4.128 Logical forms are unnumbered [number-less, but not in the sense of too numerous to count].

Therefore there are in logic no pre-eminent numbers, and therefore there is no philosophical monism or dualism, etc.

Black (p. 206) suggests ‘anumerical’ for zahllos (‘unnumbered’). He goes on: “It is nonsense to speak of counting logical forms. It is not clear what W. had in mind here: certainly in a universe containing a finite set of objects and a finite set of their combinations, a list could be made of distinct logical forms, which might then be counted. … Perhaps W. wanted to stress that ‘is a logical form’ is not an authentic predicate such as ‘is a star.’

My first reaction: Are logical forms without number (as Pears and McGuinness have it) because they cannot be counted, since their ‘existence’ is so dubious/problematic, or is it because they are more or less arbitrary inventions/conventions (like mathematical operations and stipulated first terms in series)?