Single Idea 10607

[catalogued under 6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory]

Full Idea

Frege's general logical system involves a type hierarchy, distinguishing objects from properties from properties-of-properties etc., with every item belonging to a determinate level.

Gist of Idea

Frege's logic has a hierarchy of object, property, property-of-property etc.

Source

report of Gottlob Frege (Begriffsschrift [1879]) by Peter Smith - Intro to Gödel's Theorems 14.1

Book Reference

Smith,Peter: 'An Introduction to Gödel's Theorems' [CUP 2007], p.118


A Reaction

The Theory of Types went on to apply this hierarchy to classes, where Frege's disastrous Basic Law V flattens the hierarchy of classes, putting them on the same level (Smith p.119)