Combining Texts

Ideas for 'Function and Concept', 'Properties' and 'Virtues of the Mind'

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3 ideas

5. Theory of Logic / E. Structures of Logic / 1. Logical Form
10407 Logical Form explains differing logical behaviour of similar sentences [Swoyer]
     Full Idea: 'Logical Form' is a technical notion motivated by the observation that sentences with a similar surface structure may exhibit quite different logical behaviour.
     From: Chris Swoyer (Properties [2000], 4.2)
     A reaction: [Swoyer goes on to give some nice examples] The tricky question is whether each sentence has ONE logical form. Pragmatics warns us of the dangers. One needs to check numerous inferences from a given sentences, not just one.
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.