more from Wilfrid Hodges

Single Idea 10476

[catalogued under 2. Reason / D. Definition / 7. Contextual Definition]

Full Idea

Late nineteenth century mathematicians said that, although plus, minus and 0 could not be precisely defined, they could be partially 'implicitly defined' as a group. This nonsense was rejected by Frege and others, as expressed in Russell 1903.

Gist of Idea

The idea that groups of concepts could be 'implicitly defined' was abandoned


Wilfrid Hodges (Model Theory [2005], 2)

Book Reference

'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [], p.7

A Reaction

[compressed] This is helpful in understanding what is going on in Frege's 'Grundlagen'. I won't challenge Hodges's claim that such definitions are nonsense, but there is a case for understanding groups of concepts together.