display all the ideas for this combination of texts
2 ideas
| 10032 | 'Ancestral' relations are derived by iterating back from a given relation [Frege, by George/Velleman] |
| Full Idea: Any relation will yield a new relation, called the 'ancestral', which is the iterated relation which leads up to it, as when 'x is the parent of y' can lead us to the relation 'x is an ancestor of y' | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §79) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.2 | |
| A reaction: This idea is one of Frege's notable discoveries. The ancestral seems to be a generalisation of a given relation. |
| 10606 | Frege treats properties as a kind of function, and maybe a property is its characteristic function [Frege, by Smith,P] |
| Full Idea: Frege urges us to regard properties as just a special kind of function, and in the case of numerical properties he comes close to identifying a property with its characteristic function. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Peter Smith - Intro to Gödel's Theorems 11.3 n 5 | |
| A reaction: Every now and then really interesting bits of metaphysics pop out of Frege, though it usually needs commentators to show the implications. Does the 'characteristic' imply a teleological view? |