Tractatus Logico-Philosophicus · Chapter
6.022 explained
Wittgenstein defines the concept of number as the general form common to all numbers, equating it with the variable number, and similarly treats equality of numbers as the general form of all specific numerical equalities.
What happens
Wittgenstein defines the concept of number as the general form common to all numbers, equating it with the variable number, and similarly treats equality of numbers as the general form of all specific numerical equalities.
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Narrative arc
Story tension across the book.
- Setup
- Escalation
- Breaking point
- Aftermath
- Closing
This passage marks the story’s dramatic climax because it presents the moment when the protagonist’s obsessive…
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Follow the arc while readingThemes in this chapter
- Logic and Tautology
The discussion of the general form of number and equality reflects the logical structure underlying arithmetic.
Characters to notice
- Mr. Wittgenstein
Author of the proposition, defining number and numerical equality in terms of general form.
Key passages
“The concept number is nothing else than that which is common to all numbers, the general form of a number.”
The idea of number is just what all numbers share, namely their general pattern or form.
Wittgenstein reduces the concept of number to its logical form.
“The concept number is the variable number.”
The concept of number is the same as the variable that can stand for any number.
Number is treated as a variable in logical notation.
“And the concept of equality of numbers is the general form of all special equalities of numbers.”
What it means for numbers to be equal is just the general pattern that all specific numerical equalities follow.
Equality is also understood as a formal, logical structure.
