On abortion, the United States public is strongly divided. On abortion as performance art, the nation is almost uniformly opposed, it would seem. A Yale University art student sparked controversy this week by claiming that she has repeatedly artificially inseminated herself and induced abortions for a period of nine months as a piece of performance art. She planned to exhibit films and other documentation of these miscarriages as part of her final project, until controversy found the student reviled by the public and condemned by Yale.

Whatever you think about the merits of inducing pregnancies only to induce abortions as an artistic activity, Yale's public-relations performance has been execrable. Following a very public debate about Yale senior Aliza Shvarts's controversial art project, the university has stumbled over its own message and forgotten its mission.

At the moment, it remains to be seen whether and to what extent Shvarts followed through with her "abortion as medium" project, but Yale was quick to write the whole thing off. "The entire project is an art piece, a creative fiction designed to draw attention to the ambiguity surrounding form and function of a woman's body," Yale spokeswoman Helaine Klasky told the Yale Daily News. That account has yet to be definitely confirmed, but it registers the right note - a factual account. "She is an artist and has the right to express herself through performance art."

Yet with Klasky's next breath, the university delivered judgment: "Had these acts been real, they would have violated basic ethical standards and raised serious mental and physical health concerns."

Yale calls into doubt its stated support for performance art by appealing to a set of unstated "basic ethical standards". Worse still, the university's statement - cast before faculty within the department in question had spoken - seems to undercut the autonomy of and confidence in that department. If, as Klasky claims, the project is a fiction, then why has the university disciplined two faculty members (School of Art lecturer Pia Lindman and School of Art director of undergraduate studies Henk van Assen)?

No matter. Robert Storr, a highly regarded critic and curator and the dean of the Yale School of Art, echoed the opinion of the university. "If I had known about this, I would not have permitted it to go forward," he told the university newspaper. "This is not an acceptable project in a community where the consequences go beyond the individual who initiates the project and may even endanger that individual." Presumably Storr would not feel the same way about other examples of performance art that are recognised as groundbreaking moments in the genre, if not art history. What to make of Vito Acconci's Following Piece? The work of the Viennese Actionists? Or Chris Burden's Shoot?

It is not enough to say that physical harm might have been caused by the inducement of one or several miscarriages, and that therefore the work is unacceptable. (Physical harm was definitely caused when Burden had himself shot in the arm, and his work is celebrated.) Self-mutilation and scarification have a long history in performance art. In a superficial, relative sense, Shvarts's piece barely registers on the self-administered-harm scale. Other recent performance pieces have caused a stir in university settings for better reason. When Burden resigned from his UCLA faculty post in 2005 after the school failed to reprimand a young artist for staging a game of Russian roulette in the classroom, Burden's response was both ironic and needlessly meek. As he told the Daily Bruin: "Columbine has happened; 9/11 has happened. There are restrictions." In fact, neither of those incidents affected the gun policy on campus. All notions of merit or context aside, a university cannot and should not tolerate an illegal action that potentially endangers students.

Burden was right to clarify that point - the student's Russian roulette game was illegal in the classroom, but could be judged on the merits as art in another setting. What Storr and dean of Yale Collete Peter Salovey fail to recognise is that the classroom is exactly the sort of context for the piece Shvarts has proposed: documentation of a private activity. The school is tripping over two issues related to performance art: age and credential, and quality.

Salovey says: "This piece of performance art as reported in the press bears no relation to what I consider appropriate for an undergraduate senior project." The emphasis here is on Shvarts's age - as if were she a year toward her Master's degree, she would have the credentialing to follow through with such a piece. This attitude is a problem. The market follows the work of young and emerging artists closely, and practice often really begins before a bachelor's degree is even granted. And it reeks of ageism to say that a young woman should wait until her mid-career survey before she should have anything worth saying about abortion, autonomy and sex.

Second, performance art tends to be judged within a public context that, as a rule, is openly hostile to performance art. The academic environment is supposed to protect this speech and nurture the frames for viewing the world that art establishes. The result, with good supervision and mentorship, will be good art, but it will not always be publicly palatable art. Art colleges do no good work when they snap to fit the public perception of artwork that is, pardon the expression, in utero. Whether Shvarts has made good art remains to be seen - if it is seen - but the answer will not be determined by whether or not a performance art-hating public hates her performance art.

As Shvarts explains, "the piece exists only in its telling" - proof one way or the other about the activity will be hard to come by, and perhaps that is in part the point. (Proof isn't impossible, says Discover magazine.) She's rather sidestepped the question of proof, now that the notion of a woman inducing abortions is seeing debate in the public sphere. For Yale administrators to put on an epistemological show, saying they'll only show Shvarts's work if she signs a statement declaring it inauthentic, is an embarrassment. It's prevention after the fact, censorship aimed at mollifying public opinion. What matters next is seeing the work.

If Yale faculty judge Shvarts's work and find it lacking, the school has a much more powerful tool than censorship to dissuade her from making more: They can give her a failing grade.