Recent debates in the interpretation of Kant’s theoretical philosophy have focused on the nature of Kantian intuition and, in particular, on the question of whether intuitions depend for their existence on the existence of their objects. In this paper we show how opposing answers to this question determine different accounts of the nature of Kantian cognition and we suggest that progress can be made on determining the nature of intuition by considering the implications different views have for the nature of (...) cognition. (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)

The aim of the Analytic of Concepts is to derive and deduce a set of pure concepts of the understanding, the categories, which play a central role in Kant’s explanation of the possibility of synthetic a priori cognition and judgment. This chapter is structured around two questions. First, what is a pure concept of the understanding? Second, what is involved in a deduction of a pure concept of the understanding? In answering the first, we focus on how the categories differ (...) from the pure forms of sensibility and examine whether they are known only to be the pure forms of human thinking or rather the forms of discursive cognition as such. In answering the second, we draw a distinction between the application and the exemplification of the categories and use it to identify different ways of understanding Kant’s project in the Transcendental Deduction of the Categories. These questions connect because the answer to the first determines how we should understand the kind of entitlement which is to be established in the Deduction. (shrink)

This paper gives an interpretation of Kant's argument for transcendental idealism in the Transcendental Aesthetic. I argue against a common way of reading this argument, which sees Kant as arguing that substantive a priori claims about mind-independent reality would be unintelligible because we cannot explain the source of their justification. I argue that Kant's concern with how synthetic a priori propositions are possible is not a concern with the source of their justification, but with how they can have objects. I (...) argue that Kant's notion of intuition needs to be understood as a kind of representation which involves the presence to consciousness of the object it represents, and that this means that a priori intuition cannot present us with a mind-independent feature of reality. (shrink)

:Space is not an empirical concept that has been drawn from outer experiences. For in order for certain sensations to be related to something outside me , thus in order for me to represent them as outside and next to one another, thus not merely different but as in different places, the representation of space must already be their ground. Thus the representation of space cannot be obtained from the relations of outer appearance through experience, but this outer experience is (...) itself first possible only through this representation. 1Abstract:Der Raum is kein empirischer Begriff, der von äußeren Erfahrungen abgezogen worden. Denn damit gewisse Empfindungen auf etwas außer mir bezogen werden, imgleichen damit ich sie als außer und neben einander, mithin nicht bloß verschieden, sondern als in verschiedenen Orten vorstellen können, dazu muß die Vorstellung des Raumes schon zum Grunde liegen. (shrink)

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

Because of the transcendental emphasis of his critical works, Immanuel Kant has been criticised for not being able to accommodate the notion of multiplicity. This paper outlines a complex argument designed as a means to the rescue of Kant from this repudiation. To this end, the paper proposes a new, strong reading of the doctrine of aesthetic ideas that unveils the idiosyncratic play of the mental powers, constituted of two separate acts, that equips one to intuit an unnameable mark that (...) evades both empirical apprehension and logical comprehension. By analogy with the two types of cognition, stipulated in the Stufenleiter (and elsewhere), I shall suggest that the two distinct kinds of a feeling of pleasure, stirred up by the generation of an aesthetic idea, add an overlooked, aesthetic element that renders Kant a philosopher of multiplicity. (shrink)

This review of contemporary discussions of Kantian philosophy of mathematics is timed for the publication of the essay Kant’s Philosophy of Mathematics. Volume 1: The Critical Philosophy and Its Roots (2020) edited by Carl Posy and Ofra Rechter. The main discussions and comments are based on the texts contained in this collection. I first examine the more general questions which have to do not only with the philosophy of mathematics, but also with related areas of Kant’s philosophy, e. g. the (...) question: What is intuition and singular term? Then I look at more specific questions, e. g.: What is the subject of arithmetic and what is the significance of diagrams in mathematical reasoning? As a result, the reader is presented with a fairly complete overview of modern discussions which can be used as an introduction to the problem field of Kant’s philosophy of mathematics. (shrink)

