Tractatus Logico-Philosophicus · Chapter
6.03 explained
Wittgenstein defines the general form of the cardinal number as a series starting from 0, where each successive number is obtained by adding 1 to the previous one.
What happens
Wittgenstein defines the general form of the cardinal number as a series starting from 0, where each successive number is obtained by adding 1 to the previous one.
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- Escalation
- Breaking point
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Follow the arc while readingThemes in this chapter
- Logic and Tautology
The definition of cardinal numbers as a formal series reflects Wittgenstein's view that mathematical propositions are tautologies or formal transformations.
Characters to notice
- Mr. Wittgenstein
Author of the proposition defining the general form of cardinal numbers.
Key passages
“The general form of the cardinal number is: [ 0 , ξ , ξ + 1 ] .”
Every natural number can be generated by starting at 0 and repeatedly applying the operation of adding 1.
This defines the natural numbers as a recursive series, foundational to arithmetic.
