# 6.1201 explained — Tractatus Logico-Philosophicus

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

## What happens

Wittgenstein illustrates how tautologies reveal logical relations between propositions, such as contradiction, consequence, and instantiation, by examining specific logical forms.

## Themes in this chapter

### Logic and Tautology

The chapter uses tautologies to exhibit logical relations like contradiction and consequence between propositions.

## Character check-ins

### Mr. Wittgenstein

Author of the Tractatus, presenting examples of tautologies to demonstrate logical relations.

## Key lines

> That e.g. the propositions “ p ” and “ ~ p ” in the connection “ ~ ( p . ~ p ) ” give a tautology shows that they contradict one another.

The fact that 'not (p and not p)' is a tautology demonstrates that p and not p are contradictory.

_Illustrates contradiction via tautology._

> That the propositions “ p ⊃ q ”, “ p ” and “ q ” connected together in the form “ ( p ⊃ q ) . ( p ) : ⊃ : ( q ) ” give a tautology shows that q follows from p and p ⊃ q .

The tautology of the conditional form shows that q is a logical consequence of p and 'if p then q'.

_Demonstrates logical consequence through tautology._

> That “ ( x ) . f ⁡ x : ⊃ : f ⁡ a ” is a tautology shows that f ⁡ a follows from ( x ) . f ⁡ x , etc. etc.

The tautology 'if everything is f, then a is f' shows that the particular instance follows from the universal statement.

_Shows instantiation as a logical relation via tautology._

## Links

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