Tractatus Logico-Philosophicus · Chapter
6.1221 explained
Wittgenstein explains how logical inference can be demonstrated by showing that a conditional proposition is a tautology, using the example that 'q' follows from 'p ⊃ q .
What happens
Wittgenstein explains how logical inference can be demonstrated by showing that a conditional proposition is a tautology, using the example that 'q' follows from 'p ⊃ q . p' by combining them into a tautological form.
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- Setup
- Escalation
- Breaking point
- Aftermath
- Closing
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Follow the arc while readingThemes in this chapter
- Logic and Tautology
The chapter demonstrates how logical inference is grounded in tautology, showing that the truth of a conclusion is already contained in the premises.
Characters to notice
- Mr. Wittgenstein
Author of the Tractatus, presenting the logical method for demonstrating inference through tautology.
Key passages
“If for example two propositions “ p ” and “ q ” give a tautology in the connection “ p ⊃ q ”, then it is clear that q follows from p .”
If the conditional 'if p then q' is a tautology, then q logically follows from p.
Wittgenstein illustrates the concept of logical consequence through tautology.
“E.g. that “ q ” follows from “ p ⊃ q . p ” we see from these two propositions themselves, but we can also show it by combining them to “ q ” follows from “ p ⊃ q . p : ⊃ : q ” and then showing that this is a tautology.”
For instance, we can see that q follows from the premises 'if p then q' and 'p' either directly or by forming the conditional 'if (if p then q and p) then q' and proving it is a tautology.
Wittgenstein provides a concrete example of how to demonstrate logical inference using tautology.
