Tractatus Logico-Philosophicus · Chapter
6.031 explained
Wittgenstein argues that the theory of classes is unnecessary in mathematics because the generality required in mathematics is essential, not accidental.
What happens
Wittgenstein argues that the theory of classes is unnecessary in mathematics because the generality required in mathematics is essential, not accidental.
Themes in this chapter
Logic and Tautology
The rejection of class theory as superfluous aligns with the view that mathematical propositions are tautologies or essential, not contingent on empirical classification.
Characters to notice
- Mr. Wittgenstein
Author of the proposition
Key passages
“The theory of classes is altogether superfluous in mathematics.”
Class theory is entirely unnecessary for mathematics.
Wittgenstein dismisses the need for class theory in mathematical foundations.
“This is connected with the fact that the generality which we need in mathematics is not the accidental one.”
This is because the kind of generality required in mathematics is essential, not contingent.
Distinguishes mathematical generality from empirical or accidental generality.