In 1675, Burchard de Volder (1643–1709) was the first professor to introduce the demonstration of experiment into a university physics course and built the Leiden Physics Theatre to accommodate this new pedagogy. When he requested the funds from the university to build the facility, he claimed that the performance of experiments would demonstrate the “truth and certainty” of the postulates of theoretical physics. Such a claim is interesting given de Volder’s lifelong commitment to Cartesian scientia. This chapter will examine de (...) Volder’s views on experiment and show that they are not Newtonian or inductivist, as is sometimes claimed. While de Volder thinks we need deductive reasoning from first principles to provide evidence of the certainty of the content of our physical theories, he also contends that we need experiment to provide evidence of the certainty of the existence of the particular bodies those theories discuss. This approach to experiment is based on a distinction between rational certainty and the certainty of material bodies in the actual world. While this account is deeply influenced by Descartes, it is importantly different than Descartes’ distinction between absolute and moral certainty. De Volder’s “Cartesian Empiricism” is best understood as a continuation and further development of a long tradition of teaching through observation at Leiden. (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)

Kant held that under the concept of √2 falls a geometrical magnitude, but not a number. In particular, he explicitly distinguished this root from potentially infinite converging sequences of rationals. Like Kant, Brouwer based his foundations of mathematics on the a priori intuition of time, but unlike Kant, Brouwer did identify this root with a potentially infinite sequence. In this paper I discuss the systematical reasons why in Kant's philosophy this identification is impossible.

What I will call “the deviant logician objection” [DLO] is one line of attack against the common and compelling tenet that our justification for logical truths is grounded in our understanding of their constituent concepts. This objection seeks to undermine the possibility of any deep constitutive connection, in the epistemology of logic, between understanding and justification. I will consider varieties of the deviant logician objection developed by Horwich and by Williamson. My thesis is that while the deviant logician objection falls (...) short of proving that this traditional tenet must be rejected, nonetheless it serves to bolster some important refinements. (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)

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

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)

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)

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)

Idealist Heresies in Philosophy of Science: Cassirer, Carnap, and Kuhn. As common wisdom has it, philosophy of science in the analytic tradition and idealist philosophy are incompatible. Usually, not much effort is spent for explaining what is to be understood by idealism. Rather, it is taken for granted that idealism is an obsolete and unscientific philosophical account. In this paper it is argued that this thesis needs some qualification. Taking Carnap and Kuhn as paradigmatic examples of positivist and postpositivist philosophies (...) of science it is shown that these accounts share important features with Cassirer's idealist philosophy of science developed in the first half of this century. As it turns out, often Cassirer is more modern than those classical philosophers of (post)posivitist philosophy of science. For instance, Quine's criticism against Carnap's empiricist philosophy of science launched in Two Dogmas of Empiricism is anticipated by Cassirer for several decades. (shrink)

The ‘triumph of the anti-phlogistians’ is a familiar story to the historians and philosophers of science who characterize the Chemical Revolution as a broad conceptual shift. The apparent “incommensurability” of the paradigms across the revolutionary divide has caused much anxiety. Chemists could identify phlogiston and oxygen, however, only with different sets of instrumental practices, theoretical schemes, and philosophical commitments. In addition, the substantive counterpart to phlogiston in the new chemistry was not oxygen, but caloric. By focusing on the changing visions (...) of chemical body across the revolutionary divide with a more sensitive probe into the historical actors’ material manipulations and linguistic usage, we can historicize their laboratory realities and philosophical agenda. An archeology of chemical bodies that configures the fragile stability of the material worlds chemists created in succession promises a philosophical horizon that would recognize our hybrid (natural–artificial) environment as an evolving investigative object of science. (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)

This essay aims to sharpen debates on the pros and cons of historical epistemology, which is now understood as a novel approach to the study of knowledge, by comparing it with the history of epistemology as traditionally pursued by philosophers. The many versions of both approaches are not always easily discernable. Yet, a reasoned comparison of certain versions can and should be made. In the first section of this article, I argue that the most interesting difference involves neither the subject (...) matter nor goal, but the methods used by the two approaches. In the second section, I ask which of the two approaches or methods is more promising given that both historical epistemologists and historians of epistemology claim to contribute to epistemology simpliciter . Using traditional problems concerning the epistemic role of perception, I argue that the historical epistemologies of Wartofsky and Daston and Galison fail to show that studying practices of perception is philosophically significant. Standard methods from the history of epistemology are more promising, as I show by means of reconstructing arguments in a debate about the relation between perception and judgment in psychological research on the famous moon illusion. (shrink)

