Single Idea 7742

[catalogued under 5. Theory of Logic / G. Quantification / 3. Objectual Quantification]

Full Idea

Frege treated 'everything' as basic, and suggested ways of recasting propositions containing other quantifiers so that this was the only one remaining. He recast 'something' as 'at least one thing', and defined this in terms of 'everything' and 'not'.

Gist of Idea

Frege reduced most quantifiers to 'everything' combined with 'not'

Source

report of Gottlob Frege (Begriffsschrift [1879]) by Gregory McCullogh - The Game of the Name 1.6

Book Reference

McCulloch,Gregory: 'The Game of the Name' [OUP 1989], p.19


A Reaction

Extreme parsimony seems highly desirable in logic as well as ontology, but it can lead to frustrations, especially over the crucial question of the existence of things quantified over. See Idea 6068.

Related Idea

Idea 6068 We need an Intentional Quantifier ("some of the things we talk about.."), so existence goes into the proposition [McGinn]