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Say you come up with an idea, but X already has written about it before, even though you don't know about this.
Is it plagiarism to then publish the idea, even if during publishing you still are not aware that X came up with this idea first?
That is, can you accidentally commit plagiarism in this way?
If you publish an idea that turns out to have been previously known, but you were unaware of the prior work before you published it, then it's not plagiarism. Depending on the circumstances, it could be considered poor scholarship, or even negligence if you really should have found the reference. However, it's not a form of academic dishonesty if you truly didn't know.
If you come up with an idea on your own, learn that it was previously known, and subsequently publish it as original work without disclosing the prior source, then it's definitely academic dishonesty. I wouldn't use the word "plagiarism" if you came up with the idea independently, but it's still misconduct to act like you're unaware of the idea's history.
The trickiest case is if you may have been aware of the idea in the past, but forgotten about it. That's a horrible mess, since the rest of the world has no way of knowing whether you genuinely forgot or are being dishonest. (You really don't want to have to argue that you aren't a thief, but rather massively screwed up.) This is the only case in which I think accidental plagiarism is really plausible.
This is not at all common, but it can happen more easily than you might hope, so it's best to be careful to keep track of what you've heard about. The worrisome scenario is the following: you hear Smith give a talk, but you don't really understand it or care very much, so you basically forget about it. Some years later, you are faced with a similar problem and come up with more or less the same idea to solve it. You don't realize how similar it is to Smith's talk, but you may have been influenced by subconscious memories, so you haven't really discovered it independently. When you publish your idea, Smith writes to you to say "How dare you use my idea without giving me any credit! I know you were at my talk, since we chatted afterwards, and your colleague X confirms that he remembers you there as well. Did you really think you could get away with this?"
There is such a thing as independent discovery. In the 17th century, Newton and Leibnitz apparently discovered calculus a year or two apart, but without either knowing about the work of the other. Nowadays, information travels at "warp" speed and "a year or two" would be an unacceptable time lag. Even so, it's possible that two people would publish similar findings, drawn from common sources, days or even hours apart. (And on SE sites, it gets even more intense; sometimes people "publish" similar answers minutes or even seconds apart, neither knowing of the other.) Under such circumstances, concurrent publication is usually excused, but it also behooves one to do a literature search to see if the idea has, in fact been published previously.
I have seen this happening in my field twice. Both researchers became famous because they did some research that was completed by others before its time being completely unaware of that research existence. Neither the editors, or the referees helped with this.
In one case, the researcher who was in this situation learned from colleagues that similar work was done in the 70's by a prominent Russian scientist, so he acknowledged it, and everyone is citing the Russian guy ever since. The good outcome is that the Russian guy made his re-entry in the field and made more contributions.
In the other case, the original paper was written by a Japanese scientist, who was a postdoc at the time, and everyone forgot about it. Three years later, another researcher wrote a very similar paper, became famous for it, but never cited the Japanese guy. In fact, very few people in the field cite him.
Since many fields are becoming increasingly multidisciplinary, I don't believe a single guy can do proper literature search. You can use google and web of science and whatever tools, but unless you are specialist in a field, you are very likely to miss something. Even if your random walk from citation to citation takes a significant percentage of your time, it may not be ergodic. For better ergodicity is good to have conversations with older scientists who might have stumbled upon your reference in the past. In any case, if you succeed to do your literature search properly, you will notice that there are a few others who didn't. The most unpleasant are the ones that should have cited you, and don't even answer the email you send them.
To answer the question, I don't believe it's plagiarism. In fact, before the advent of specialized science journals, it was quite a common situation in science. -- Remember all those two-name theorems from mathematics. Many of them were developed years apart by different scientists.
Building on David's comment:
If you inadvertently reinvent the wheel, without contributing anything additional and meaningful, your paper is unlikely to get published anyway. So let's start with the assumption that you inadvertently reinvented the wheel, did not credit the original inventor, and then added something meaningful. It is likely the review process would trigger a correction in this situation.
I think it would be helpful to review what plagiarism tends to look like. I have seen the following, as a copy editor:
Neglect to give credit for a creative assertion
Lift text from someone else's work, without putting quotes around it
Same as 1 or 2, but from your own previously published work
Other types of sloppiness I've seen:
Cite the wrong author(s) for a creative assertion or quote
Make a significant mistake in the citation
Cite the wrong work (but at least getting the researcher right)
As addition to the other answers: I think it is possible to distinguish if you are academically dishonest or that you really invented the wheel again.
If you reinvented the wheel, you will have worked with the new method a longer time to verify that it really works and you will therefore know its merits and its disadvantages. Moreover the path how you invented will be almost always different from the original author, so it will give you very specific insights which you intuitively grasp, but it does not give you the insights if you followed another path.
So a short interview (preferably with the original author if he/she is not malignant) would settle with high probability if you really invented the method yourself.
The Newton-Leibniz controversy is a good example: Newton used the "fluxion" approach, always dividing out the resulting equation and neglecting the remaining part while Leibniz see them as "differential", a ratio of infinitesimal changes, so he could cancel out e.g. (dy/dx) * dx = dy. Both used the same method to finally get the derivative at one point, but their interpretation varied. Both methods were attacked for their lack of rigour, but Leibniz approach was formally more elegant and easier to handle, so his integral notation prevailed.
Some assumptions here are that you are intellectually honest, you use a reputable publisher, and the prior work in question was done some time before yours. If your due diligence (and your publishers) didn't discover it in mainstream publishing in your field, it couldn't be considered plagiarism. While this answers your question, it still leaves open the likelihood of conflict over credit. Even without political considerations, history is replete with antagonism that carries for generations. While we as a society consider publishing important work of any kind to serve mankind, you can see how vital it can be to the author.
There is a famous example for this question. Some people re-discovered calculus in the following paper:
“A Mathematical Model for the Determination of Total Area Under Glucose Tolerance and Other Metabolic Curves”, Mary M. Tai, Diabetes Care, 1994, 17, 152–154.
You can laugh, but no, they did not commit plagiarism.
Real plagiarism involves deliberately copying someone else's work. I saw this when editing a paper for a PhD candidate who was worried about his English. Parts of the paper were badly constructed, but other parts were letter perfect. So I used Google to check for some of the unique phrases in the well-written section. Bingo! Wikipedia!
I did not tell him what I found. Instead I fixed the most glaring of his errors in English, gave him a note that Wikipedia was not an acceptable source, and hoped that his advisor and his examination committee would discover his malfeasance. They needed to hang him by his thumbs.
Generally if you find that you have inadvertently used someone else's idea without attribution it is good if you can later publish something that corrects the situation. It's better to do it that way than to have someone else point you out as a possible thief.
