# 5.43 explained — Tractatus Logico-Philosophicus

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

## What happens

Wittgenstein argues that from a single fact p, an infinite number of logical propositions (like ~~p, ~~~~p, etc.) follow, which seems unbelievable. He notes that it is equally remarkable that all logical and mathematical propositions follow from a few primitive propositions, but explains that all such logical propositions say the same thing—namely, nothing.

## Themes in this chapter

### Logic and Tautology

Wittgenstein asserts that all logical propositions say the same thing—nothing—highlighting their tautological nature.

### Nonsense and Meaning

The claim that logical propositions say nothing touches on the boundary between sense and nonsense.

## Character check-ins

### Mr. Wittgenstein

Author of the proposition; presents the argument about the infinite consequences of a fact and the nature of logical propositions.

## Key lines

> That from a fact p an infinite number of others should follow, namely, ~ ~ p , ~ ~ ~ ~ p , etc. , is indeed hardly to be believed, and it is no less wonderful that the infinite number of propositions of logic (of mathematics) should follow from half a dozen 'primitive propositions.'

It is hard to accept that from a single fact p, an endless series of negated propositions (like not-not-p, not-not-not-not-p, etc.) follows, and it is equally astonishing that all logical and mathematical truths can be derived from just a few basic axioms.

_Wittgenstein highlights the seemingly paradoxical fecundity of logical inference from simple facts and axioms._

> But the propositions of logic say the same thing. That is, nothing.

However, all logical propositions are equivalent in meaning—they express nothing at all.

_This underscores the tautological and contentless nature of logical truths._

## Links

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