Tractatus Logico-Philosophicus · Chapter
5.15 explained
Wittgenstein defines the measure of probability that one proposition gives to another as the ratio of the number of truth-grounds common to both propositions to the number of truth-grounds of the first proposition.
What happens
Wittgenstein defines the measure of probability that one proposition gives to another as the ratio of the number of truth-grounds common to both propositions to the number of truth-grounds of the first proposition.
Free preview opens on this chapter — companions, themes, and character notes appear beside the text.
Narrative arc
Story tension across the book — this chapter sits in Climax.
- Setup
- Escalation
- Breaking point
- Aftermath
- Closing
This passage marks the story’s dramatic climax because it presents the moment when the protagonist’s obsessive…
Full beat labels and climax notes unlock in the reader.
Follow the arc while readingThemes in this chapter
- Logic and Tautology
Probability is defined in terms of truth-grounds, linking logical structure to quantitative measure.
Characters to notice
- Mr. Wittgenstein
Author of the Tractatus, presenting a logical definition of probability.
Key passages
“If T r is the number of the truth-grounds of the proposition “ r ”, T r s the number of those truth-grounds of the proposition “ s ” which are at the same time truth-grounds of “ r ”, then we call the ratio T r s : T r the measure of the probability which the proposition “ r ” gives to the proposition “ s ”.”
The probability that proposition r confers on proposition s is the ratio of the number of truth-grounds they share to the total truth-grounds of r.
Wittgenstein reduces probability to a logical relation between truth-grounds.
