Back to the original post again, this is paragraph 3.333 of Ludwig Wittgenstein's Tractatus Logico-philosophicus (in the original post the Greek and mathematical characters were lost):

3.333 The reason why a function cannot be its own argument is that the sign for a function already contains the prototype of its argument, and it cannot contain itself.
For let us suppose that the function F(fx) could be its own argument: in that case there would be a proposition ‘F(F(fx))’, in which the outer function F and the inner function F must have different meanings, since the inner one has the form φ(fx) and the outer one has the form ψ(φ(fx)). Only the letter ‘F’ is common to the two functions, but the letter by itself signifies nothing.
This immediately becomes clear if instead of ‘F(Fu)’ we write ‘(∃φ): F(φu).φu = Fu’.
That disposes of Russell’s paradox.

You can take this at face value. No normal mathematical function could operate on itself as an argument. For example, considering a function from real numbers to real numbers like cosine. The type of the function is a real-to-real mapping, the type of the argument is real - two very different things. We are not talking about function composition -many of the comments have gone onto that but it is another subject entirely. (The book by Black mentioned below is clear on that.)

Wittgenstein's target is evidently Russell's paradox. Russell's paradox concerns sets that may include themselves. If we disallow sets from including themselves by making some analogy with functions then Russell's paradox could not arise. This is obvious in itself.

Some decent articles on the internet explain the importance of Russell's paradox to mathematical logic. It can be seen that Wittgenstein's suggestion made no impact in this field. He is known as a philosopher not a mathematician. It can also be understood how he came to be aware of it since he was close to Russell, who was both. In any case, the reference to Russell's paradox in the Tractatus just looks like an aside. It does not figure in anything that follows in the Tractatus.

The part that does not have an obvious interpretation is the second last line, which is a mathematical expression. Presumably this line would make the point clear and so we can turn to commentaries to explain it to us. I know of two commentaries on the Tractatus, the Routledge 'study guide' by Michael Morris and the Companion by Max Black (see below for links). Morris ignores the second last line entirely and Black offers a lame kind of comment that is not worth quoting. Neither of these commentaries otherwise advances us beyond the face value understanding that I have expressed.

The only conclusion is that the whole of the 3.333 paragraphs are a waste of words, being amateurish contributions on a specialised topic made to look more intelligent than they are by being obscure. In a way I hope I am wrong. I was expecting something else when I got around to reading Wittgenstein.

No longer giving W the benefit of the doubt, the talk about F have two unrelated meanings is also a waste of words. When one uses a mathematical symbol twice, the meaning is the same each time. W should simply say that it is being used incompatibly in the two occurrences.

Are the 3.333 statements as poor as they appear and if they are how can we take the rest of the Tractatus seriously, when we are forever trying to fill in the gaps in order to discern the meaning? Perhaps there is nothing there to be found.

Commentaries on the Tractatus

https://www.routledge.com/Routledge-Philosophy-GuideBook-to-Wittgenstein-and-the-Tractatus/Morris/p/book/9780415357227
https://www.google.com.au/books/edition/A_Companion_to_Wittgenstein_s_Tractatus/uzY9AAAAIAAJ?hl=en

Russell's Paradox

https://plato.stanford.edu/entries/russell-paradox/
https://www.britannica.com/topic/Russells-paradox , etc

yes I think that is the correct term. But then what is a function of a functional - a functionalal?

If we could go back right to the start, this is paragraph 3.333 of Ludwig Wittgenstein's Tractatus Logico-philosophicus (in the original post the Greek and mathematical characters were lost):

3.333 The reason why a function cannot be its own argument is that the sign for a function already contains the prototype of its argument, and it cannot contain itself.
For let us suppose that the function F(fx) could be its own argument: in that case there would be a proposition ‘F(F(fx))’, in which the outer function F and the inner function F must have different meanings, since the inner one has the form φ(fx) and the outer one has the form ψ(φ(fx)). Only the letter ‘F’ is common to the two functions, but the letter by itself signifies nothing.
This immediately becomes clear if instead of ‘F(Fu)’ we write ‘(∃φ): F(φu).φu = Fu’.
That disposes of Russell’s paradox.

This statement looks like it should be plain enough, but it seems that no-one in the world really knows what the point of the second last line is. That is how I got here. Some clues that I have picked up: Although it seems to be a sensible discussion about mathematical functions it may be more particularly aimed at logical propositions expressed as functions or set theory propositions expressed as functions. The notation seems to be non-standard but guessable, however it supposedly goes back to Principia Mathematica as described in [url=https:// plato.stanford.edu/entries/pm-notation/] plato.stanford.edu/entries/pm-notation/[/url]

F(F(x)) is allowed only if the co-domain is equal to or a subset of the domain of F(x). Beyond that, I don't see what the problem is with the repeated application of functions. — alcontali

alcontali is taking the expression F(F(x)) as function composition, ie compute x1 = F(x) and then compute F(x1) , and x could be an integer and F(x) returns an integer. That is different from the question considered by Wittgentstein, which is could there be a function which takes the function itself (the mapping) as an argument? An example of a function which accepts a function as an argument would be something that integrates the supplied argument function over some interval and returns the result. Made up example: Int (cos) integrates cos() over a quarter cycle from 0 to pi/2 and returns 1. But in this case the integrating function is nothing like the functions which it takes as an argument - you could not think of operating the integrating function with itself as an argument, ie Int(Int). There is no difficulty in coming up with functions that can be composed with themselves, F(F(x)) where x is supplied, but very hard to think of a function that operates itself, and we would write it as F(F) because we are not supplying any x value.