Space, Number, and Geometry from Helmholtz to Cassirer by Francesca Biagioli

By Francesca Biagioli

This publication 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 types 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 used to be generally thought of to be a version of sure bet at his time. despite the fact that, such later medical advancements as non-Euclidean geometries and Einstein’s normal concept 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 information to an item of analysis should be traced again to a convention, along with such mathematicians as Carl Friedrich Gauss, Bernhard Riemann, Richard Dedekind, Felix Klein, and Henri Poincaré, and which unearths considered one of its clearest expressions in Hermann von Helmholtz’s epistemological works. even if Helmholtz formulated compelling objections to Kant, the writer reconsiders diverse options for a philosophical account of an analogous transformation from a neo-Kantian viewpoint, and particularly Hermann Cohen’s account of the aprioricity of arithmetic when it comes to applicability and Ernst Cassirer’s reformulation of the a priori of area by way of a method of hypotheses. This publication is perfect for college students, students and researchers who desire to increase their wisdom of non-Euclidean geometry or neo-Kantianism.

Show description

Read or Download Space, Number, and Geometry from Helmholtz to Cassirer (Archimedes) PDF

Best geometry & topology books

Finsler Geometry: An Approach via Randers Spaces

"Finsler Geometry: An strategy through Randers areas" solely bargains with a unique classification of Finsler metrics -- Randers metrics, that are outlined because the sum of a Riemannian metric and a 1-form. Randers metrics derive from the study on common Relativity idea and feature been utilized in lots of components of the ordinary sciences.

Mathematical Concepts

The most purpose of this booklet is to explain and enhance the conceptual, structural and summary deliberating arithmetic. particular mathematical constructions are used to demonstrate the conceptual method; offering a deeper perception into mutual relationships and summary universal positive aspects. those principles are conscientiously influenced, defined and illustrated through examples in order that a number of the extra technical proofs could be passed over.

Modern General Topology (Bibliotheca Mathematica)

Bibliotheca Mathematica: a chain of Monographs on natural and utilized arithmetic, quantity VII: sleek normal Topology makes a speciality of the methods, operations, ideas, and techniques hired in natural and utilized arithmetic, together with areas, cardinal and ordinal numbers, and mappings. The e-book first elaborates on set, cardinal and ordinal numbers, uncomplicated suggestions in topological areas, and numerous topological areas.

Fractal Functions, Fractal Surfaces, and Wavelets

Fractal features, Fractal Surfaces, and Wavelets, moment version, is the 1st systematic exposition of the idea of neighborhood iterated functionality platforms, neighborhood fractal features and fractal surfaces, and their connections to wavelets and wavelet units. The publication relies on Massopust’s paintings on and contributions to the speculation of fractal interpolation, and the writer makes use of a couple of tools—including research, topology, algebra, and likelihood theory—to introduce readers to this intriguing topic.

Additional resources for Space, Number, and Geometry from Helmholtz to Cassirer (Archimedes)

Sample text

Download PDF sample

Rated 4.40 of 5 – based on 46 votes