Logic of Division

Mon, 01 Jan 0001 00:00:00 +0000

Logical division is the operation that produces a hierarchy: a class, the genus, is split into subclasses, the species, on one characteristic, called the basis of division or, in the logic textbooks, the fundamentum divisionis. Jevons: “Logical division is the name of the process by which we distinguish the species of which a genus is composed. Thus we are said to divide the genus ‘book’ when we consider it as made up of the groups folio, quarto, octavo, duodecimo books, &c., and the size of the books is in this case the ground, basis, or principle of division”. A directory tree, a taxonomy and a class hierarchy are all products of repeated division, and the rules for doing it soundly were written down long before any of them existed. This page states the rules and then applies them to the two orders software/microsoft and microsoft/software, which turn out not to be mirror images: one is a hierarchy and the other is a grouping wearing a hierarchy’s clothes.

Escapes From the Tree

Mon, 01 Jan 0001 00:00:00 +0000

A tree gives each thing one path, so it can collocate one facet and must scatter the rest — the citation order problem. Five mechanisms let a reader reach a thing by a facet other than the first-cited one. Each keeps a single physical location and adds a second route to it, and each pays for the route in a different currency: a polyhierarchy gives a node more than one parent; a link or alias is a second name that resolves to the first; postcoordination defers the combination of facets to query time; rotation generates every citation order in advance; and a lattice stores every combination of facets as a node of its own. What the evidence says people actually do comes last, because it is not what the mechanisms predict.

Citation Order on Bitsy Wiki

Logic of Division

Escapes From the Tree