There are two “facets” to the numbering system of Tractatus Logico-Philosophicus. One is to show the logical importance the comments to propositions/comments. The other is to show to which of the propositions/comments are they a comment of.
Two “problems” immediately come to mind when I look at the system:
- In certain parts the less important comments come first before the more important ones.
- There can never be more than ten comments to a comment.
Let’s start with the quote (Ogden’s translation) of the one and only footnote which accompanies the text
“The decimal figures as numbers of the separate propositions indicate the logical importance of the propositions, the emphasis laid upon them in my exposition. The propositions n.1, n.2, n.3, etc., are comments on proposition No. n; the propositions n.m1, n.m2, etc., are comments on the proposition No. n.m; and so on.”
There is only one comment in which the final digit reaches ‘9’. It is comment 2.19 (what the comment is is unimportant here). 2.19 is a comment on 2.1 as defined by Wittgenstein’s (reluctantly included) footnote. If for example there were to be another comment to 2.1 after 2.19 then it would be 2.110. If there happened to be another comment then it should be 2.111.
But would not 2.111 be a comment to 2.11 and not 2.19?
Let us just say it was fortunate that he did not reach this number for he may have had to do something drastic to recover from the illogicalness of this.
The second problem is that Wittgenstein starts some comments with “odd” numbers. The first one in the text is 2.01 after proposition 2. While in proposition 1 the next comment was 1.1 as explained in the footnote this was different here. One has to assume then 2.01 is less important than 2.1 which happens to be there 42 comments later. By sheer quantity the comments on the non-existent “2.0” comment must be somehow important then.
Furthermore 2.01 comes before the more important comments like 2.1 etc. Should not they come after these? Most likely because ‘0’ comes before ‘1’ that they are arranged in this manner. Linearly this makes sense. But in terms of commentary priority it should come afterwards.
I can see what Wittgenstein wants to do (it was a good attempt) but the logic of his numbering system leaves much to be desired.
Modern systems of numbering use multiple periods (for example: 2.1.1, 2.1.11, 18.104.22.168 , etc). This system was non-existent in Wittgenstien’s time. Would the order of his comments been different if he had the benefit of such a system? Would we read Tractatus different under this more logical numbering system? That, we shall never know.