Hernán Pringe’s research while affiliated with University of Buenos Aires and other places

En este trabajo comparamos la interpretación del cálculo diferencial que Hegel propone en la Ciencia de la lógica con la que Cohen desarrolla en El principio del método infinitesimal y su historia y en la segunda edición de la Teoría kantiana de la experiencia. Si bien ambos filósofos encuentran en el cálculo el principio cualitativo fundante de lo cuantitativo, Cohen sostiene que Hegel no resuelve el problema de la relación entre matemática y ciencia natural.

The aim of this paper is to analyze Dimitry Gawronsky’s doctrine of actual infinitesimals. I examine the peculiar connection that his critical idealism establishes between transcendental philosophy and mathematics. In particular, I reconstruct the relationship between Gawronsky’s differentials, Cantor’s transfinite numbers, Veronese’s trans-Archimedean numbers and Robinson’s hyperreal numbers. I argue that by means of his doctrine of actual infinitesimals, Gawronsky aims to provide an interpretation of calculus that eliminates any alleged given element in knowledge. The author emphasizes not the mathematical, but the transcendental or metaphysical aspect of Gavronsky’s teaching. It follows from Gavronsky’s doctrine that infinitesimals are the key to a correct philosophical explanation of the relationship between thinking and being: mathematics, and differential calculus in particular, turns out to be the means by which pure thought constructs being. Thus, we are talking about the conception of transcendental mathematics, which solves the problem of the applicability of mathematics to nature. Thus, nature is understood as a product of thought, created in accordance with the infinitesimal method: since thought creates natural objects in accordance with mathematical methods, the latter have the necessary reliability in relation to the former. The relevance of infinitesimals turns out to be Gavronsky’s relevance of pure thought in the generation of being, and the first relevant product of pure thought is the reality of being

The aim of this paper is to analyze Dimitry Gawronsky’s doctrine of actual infinitesimals. I examine the peculiar connection that his critical idealism establishes between transcendental philosophy and mathematics. In particular, I reconstruct the relationship between Gawronsky’s differentials, Cantor’s transfinite numbers, Veronese’s trans-Archimedean numbers and Robinson’s hyperreal numbers. I argue that by means of his doctrine of actual infinitesimals, Gawronsky aims to provide an interpretation of calculus that eliminates any alleged given element in knowledge.

The goal of this paper is to explain Hermann Cohen´s logic of origin and the role that negativity plays in it. In the first section, we will consider Cohen´s transcendental method. This will lead us to Cohen´s early interpretation of differential calculus, that contains the presuppositions necessary to understand his logic of origin. In the second section, we will analyze Cohen´s mature doctrine of pure thinking in order to study the connections that Cohen establishes between the concepts of origin, something and nothing.

La crítica kantiana de la razón tiene como principal propósito determinar la posibilidad de la metafísica como ciencia. El objetivo de este trabajo es presentar un panorama de aquella metafísica cuya posibilidad resulta finalmente establecida. Distinguiremos tres tipos de conocimiento metafísico posible: la metafísica de la experiencia, la metafísica de las costumbres y la metafísica práctico-dogmática. Posteriormente, discutiremos el modo en el que estas metafísicas se ordenan en un sistema.

In this paper we analyze the historical roots of the Bohrian concept of symbol. More precisely, we argue that Bohr takes Kantian elements from Høffding´s philosophy in order to develop his own concept of symbol. For this purpose, firstly, we focus on the two different senses that Bohr gives to the concept of symbol. Then, we study how each of these senses is related to different aspects of Høffding’s philosophy and we show the connection between the Bohrian and the Kantian concept of symbol by means of Høffding’s mediation.

En este trabajo nos proponemos analizar uno de los aspectos centrales de la filosofía de Hermann Cohen: la relación que su Lógica del conocimiento puro establece entre el pensar puro y el cálculo infinitesimal. Mostraremos que la interpretación coheniana del cálculo se orienta a fundamentar en el pensar puro todos los elementos que Kant distingue en la intuición empírica: tanto su materia (la sensación), como su forma (el tiempo y el espacio). De tal modo, mediante el cálculo infinitesimal, Cohen buscará dar cuenta del conocimiento sin recurrir a ninguna receptividad.

This paper compares Cohen’s Logic of Pure Knowledge and Cassirer’s Substance and Function in order to evaluate how in these works Cohen and Cassirer go beyond the limits established by Kantian philosophy. In his Logic , Cohen seeks to ground in pure thought all the elements which Kant distinguishes in empirical intuition: its matter (sensation) as well as its form (time and space). In this way, Cohen tries to provide an account of knowledge without appealing to any receptivity. In accordance with Cohen’s project of reformulating the Kantian theory of sensibility, Cassirer undertakes in Substance and Function the task of developing an alternative doctrine of pure and empirical manifolds. But whereas Cohen analyzes the laws of pure thought, Cassirer aims to highlight the functional character of concepts in the development of modern mathematics and physics. I will discuss these two different approaches to the problems raised by Kantian philosophy and I will argue that Cassirer went further than Cohen in the project of critical idealism.

Artykuł omawia krytykę stanowiska Immanuela Kanta dotyczących zastosowania czystych pojęć intelektu do przedmiotów empirycznych, jaką przedstawił Salomon Maimon (1753–1800). Wedle Maimona stanowisko Kanta jest niewystarczające ze względu na swój formalizm i choć wyjaśnia zastosowanie kategorii do doświadczenia w ogóle, to nie odpowiada na pytanie o to, w jaki sposób można subsumować pod kategorie konkretne przedmioty doświadczenia. Zdaniem Maimona jest to możliwe tylko wówczas, gdy te dwa elementy – nie tylko czyste pojęcia, ale także przedmioty empiryczne, uzna się za wynik spontaniczności ludzkiego rozumu. Relacja reguły wytwarzającej materię zjawisk i samej materii, miałaby być jego zdaniem analogiczna do relacji funkcji i jej pochodnych. Ponieważ jednak reguła ta znana mogłaby być tylko domniemanemu rozumowi absolutnemu, Maimon określa swe stanowisko mianem sceptycyzmu empirycznego.

The aim of this paper is to discuss Maimon's criticism of Kant's doctrine of mathematical cognition. In particular, we will focus on the consequences of this criticism for the problem of the possibility of metaphysics as a science. Maimon criticizes Kant's explanation of the synthetic a priori character of mathematics and develops a philosophical interpretation of differential calculus according to which mathematics and metaphysics become deeply interwoven. Maimon establishes a parallelism between two relationships: on the one hand, the mathematical relationship between the integral and the differential and on the other, the metaphysical relationship between the sensible and the supersensible. Such a parallelism will be the clue to the Maimonian solution to the Kantian problem of the possibility of metaphysics as a science.