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Ideas for 'Function and Concept', 'Conditionals (Stanf)' and 'Laws of Nature'

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4 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.
5. Theory of Logic / G. Quantification / 1. Quantification
15891 Traditional quantifiers combine ordinary language generality and ontology assumptions [Harré]
     Full Idea: The generalising function and the ontological function of discourse are elided in the traditional quantifier.
     From: Rom Harré (Laws of Nature [1993], 5)
     A reaction: This simple point strikes me as helping enormously to disentangle the mess created by over-emphasis on formal logic in ontology, and especially in the Quinean concept of 'ontological commitment'.
5. Theory of Logic / G. Quantification / 7. Unorthodox Quantification
15878 Some quantifiers, such as 'any', rule out any notion of order within their range [Harré]
     Full Idea: The quantifier 'any' unambiguously rules out any presupposition of order in the members of the range of individuals quantified.
     From: Rom Harré (Laws of Nature [1993], 3)
     A reaction: He contrasts this with 'all', 'each' and 'every', which are ambiguous in this respect.