Combining Texts

Ideas for 'Reply to Professor Marcus', 'Models' and 'Function and Concept'

unexpand these ideas     |    start again     |     choose another area for these texts

display all the ideas for this combination of texts

3 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 / 4. Substitutional Quantification
10801 Either reference really matters, or we don't need to replace it with substitutions [Quine]
     Full Idea: When we reconstrue quantification in terms of substituted expressions rather than real values, we waive reference. ...but if reference matters, we cannot afford to waive it as a category; and if it does not, we do not need to.
     From: Willard Quine (Reply to Professor Marcus [1962], p.183)
     A reaction: An odd dilemma to pose. Presumably the substitution account is an attempt to explain how language actually works, without mentioning dubious direct ontological commitment in the quantifiers.