Russellâs Unknown Logicism : A Study in the History and Philosophy of Mathematics
Mathematics-Philosophy Philosophy, modern Analysis (Philosophy) Logic Philosophy of Mathematics Modern Philosophy Analytic Philosophy
Imprint: Palgrave Macmillan
2012
EISBN 1283588447
Cover; Contents; List of Figures and Tables; Acknowledgements; Series Editor's Foreword; Introduction; 1 Projective Geometry; 1.1 Projective and metrical properties; 1.2 The status of the fundamental theorem of projective geometry; 1.3 Russell's twofold analysis; 1.4 Russell's choice; 1.5 Space as an incidence structure; 1.6 Conclusion; 2 Metrical Geometry; 2.1 Logicism, if-thenism and non-Euclidean geometries; 2.2 The projective definition of a metric; 2.3 Metrical geometry, distance and stretch; 2.4 PoincareÌ and Russell on the perception of distance
2.5 Metrical geometry as an empirical science2.6 Conclusion; 3 Geometry, Logicism and 'If-Thenism'; 3.1 Russell's if-thenism (I): definitions; 3.2 Russell's if-thenism (II): existence-theorems; 3.3 Topic specificities and psychologism; 3.4 The types of relations and the architecture of mathematics; 3.5 The interaction between logic and mathematics: a persistent difficulty?; 3.6 Conclusion; 4 Quantity in The Principles of Mathematics; 4.1 Magnitude and quantity; 4.2 The concept of a measurable magnitude; 4.3 The absolutist theory and the concept of a kind of magnitude
4.4 The relational theory of distance4.5 Conclusion; 5 Quantity in Principia Mathematica; 5.1 Dedekind, Burali-Forti and Frege on real numbers; 5.2 Russell and Whitehead's theory of numbers; 5.3 The relational theory of vector family; 5.4 Hale's Fregean axiomatic definition versus Russell and Whitehead's relational theory; 5.5 Conclusion; 6 Application Constraint in Principia Mathematica; 6.1 Whitehead's conception of applied mathematics; 6.2 Real analysis and real numbers; 6.3 The architectonic use of Applic; 6.4 Applic in neo-logicism
6.5 Applic and the distinction between logical and apparent forms of propositions6.6 Conclusion; 7 Russell's Universalism and Topic-Specificity; 7.1 Pre-logicized and logicized mathematics; 7.2 Russell's positive universalism; 7.3 Logicism and the definition of the mathematical content; 7.4 Russell's logicism and practice-based philosophy of mathematics; 7.5 Conclusion; Notes; Bibliography; Index
In this excellent book Sebastien Gandon focuses mainly on Russell's two major texts, Principa Mathematica and Principle of Mathematics , meticulously unpicking the details of these texts and bringing a new interpretation of both the mathematical and the philosophical content. Winner of The Bertrand Russell Society Book Award 2013.
2.5 Metrical geometry as an empirical science2.6 Conclusion; 3 Geometry, Logicism and 'If-Thenism'; 3.1 Russell's if-thenism (I): definitions; 3.2 Russell's if-thenism (II): existence-theorems; 3.3 Topic specificities and psychologism; 3.4 The types of relations and the architecture of mathematics; 3.5 The interaction between logic and mathematics: a persistent difficulty?; 3.6 Conclusion; 4 Quantity in The Principles of Mathematics; 4.1 Magnitude and quantity; 4.2 The concept of a measurable magnitude; 4.3 The absolutist theory and the concept of a kind of magnitude
4.4 The relational theory of distance4.5 Conclusion; 5 Quantity in Principia Mathematica; 5.1 Dedekind, Burali-Forti and Frege on real numbers; 5.2 Russell and Whitehead's theory of numbers; 5.3 The relational theory of vector family; 5.4 Hale's Fregean axiomatic definition versus Russell and Whitehead's relational theory; 5.5 Conclusion; 6 Application Constraint in Principia Mathematica; 6.1 Whitehead's conception of applied mathematics; 6.2 Real analysis and real numbers; 6.3 The architectonic use of Applic; 6.4 Applic in neo-logicism
6.5 Applic and the distinction between logical and apparent forms of propositions6.6 Conclusion; 7 Russell's Universalism and Topic-Specificity; 7.1 Pre-logicized and logicized mathematics; 7.2 Russell's positive universalism; 7.3 Logicism and the definition of the mathematical content; 7.4 Russell's logicism and practice-based philosophy of mathematics; 7.5 Conclusion; Notes; Bibliography; Index
In this excellent book Sebastien Gandon focuses mainly on Russell's two major texts, Principa Mathematica and Principle of Mathematics , meticulously unpicking the details of these texts and bringing a new interpretation of both the mathematical and the philosophical content. Winner of The Bertrand Russell Society Book Award 2013.
