The Neo-Kantians and the Logicist Definition of Number :: Mathematics Math Mathematical Papers

The Neo-Kantians and the Logicist Definition of name compend The publication of Russells The Principles of Mathematics (1903) and Couturats Les principes des mathsematiques (1905) incited several prominent neo-Kantians to make up their mind about the system of logicist program. In this paper, I shall discuss the critiques presented by the adjacent neo-Kantians Paul Natorp, Ernst Cassirer and Jonas Cohn. They argued that Russells attempt to deduce the number creationion from the line concept is a petitio principii. Russell replied that the sense in which every object is ane essential be distinguished from the sense in which wizard is a number. I aim that Russell was wrong in dismissing the neo-Kantian argument as an elementary logical error. To stomach Russells distinction would be to get at least part of Russells logicist program. The feeling a sectionalisation with one member would presuppose the number one only if one at the same time accepted the analysis which numeric logic provides for it (the class u has one member when u is not null and x and y are us implies x and y are identical). My point is that the aforementioned analysis provided by numeral logic was something that the neo-Kantians were not ready to accept. Although Frege published the low gear informal exposition of his logicist political program in Die Grundlagen der Arithmetik (1884), his thesis that all math follows from logic was close to completely neglected in Germany for a long time. Frege remained an isolated identification number whose works were either strongly criticised or completely neglected by German philosophers. Freges ideas started to have an impact in Germany only in the head start decade of the twentieth century. In particular, the publication of Bertand Russells The Principles of Mathematics (1903) and Louis Couturats Les principes des mathmatiques (1905) incited several prominent German philosophers to state their opinion about mathematical logic an d the logicist plan. In this paper I shall discuss how the neo-Kantians Paul Natorp (1854-1924), Ernst Cassirer (1874-1945) and Jonas Cohn (1869-1947) criticised Russells and Freges theories of number. The education of their criticism will also throw some light on the historical origins of the current situation in philosophy, that is, on the split amidst analytic and Continental philosophy. 1. The logicist definition of number as a class of classesAccording to Russell, the goal of the logicist programme is to show thatall pure math deals exclusively with concepts definable in terms of a very olive-sized number of fundamental logical concepts, and that all its propositions are deducible from a very crushed number of fundamental logical principles (Russell 1903 v).The Neo-Kantians and the Logicist Definition of Number Mathematics Math Mathematical PapersThe Neo-Kantians and the Logicist Definition of Number bring up The publication of Russells The Principles of Mathematics (1 903) and Couturats Les principes des mathematiques (1905) incited several prominent neo-Kantians to make up their mind about the logicist program. In this paper, I shall discuss the critiques presented by the adjacent neo-Kantians Paul Natorp, Ernst Cassirer and Jonas Cohn. They argued that Russells attempt to deduce the number concept from the class concept is a petitio principii. Russell replied that the sense in which every object is one must be distinguished from the sense in which one is a number. I remove that Russell was wrong in dismissing the neo-Kantian argument as an elementary logical error. To accept Russells distinction would be to accept at least part of Russells logicist program. The panorama a class with one member would presuppose the number one only if one simultaneously accepted the analysis which mathematical logic provides for it (the class u has one member when u is not null and x and y are us implies x and y are identical). My point is that the aforementio ned analysis provided by mathematical logic was something that the neo-Kantians were not ready to accept. Although Frege published the first informal exposition of his logicist programme in Die Grundlagen der Arithmetik (1884), his thesis that all mathematics follows from logic was near completely neglected in Germany for a long time. Frege remained an isolated grade whose works were either strongly criticised or completely neglected by German philosophers. Freges ideas started to have an impact in Germany only in the first decade of the twentieth century. In particular, the publication of Bertand Russells The Principles of Mathematics (1903) and Louis Couturats Les principes des mathmatiques (1905) incited several prominent German philosophers to state their opinion about mathematical logic and the logicist programme. In this paper I shall discuss how the neo-Kantians Paul Natorp (1854-1924), Ernst Cassirer (1874-1945) and Jonas Cohn (1869-1947) criticised Russells and Freges the ories of number. The prove of their criticism will also throw some light on the historical origins of the current situation in philosophy, that is, on the split amidst analytic and Continental philosophy. 1. The logicist definition of number as a class of classesAccording to Russell, the goal of the logicist programme is to show thatall pure mathematics deals exclusively with concepts definable in terms of a very small number of fundamental logical concepts, and that all its propositions are deducible from a very small number of fundamental logical principles (Russell 1903 v).