Tractatus Logico-Philosophicus · Chapter
5.131 explained
Wittgenstein argues that logical inference is grounded in internal relations between the forms of propositions, not in external connections.
What happens
Wittgenstein argues that logical inference is grounded in internal relations between the forms of propositions, not in external connections. The truth of one proposition following from others is expressed by these inherent structural relations, which exist as soon as the propositions themselves exist.
Themes in this chapter
Logical Atomism
The internal relations between propositional forms are central to logical atomism, as they determine logical consequence without external mediation.
Limits of Language and Thought
The internal nature of logical relations shows the limits of what can be expressed: inference is already contained in the structure of propositions.
Characters to notice
- Mr. Wittgenstein
Author of the Tractatus, presenting the theory of logical inference based on internal relations of propositional forms.
Key passages
“If the truth of one proposition follows from the truth of others, this expresses itself in relations in which the forms of these propositions stand to one another, and we do not need to put them in these relations first by connecting them with one another in a proposition; for these relations are internal, and exist as soon as, and by the very fact that, the propositions exist.”
When one proposition is logically implied by others, this is shown by the inherent structural relationships between the forms of those propositions. No additional linking proposition is needed, because these relationships are internal and arise automatically from the mere existence of the propositions.
Clarifies Wittgenstein's view that logical consequence is an internal feature of propositional forms, not something added externally.