Tractatus Logico-Philosophicus · Chapter
6.1233 explained
Wittgenstein argues that the axiom of reducibility is not a logical truth, as we can conceive of a world where it fails, and logic is indifferent to the actual constitution of the world.
What happens
Wittgenstein argues that the axiom of reducibility is not a logical truth, as we can conceive of a world where it fails, and logic is indifferent to the actual constitution of the world.
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Narrative arc
Story tension across the book.
- Setup
- Escalation
- Breaking point
- Aftermath
- Closing
This passage marks the story’s dramatic climax because it presents the moment when the protagonist’s obsessive…
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Follow the arc while readingThemes in this chapter
- Logic and Tautology
The passage underscores that logical propositions are tautologies, independent of empirical facts; the axiom of reducibility is not a tautology since its negation is conceivable.
Characters to notice
- Mr. Wittgenstein
Author of the proposition, asserting the contingency of the axiom of reducibility and the independence of logic from empirical fact.
Key passages
“We can imagine a world in which the axiom of reducibility is not valid. But it is clear that logic has nothing to do with the question whether our world is really of this kind or not.”
It is possible to conceive of a universe where the axiom of reducibility does not hold; however, logic is unconcerned with whether our actual world is such a universe.
Wittgenstein emphasizes the non-logical, contingent status of the axiom of reducibility.
