Project Gutenberg #41654
Introduction to Mathematical Philosophy
Bertrand Russell
1919Russell's bridge between mathematics and philosophy, seeded from Project Gutenberg HTML in ordered sections.
Project Gutenberg #41654 Public domain in the United States Cover source Local typographic cover created for MojiMori from public-domain source metadata
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Chapter 9 — CHAPTER IX INFINITE SERIES AND ORDINALS Central question How do infinite order-types differ from infinite cardinalities? Main argument Russell turns from size to order. Infinite series can have the...
using notions which are comparatively "simple" in the logical sense than in manipulating more complex notions which are [Pg 95] more akin to their ordinary practice. For these reasons, it was only gradually that the true importance of cardinals in mathematical philosophy was recognised. The importance of ordinals, though by no means small, is distinctly less than that of cardinals, and is very largely merged in that of the more general conception of relation-numbers. [Pg 96]