Combining Texts

Ideas for 'Universal Prescriptivism', 'Logical Atomism' and 'Enquiry Conc Human Understanding'

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2 ideas

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism

2197	Reason assists experience in discovering laws, and in measuring their application [Hume]
	Full Idea: Abstract reasonings are employed, either to assist experience in the discovery of natural laws, or to determine their influence in particular instances, where it depends upon any precise degree of distance or quantity.
	From: David Hume (Enquiry Conc Human Understanding [1748], IV.I.27)

6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism

6108	Maths can be deduced from logical axioms and the logic of relations [Russell]
	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.
	From: Bertrand Russell (Logical Atomism [1924], 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.