Tractatus Logico-Philosophicus · Chapter
6.211 explained
Wittgenstein argues that mathematical propositions are never needed in life itself; rather, they serve as tools for inference between non-mathematical propositions.
What happens
Wittgenstein argues that mathematical propositions are never needed in life itself; rather, they serve as tools for inference between non-mathematical propositions. He also notes that in philosophy, asking why we use a particular word or proposition often yields valuable insights.
Themes in this chapter
Logic and Tautology
Mathematical propositions are used only as inferential tools, not as substantive truths in life, aligning with their tautological nature.
Critique of Traditional Philosophy
The remark about questioning word usage in philosophy reflects a critique of traditional philosophical methods.
Characters to notice
- Mr. Wittgenstein
Author of the proposition, presenting his view on the role of mathematical propositions in life and philosophy.
Key passages
“In life it is never a mathematical proposition which we need, but we use mathematical propositions only in order to infer from propositions which do not belong to mathematics to others which equally do not belong to mathematics.”
We never require a mathematical statement in practical life; instead, we employ mathematical statements solely to reason from one non-mathematical claim to another.
Wittgenstein emphasizes the instrumental role of mathematics, distinct from its content.
“In philosophy the question 'Why do we really use that word, that proposition?' constantly leads to valuable results.”
In philosophical inquiry, asking why we actually employ a particular word or statement frequently yields important insights.
This highlights Wittgenstein's method of examining ordinary language use.