### Chapter XI. Definition of Cardinal Numbers

### Chapter XII. Addition and Multiplication

### Chapter XIII. Finite and Infinite

### Chapter XIV. Theory of Finite Numbers

### Chapter XV. Addition of Terms and Addition of Classes

- § 124. Philosophy and mathematics distinguished
- § 125. Is there a more fundamental sense of number than that defined above?
- § 126. Numbers must be classes
- § 127. Numbers apply to classes as many
- § 128. One is to be asserted, not of terms, but of unit classes
- § 129. Counting not fundamental in arithmetic
- § 130. Numerical conjunction and plurality
- § 131. Addition of terms generates classes primarily, not numbers
- § 132.
*A term*is indefinable, but not the number 1

### Chapter XVI. Whole and Part

- § 133. Single terms may be either simple or complex
- § 134. Whole and part cannot be defined by logical priority
- § 135. Three kinds of relation of whole and part distinguished
- § 136. Two kinds of wholes distinguished
- § 137. A whole is distinct from the numerical conjunctions of its parts
- § 138. How far analysis is falsification
- § 139. A class as one is an aggregate

### Chapter XVII. Infinite Wholes

### Chapter XVIII. Ratios and Fractions

The Principles of Mathematics was written by Bertrand Russell, and published in in 1903. It is now available in the Public Domain.