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Many sources for Wikipedia articles refer to Wikipedia without citing it. Many journalists will work from Wikipedia, and most of Wikipedia's sources are journalistic articles. It happens to be that often this isn't noticed because the information obtained this way is true and uncontroversial. Citogenesis only documents examples where, by bad luck, the result is untrue information.
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No citogenesis is present regardless of whether the information is "true". The concept of "truth" on wikipedia doesn't have much weight, mainly because it would be impractical, out of scope and original research to determine truthfulness.
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> It is only when articles posing as secondary sources fail to cite wikipedia that a recursive quality loss can occur

I've seen a college professor cite wikipedia in support of a false claim. On investigation, the text in wikipedia was cited to an earlier blog post by that same professor.

I wasn't convinced.

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I don't think it's entirely illegitimate.

1- citing wikipedia (or any tertiary source) is valid, the problem is just when the source is not cited. And also it's against wikipedia policy, but you are free to cite it elsewhere.

2- citing the tertiary source and citing the secondary source are distinct and valid. There is no "rule", in wikipedia or otherwise, that says you need to cite the underlying source. In fact citation chains can become quite deep, it would be very impractical. An example would be, you could cite the gospels when jesus talks with the devil. If we had it your way then you wouldn't be able to cite an apostle, you would have to attribute the quote to jesus, and furthermore if jesus quoted the old testament you would have to cite that? If you think the bible is an exception, consider case law, if you were to cite an attorney's defense and the attorney cited some cases, would you have to cite the original cases? If so, then which? There might be multiple, it's not just a citation chain but a graph.

In this specific example your professor was not just quoting himself, but his work is now part of wikipedia and importantly was not contested or was not successfully contested. Similarly to how a trademark works, you claim you own the trademark, and if a year or so no one contends it, you have a stronger case that it's yours.

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