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Ideas for 'The Epistemology of Modality', 'Sapiens: brief history of humankind' and 'Function and Concept'

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2 ideas

5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic

8490	First-level functions have objects as arguments; second-level functions take functions as arguments [Frege]
	Full Idea: Just as functions are fundamentally different from objects, so also functions whose arguments are and must be functions are fundamentally different from functions whose arguments are objects. The latter are first-level, the former second-level, functions.
	From: Gottlob Frege (Function and Concept [1891], p.38)
	A reaction: In 1884 he called it 'second-order'. This is the standard distinction between first- and second-order logic. The first quantifies over objects, the second over intensional entities such as properties and propositions.

5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic

8492	Relations are functions with two arguments [Frege]
	Full Idea: Functions of one argument are concepts; functions of two arguments are relations.
	From: Gottlob Frege (Function and Concept [1891], p.39)
	A reaction: Nowadays we would say 'two or more'. Another interesting move in the aim of analytic philosophy to reduce the puzzling features of the world to mathematical logic. There is, of course, rather more to some relations than being two-argument functions.