I wrote once before about staunch criticisms of Wikipedia I heard in a faculty development seminar. Since then I've been thinking about different kinds of knowledge, the nature of truth, citation, and verification.
In my professional life, I have used Wikipedia for background on some mathematical concept or details on some algorithm I'm teaching. In these areas, knowledge has a sort of self-consistency, and appeals to authority are worth very little. Suppose a Wikipedia article says, “The following algorithm searches for a number in an ordered list in logarithmic time,” and provides the algorithm. The claim is something that an informed reader can verify for herself, independent of any works cited. The algorithm either works or it doesn't.
Now, suppose the article also claims that “This algorithm was invented by Charles Babbage in 1856.” It seems to me that this is an entirely different kind of knowledge. There's no self-consistency, no way to verify this on its own terms. A citation – an appeal to authority – is critical. And probably the cited authoritative work will cite other works, and so on, like a house of cards.
This is a curious situation. We're not marshaling evidence to support an opinion, but a claim of fact. It's either true or false. And yet there's no way to convince you either way except by appealing to a vast network of authorities.
To someone versed in mathematical logic and proof, this is deeply unsatisfying. And yet for most people, in most fields, I guess it's just the nature of knowledge. If a vast network of authorities is the only handle you have on the truth, then I could understand getting a little anxious at the thought of Wikipedia entering that space.
I have distinguished mathematical truth (e.g., “the real numbers are uncountably infinite”) from historical truth (e.g., “Cantor proved the real numbers are uncountably infinite in 1891”). Perhaps the ‘hard’ sciences offer something in between. Part of the purpose of claims made in scientific papers is that the evidence can – albeit at great expense – be replicated by readers. But still there's no self-consistency in, for example, biology. Maybe because it deals in knowledge about the real world, you can't just consider a claim on its own and verify its truth.
Mathematics is not about the real world. If anything, mathematics is about itself. Mathematical truth is meaningful and accessible, but no amount of observing, measuring, or citing esteemed scholars will get you there.
