Tractatus Logico-Philosophicus · Chapter
5.152 explained
Wittgenstein defines independent propositions as those sharing no truth-arguments, assigning them a probability of 1/2.
What happens
Wittgenstein defines independent propositions as those sharing no truth-arguments, assigning them a probability of 1/2. He explains that logical consequence yields probability 1, making logical certainty a limiting case of probability, with application to tautology and contradiction.
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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 limiting case of probability is applied to tautology and contradiction, showing logical certainty as a boundary of probabilistic reasoning.
Characters to notice
- Mr. Wittgenstein
Author of the Tractatus, presenting the logical relationship between independence, probability, and logical consequence.
Key passages
“Propositions which have no truth-arguments in common with one another we call independent.”
Propositions that share no truth-arguments are termed independent.
Defines independence in terms of disjoint truth-arguments.
“Independent propositions ( e.g. any two elementary propositions) give to one another the probability ½.”
Any two independent propositions, such as elementary propositions, each confer a probability of 1/2 on the other.
Establishes the baseline probability for independent propositions.
“If p follows from q , the proposition q gives to the proposition p the probability 1.”
When q entails p, q assigns probability 1 to p.
Logical consequence yields certainty.
“The certainty of logical conclusion is a limiting case of probability.”
Logical certainty represents the extreme case within the spectrum of probability.
Probability theory subsumes logical deduction as a boundary case.
