Tractatus Logico-Philosophicus · Chapter
5.441 explained
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'.
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.
Characters to notice
- Mr. Wittgenstein
Author of the proposition, presenting the disappearance of apparent logical constants through equivalence.
Key passages
“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.