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.
Themes 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.