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

Ernst Mayr argued that the emergence of biology as a special science in the early nineteenth century was possible due to the demise of the mathematical model of science and its insistence on demonstrative knowledge. More recently, John Zammito has claimed that the rise of biology as a special science was due to a distinctive experimental, anti-metaphysical, anti-mathematical, and anti-rationalist strand of thought coming from outside of Germany. In this paper we argue that this narrative neglects the important role played (...) by the mathematical and axiomatic model of science in the emergence of biology as a special science. We show that several major actors involved in the emergence of biology as a science in Germany were working with an axiomatic conception of science that goes back at least to Aristotle and was popular in mid-eighteenth-century German academic circles due to its endorsement by Christian Wolff. More specifically, we show that at least two major contributors to the emergence of biology in Germany—Caspar Friedrich Wolff and Gottfried Reinhold Treviranus—sought to provide a conception of the new science of life that satisfies the criteria of a traditional axiomatic ideal of science. Both C.F. Wolff and Treviranus took over strong commitments to the axiomatic model of science from major philosophers of their time, Christian Wolff and Friedrich Wilhelm Joseph Schelling, respectively. The ideal of biology as an axiomatic science with specific biological fundamental concepts and principles thus played a role in the emergence of biology as a special science. (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)

J. H. Lambert proved important results of what we now think of as non-Euclidean geometries, and gave examples of surfaces satisfying their theorems. I use his philosophical views to explain why he did not think the certainty of Euclidean geometry was threatened by the development of what we regard as alternatives to it. Lambert holds that theories other than Euclid's fall prey to skeptical doubt. So despite their satisfiability, for him these theories are not equal to Euclid's in justification. Contrary (...) to recent interpretations, then, Lambert does not conceive of mathematical justification as semantic. According to Lambert, Euclid overcomes doubt by means of postulates. Euclid's theory thus owes its justification not to the existence of the surfaces that satisfy it, but to the postulates according to which these "models" are constructed. To understand Lambert's view of postulates and the doubt they answer, I examine his criticism of Christian Wolff's views. I argue that Lambert's view reflects insight into traditional mathematical practice and has value as a foil for contemporary, model-theoretic, views of justification. (shrink)

Immanuel Kant has built up a dualistic epistemology that seems to fit to the peculiarities of chemistry quite well. Friedrich Paneth used Kant’s concept and characterised simple and basic substances which refer to the empirical and to the transcendental world, respectively. This paper takes account of the Kantian influences in Paneth’s philosophy of chemistry, and discusses pertinent topics, like observables, atomism and realism.

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)

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)

This book brings together philosophers, mathematicians and logicians to penetrate important problems in the philosophy and foundations of mathematics. In philosophy, one has been concerned with the opposition between constructivism and classical mathematics and the different ontological and epistemological views that are reflected in this opposition. The dominant foundational framework for current mathematics is classical logic and set theory with the axiom of choice. This framework is, however, laden with philosophical difficulties. One important alternative foundational programme that is actively pursued (...) today is predicativistic constructivism based on Martin-Löf type theory. Associated philosophical foundations are meaning theories in the tradition of Wittgenstein, Dummett, Prawitz and Martin-Löf. What is the relation between proof-theoretical semantics in the tradition of Gentzen, Prawitz, and Martin-Löf and Wittgensteinian or other accounts of meaning-as-use? What can proof-theoretical analyses tell us about the scope and limits of constructive and predicative mathematics? (shrink)

Collection of papers presented at the 2nd and 3rd Budapest Seminar in Early Modern Philosophy.

In 1792 and 1798 Kant noticed two basic problems with hisMetaphysical Foundations of Natural Science (MAdN) which opened a crucial gap in the Critical system as a whole. Why is theMAdN so important? I show that the Analogies of Experience form an integrated proof of transeunt causality. This is central to Kant's answer to Hume. This proof requires explicating the empirical concept of matter as the moveable in space, it requires the specifically metaphysical principle that every physical event has an (...) external cause, and it requires a metaphysical principle regarding the individuation of spatio-temporal things. These three doctrines are not defended in the firstCritique, but only in theMAdN. Kant's transcendental analysis of the conditions of experience thus requires the special metaphysics of theMAdN. This marks an important shift in Kant's view of the metaphysical basis of the transcendental philosophy. (shrink)

My contribution to a book symposium on Graham’s commentary on Kant’s Critique of Pure Reason, sponsored by the North American and the UK Kant Societies, held in conjunction with the Central Division Meeting of the American Philosophical Association, Chicago, 20 February 2009. Comments also delivered by Adrian Moore, Gary Banham, Jill Buroker and Manfred Kuehn, with relplies by Graham Bird.

