4.1272 Thus the variable name “x” is the proper sign of the pseudo-concept object.
Wherever the word “object” (“thing,” “item,” etc.) is used rightly, it is expressed in the concept-script by a variable name.
For example in the proposition “there are two objects, such that …” by “(Ex,y)…”.
Wherever it is used otherwise, thus as a proper concept word, nonsensical [unsinnige] pseudo-propositions arise.
Thus one cannot, e.g., say “There are objects,” as one says “There are books.” Just as little can one say “There are 100 objects” or “There are א0 objects.”
And it is nonsensical [unsinnig] to speak of the number of all objects.
The same goes for the words “complex,” “fact,” “function,” “number,” etc.
They all signify formal concepts and are represented in the concept-script by variables, not by functions or classes. (As Frege and Russell believed.)
Expressions like “1 is a number,” “there is only one zero,” and all such are nonsensical [unsinnig].
(It is equally nonsensical [unsinnig] to say “there is only one 1,” as it would be nonsensical [unsinnig] to say: 2+2 is at equal to 4.)
Quite a bit of Frege- and Russell-bashing going on here, it seems. But what concept-script is he talking about? His own, or the only possible correct one? In other words, is he stipulating how he wants these things to be done, or claiming that Frege and Russell are wrong in some more objective sense? Perhaps it comes to the same thing if he is here developing Frege's and Russell’s ideas as well as they can be developed. But in what sense, if any, is it nonsensical to say there are objects or that 1 is a number? Surely in teaching a child or doing philosophy we make such assertions often. They do not, presumably, count as propositions though for Wittgenstein. They are what he later called grammatical remarks, not (metaphysical) facts. To treat them as facts is to misuse them, i.e. to speak nonsense. Certainly attempts to specify the minimum number of objects there must be are badly mistaken, in Wittgenstein’s view. The Hebrew letter Aleph with the suffix 0 is used in mathematics, including in Principia Mathematica, says Wittgenstein in Letters to
Ostrow (p. 77): “In acknowledging the weakness of our grasp on “object” we are acknowledging the same about “complex,” “fact,” “function,” “number,” and so on.” On p. 78 he says: “We do not by means of this text arrive at new, superior accounts of “fact,” “object,” and “number.” What the Tractatus seeks instead is to lead us to regard in a new way our attempts to gain clarity about all such notions; it seeks to get us to go on differently in our efforts to know the world. We are called to go on without philosophy.”