Take a look at some WikiFarms out there. Many of the wikis in these farms are focused on sex, (what`s our problem about sex?) have only one test page, or the wikizens have left a long time ago. They are purposeless wikis.
It's not enough to throw up a wiki onto the web, sit back, and wait for something to happen. If you don't have a vision, there is no reason for people to contribute. If you don't invite people, no-one will come. If you don't put effort into your wiki, no one else will. See SeedPosting.
Consequences: The purposeless wiki turns into dead pages on the web. SoftSecurity fails due to lack of community and the wiki becomes vulnerable to vandalism.
Treatments: Zen it. There's no point in getting upset. Dead wikis join the huge pile of purposeless homepages on the web, there's nothing wrong with that. If you don't want to read it, don't.
If, however, you are responsible for a purposeless wiki, there are only two solutions: find a purpose and actively pursue it, or dump the whole thing. If you dump the wiki, then find another place to host any valuable content (assuming no CopyrightTrap) and leave a pointer there.
I think MultiPurposeWiki? is a TargetGroup intersection problem. PurposelessWiki is similar because any visitor will either have no target or he will become a contributor with a target. In this case the chance of similar targets is near null and - again - the intersection problem hits. CommunityWiki:TooFewWiki is uninspiring because it doesn't take the most basic experience into account that ownership and leadership do make a difference in how a wiki develops. -- HelmutLeitner
CommunityWiki:TooFewWiki offers one particularly interesting semi-PurposelessWiki idea that I had in mind: The idea of a wiki where people can develop pages and then have squatters rights. In this setting, the owner simply offers up hosting and some rules to force communities to be productive or be deleted. Thus, the wiki where all of this growth takes place has no specific purpose, but does promote community development and could be a solution for problems posited on TooFewWiki?. The page does really need a refactor though... -- MattBowen