending this claim, I propose a view on which shape experience presents familiar Euclidean spatial properties veridically, while implicitly representing those properties as instantiated in a particular manner — namely, relative to our own frame of reference. (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)

In theCritique of Pure Reason,Kant argues for two principles that concern magnitudes. The first is the principle that ‘All intuitions are extensive magnitudes,’ which appears in the Axioms of Intuition (B202); the second is the principle that ‘In all appearances the real, which is an object of sensation, has an intensive magnitude, that is, a degree,’ which appears in the Anticipations of Perception (B207). A circle drawn in geometry and the space occupied by an object such as a book are (...) paradigm examples of extensive magnitudes, while the intensity of a light is a paradigm example of an intensive magnitude. These principles justify and explain the possibility of applying mathematics to objects of experience. The Axioms principle also explains the possibility of any mathematical cognition at all. (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.

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)

There has been considerable recent debate about whether Kant's account of intuitions implies that their content is conceptual. This debate, however, has failed to make significant progress because of the absence of discussion, let alone consensus, as to the meaning of ‘content’ in this context. Here I try to move things forward by focusing on the kind of content associated with Frege's notion of ‘sense ’, understood as a mode of presentation of some object or property. I argue, first, that (...) Kant takes intuitions to have a content in this sense, and, secondly, that Kant clearly takes the content of intuitions, so understood, to be distinct in kind from that possessed by concepts. I then show how my account can respond to the most serious objections to previous non-conceptualist interpretations.Send article to KindleTo send this article to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle. Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply. Find out more about the Kindle Personal Document Service.The Non-Conceptuality of the Content of Intuitions: A New ApproachVolume 18, Issue 1Clinton Tolley DOI: https://doi.org/10.1017/S1369415412000313Your Kindle email address Please provide your Kindle [email protected]@kindle.com Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Dropbox To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Dropbox. The Non-Conceptuality of the Content of Intuitions: A New ApproachVolume 18, Issue 1Clinton Tolley DOI: https://doi.org/10.1017/S1369415412000313Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Google Drive To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Google Drive. The Non-Conceptuality of the Content of Intuitions: A New ApproachVolume 18, Issue 1Clinton Tolley DOI: https://doi.org/10.1017/S1369415412000313Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Export citation. (shrink)

As far as the law of preservation of matter and the existence of ether are concerned, Kant, Lomonossow and Lavoisier had very similar views. Nevertheless, according to historical evidence they worked out their theories never taking each other's results for granted. Whereas it is well known that Lavoisier did not base his experiments on the former ones by Lomonossow, it has been argued that Kant based his philosophy of nature on Lavoisier's experiments. I try to show here, that Kant had (...) his philosophy of nature done, prior to Lavoisier's Elements of Chemistry. Further that the only one to have been able to influence Kant was not Lavoisier but Lomonossow. But Kant never mentioned Lomonossow. There is strong evidence that the similarity of views in Kant, Lomonossow and Lavoisier is not due to any kind of interaction between them. This also holds of the mistakes, which Kant and Lomonossow made. The only substantial difference is that Kant thought, that some laws of nature may be logically inferred without experiments. (shrink)

This paper will argue that the puzzles about instantaneous velocity, and rates of change more generally, are the result of a failure to recognize an ambiguity in the concept of an instant, and therefore of an instantaneous state. We will conclude that there are two distinct conceptions of a temporal instant: (i) instants conceived as fundamentally distinct zero-duration temporal atoms and (ii) instants conceived as the boundary of, or between,temporally extended durations. Since the concept of classical instantaneous velocity is well- (...) defined only on the second conception of instants, we will conclude that this distinction allows us to avoid the above dilemma. If instantaneous velocity is well-defined then the states of a system at various instants are not logically distinct and thus we cannot generate Zeno’s paradox. However, if we assume that the instants are metaphysically distinct, then instantaneous velocity is not well-defined and thus the second horn of the dilemma about the causal-explanatory role of instantaneous velocity cannot be generated. (shrink)

