We shall address from a conceptual perspective the duality between algebra and geometry in the framework of the refoundation of algebraic geometry associated to Grothendieck’s theory of schemes. To do so, we shall revisit scheme theory from the standpoint provided by the problem of recovering a mathematical structure A from its representations \ into other similar structures B. This vantage point will allow us to analyze the relationship between the algebra-geometry duality and the structure-semiotics duality. Whereas in classical algebraic geometry (...) a certain kind of rings can be recovered by considering their representations with respect to a unique codomain B, Grothendieck’s theory of schemes permits to reconstruct general rings by considering representations with respect to a category of codomains. The strategy to reconstruct the object from its representations remains the same in both frameworks: the elements of the ring A can be realized—by means of what we shall generally call Gelfand transform—as quantities on a topological space that parameterizes the relevant representations of A. As we shall argue, important dualities in different areas of mathematics can be understood as particular cases of this general pattern. In the wake of Majid’s analysis of the Pontryagin duality, we shall propose a Kantian-oriented interpretation of this pattern. We shall use this conceptual framework to argue that Grothendieck’s notion of functor of points can be understood as a “relativization of the a priori” that generalizes the relativization already conveyed by the notion of domain extension to more general variations of the corresponding domains. (shrink)

We shall examine some conceptual tensions in Hick’s ‘pluralism’ in the light of S. Radhakrishnan’s reformulation of classical Advaita. Hick himself often quoted Radhakrishnan’s translations from the Hindu scriptures in support of his own claims about divine ineffability, transformative experience and religious pluralism. However, while Hick developed these themes partly through an adaptation of Kantian epistemology, Radhakrishnan derived them ultimately from Śaṁkara, and these two distinctive points of origin lead to somewhat different types of reconstruction of the diversity of world (...) religions. Our argument will highlight the point that Radhakrishnan is not a ‘pluralist’ in terms of Hick’s understanding of the Real. The Advaitin ultimate, while it too like Hick’s Real cannot be encapsulated by human categories, is, however, not strongly ineffable, because some substantive descriptions, according to the Advaitic tradition, are more accurate than others. Our comparative analysis will reveal that they differ because they are located in two somewhat divergent metaphysical schemes. In turn, we will be able to revisit, through this dialogue between Hick and Radhakrishnan, the intensely vexed question of whether Hick’s version of pluralism is in fact a form of covert exclusivism. (shrink)

This paper argues that there is an important respect in which Rae Langton's recent interpretation of Kant is correct: Kant's claim that we cannot know things in themselves should be understood as the claim that we cannot know the intrinsic nature of things. However, I dispute Langton's account of intrinsic properties, and therefore her version of what this claim amounts to. Langton's distinction between intrinsic, causally inert properties and causal powers is problematic, both as an interpretation of Kant, and as (...) an independent metaphysical position. I propose a different reading of the claim that we cannot know things intrinsically. I distinguish between two ways of knowing things: in terms of their effects on other things, and as they are apart from these. I argue that knowing things' powers is knowing things in terms of effects on other things, and therefore is not knowing them as they are in themselves, and that there are textual grounds for attributing this position to Kant. (shrink)

This paper argues that there is an important respect in which Rae Langton's recent interpretation of Kant is correct: Kant's claim that we cannot know things in themselves should be understood as the claim that we cannot know the intrinsic nature of things. However, I dispute Langton's account of intrinsic properties, and therefore her version of what this claim amounts to. Langton's distinction between intrinsic, causally inert properties and causal powers is problematic, both as an interpretation of Kant, and as (...) an independent metaphysical position. I propose a different reading of the claim that we cannot know things intrinsically. I distinguish between two ways of knowing things: in terms of their effects on other things, and as they are apart from these. 1 argue that knowing things' powers is knowing things in terms of effects on other things, and therefore is not knowing them as they are in themselves, and that there are textual grounds for attributing this position to Kant. (shrink)

The paper is an interpretation and defense of Kant's conception of things in themselves as noumena, along the following lines. Noumena are transempirical realities. As such they have several important roles in Kant's critical philosophy (Section 1). Our theoretical faculties cannot obtain enough content for a conception of noumena that would assure their real possibility as objects, but can establish their merely formal logical possibility (Sections 2-3). Our practical reason, however, grounds belief in the real possibility of some noumena, and (...) even knowledge of the noumenal reality of a free will (Section 4). Section 5 defends Kant's conception of noumena as a good piece of philosophy, particularly with respect to its distinction between logical and real possibility. Are noumena numerically identical with experienced (phenomenal) objects? Kantian principles yield the answers that human selves are, God isn't, and it's harder to say about bodies (Section 6). (shrink)

