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Single Idea 6408

[filed under theme 6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism ]

Full Idea

In order to deduce the theorems of mathematics from purely logical axioms, Russell had to add three new axioms to those of standards logic, which were: the axiom of infinity, the axiom of choice, and the axiom of reducibility.

Gist of Idea

Russell needed three extra axioms to reduce maths to logic: infinity, choice and reducibility

Source

A.C. Grayling (Russell [1996], Ch.2)

Book Ref

Grayling,A.C.: 'Russell' [OUP 1996], p.31

A Reaction

The third one was adopted to avoid his 'barber' paradox, but many thinkers do not accept it. The interesting question is why anyone would 'accept' or 'reject' an axiom.

The 20 ideas from A.C. Grayling

7293 It is legitimate to do harm if it is the unintended side-effect of an effort to achieve a good [Grayling]
7292 War must also have a good chance of success, and be waged with moderation [Grayling]
6408 Russell needed three extra axioms to reduce maths to logic: infinity, choice and reducibility [Grayling]
6414 Two propositions might seem self-evident, but contradict one another [Grayling]
23253 Majority decisions are only acceptable if the minority interests are not vital [Grayling]
23256 Liberty and equality cannot be reconciled [Grayling]
23258 The very concept of democracy entails a need for justice [Grayling]
23259 There should be separate legislative, executive and judicial institutions [Grayling]
23260 A cap on time of service would restrict party control and career ambitions [Grayling]
23262 Experience, sympathy and history are sensible grounds for laying claim to rights [Grayling]
23263 Politics is driven by power cliques [Grayling]
23254 Democracies should require a supermajority for major questions [Grayling]
23255 It is essential for democracy that voting is free and well informed [Grayling]
7809 In an honour code shame is the supreme punishment, and revenge is a duty [Grayling]
7818 In Greek mythology only heroes can go to heaven [Grayling]
7819 Religion gives answers, comforts, creates social order, and panders to superstition [Grayling]
7817 To make an afterlife appealing, this life has to be denigrated [Grayling]
7823 Lucretius was rediscovered in 1417 [Grayling]
7824 If suicide is lawful, but assisting suicide is unlawful, powerless people are denied their rights [Grayling]
7091 The argument from analogy is not a strong inference, since the other being might be an actor or a robot [Grayling]