The 13th International Kant Congress was held on August 6-9, 2019 in Oslo, Norway. The main tasks of this review are to analyse the central theme of the Congress, “The Court of Reason”, the related spheres of philosophical inquiry such as metaphilosophy and philosophical methodology, as well as to reveal the main approaches and development trends of transcendental philosophy in “theoretical” and “practical” fields and modern Kant studies, notably transcendental philosophy of language and consciousness. The solution of these tasks will (...) make it possible to raise the question of the prospects of Kantian transcendentalism in relation to the pressing problems of our time and to chart the paths of such development. (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)

This paper argues that the famous passage that compares Kant’s efforts to reform metaphysics with his transcendental idealism to the earlier Copernican revolution in astronomy has a more systematic significance than many recognize. By examining the totality of Kant’s references to Copernicus, one can see that Kant’s analogy points to more than just a similar reversal of perspective. By situating Kant’s comments about Copernicus in relation to his understanding of the logic implicit in the great revolutions in mathematics and natural (...) science, this paper argues that Kant’s appeal to the Copernican revolution in astronomy as a forebear to his own transcendental project indicates that his attempt to revolutionize metaphysics by setting it on the secure path of the sciences demands a shift in how we think of the proper object of metaphysics. (shrink)

In the following paper, the author will try to test the meaning of the transcendental approach in respect of the inner changes implied by the idea of quantum gravity. He will firstly describe the basic methodological Kant’s aim, viz. the grounding of a meta-science of physics as the a priori corpus of physical knowledge. After that, he will take into account the problematic physical and philosophical relationship between the theory of relativity and the quantum mechanics; in showing how the elementary (...) ontological and epistemological assumptions of experience result to be changed within them, he will also show the further modifications occurred in the development of the loop quantum gravity. He will particularly focus on the tough problem of the relationship space-matter, in order to settle the decisive question about the possibility of keeping a transcendental approach in the light of quantum gravity. He will positively answer by recalling Cassirer’s theory of the invariants of experience, although he will also add some problematic issues arising from the new physical context. (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 essay examines Friedman's recent approach to the analysis of physical theories. Friedman argues against Quine that the identification of certain principles as ‘constitutive’ is essential to a satisfactory methodological analysis of physics. I explicate Friedman's characterization of a constitutive principle, and I evaluate his account of the constitutive principles that Newtonian and Einsteinian gravitation presuppose for their formulation. I argue that something close to Friedman's thesis is defensible.

This dissertation investigates the origin, intellectual development and use of a semantic variant of the idea of logical space found implicitly in Kant and explicitly in early Wittgenstein and van Fraassen. It elucidates the idea of logical space as the idea of images or pictures representative of reality organized into a logico-mathematical structure circumscribing a form of all possible worlds. Its main claim is that application of these images or pictures to reality is through a certain conception of self. The (...) first chapter presents a novel interpretation of Kant’s semantic theory of schemata in the Critique of Pure Reason, showing that a structure of the imagination induced by the transcendental self informs an implicit idea of logical space. The second chapter offers an intellectual history of the idea through developments in the organization of images introduced by Helmholtz and Hertz. The third chapter reveals early Wittgenstein’s idea of logical space to be his notion of the self, demonstrating how this serves to unify propositions of the Tractatus Logico-Philosophicus concerning solipsism, realism, ethics, aesthetics and mysticism with those pertaining to the picture theory of meaning. The fourth chapter provides a historical overview of the development of van Fraassen’s empiricism in relation to his adaptation of logical space, and evaluates his recent proposal in Scientific Representation: Paradoxes of Perspective that the problem of coordination in the semantic view of theories is dissolved through self-location in logical space. After identifying a number of problems this proposal creates for his empiricism, a brief suggestion is made about how van Fraassen might improve upon his conception of logical space, and how an empiricist view of scientific representation might be understood as a result. (shrink)

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)