Tractatus Logico-Philosophicus · Chapter
5.473 explained
Wittgenstein argues that logic is self-contained and self-justifying: any possible sign can signify, and whatever is logically possible is permitted.
What happens
Wittgenstein argues that logic is self-contained and self-justifying: any possible sign can signify, and whatever is logically possible is permitted. He illustrates with the nonsensical proposition 'Socrates is identical,' which fails not because the symbol is inherently impermissible but because no arbitrary determination has been made to give it meaning. Thus, in a certain sense, mistakes in logic are impossible.
Themes in this chapter
Nonsense and Meaning
The proposition 'Socrates is identical' is senseless due to lack of arbitrary determination, not because the symbol is inherently impermissible.
Logic and Tautology
Logic must take care of itself; in a certain sense we cannot make mistakes in logic.
Characters to notice
- Mr. Wittgenstein
Author of the Tractatus, presenting the self-sufficiency of logic.
- Socrates
Used as an example in the proposition 'Socrates is identical' to illustrate nonsense.
Key passages
“Logic must take care of itself.”
Logic is autonomous and requires no external justification.
Wittgenstein asserts the self-sufficiency of logical rules.
“A possible sign must also be able to signify.”
Any sign that can exist in logical space is capable of meaning.
The possibility of a sign guarantees its potential for signification.
“Everything which is possible in logic is also permitted.”
Whatever is logically possible is allowed within the logical framework.
Logical possibility entails permissibility.
““Socrates is identical” means nothing because there is no property which is called “identical.””
The sentence 'Socrates is identical' is meaningless because 'identical' does not denote a property.
Illustrates how lack of determination leads to nonsense.
“In a certain sense we cannot make mistakes in logic.”
Errors in logic are impossible in a fundamental sense.
Logic is infallible when properly understood.