Wiki is perhaps the only web idiom that is not a child of BBS culture. It derives historically from pre-web models of hypertext, with an emphasis on the pre. The immediate ancestor of wiki was a Hypercard stack maintained by Ward Cunningham that attempted to capture community knowledge among programmers. Its philosophical godfather was the dead-tree hypertext A Pattern Language written by Christopher Alexander in the 1970s.
What wiki brought to these models, which were personal to start with, was collaboration. Wiki values are often polar opposites of blogging values. Personal voice is meant to be minimized. Voices are meant to be merged.
Not so true for the personal wiki. Maybe a personal wiki is wiki software but with different values for the output?
Rather than serial presentation, wiki values treating pages as nodes that stand outside of any particular narrative, and attempt to be timeless rather than timebound reactions.
This is still true for personal wikis.
Wiki iterates not through the creation of new posts, but through the refactoring of old posts. It shows not a mind in motion, but the clearest and fairest description of what that mind has (or more usually, what those minds have) arrived at. It values reuse over reply, and links are not pointers to related conversations but to related ideas.