WHEN THE JUSTICES of the Supreme Court meet in conference this morning, they will confront a problem of their own making. Last July, the court ruled -- or so it appeared at the time -- that the public has no right to attend criminal trials. It wasn't long, however, before some members of the slender (5 to 4) majority began to back away from the idea. Now, the justices face head-on the issue of secret trials and have to square what they said officially last summer with what some of them have said unofficially since.

The court should admit it made a mistake. True, the court has rarely reversed its position on anything this soon. But rarely has a decision been so thoughtfully attacked and so soon discredited.

The idea that individual Americans can be tried and convicted in secret is repugnant to the Constitution and to the philosophy on which the nation's entire legal system rests. It assumes that the public has no legitimate interest in how justice is administered and how its courts operate.It elevates what a majority of the court has determined to be a right of an individual -- the right to be tried in secret -- over the right of the public to know that justice has been done.

This is not a matter of conflict between the First and Sixth Amendments, as some lawyers and justices perceive it to be. The right of the press to attend and report criminal trials cannot be greater than the right of the public because the press is acting in such instances as the public's surrogate. To play the two amendments against each other is only to complicate a straightforward issue.

The history of secret legal systems is terrible. The history of this nation -- until recent years -- shows only a deep aversion to closed courtrooms. The danger of secrecy to the judicial system is obvious since the courts depend totally for their power on the public's belief in their integrity. There are instances in which a particular defendant believes he is better off being tried in secret. But there can be no instance in which the essence of a criminal trial -- the vindication of the public's right to justice -- can be realized by secrecy. The Supreme Court should change its mind.