This article offers the first systematic investigation of the linguistic forms in which Kant expresses his transcendental idealism since Gerold Prauss’ seminal book Kant und das Problem der Dinge an sich. It is argued that Prauss’ own argument for the claim that ‘in itself’ is an adverbial expression that standardly modifies verbs of philosophical reflection is flawed and that there is hence very poor exegetical evidence for so-called ‘methodological two-aspect’ interpretations of Kant’s transcendental idealism. A comprehensive investigation of Kant’s adverbial (...) uses of ‘in itself’ rather reveals that there are various groups of verbs that ‘in itself’ modifies, which can more or less all be reduced to a standard use in which ‘in itself’ modifies verbs of predicative being such as the copula. It is also discussed how these findings can be accommodated by the two main alternative kinds of interpretations, that is, two-object and ontological two-aspect interpretations. (shrink)

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

In the first part of this chapter, I summarise some of the issues in the philosophy of mind which are addressed in Kant’s Critical writings. In the second part, I chart some of the ways in which that discussion influenced twentieth-century analytic philosophy of mind and identify some of the themes which characterise Kantian approaches in the philosophy of mind.

It has long been disputed whether Kant's transcendental idealism requires two worlds ? one of appearances and one of things in themselves ? or only one. The one-world view must be wrong if it claims that individual spatio-temporal things can be identified with particular things in themselves, and if it fails to take seriously the doctrine of double affection; versions that insist on one world, without making claims about the identity of individual things, cannot say in what way the world (...) as we know it and the world of things in themselves can be ?the same?. The two-world view must be wrong if it denies Kant's empirical realism, or offers a phenomenalist interpretation of it. On moral grounds Kant ?identifies? each human person with a particular thing in itself, but the relationship here cannot be strict identity; instead its closeness may warrant regarding the two distinct entities as part of a composite whole. Perhaps up to the first edition of the Critique, Kant thought that empirical knowledge required a particular kind of close correspondence between appearances and things in themselves, one that would make it appropriate to speak of composite wholes here also. By the time of the second edition, he saw that there could be no good grounds for thinking that. In this respect something a bit like the one-world theory might make more sense for the first edition than for the second; but in both cases there is room to speak of two worlds as well. Talk of the number of worlds is metaphorical, and both metaphors have their dangers. (shrink)

According to the ‘One Object’ reading of Kant's transcendental idealism, the distinction between the appearance and the thing in itself is not a distinction between two objects, but between two ways of considering one and the same object. On the ‘Metaphysical’ version of the One Object reading, it is a distinction between two kinds of properties possessed by one and the same object. Consequently, the Metaphysical One Object view holds that a given appearance, an empirical object, is numerically identical to (...) the thing in itself that appears as that object. I raise various indiscernibility arguments against that view; because an appearance has different spatiotemporal and modal properties than a thing in itself, no appearance can be identical to a thing in itself. I point out that these arguments are similar to arguments against Monism, the view that material objects are numerically identical to the matter of which they are made. I outline some strategies Monists have developed to respond to these indiscernibility arguments and then develop parallel responses on behalf of the Metaphysical One Object view. However, I then raise another indiscernibility argument, to which, I argue, the Metaphysical One Object view cannot respond, even using the resources I have developed thus far. I develop a modified version of the Metaphysical One Object view that can respond to this new indiscernibility argument, but, I argue, this modified version of the One Object view is only a terminological variant of the Two Object view. When the Metaphysical One Object view is fully thought through it becomes the Two Object view. I conclude that Kantian appearances are not numerically identical to the things in themselves that appear to us. (shrink)

According to the ‘One Object’ reading of Kant's transcendental idealism, the distinction between the appearance and the thing in itself is not a distinction between two objects, but between two ways of considering one and the same object. On the ‘Metaphysical’ version of the One Object reading, it is a distinction between two kinds of properties possessed by one and the same object. Consequently, the Metaphysical One Object view holds that a given appearance, an empirical object, is numerically identical to (...) the thing in itself that appears as that object. I raise various indiscernibility arguments against that view; because an appearance has different spatiotemporal and modal properties than a thing in itself, no appearance can be identical to a thing in itself. I point out that these arguments are similar to arguments against Monism, the view that material objects are numerically identical to the matter of which they are made. I outline some strategies Monists have developed to respond to these indiscernibility arguments and then develop parallel responses on behalf of the Metaphysical One Object view. However, I then raise another indiscernibility argument, to which, I argue, the Metaphysical One Object view cannot respond, even using the resources I have developed thus far. I develop a modified version of the Metaphysical One Object view that can respond to this new indiscernibility argument, but, I argue, this modified version of the One Object view is only a terminological variant of the Two Object view. When the Metaphysical One Object view is fully thought through it becomes the Two Object view. I conclude that Kantian appearances are not numerically identical to the things in themselves that appear to us. (shrink)

European Journal of Philosophy, EarlyView.

