Tractatus Logico-Philosophicus · Chapter
5.452 explained
Wittgenstein argues that any new symbol or expedient introduced into logical symbolism must be fully justified and its place clearly established, criticizing Russell and Whitehead's Principia Mathematica for using words without proper justi
What happens
Wittgenstein argues that any new symbol or expedient introduced into logical symbolism must be fully justified and its place clearly established, criticizing Russell and Whitehead's Principia Mathematica for using words without proper justification.
Themes in this chapter
Limits of Language and Thought
Wittgenstein insists that logical symbolism must be self-contained and not rely on informal language, highlighting the boundaries of meaningful expression.
Critique of Traditional Philosophy
Direct critique of Russell and Whitehead's method in Principia Mathematica, challenging the legitimacy of their use of words in logical definitions.
Characters to notice
- Mr. Wittgenstein
Author of the Tractatus, presenting a critique of logical notation practices.
- Bertrand Russell
Co-author of Principia Mathematica, criticized for introducing words without justification.
Key passages
“The introduction of a new expedient in the symbolism of logic must always be an event full of consequences.”
Adding any new device to logical notation is a significant move with far-reaching implications.
Wittgenstein emphasizes the gravity of altering logical symbolism.
“No new symbol may be introduced in logic in brackets or in the margin—with, so to speak, an entirely innocent face.”
You cannot sneak a new symbol into logic as if it were harmless or trivial.
Critique of casual or unexamined additions to logical systems.
“Thus in the Principia Mathematica of Russell and Whitehead there occur definitions and primitive propositions in words. Why suddenly words here? This would need a justification. There was none, and can be none for the process is actually not allowed.”
Russell and Whitehead used ordinary language in their logical work without any justification, but such a move is illegitimate.
Direct criticism of a specific flaw in Principia Mathematica.
“But if the introduction of a new expedient has proved necessary in one place, we must immediately ask: Where is this expedient always to be used? Its position in logic must be made clear.”
Whenever a new logical device is needed, we must determine its general application and clarify its role in the system.
Wittgenstein demands systematic consistency in logical notation.