# 5.441 explained — Tractatus Logico-Philosophicus

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

## What happens

Wittgenstein argues that apparent logical constants disappear when equivalent expressions are shown to say the same thing, such as the equivalence of '~(∃x).~fx' and '(x).fx', or '(∃x).fx.x=a' and 'fa'.

## Themes in this chapter

### Logic and Tautology

The equivalence of expressions like '~(∃x).~fx' and '(x).fx' illustrates the tautological nature of logical constants.

## Character check-ins

### Mr. Wittgenstein

Author of the proposition, presenting the disappearance of apparent logical constants through equivalence.

## Key lines

> This disappearance of the apparent logical constants also occurs if “ ~ ( ∃ x ) . ~ f ⁡ x ” says the same as “ ( x ) . f ⁡ x ”, or “ ( ∃ x ) . f ⁡ x . x = a ” the same as “ f ⁡ a ”.

The apparent logical constants vanish when, for example, 'not there exists an x such that not fx' is equivalent to 'for all x, fx', or 'there exists an x such that fx and x equals a' is equivalent to 'fa'.

_Wittgenstein demonstrates that logical constants are not genuine constituents of propositions but are revealed through equivalence._

## Links

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