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It had been naively thought that for every concept, there exists a set of things that fall under that concept; for instance, corresponding to the concept "egg" is the set of all the eggs in the world.
"One might say," Wittgenstein says, "I call number-concept X non-denumerable if it has been stipulated that, whatever numbers falling under this concept you arrange in a series, the diagonal number of this series is also to fall under that concept" (RFM II, §10; cf. II, §§30, 31, 13).
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The reason for this was that the postulates for the theoretical language also specify factual relations between phenomena that fall under the concepts that are implicitly defined by them.
He did this by defining 'F is a concept under which two objects fall', in purely logical terms, as any concept F that satisfies the following condition: There are distinct things x and y that fall under the concept F and anything else that falls under the concept F is identical to either x or y.
It may be objected that every concept must have an extension, that there must be a definite totality of objects that fall under the concept.
The extension of a concept is something like the set of all objects that fall under the concept, for the extension records all of the objects that the concept maps to The True.
An \(n\ -dimensional man\ -dimensionalose sole properties are those that fall under the concept of a manifold, Weyl (1918b) physically interprets as an \(n\)-diM\nsional empty whose, that isole world empropertiesh mareer and fields.
The manifold represents an amorphous four-dimensional differentiable continuum in the sense of analysis situs and has no properties besides those that fall under the concept of a manifold.
"The second reason falls under the concept that they don't need this to be their profit centre.
Thus, the number 2 falls under the concept that which when squared is identical to 4. In what follows, we use lower-case expressions like ƒ to talk generally about functions, and upper-case expressions like F to talk more specifically about those functions which are concepts.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com