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Single Idea 6108

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

Full Idea

I think that no one will dispute that from certain ideas and axioms of formal logic, but with the help of the logic of relations, all pure mathematics can be deduced.

Gist of Idea

Maths can be deduced from logical axioms and the logic of relations

Source

Bertrand Russell (Logical Atomism [1924], p.145)

Book Ref

Russell,Bertrand: 'Russell's Logical Atomism', ed/tr. Pears,David [Fontana 1972], p.145

A Reaction

It has been said for a long time that Gödel's Incompleteness Theorems of 1930 disproved this claim, though recently there have been defenders of logicism. Beginning with 'certain ideas' sounds like begging the question.

The 14 ideas from 'Logical Atomism'

10968 Russell gave up logical atomism because of negative, general and belief propositions [Russell, by Read]
6107 It is logic, not metaphysics, that is fundamental to philosophy [Russell]
6109 Some axioms may only become accepted when they lead to obvious conclusions [Russell]
6108 Maths can be deduced from logical axioms and the logic of relations [Russell]
6110 Subject-predicate logic (and substance-attribute metaphysics) arise from Aryan languages [Russell]
6111 As propositions can be put in subject-predicate form, we wrongly infer that facts have substance-quality form [Russell]
6112 Meaning takes many different forms, depending on different logical types [Russell]
6113 To mean facts we assert them; to mean simples we name them [Russell]
6114 'Simples' are not experienced, but are inferred at the limits of analysis [Russell]
6116 A logical language would show up the fallacy of inferring reality from ordinary language [Russell]
6115 Vagueness, and simples being beyond experience, are obstacles to a logical language [Russell]
6117 Philosophy should be built on science, to reduce error [Russell]
21722 Better to construct from what is known, than to infer what is unknown [Russell]
6118 Philosophy is logical analysis, followed by synthesis [Russell]