5.526 One can describe the world completely with completely generalized propositions, which means therefore without initially [or: a priori?] coordinating any name with a particular object.
In order then to get to the usual means of expression one must simply say “And this x is a” after an expression “There is one and only one x, such that…..”
Doesn’t this contradict what came earlier? How could a completely generalized proposition mean anything without being made up of elementary propositions, which must have names as their parts?
Fahrnkopf (p. 49) argues that "The second paragraph, which shows the replacement of an apparent variable by a name only for the case of 'a', a letter customarily used to represent an argument (i.e., a particular), is slightly misleading, because the point of talking about completely generalized propositions--as is made clear by 5.5621 as well as by the comparable discussion of completely generalized propositions in the Notebooks--is that in such propositions even the function is generalized.""The point, then," he continues, "of the statement in 5.562 that the description of the world can take place 'without first correlating any name with a particular object' is surely to stress that even those objects which are universals, and thus represented by function-signs, can be represented by apparent variables rather than by constants."
Black (p. 288): “W. does not mean that names are theoretically superfluous: as he explains in the Notebooks, ‘Names are necessary for an assertion that this thing possesses that property and so on.’ (53 (8,9)). W.’s point is that general propositions describe, without any imprecision, the general structural features—the make-up or constitution—of the actual universe. However, such a description cannot express the respects in which the actual universe differs from an isomorphic one that might have existed in its place.”