Tractatus Logico-Philosophicus · Chapter
5.532 explained
Wittgenstein critiques Russell's notation for existence statements, arguing that identity signs are unnecessary and can be replaced by more perspicuous logical forms that avoid pseudo-propositions about identity.
What happens
Wittgenstein critiques Russell's notation for existence statements, arguing that identity signs are unnecessary and can be replaced by more perspicuous logical forms that avoid pseudo-propositions about identity.
Themes in this chapter
Logical Atomism
Wittgenstein's reformulation of existence statements reflects the logical atomist project of analyzing propositions into elementary components without superfluous signs like identity.
Nonsense and Meaning
By eliminating the identity sign, Wittgenstein aims to avoid pseudo-propositions that appear meaningful but are logically empty.
Characters to notice
- Mr. Wittgenstein
Author of the Tractatus, presenting a refined logical notation that eliminates the identity sign.
- Bertrand Russell
His notation for existence statements is critiqued and reformulated by Wittgenstein.
Key passages
“And analogously: not “ ( ∃ x , y ) . f ( x , y ) . x = y ”, but “ ( ∃ x ) . f ( x , x ) ”; and not “ ( ∃ x , y ) . f ( x , y ) . ~ x = y ”, but “ ( ∃ x , y ) . f ( x , y ) ”.”
Instead of writing 'there exist x and y such that f(x,y) and x equals y', we should write 'there exists an x such that f(x,x)'. And instead of 'there exist x and y such that f(x,y) and x is not equal to y', we should simply write 'there exist x and y such that f(x,y)'.
Wittgenstein shows how to eliminate the identity sign by using distinct variables or repeated variables, making the logical form more perspicuous.