Kant's distinction between things in themselves and things as they appear, or appearances, is commonly attacked on the ground that it delivers a radical and incoherent ‘two world’ picture of what there is. I attempt to deflect this attack by questioning these terms of dismissal. Distinctions of the kind Kant draws on are in fact legion, and they make perfectly good sense. The way to make sense of them, however, is not by buying into a profligate ontology but by using (...) some rather different tools – surprisingly enough, tools first developed in the area of aesthetics. Once this is done, much of what Kant says begins to look perfectly coherent. In the final part of the paper, I point out that none the less all is not well. Kant's Critical doctrines make it hard for us to accept Kant's own version of this otherwise coherent distinction. (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)

This article argues that many (often Anglophone) interpreters of the Deduction have mistakenly identified Kant's aim as vindicating ordinary knowledge of objects and as refuting Hume's (alleged) skepticism about such knowledge. Instead, the article contends that Kant's aims were primarily negative. His primary mission (in the Deduction) was not to justify application of the categories to experience, but to show that any use beyond the domain of experience could not be justified. To do this, he needed to show that their (...) proper use in attaining metaphysical knowledge was restricted to (actual and possible) experience. The central theoretical claims of previous metaphysics were thus rendered void. Kant was not out to save ordinary knowledge from the skeptic, at least not originally, since he did not think such knowledge was in danger. Rather, he wanted to sustain the skeptical claim that we cannot justify metaphysical claims about things in themselves, hence that we cannot gain metaphysical knowledge about the existence of God, the immortality of the soul, the beginning of time, and the least parts of matter. He wanted to achieve this result in a more theoretically satisfying manner than had skeptical authors. Doing so would also allow him to curb certain forms of skeptical empiricism, by showing that we cannot disprove, or rule out as unintelligible, human freedom, an afterlife, or divine providence. The article ends by considering the retrospective rereadings of the Deduction by Hermann Cohen and P. F. Strawson, concluding that these rereadings force Kant's text into an alien mold, thereby diminishing its philosophical value as a work with its own distinctive aims and methods. (shrink)

The present work proposes to examine the problem of the empirical thing in itself and the objective sensation as an access route to the concrete content of empirical reality in Kant’s transcendental philosophy. The main notion of ‘empirical thing in itself’, offered by Gerold Prauss’ interpretation, provides a key to understand and solve central problems of transcendental philosophy. Nevertheless Prauss’s position still exhibits certain imperfections that might lead any lecture of Kant towards a phenomenalist understanding. In order to avoid this (...) misleading, it will be intended to complement Prauss’s interpretation, analyzing the objectivity of sensation, trying within to restore the objectivity of appearance. Finally, it will be possible to make an evaluation about advantages and limits of Prauss’s hermeneutical reconstruction of this problematic. (shrink)

I begin by considering a question that has driven much scholarship on transcendental idealism: are appearances numerically identical to the things in themselves that appear, or numerically distinct? I point out that much of the debate on this question has assumed that this is equivalent to the question of whether they are the same objects, but go on to provide textual, historical, and philosophical evidence that “object” (Gegenstand) and “thing” (Ding) have different meanings for Kant. A thing is a locus (...) of intensively gradable causal force, reality. I argue that appearances and things in themselves are not identical as objects, because the very concept of object-identity is tied, for Kant, to the concept of an intellect that would cognize the numerical identity of the objects in question. Because no intellect can be both discursive and intellectual, no intellect could cognize the numerical identity of objects across the phenomenal/noumenal divide, and thus the claim that they are identical has no content. However, the very same things, the same reality, can be given to our sensible intellects, and to divine intuitive intellect, as two non-overlapping domains of objects. Identity readers are thus shown to be right about the same thing relation, while non-identity readers are vindicated on the numerical identity of objects. (shrink)

This thesis argues that Kant is able to maintain the distinctiveness of his position in opposition to Hume's naturalism (contrary to the arguments of R. A. Mall and L. W. Beck) without invoking premises which are question begging with regard to Hume's scepticism. The argument of Kant's Transcendental Deduction of the Categories, as presented in the second edition of the Critique of Pure Reason, is considered in relation to the two sets of criticism that have been levelled at it from (...) its publication up to the present day, both of which aim to demonstrate that synthetic a priori judgements are subjectively necessary but without objective validity. The first set of criticisms involves problems raised with regard to the status of transcendental arguments. The difficulties identified here (by B. Stroud, M. S. Gram, and others) are that the Deduction can either, at best, show that it is necessary for experience to be regarded in a certain way without demonstrating anything as to the nature of experience as such, or the argument is circular in that it begins by making assumptions regarding the nature of our experience. Alternatively, if the Deduction is taken to establish the objective nature of concepts via an analysis of the conditions under which it is possible for us to have some knowledge of ourselves, then incoherence is said to arise because this requires either an implausible reflective theory of consciousness (according to D. Henrich) or that we have knowledge of the subject-in-itself (as held by J. G. Fichte and other contemporaries of Kant). Through a consideration of both the historical and contemporary manifestations of these criticisms, the thesis advances an interpretation of the Deduction, with special attention paid to the role and nature of the subject, which does not fall prey to the alleged incoherence. As such, the thesis defends both the distinctiveness and legitimacy of transcendental philosophy. (shrink)