Combining Texts

Ideas for 'fragments/reports', 'works' and 'The Principles of Mathematics'

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4 ideas

4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set

14113	The null class is a fiction [Russell]
	Full Idea: The null class is a fiction.
	From: Bertrand Russell (The Principles of Mathematics [1903], §079)
	A reaction: This does not commit him to regarding all classes as fictions - though he seems to have eventually come to believe that. The null class seems to have a role something like 'Once upon a time...' in story-telling. You can then tell truth or fiction.

4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets

15894	Russell invented the naïve set theory usually attributed to Cantor [Russell, by Lavine]
	Full Idea: Russell was the inventor of the naïve set theory so often attributed to Cantor.
	From: report of Bertrand Russell (The Principles of Mathematics [1903]) by Shaughan Lavine - Understanding the Infinite I

4. Formal Logic / F. Set Theory ST / 6. Ordering in Sets

14126	Order rests on 'between' and 'separation' [Russell]
	Full Idea: The two sources of order are 'between' and 'separation'.
	From: Bertrand Russell (The Principles of Mathematics [1903], §204)

14127	Order depends on transitive asymmetrical relations [Russell]
	Full Idea: All order depends upon transitive asymmetrical relations.
	From: Bertrand Russell (The Principles of Mathematics [1903], §208)