Download Space, Number, and Geometry from Helmholtz to Cassirer by Francesca Biagioli PDF
By Francesca Biagioli
This ebook deals a reconstruction of the talk on non-Euclidean geometry in neo-Kantianism among the second one 1/2 the 19th century and the 1st a long time of the 20 th century. Kant famously characterised area and time as a priori varieties of intuitions, which lie on the beginning of mathematical wisdom. The good fortune of his philosophical account of area used to be due now not least to the truth that Euclidean geometry was once extensively thought of to be a version of simple task at his time. despite the fact that, such later medical advancements as non-Euclidean geometries and Einstein’s normal idea of relativity known as into query the knowledge of Euclidean geometry and posed the matter of reconsidering house as an open query for empirical learn. The transformation of the idea that of house from a resource of data to an item of study may be traced again to a convention, inclusive of such mathematicians as Carl Friedrich Gauss, Bernhard Riemann, Richard Dedekind, Felix Klein, and Henri Poincaré, and which reveals one among its clearest expressions in Hermann von Helmholtz’s epistemological works. even supposing Helmholtz formulated compelling objections to Kant, the writer reconsiders assorted thoughts for a philosophical account of an analogous transformation from a neo-Kantian standpoint, and particularly Hermann Cohen’s account of the aprioricity of arithmetic by way of applicability and Ernst Cassirer’s reformulation of the a priori of house when it comes to a process of hypotheses. This ebook is perfect for college students, students and researchers who desire to increase their wisdom of non-Euclidean geometry or neo-Kantianism.
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Additional resources for Space, Number, and Geometry from Helmholtz to Cassirer
Sample text
Given Schlick’s account of geometrical knowledge, such a definition can only be consistent if it tacitly presupposes a conventional definition of rigidity. In this regard, Schlick distanced himself from Helmholtz’s empiricism and defended a conventionalist approach to the foundations of geometry. In order to highlight the contrast between Kantianism, empiricism, and conventionalism, which occupies us on several occasions in the rest of the book, the following section provides an introduction to Helmholtz’s considerations about the Kantian theory of space.
Not only did Helmholtz consider the free mobility of rigid bodies an empirical generalization, but the structure thus characterized includes both Euclidean and non-Euclidean geometries as special cases. Therefore, Helmholtz contrasted this picture of spatial intuition with the older view that spatial intuition is a simple and immediate psychological act and provides us with evident truths. 201). In this connection, Friedman reconsiders his original stance by admitting that such a conception would enable us to overcome the limits of the logical approach to the Kantian notion of intuition.
XII–XIII). 3 The Trendelenburg-Fischer Controversy 29 that emerged from Cohen’s study enabled him and Cassirer to present their shift in emphasis from sensation to constructive thought as a consistent development of the Kantian philosophy of mathematics and, at the same time, to engage in the nineteenth-century debate about the foundations of geometry from a new perspective. 3 The Trendelenburg-Fischer Controversy The neo-Aristotelian Friedrich Adolf Trendelenburg discussed Kant’s metaphysical exposition of the concepts of space and time in Logical Investigations (1840) as follows.