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ThesaHelp:
references p-r
Topic:
history of mathematics
Topic:
number as a progression for counting and 1-1 relations
Topic:
what is a number
Topic:
set definition by extension or intension
Topic:
names as abbreviations for descriptions
Topic:
number as the extension of a class of equinumerous classes
Topic:
kinds of numbers
Topic:
mathematical proof
Topic:
infinite sequences
Topic:
infinity and infinitesimal
Group:
mathematics
Topic:
ordered data types
Topic:
logic
Topic:
integer values and operations
Topic:
real numbers and floating point numbers
Topic:
meaning without reference
Topic:
metaphysics and epistemology
Topic:
proper names
Topic:
denoting phrases and definite descriptions
Topic:
problems with analytic truth
Topic:
names as rigid designators
Topic:
names independent of objects
Topic:
mathematics as a formal system
Topic:
abstraction

Reference

Russell, B., Introduction to Mathematical Philosophy, London, George Allen and Unwin Ltd., 1919. Google

Other Reference

p. 167-180 is reproduced as "Descriptions", p. 212-218 in Martinich, A.P. (ed), The Philosophy of Language, 2nd edition, New York: Oxford University Press, 1990.

Published before 1923

Quotations
 5 ;;Quote: Peano's axioms for number concern 0, unique successors, and induction 7 ;;Quote: any progression matches Peano's five axioms for numbers; so the axioms do not define '0', 'number' and 'successor' 7+;;Quote: the concept of number should apply in the right way to common objects 12 ;;Quote: can define a class by extension (enumerate its members) or intension (a defining property); can reduce extension to intension 13 ;;Quote: the difference between a class and its definition is that a class has many defining characteristics but only one set of members 15 ;;Quote: a number is the number of some class, i.e., the class of those classes that are similar to it; discovered by Frege 15+;;Quote: two classes are similar when there is a one-one relation between them 21 ;;Quote: the natural numbers are the posterity of 0 w.r.t. immediate predecessor; i.e., all larger numbers, by hereditary; includes Peano's 0 and induction 27 ;;Quote: for Russell, mathematical induction is a definition, not a principle as for Poincare 27+;;Quote: we define the natural numbers as those to which proofs by mathematical induction can be applied 27 ;;Quote: mathematical induction is the essential characteristic that distinguishes the finite from the infinite 31 ;;Quote: an ordering relation has three properties: x not y

Related Topics

ThesaHelp: references p-r (245 items)
Topic: history of mathematics (57 items)
Topic: number as a progression for counting and 1-1 relations (22 items)
Topic: what is a number (55 items)
Topic: set definition by extension or intension (18 items)
Topic: names as abbreviations for descriptions (35 items)
Topic: number as the extension of a class of equinumerous classes (23 items)
Topic: kinds of numbers (24 items)
Topic: mathematical proof (23 items)
Topic: infinite sequences (7 items)
Topic: infinity and infinitesimal (37 items)
Group: mathematics   (23 topics, 560 quotes)
Topic: ordered data types (8 items)
Topic: logic (84 items)
Topic: integer values and operations (13 items)
Topic: real numbers and floating point numbers (37 items)
Topic: meaning without reference (31 items)
Topic: metaphysics and epistemology (99 items)
Topic: proper names (35 items)
Topic: denoting phrases and definite descriptions (21 items)
Topic: problems with analytic truth (20 items)
Topic: names as rigid designators (43 items)
Topic: names independent of objects (34 items)
Topic: mathematics as a formal system (30 items)
Topic: abstraction (62 items)

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