Quote: for Russell, mathematical induction is a definition, not a principle as for Poincare

Quotation

Poincare [ref] considered [induction] to be a principle of the utmost importance, by means of which an infinite number of syllogisms could be condensed into one argument. We now know that all such views are mistaken, and that mathematical induction is a definition, not a principle. ... We define the "natural numbers" as those to which proofs by mathematical induction can be applied, i.e. as those that possess all inductive properties.   Google-1   Google-2

Published before 1923

Additional Titles

Quote: we define the natural numbers as those to which proofs by mathematical induction can be applied

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