Are citation mistakes and mistakes in paraphrasing considered plagiarism?
I read opposite opinions on if this could be considered plagiarism or it is simply something else.
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This is a very clear-cut case.
Taking someone else's work and presenting it as your own is plagiarism, full stop. No amount of paraphrasing could ever save that, and teaching the connection between paraphrasing and plagiarism is quite terrible, honestly. These are two separate things entirely - one is proper credit attribution and another is an ability to synthesize and interpret information from different sources.
Misrepresenting others' work is also bad, of course, but it is yet another topic. Going by the example by Bryan Krause in the comments:
Kittey et al says "Lions are cats"
Only two of the above are acceptable. If the last one could be traced to its origin with a high degree of certainty, this is a pretty serious offense of trying to steal others' intellectual work and cover the tracks. There is also being too sloppy to do so convincingly, probably for the better.
If anyone makes mistakes in citations out of the desire to paraphrase in order to avoid plagiarism, they need to go way back and understand what plagiarism is. And also figure out why are they even paraphrasing in the first place.
An action needs to have an element of will for it in order to constitute plagiarism. A honest mistake
is not plagiarism, nor is an accidental citation error
They still reflect negatively on the writer and they run the risk of being taken for plagiarism as many engaged in plagiarism talk excuse their bad action by a "honest mistake".
There has been at least one high profile case where an academic committee decided that an action was not plagiarism because the idea of someone else made it through iterative versions of lecture notes through years of teaching, evolving, and finally being made part of a text book. Somewhere along this line, the author forgot that it was not his work only. That is an exception, but shows that in practice, plagiarism is usually not so well defined.
Another source of confusion is the rediscovery of certain facts. It is quite common in the Engineering field or in Mathematics to rediscover the same fact. Some well-known theorems suddenly get different names because of this.