# 5.15 explained — Tractatus Logico-Philosophicus

> Chapter companion for Tractatus Logico-Philosophicus by Ludwig Wittgenstein.

## 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.

## Character check-ins

### Mr. Wittgenstein

Author of the Tractatus, presenting a logical definition of probability.

## Key lines

> 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._

## Links

- HTML: https://www.betterreads.online/discover/tractatus_logico_philosophicus_se/chapters/5-15
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