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Single Idea 8745

[from 'Introduction to Mathematical Philosophy' by Bertrand Russell, in 4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory ]

Full Idea

The symbols for classes are mere conveniences, not representing objects called 'classes'. Classes are in fact logical fictions; they cannot be regarded as part of the ultimate furniture of the world.

Gist of Idea

Classes are logical fictions, and are not part of the ultimate furniture of the world

Source

Bertrand Russell (Introduction to Mathematical Philosophy [1919], Ch.18), quoted by Stewart Shapiro - Thinking About Mathematics 5.2

Book Reference

Shapiro,Stewart: 'Thinking About Mathematics' [OUP 2000], p.123


A Reaction

I agree. For 'logical fictions' read 'abstractions'. To equate abstractions with fictions is to underline the fact that they are a human creation. They are either that or platonic objects - there is no middle way.