É comum a literatura secundária reduzir o ensaio kantiano Do primeiro princípio da diferença das regiões no espaço a um ataque à concepção leibniziana de espaço relativo em defesa da concepção newtoniana de espaço absoluto. Até que ponto, porém, essa imagem não é obstáculo para compreender o Ensaio como um todo e o alcance de sua reflexão? A pergunta se impõe, porque não é claro o que o Ensaio pretende provar, uma vez que propõe quatro diferentes formulações de uma prova (...) que denomina evidente. Tampouco é claro, por isso mesmo, como pretende conduzir a demonstração segundo o método que denomina a posteriori. Para compreender o Ensaio, é necessário entender qual é o objetivo último da prova e o método de demonstração. Dessa investigação decorrem alguns pontos, de outro modo, insuspeitos: (1) Kant critica não apenas a concepção de espaço leibniziana, mas também princípios adotados pelos leibnizianos, em particular, o princípio de determinação completa como princípio de individuação para as coisas em geral; (2) o Ensaio propõe uma concepção inaudita de espaço absoluto como: conceito, radicado no corpo humano e primeiro fundamento das relações espaciais e de sua cognição; (3) assim entendido, o Ensaio kantiano mostra-se, do ponto de vista genético, estratégico para tornar compreensível a concepção, introduzida pela Estética Transcendental da Crítica da razão pura, de aparecimento (Erscheinung) como objeto indeterminado da intuição empírica. Palavras-chave: Kant; Leibniz; Baumgarten; Espaço; Princípio de determinação completa. Transcendental Aesthetic and the 1768 Essay: Space and Complete Determination Abstract: It is common for secondary literature to reduce Kant's 1768 essay On the First Ground of the Difference of Regions in Space to an attack on the Leibnizian conception of relative space in defense of the Newtonian conception of absolute space. To what extent, however, is this picture an obstacle to understanding the essay as a whole and the scope of its reflection? The question arises because it is not clear what the essay intends to prove, since it proposes four different formulations of a proof that it calls evident. Nor is it clear, therefore, how the essay intends to conduct the demonstration according to its a posteriori method. To understand Kant's argument, it is necessary to determine the ultimate objective of his proof and his method of demonstration. Some otherwise unsuspected points arise from this investigation: (1) Kant criticizes not only the conception of relative space but also the Leibnizian principle of thoroughgoing determination as a principle of individuation for things in general; (2) Kant proposes an unprecedented conception of absolute space as a fundamental concept, rooted in the human body, as the first ground of spatial relations and its cognition; (3) the Kantian essay appears, from a genetic point of view, strategic to make comprehensible the conception introduced by the Transcendental Aesthetics of the Critique of Pure Reason, of appearance as an indeterminate object of empirical intuition. Keywords: Kant; Leibniz; Baumgarten; Space; Principle of thoroughgoing determination. Estética transcendental y el Ensayo de 1768: espacio y determinación completa Resumen: Es común en la literatura secundaria reducir el ensayo kantiano Del primer fundamento de la diferencia de las regiones del espacio a un ataque a la concepción leibniziana de espacio relativo en defensa de la concepción newtoniana de espacio absoluto ¿Hasta qué punto, pero, esa imagen no es obstáculo para la comprensión del Ensayo en general y el alcance de su reflexión? La pregunta se impone, porque no es claro lo que el Ensayo pretende comprobar, una vez que propone cuatro diferentes formulaciones de una prueba que denomina evidente. Tampoco es nítido, por eso incluso, cómo pretende conducir la demostración, según el método que denomina a posteriori. Para comprender el Ensayo, es necesario entender cuál es el objetivo último de la prueba y el método de demostración. De esa investigación decurren algunos puntos, de otro modo, insospechados: (1) Kant critica no solamente la concepción de espacio leibniziana, sino también los principios adoptados por los leibnizianos, en particular el principio de determinación completa como: principio de individuación para las cosas en general; (2) el Ensayo propone una concepción inaudita de espacio absoluto como: concepto, radicado en el cuerpo humano y el primer fundamento de las relaciones espaciales y de su cognición; (3) de ese modo, el Ensayo kantiano se muestra, del punto de vista genético, estratégico para que se vuelva comprensible la concepción, introducida por la Estética Transcendental de la Crítica de la razón pura, de aparecimiento (Erscheinung) como objeto indeterminado de la intuición empírica. Palabras-clave: Kant; Leibniz; Baumgarten; Espacio; Principio de determinación completa. 1 Pesquisador de produtividade CNPq. Agradeço aos organizadores do I Colóquio da Seção do Cerrado da SKB, pela oportunidade de apresentar e discutir parte significativa deste trabalho; a Marcos Seneda e demais organizadores do presente volume, por terem esperado, pacientemente, a entrega da versão final de meu artigo; a Luciano Codato, pelas observações e pelo constante diálogo; a Ivanilde Fracalossi, pelas sugestões ao texto e a Rafael Tessari Dias, pela revisão das referências bibliográficas; ao CNPq, pelo fomento da pesquisa (Processo: 313393/2020-6). Modesta homenagem a meus professores, sempre presentes: José Arthur Giannotti, Rubens Rodrigues Torres Filho e Oswaldo Porchat. Data de registro: 30/07/2024 Data de aceite: 30/10/2024. (shrink)

