Philosophy of Arithmetic: Psychological and Logical Investigations

Description

This volume is a window on a period of rich and illuminating philosophical activity that has been rendered generally inaccessible by the supposed "revolution" attributed to "Analytic Philosophy" so-called. Careful exposition and critique is given to every serious alternative account of number and number relations available at the time. Front Matter....Pages i-lxiv Front Matter....Pages 9-9 Introduction....Pages 11-14 The Origination of the Concept of Multiplicity Through that of the Collective Combination....Pages 15-22 Critical Developments....Pages 23-65 The Psychological Nature of the Collective Combination....Pages 67-79 Analysis of the Concept of Number in Terms of its Origin and Content....Pages 81-93 The Relations “More” and “Less”....Pages 95-100 The Definition of Number-Equality Through the Concept of Reciprocal One-to-One Correlation....Pages 101-115 Definitions of Number in Terms of Equivalence....Pages 117-132 Discussions Concerning Unity and Multiplicity....Pages 133-167 The Sense of the Statement of Number....Pages 169-177 Front Matter....Pages 189-189 Operations on Numbers and the Authentic Number Concepts....Pages 191-203 Symbolic Representations of Multiplicities....Pages 205-234 The Symbolic Representations of Numbers....Pages 235-269 The Logical Sources of Arithmetic....Pages 271-301 Front Matter....Pages 303-303 Original Version of the Text Through Chapter IV....Pages 305-357 Essays....Pages 359-503 Back Matter....Pages 505-515