Librarians have systems that can classify every published book. And scientific publishers can classify every paper. Those don't add up to a complete classification of all human knowledge, but it's a substantial fraction of it.

If you skim the high-level book categories at https://en.wikipedia.org/wiki/List_of_Dewey_Decimal_classes, you may conclude this is is beyond a lifetime's work.

Mmhmm. A talented cataloger in a research library understands where the 'fuzz' in these systems is - where the margins intersect - and they have a process for helping systematize those classifications in a way that they can socialize with other librarians across the world. (If nobody has ever cataloged a particular book before... your record is probably going into OCLC WorldCat and other people will borrow the output of your thinking process later... making things more and more definitive.)