Tractatus Logico-Philosophicus · Chapter
5.47 explained
Wittgenstein argues that the general form of proposition is already implicit in the elementary proposition, as all logical operations are contained within it.
What happens
Wittgenstein argues that the general form of proposition is already implicit in the elementary proposition, as all logical operations are contained within it. He illustrates that a proposition like 'f a' is equivalent to '(∃x). f x . x = a', showing that composition, argument, and function inherently include all logical constants. The one logical constant common to all propositions is their general form.
Themes in this chapter
Logical Atomism
The chapter asserts that elementary propositions contain all logical operations, reinforcing the atomistic view that complex propositions are built from simple elements.
Logic and Tautology
Discussion of the general form of proposition and the logical constant common to all propositions relates to the nature of logical truth and tautology.
Characters to notice
- Mr. Wittgenstein
Author of the proposition; presents the argument that all logical operations are contained in the elementary proposition.
Key passages
“For all logical operations are already contained in the elementary proposition.”
Every logical operation is already present within the simplest proposition.
Wittgenstein emphasizes that logical complexity is inherent in the basic units of language.
“One could say: the one logical constant is that which all propositions, according to their nature, have in common with one another. That however is the general form of proposition.”
The single logical constant is what all propositions share by their very nature, which is their general form.
This identifies the general form of proposition as the fundamental logical constant.