This article examines how Quine and Sellars develop informatively contrasting responses to a fundamental tension in Carnap’s semantics ca. 1950. Quine’s philosophy could well be styled ‘Essays in Radical Empiricism’; his assay of radical empiricism is invaluable for what it reveals about the inherent limits of empiricism. Careful examination shows that Quine’s criticism of Carnap’s semantics in ‘Two Dogmas of Empiricism’ fails, that at its core Quine’s semantics is for two key reasons incoherent and that his hallmark Thesis of Extensionalism (...) is untenable. The tension in Carnap’s semantics together with Quine’s exposure of the severe limits of radical empiricism illuminate central features of Sellars’s philosophy: the fully general form of the myth of givenness, together with Sellars’s alternative Kantian characterisation of understanding; the full significance of Carnap’s distinction between conceptual analysis and conceptual explication, and its important methodological implications; the specifically pragmatic character of Sellars’s realism; and Sellars’s methodological reasons for holding that philosophy must be systematic and that systematic philosophy must be deeply historically and textually informed. This paper thus re-examines this recent episode of philosophical history for its philosophical benefits and systematic insights. (shrink)

The paper discusses the Kantian legacy in modern views about scientific theories. The aim of this paper is to show how Einstein's philosophy of science, which was inspired by his physics, offers a specialized version of the Kantian synthesis of Empiricism and Rationalism. In modern physical theories Kant's a priori conditions become “constraints,” as shown in Einstein's use of principle theories. Einstein's use of principle theories shows how constraints are used to steer the mapping of the rational onto the empirical (...) elements of scientific theories. (shrink)

It is often claimed that Kant intended to justify Newton’s most fundamental claims expressed in the Principia, such as his laws of motion and the law of universal gravitation. In this article, I argue that the differences between Newton’s laws of motion and Kant’s laws of mechanics are not superficial or merely apparent. Rather, they reflect fundamental differences in their respective projects. This point can be seen especially clearly by considering the nature of the various projects undertaken in Germany prior (...) to Kant that discuss the laws of motion. Wolff and his followers qua metaphysicians were especially interested in providing nonempirical justifications of their laws of motion as well as an intelligible account of the fundamental properties of bodies in terms of substance, accident, and force. Maupertuis and Euler, despite often being seen as Newtonians, both drew on traditions other than Newton’s. Physics textbooks vary considerably in their aims, but in none of these cases is Newton’s main argument of the Principia presented. In light of the fact that these projects are distinct in significant ways from Newton’s project, the differences between Newton’s laws of motion and Kant’s laws of mechanics are most likely not merely apparent but reflect the fact that Kant, too, was pursuing a project fundamentally distinct from Newton’s. (shrink)

Unity is a central concept in the Critique of Pure Reason, since it is only through the unifying act of our spontaneous faculties that an experience can emerge, according to Kant. However, the faculty of reason brings forth a different unity than that of the understanding: Kant characterizes the former as a collective unity, while the latter as a distributive unity. This article aims to explain the meaning of these terms, with reference to the Nachlass on metaphysics and the writings (...) on right where Kant employs them in a clearer manner. This explanation can provide a basis to understand the difference between the faculty of understanding and the faculty of reason within the first Critique, a difference rather neglected by scholars, who have focused mainly on Kant’s distinction between sensibility and understanding. (shrink)

This paper analyses the actual meaning of a transcendental philosophy of biology, and does so by exploring and actualising the epistemological and metaphysical value of Kant's viewpoint on living systems. It finds inspiration in the Kantian idea of living systems intrinsically resisting objectification, but critically departs from Kant's philosophical solution in as far as it is based in a subjectivist dogmatism. It attempts to overcome this dogmatism, on the one hand by explicitly taking into account the conditions of possibility at (...) the side of the subject, and on the other hand by embedding both the living and the knowing system into an ontology of complexly organized dynamical systems. This paper fits into the transcendental perspective in acknowledging the need to analyse the conditions of knowability, prior to the contents of what is known. But it also contributes to an expansion and an actualisation of the issue of transcendentality itself by considering the conditions of possibility at the side of the object as intrinsically linked to the conditions of possibility at the side of the subject. (shrink)

Defences of Kant's foundations of geometry fall short if they are unable to equally ground Euclidean and non-Euclidean geometries. Thus, Kant's account must be separated from geometrical postulates. I argue that characterizing space as the form of outer intuition must be independent of postulates. Geometrical postulates are then expressions of particular spatializing activities made possible by the a priori intuition of space. While Amit Hagar contends that this is to speak of noumena, I argue that a Kantian account of space (...) as the form of outer attention-directing remains seated in the subject. (shrink)

