Single Idea 11029

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers]

Full Idea

To the question 'How many gallons of water are in the tank', the correct answer might be 'exactly ten'. But this does not mean that exactly ten things instantiate the concept 'gallon of water in the tank'.

Gist of Idea

'Exactly ten gallons' may not mean ten things instantiate 'gallon'

Source

comment on Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §46) by Ian Rumfitt - Concepts and Counting p.43

Book Reference

-: 'Aristotelian Society' [], p.43


A Reaction

The difficulty for Frege that is being raised is that whole numbers are used to designate quantities of stuff, as well as for counting denumerable things. Rumfitt notes that 'ten' answers 'how much?' as well as Frege's 'how many?'.