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