Michael Friedman’s Dynamics of Reason is a welcome contribution to the ongoing articulation of philosophical perspectives for understanding the sciences in the context of post-positivist philosophy of science. Two perspectives that have gained advocacy since the demise of the “received view” are Quinean naturalism and Kuhnian relativism. In his 1999 Stanford lectures, Friedman articulates and defends a neo-Kantian perspective for philosophy of science that opposes both of these perspectives. His proffered neo-Kantian perspective is presented within the context of the problem (...) of theory change or “scientific revolutions,” and its main feature is a conception of scientific knowledge that requires “relativized constitutive a priori principles.” The lectures make up the first part of the book; the second part of the book, “Fruits of Discussion,” is a further elaboration and defence of the ideas advanced in the lectures. The resulting book serves as a useful sequel to Friedman’s impressive historical studies in Foundations of Space-Time Theories, Kant and the Exact Sciences, and Reconsidering Logical Positivism. In the preface, Friedman tells us that this book represents the philosophical viewpoint that he has arrived at as a result of completing these works. As such, it is not surprising that the prominent themes of the book are ones that have occupied Friedman’s attention in the past, viz., the importance of a priori principles in the exact sciences, the conventionalism of the logical positivists, and, more generally, an articulation of what remains defensible in neo-Kantian philosophy of science. (shrink)

It makes sense to ask from time to time where we are in the philosophical discussion. This article reviews the debate in the twentieth century. Michael Friedman has recently argued that the split between Continental and analytic philosophy is due to the inability, because of war, to carry forward a genuine debate begun by Heidegger and Carnap around the time of Heidegger's public controversy with Cassirer at Davos in 1929. I, however, argue that there was not even the beginning of (...) a genuine debate between Heidegger and Carnap. I argue further that the split between analytic and Continental philosophy originated earlier, in the analytic attack on idealism at the beginning of the century. And finally, I argue that the differences among analytic philosophy, Continental philosophy, and pragmatism, the third main current of twentieth-century philosophy, can be traced to differing reactions to Kant. (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)

This essay investigates the transformation of the faculty of understanding in Kant’s Transition from Metaphysical Foundations of Natural Science to Physics drafts found in Opus postumum. I argue that in fascicles X and XI Kant implicitly reverses the architectonic order of sensibility and understanding. Without an account of this reversal, Kant’s critique of Isaac Newton’s conception of phenomena and the so called Selbstsetzungslehre in fascicle VII fall apart. I argue that what is at stake is a challenge Kant makes to (...) his own presuppositions and a challenge to the Kantian philosopher who wishes to stay with a strictly ‘critical’ Kant. (shrink)

This paper develops some respects in which the philosophy of mathematics can fruitfully be informed by mathematical practice, through examining Frege's Grundlagen in its historical setting. The first sections of the paper are devoted to elaborating some aspects of nineteenth century mathematics which informed Frege's early work. (These events are of considerable philosophical significance even apart from the connection with Frege.) In the middle sections, some minor themes of Grundlagen are developed: the relationship Frege envisions between arithmetic and geometry and (...) the way in which the study of reasoning is to illuminate this. In the final section, it is argued that the sorts of issues Frege attempted to address concerning the character of mathematical reasoning are still in need of a satisfying answer. (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)

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)

Hermann Cohen’s 1871 classic, Kants Theorie der Erfahrung, had a formative influence, not only on the Marburg school’s reading of Kant, but on their entire conception of philosophy. This influence was further magnified by the substantially revised and expanded second edition of 1885 and the yet further expanded third edition of 1918. Neo-Kantianism was the dominant philosophical movement in Germany in the late nineteenth and twentieth centuries, which means that a work, ostensibly, of Kant scholarship had an influence on the (...) development of German philosophy that few works of secondary literature can claim. (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)

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

This paper reconstructs the Peircean interpretation of Kant's doctrine on the syntheticity of mathematics. Peirce correctly locates Kant's distinction in two different sources: Kant's lack of access to polyadic logic and, more interestingly, Kant's insight into the role of ingenious experiments required in theorem-proving. In this second respect, Kant's analytic/synthetic distinction is identical with the distinction Peirce discovered among types of mathematical reasoning. I contrast this Peircean theory with two other prominent views on Kant's syntheticity, i.e. the Russellian and the (...) Beckian views, and show how Peirce's interpretation of Kant solves the dilemma that each of these two views faces. I also show that Hintikka's criterion for Kant's synthetic judgments, i.e. a new individual introduced by the -instantiation rule, does not capture the most important characteristic of Peirce's theorematic reasoning, i.e. the process of choosing a correct individual. (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)