# 6.1221 explained — Tractatus Logico-Philosophicus

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

## What happens

Wittgenstein explains how logical inference can be demonstrated by showing that a conditional proposition is a tautology, using the example that 'q' follows from 'p ⊃ q . p' by combining them into a tautological form.

## Themes in this chapter

### Logic and Tautology

The chapter demonstrates how logical inference is grounded in tautology, showing that the truth of a conclusion is already contained in the premises.

## Character check-ins

### Mr. Wittgenstein

Author of the Tractatus, presenting the logical method for demonstrating inference through tautology.

## Key lines

> If for example two propositions “ p ” and “ q ” give a tautology in the connection “ p ⊃ q ”, then it is clear that q follows from p .

If the conditional 'if p then q' is a tautology, then q logically follows from p.

_Wittgenstein illustrates the concept of logical consequence through tautology._

> E.g. that “ q ” follows from “ p ⊃ q . p ” we see from these two propositions themselves, but we can also show it by combining them to “ q ” follows from “ p ⊃ q . p : ⊃ : q ” and then showing that this is a tautology.

For instance, we can see that q follows from the premises 'if p then q' and 'p' either directly or by forming the conditional 'if (if p then q and p) then q' and proving it is a tautology.

_Wittgenstein provides a concrete example of how to demonstrate logical inference using tautology._

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