A Estética Transcendental é uma peça chave no programa de pesquisa que Kant desenvolveu e nomeou de filosofia transcendental. Ela se anuncia na Dissertação de 1770 e se configura de forma bem explícita na primeira edição da Crítica da razão pura, de 1781. O modo como Kant a concebeu permitiu-lhe separar radicalmente intelecto e sensibilidade, mas seria importante compreender a raiz dessa separação. Nesse texto procuramos mostrar que o opúsculo “Sobre o primeiro fundamento da distinção de direções no espaço”, de (...) 1768, traz características bastante decisivas para a estética proposta no período crítico. Para evidenciar isso, expusemos ideias marcantes do texto sobre as contrapartidas incongruentes e as cotejamos com as reflexões expostas nos itens 3 e 4 relativos à Exposição Metafísica do conceito de espaço e aquelas apresentadas nos itens 4 e 5 relativos à Exposição Metafísica do conceito de tempo. (shrink)

En un pasaje famoso, Kant dijo que "los pensamientos sin contenido son vacíos, las intuiciones sin conceptos son ciegas", lo cual ha dado lugar -de la mano de filósofos y exégetas clásicos y contemporáneos como McDowell- a la idea de que los estados mentales que Kant denomina intuiciones poseen ya un contenido conceptual. En este artículo se propone una lectura que hace énfasis en la independencia o separabilidad de intuiciones y conceptos, y cómo las primeras constituyen un tipo de cognición (...) que, sin ser conceptual, es suficiente para la individuación de particulares. In a famous passage, Kant said that "the thoughts without content are empties, the intuitions without concepts are blind", which has given place, from the hand of classical and contemporaries philosophers and scholars, like McDowell, to the idea that the mental states which Kant calls intuitions have conceptual content. This article proposes a lecture that makes emphasis on independence or separability between intuitions and concepts, and how the firsts constitutes a kind of cognition that while is non-conceptual, is enough for the individuation of particulars. (shrink)

Kant’s philosophy of mathematics presents two fundamental problems of interpretation: (1) Kant claims that mathematical truths or “judgments” are synthetic a priori; and (2) Kant maintains that intuition is required for generating and/or understanding mathematical statements. Both of these problems arise for us because of developments in mathematics since Kant. In particular, the axiomatization of geometry--Kant’s paradigm of mathematical thinking--has made it seem to some commentators as, for example, Russell, that both (1) and (2) are false (Russell 1919, p. 145).2 (...) If virtually all of mathematics, including geometry, is axiomatizable, it would seem that mathematics results in analytic judgments that are totally independent of sensibility, the source, according to Kant, of intuition. In this paper I will address both of these difficulties. I shall argue that Kant’s understanding of both “synthetic” and “intuition” make his position immune to these criticisms. (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)

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)

Recent work on Kant’s conception of space has largely put to rest the view that Kant is hostile to actual infinity. Far from limiting our cognition to quantities that are finite or merely potentially infinite, Kant characterizes the ground of all spatial representation as an actually infinite magnitude. I advance this reevaluation a step further by arguing that Kant judges some actual infinities to be greater than others: he claims, for instance, that an infinity of miles is strictly smaller than (...) an infinity of earth-diameters. This inequality follows from Kant’s mereological conception of magnitudes (quanta): the part is (analytically) less than the whole, and an infinity of miles is equal to only a part of an infinity of earth-diameters. This inequality does not, however, imply that Kant’s infinities have transfinite and unequal sizes (quantitates). Because Kant’s conception of size (quantitas) is based on the Eudoxian theory of proportions, infinite magnitudes (quanta) cannot be assigned exact sizes. Infinite magnitudes are immeasurable, but some are greater than others. (shrink)

The role of intuition in Kant's theory of mathematics is similar to instantiation rules in first-order logic according to Jaakko Hintikka. This paper is a critical examination of Hintikka's interpretation and reconstruction of Kant's theory. It is argued that Kant's position is question-begging on this interpretation.