Kant’s treatments of incongruent counterparts have been criticized in the recent literature. His 1768 essay has been charged with an ambiguous use of the notion of ‘inner ground’, and his 1770 claim that those differences cannot be apprehended conceptually is thought to be false. The author argues that those two charges rest on an uncharitable reading. ‘Inner ground’ is equivocal only if misread as mapping onto Leibniz notion of quality. Concepts suffice to distinguish counterparts, but are insufficient to specify their (...) spatial forms. Kant’s claims are reasonable and plausible, and have been reaffirmed repeatedly in contemporary discussions of demonstrative identification. (shrink)

I propose that we interpret Kant’s argument from incongruent counterparts in the 1768 article ‘Concerning the Ultimate Ground of the Differentiation of Directions in Space’ in light of a theory of dynamic absolute space that he accepted throughout the 1750s and 1760s. This force-based or material conception of space was not an unusual interpretation of the Newtonian notion of absolute space. Nevertheless, commentators have continually argued that Kant’s argument is an utter failure that shifts from the metaphysics of space to (...) its epistemology, because he has no way to connect ‘directionality’ and ‘handedness’ to absolute space. This supposed failure is based on an understanding of absolute space in purely mathematical terms and as an absolute void that lacks any qualitative or dynamic features. If we recognize that Kant held that space had an intrinsic directional asymmetry then his argument successfully connects incongruent counterparts to absolute space. The presence of this notion in Kant’s pre-Critical thought is rarely noted, and its necessity in understanding his incongruence argument is novel. (shrink)

The concept of athleticism seems, at first glance, to be a minor component of Deleuze's analysis in Francis Bacon, appearing by name in the text only six times. In this article, I draw out the close link between athleticism and Deleuze's fundamental concept of intensity, arguing that this ostensibly minor term is in fact central to his account of the ‘clear and durable sensation’ produced by Bacon's painting. In tracing links between athleticism, Deleuze's aesthetic concept of ‘the fall’, and his (...) reliance on and critique of Kant's theory of intensive magnitudes, I show that athleticism in Francis Bacon names the form of intensity proper to painting. (shrink)

This paper develops a novel interpretation of Kant's argument from incongruent counterparts to the effect that the representations of space and time are intuitions rather than concepts. When properly understood, the argument anticipates the contemporary position whereby the meaning of indexicals cannot be captured by descriptive contents.

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)

Kant uses incongruent counterparts in his work before and after 1781, but not in the first Critique. Given the relevance that incongruent counterparts had for his thought on space, and their persistence in his work during the 1780s, it is plausible to think that he had a reason for leaving them out of both editions of the Critique. Two implausible conjectures for their absence are here considered and rejected. A more plausible alternative is put forth, which explains that textual absence (...) as a result of the synthetic method of presentation intended for the Critique. (shrink)

I argue that, by the time of his essay "Concerning the Ultimate Ground of the Differentiation of Directions in Space" (1768), Kant had come to question the status of the Principle of Sufficient Reason as a result, at least in part, of his recognition of the existence of incongruent counterparts. Though Kant's argument against absolute space based on the existence of incongruent counterparts has been much discussed in recent years, its importance as a useful benchmark by which to judge the (...) direction of Kant’s thinking during this period has gone unnoticed. This paper is a modest attempt to remedy this deficiency. (shrink)

Se defiende la tesis de que la teoría kantiana del espacio, en el contexto del idealis-mo trascendental, constituye un marco adecuado para solucionar la paradoja de las contrapartidas incongruentes. Se incluyen dos hipótesis: a) la solución kantiana implica una referencia a la conciencia de la propia corporalidad, para comprender cómo poseemos la capacidad para orientarnos en el espacio; b) no existe contradicción en el uso kantiano de las contrapartidas incongruentes en diferentes estadios de su pensamiento. La solución kantiana de 1768 (...) constituye una versión germinal del desarrollo que culminará en la teoría idealista trascendental acerca del espacio como una forma de nuestra sensibilidad. (shrink)

RESUMEN Se defiende la tesis de que la teoría kantiana del espacio, en el contexto del idealismo trascendental, constituye un marco adecuado para solucionar la paradoja de las contrapartidas incongruentes. Se incluyen dos hipótesis: a) la solución kantiana implica una referencia a la conciencia de la propia corporalidad, para comprender cómo poseemos la capacidad para orientarnos en el espacio; b) no existe contradicción en el uso kantiano de las contrapartidas incongruentes en diferentes estadios de su pensamiento. La solución kantiana de (...) 1768 constituye una versión germinal del desarrollo que culminará en la teoría idealista trascendental acerca del espacio como una forma de nuestra sensibilidad. ABSTRACT The article argues that the Kantian theory of space, in the context of transcendental idealism, constitutes an adequate framework to resolve the paradox of incongruent counterparts. Two hypotheses are considered: a) the Kantian solution implies a reference to the awareness of one's corporeity in order to understand how we have the capacity to orient ourselves in space; b) there is no contradiction in the Kantian use of incongruent counterparts throughout the different stages of his thought. The Kantian solution of 1768 is a germinal version of the development leading up to the transcendental idealist theory of space as a form of our sensibility. (shrink)