# 5.151 explained — Tractatus Logico-Philosophicus

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

## What happens

Wittgenstein introduces a formal schema for calculating the probability that one proposition gives to another, based on the ratio of shared truth-conditions.

## Themes in this chapter

### Logic and Tautology

The probability ratio is grounded in the logical structure of truth-conditions.

## Character check-ins

### Mr. Wittgenstein

Author of the Tractatus, presenting a formal definition of probability between propositions.

## Key lines

> Suppose in a schema like that above in No. 5.101 T r is the number of the “ T ”’s in the proposition r , T r s the number of those “ T ”’s in the proposition s , which stand in the same columns as “ T ”’s of the proposition r ; then the proposition r gives to the proposition s the probability T r s : T r .

If we count the truth-conditions (T's) in a truth-table for proposition r, and then count how many of those same truth-conditions are also T's in proposition s, the ratio of the latter to the former is the probability that r confers on s.

_Wittgenstein defines logical probability as a ratio of shared truth-conditions._

## Links

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