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Ideas for 'Function and Concept', 'On Medical Experience' and 'Regressive Method for Premises in Mathematics'

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

17628	Arithmetic was probably inferred from relationships between physical objects [Russell]
	Full Idea: When 2 + 2 =4 was first discovered, it was probably inferred from the case of sheep and other concrete cases.
	From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.272)

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

8487	Arithmetic is a development of logic, so arithmetical symbolism must expand into logical symbolism [Frege]
	Full Idea: I am of the opinion that arithmetic is a further development of logic, which leads to the requirement that the symbolic language of arithmetic must be expanded into a logical symbolism.
	From: Gottlob Frege (Function and Concept [1891], p.30)
	A reaction: This may the the one key idea at the heart of modern analytic philosophy (even though logicism may be a total mistake!). Logic and arithmetical foundations become the master of ontology, instead of the servant. The jury is out on the whole enterprise.