Pro and con? Perhaps you think this is a deliberately provocative title. Every teacher, after all, is vehemently against plagiarism, right? We are justifiably outraged when a student turns in a paper in which whole paragraphs are cribbed unattributed from Wikipedia…or, worse yet, the whole paper is stolen from another author. The issue is black and white, isn’t it?
Flagrant violations are indeed fairly easy to spot and extremely easy to condemn. But if you think that that’s the end of the story, not the beginning, then you should read The Little Book of Plagiarism, by Judge Richard Posner. It will make you think again. Despite having attitudes that often border on (or cross the line to) obnoxiousness, Posner raises a large number of valid issues, which he discusses in a style that ranges from dryly legalistic in spots to anecdotally interesting most of the time. We are reminded of the remarks that Tom Lehrer makes in his well-known song, Lobachevky:
I am never forget the day my first book is published.
Every chapter I stole from somewhere else.
Let no one else’s work evade your eyes,
Remember why the good Lord made your eyes,
So don’t shade your eyes,
But plagiarize, plagiarize, plagiarize –
Only be sure always to call it please ‘research’.
Some of Posner’s examples are familiar ones. It is well known that poets from William Shakespeare to Bob Dylan “borrowed” extensively from earlier works, and no one accuses them of plagiarizing. What counts is the originality with which they treat the ideas that they have “borrowed,” not the fact that they didn’t come up with them in the first place. Perhaps less well known is the fact that judges routinely put their name on opinions that their clerks have written, and no one accuses them of plagiarizing. Posner does discuss the question of who is harmed in a plagiarism case, but I wish he had gone into greater depth on this issue; of course this is a major concern to him as a judge, but it’s not quite the point for a teacher.
Speaking of teachers, I wish he had brought up the subject of plagiarizing in teaching, both teaching in general and math teaching in particular. We all plagiarize, and it’s a little tricky to see how we can maintain our moral authority when we condemn plagiarizing in our students. The position goes something like this:
When I turn in a paper with my name on it — whether an article I write for a journal or a paper I turn in as part of a course I’m taking — I am taking credit for the ideas and words contained within it. Whatever I got from elsewhere, I need to cite. In that way I am not given credit for someone else’s work. But when I’m teaching a class, there is no presumption that I am taking credit for all the words and ideas in the lecture or in my discussions. It’s understood that I have synthesized what I say from many sources over my years of experience, and I neither claim originality nor do I even know where everything came form.
Well, OK. If I say that with firm conviction, maybe I can convince you. Certainly 92% of all teachers actually believe it. (I just made up that figure, so I can’t cite the source.) But as Posner would point out — even if he doesn’t actually discuss the issue — it’s not the least bit obvious why we expect originality in our authors and not in our teachers. Perhaps students are being harmed by not knowing where our words and ideas come from; perhaps readers are not being harmed by the same lack of knowledge. And yet it’s plagiarism in the case of authors but not in the case of teachers.
One last point: the thorny case of mathematics. Unlike other disciplines, it is assumed that mathematical ideas are the property of the community and do not require citation. (This is why mathematicians become so uncomfortable about the modern idea that algorithms can be patented.) Of course it’s good form to credit a mathematician if you know that you got your ideas from her, but most of the time you simply don’t know: I get a problem from A, who got it from B, who based it on something from C, who wrote the original problem by collaborating with D. Who do I credit? A, whom I got it from though I might not remember that? Or C, whom I’m not even aware of? And perhaps the idea is 2000 or 4000 years old, in which case the self-appointed plagiarism experts say that it’s “common knowledge” and doesn’t need to be credited, but I can find plenty of material that I have used (from 2000 or 4000 years ago) that is not in the least bit common — in any reasonable sense of the words “common knowledge.” So where does that leave us in math teaching? It leaves us with condemning acts of blatant theft of whole chunks of text and putting them in a document without citation, but otherwise we just live with the gray cases because we simply can’t draw the line in any plausibly consistent way. Math may seem to be the most black-and-white subject, but at least in this case it’s shades of gray.