The Principles of Mathematics (1903)

Part IV. Order
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Part IV. Order

Table of Contents

  1. Chapter XXIV. The Genesis of Series

    1. § 187. Importance of order
    2. § 188. Between and separation of couples
    3. § 189. Generation of order by one-one relations
    4. § 190. By transitive asymmetrical relations
    5. § 191. By distances
    6. § 192. By triangular relations
    7. § 193. By relations between asymmetrical relations
    8. § 194. And by separation of couples

  2. Chapter XXV. The Meaning of Order

    1. § 195. What is order?
    2. § 196. Three theories of between
    3. § 197. First theory
    4. § 198. A relation is not between its terms
    5. § 199. Second theory of between
    6. § 200. There appear to be ultimate triangular relations
    7. § 201. Reasons for rejecting the second theory
    8. § 202. Third theory of between to be rejected
    9. § 203. Meaning of separation of couples
    10. § 204. Reduction to transitive asymmetrical relations
    11. § 205. This reduction is formal
    12. § 206. But is the reason why separation leads to order
    13. § 207. The second way of generating series is alone fundamental, and gives the meaning of order

  3. Chapter XXVI. Asymmetrical Relations

    1. § 208. Classification of relations as regards symmetry and transitiveness
    2. § 209. Symmetrical transitive relations
    3. § 210. Reflexiveness and the principle of abstraction
    4. § 211. Relative position
    5. § 212. Are relations reducible to predications?
    6. § 213. Monadistic theory of relations
    7. § 214. Reasons for rejecting the theory
    8. § 215. Monistic theory and the reasons for rejecting it
    9. § 216. Order requires that relations should be ultimate

  4. Chapter XXVII. Difference of Sense and Difference of Sign

    1. § 217. Kant on difference of sense
    2. § 218. Meaning of difference of sense
    3. § 219. Difference of sign
    4. § 220. In the cases of finite numbers
    5. § 221. And of magnitudes
    6. § 222. Right and left
    7. § 223. Difference of sign arises from difference of sense among transitive asymmetrical relations

  5. Chapter XXVIII. On the Difference Between Open and Closed Series

    1. § 224. What is the difference between open and closed series?
    2. § 225. Finite closed series
    3. § 226. Series generated by triangular relations
    4. § 227. Four-term relations
    5. § 228. Closed series are such as have an arbitrary first term

  6. Chapter XXIX. Progressions and Ordinal Numbers

    1. § 229. Definition of progressions
    2. § 230. All finite arithmetic applies to every progression
    3. § 231. Definition of ordinal numbers
    4. § 232. Definition of nth
    5. § 233. Positive and negative ordinals

  7. Chapter XXX. Dedekind's Theory of Number

    1. § 234. Dedekind's principal ideas
    2. § 235. Representation of a system
    3. § 236. The notion of a chain
    4. § 237. The chain of an element
    5. § 238. Generalized form of mathematical induction
    6. § 239. Definition of a singly infinite system
    7. § 240. Definition of cardinals
    8. § 241. Dedekind's proof of mathematical induction
    9. § 242. Objections to his definition of ordinals
    10. § 243. And of cardinals

  8. Chapter XXXI. Distance

    1. § 244. Distance not essential to order
    2. § 245. Definition of distance
    3. § 246. Measurement of distances
    4. § 247. In most series, the existence of distances is doubtful
    5. § 248. Summary of Part IV
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