Mental representations—like many other things—seem to have parts. However, it isn’t clear how to properly understand the idea of a part of a representation. In this paper I shed new light on how representations can have a mereology. In particular, it has been recognized that there is a mereological element to Kant’s distinction between two kinds of representations: intuitions and concepts. A concept depends upon its parts, whereas an intuition is prior to its parts. The paper thus focuses on an (...) exploration of how to make sense of the parts and wholes of intuitions and concepts. (shrink)

Overview of the (non)conceptualism debate in Kant studies.

Istnieje spór w obrębie filozofii sięgający już starożytności i polemiki Platona z Sofistami, dotyczący ugruntowania metafizyki jako dziedziny autonomicznej, która byłaby zdolna do badania swoistych elementów rzeczywistości, przysługujących tylko i wyłącznie metafizyce. We wstępnych rozważaniach przedstawiamy sposób, w jaki ten spór można rozumieć oraz jak można go rozwiązać. Tezą metafilozoficzną naszych analiz będzie stwierdzenie, że w celu ugruntowania metafizyki musimy wskazać na swoiste doświadczenie, które mogłoby zapewnić bezpośredni dostęp poznawczy do abstrakcyjnego przedmiotu metafizyki. W niniejszych badaniach, rolę tego doświadczenia będzie (...) pełnić intuicja, którą utożsamiamy z poznaniem apriorycznym – ujmowanym jednak nie jako poznanie pojęciowe bądź dedukcyjne – lecz jako poznanie naoczne, które (używając języka fenomenologii) źródłowo (materialnie) prezentuje nam swoistą sferę przedmiotową. By lepiej zrozumieć zjawisko intuitywnego poznania do którego bardzo często filozofowie implicite się odnosili (rzadziej zaś wprost) zrekonstruujemy stanowisko E. Chudnoffa. W trakcie rekonstrukcji skupimy się na najistotniejszych cechach poznania intuitywnego, które będą kluczem zarówno do zrozumienia wielości tradycyjnych już odniesień i niejawnych odwoływań do intuicji, jak i sposobem poprzez który możliwe stanie się ustalenie warunków możliwości ugruntowania metafizyki jako dziedziny autonomicznego badania rzeczywistości. (shrink)

In this dissertation I defend a Kantian notion of the given. I show that something akin to Kant's theory of intuition is necessary to make sense of the normative role perception has in forming perceptual knowledge. ;Perceptual judgments require guidance from the objects they represent. I argue that this normative aspect of perception can be explained only by appeal to a non-conceptual content caused by the object perceived. But isn't this to appeal to the mythical given? I show that it (...) is not by comparing it to the result of Sellars' famous Myth of the Given argument. Contrary to the generally accepted view, what follows from Sellars' argument is not that the given is a myth, but rather that what is immediately present to mind cannot be known. This result leaves an explanatory option which the Sellars' critique does not consider. The given might be a part of knowledge while not itself being independently knowable. ;However, because the possibility of an immediate cognitive content is thought to have been foreclosed by the Sellars argument, much subsequent epistemology has overlooked this alternative. One widespread response has been to embrace coherence theories according to which justification is regarded as a relation between beliefs. These theories regard perception as a thoroughly causal phenomenon and consequently allow no role for perception in the justification of perceptual or other beliefs. ;I argue that in perceptual contexts only perception can decide the case between equally coherent conceptual determinations. But according to the coherentist this kind of justificatory function could not involve perception since perception is a thoroughly causal phenomenon. Against this view, I argue that some notion of the given, one which circumvents Sellars' criticism, is necessary to account for the normative role perception plays in perceptual belief. I show that Kant's notion of sensible intuition circumvents the Sellars critique. The idea of the given is redeemed in Kant's account, since it makes possible a theory of the normative role that perception plays in knowledge. (shrink)