Tractatus Logico-Philosophicus · Chapter
6.2321 explained
Wittgenstein argues that the provability of mathematical propositions lies in their internal self-evidence, not in empirical comparison with facts.
What happens
Wittgenstein argues that the provability of mathematical propositions lies in their internal self-evidence, not in empirical comparison with facts.
Themes in this chapter
Logic and Tautology
The proposition suggests that mathematical truths are tautological in nature, requiring no external verification.
Characters to notice
- Mr. Wittgenstein
Author of the proposition, presenting the view that mathematical proof is a matter of internal insight rather than factual correspondence.
Key passages
“And, that the propositions of mathematics can be proved means nothing else than that their correctness can be seen without our having to compare what they express with the facts as regards correctness.”
The provability of mathematical statements simply means that their truth is evident internally, without needing to check them against external reality.
Wittgenstein emphasizes the self-contained nature of mathematical proof, independent of empirical facts.