Tractatus Logico-Philosophicus · Chapter
6.1203 explained
Wittgenstein describes an intuitive method for recognizing tautologies by using a truth-table notation with 'T p F' and brackets, demonstrating how the proposition ~(p.~p) (the Law of Contradiction) is shown to be a tautology by coordinatin
What happens
Wittgenstein describes an intuitive method for recognizing tautologies by using a truth-table notation with 'T p F' and brackets, demonstrating how the proposition ~(p.~p) (the Law of Contradiction) is shown to be a tautology by coordinating truth-combinations.
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- Closing
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Follow the arc while readingThemes in this chapter
- Logic and Tautology
The chapter demonstrates a method for identifying tautologies, such as the Law of Contradiction, through truth-table notation.
Characters to notice
- Mr. Wittgenstein
Author of the Tractatus, presenting a method for recognizing tautologies.
Key passages
“In order to recognize a tautology as such, we can, in cases in which no sign of generality occurs in the tautology, make use of the following intuitive method: I write instead of “ p ”, “ q ”, “ r ”, etc. , “ T p F ”, “ T q F ”, “ T r F ”, etc.”
To identify a tautology when no generality symbol appears, we can use a simple method: replace propositional variables with a notation indicating truth and falsity.
Wittgenstein introduces a truth-table method for detecting tautologies.
“If here we put “ p ” instead of “ q ” and examine the combination of the outermost T and F with the innermost, it is seen that the truth of the whole proposition is coordinated with all the truth-combinations of its argument, its falsity with none of the truth-combinations.”
By substituting 'p' for 'q' and analyzing the truth-value patterns, we see that the proposition is true for every possible truth assignment, and false for none.
This demonstrates that ~(p.~p) is a tautology.
