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Ideas for 'Function and Concept', 'Of the standard of taste' and 'Knowledge and the Philosophy of Number'

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4 ideas

5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / d. and

23628	The connective 'and' can have an order-sensitive meaning, as 'and then' [Hossack]
	Full Idea: The sentence connective 'and' also has an order-sensitive meaning, when it means something like 'and then'.
	From: Keith Hossack (Knowledge and the Philosophy of Number [2020], 10.4)
	A reaction: This is support the idea that orders are a feature of reality, just as much as possible concatenation. Relational predicates, he says, refer to series rather than to individuals. Nice point.

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.

23627	'Before' and 'after' are not two relations, but one relation with two orders [Hossack]
	Full Idea: The reason the two predicates 'before' and 'after' are needed is not to express different relations, but to indicate its order. Since there can be difference of order without difference of relation, the nature of relations is not the source of order.
	From: Keith Hossack (Knowledge and the Philosophy of Number [2020], 10.3)
	A reaction: This point is to refute Russell's 1903 claim that order arises from the nature of relations. Hossack claims that it is ordered series which are basic. I'm inclined to agree with him.