Tractatus Logico-Philosophicus · Chapter
4.12721 explained
Wittgenstein argues that a formal concept is already given with any object that falls under it, so it is a mistake to introduce both the formal concept and its instances as primitive ideas.
What happens
Wittgenstein argues that a formal concept is already given with any object that falls under it, so it is a mistake to introduce both the formal concept and its instances as primitive ideas. He criticizes Russell for doing this with the concept of function and specific functions, and with the concept of number and definite numbers.
Themes in this chapter
Logical Atomism
Wittgenstein's critique of introducing formal concepts and their instances as separate primitives challenges the atomistic approach to logical foundations.
Critique of Traditional Philosophy
Directly criticizes Russell's method of introducing concepts and their instances, highlighting a philosophical confusion in logical theory.
Characters to notice
- Mr. Wittgenstein
Author of the argument that formal concepts and their instances cannot both be primitive ideas.
- Bertrand Russell
Criticized for introducing both the concept of function and special functions as primitive ideas, and similarly for number.
Key passages
“The formal concept is already given with an object, which falls under it.”
A formal concept is inherently present in any object that belongs to it.
Clarifies that formal concepts are not separate from their instances.
“One cannot, therefore, introduce both, the objects which fall under a formal concept and the formal concept itself, as primitive ideas.”
It is impossible to treat both the instances of a formal concept and the concept itself as fundamental, unanalyzable notions.
Highlights the logical error in treating concept and instance as equally primitive.
“One cannot, therefore, e.g. introduce (as Russell does) the concept of function and also special functions as primitive ideas; or the concept of number and definite numbers.”
For example, Russell is wrong to treat both the general notion of function and particular functions as basic, or both the concept of number and specific numbers as basic.
Concrete example of the error Wittgenstein identifies in Russell's logical system.