TO EMPHASIZE the difference between words and reality, Abraham Lincoln liked to pose a well-worn riddle: Suppose you call a sheep’s tail a leg. How many legs will the sheep then have?

The answer, of course, was four. Calling a tail a leg doesn’t make it a leg.

Now, suppose you call St. Isidore of Seville Catholic Virtual School a public school. Does that make it public?

That’s the question at the heart of a legal battle pitting Oklahoma’s attorney general against its charter school board, with St. Isidore’s fate hanging in the balance. The state’s highest court ruled recently in favor of the attorney general and against the Catholic school. Now the US Supreme Court is being asked to take the case and reverse. It should do so to uphold religious liberty under the First Amendment. And because, as Lincoln knew, a false label cannot alter the truth.

Here is the background.

Last year the Catholic Archdiocese of Oklahoma City and the Diocese of Tulsa created St. Isidore and applied to be certified as a charter school under Oklahoma law. Many such schools exist in the state. Charter schools, which are exempt from regulation and oversight by local school committees, must meet basic health and safety standards. They must also be tuition-free and open to all students. But their essential purpose is to provide “a diversity of educational choices” — an array of distinctive teaching methods, curricula, priorities, and values from which parents can choose the option that is best for their children.

Thus, there is an Oklahoma charter school that emphasizes Spanish/English bilingual education. Another offers education with a focus on computer science and technology. A third embraces an international approach, with a staff drawn from 18 countries. Yet another places high value on the fine arts and teaches dance, music, and theater. Still one more immerses students in Cherokee language, history, and culture.

The mission of St. Isidore? To provide a rigorous Catholic education, through a curriculum rooted in “virtue, rigor, and innovation.” Catholic schools have an admirable record of achievement in the United States. So with every reason for confidence in St. Isidore’s prospects for success, the Oklahoma charter school board approved its application.

Which triggered an uproar.

Oklahoma Attorney General Gentner Drummond promptly sued the charter board, demanding that St. Isidore’s contract with the state be rescinded on the grounds that Oklahoma law requires all charter schools to be “nonsectarian” — i.e., not affiliated with a religious institution. But the board had reasoned that to reject an application because of a school’s religious character would violate the First Amendment, which forbids government officials from impeding the “free exercise” of religion.

In a string of rulings in recent decades, the US Supreme Court has repeatedly affirmed that a state cannot bar religious schools, parents, or students from public benefits simply because of their religion. It is by now well-established that if a state provides public funds for education in the form of vouchers, parents may use those vouchers to pay for tuition at a religious school. As recently as two years ago, the Supreme Court drove home the point, ruling that Maine’s tuition assistance program could not be limited only to students in “nonsectarian” schools.

But Drummond argued before the Oklahoma Supreme Court that public funds spent on charter schools were different because state law labels them “public schools.” That means every charter school must be seen as a state entity. And state entities may not promote religion.

A majority of the Oklahoma justices accepted that argument. But in a forceful dissent, Justice Dana Kuehn made Lincoln’s point: St. Isidore — a Catholic academy created and run by the church — is not a “public school” just because a state statute calls it that. The whole point of the charter school law is to enable private entities of every description to offer unique, experimental, or specialized educational options the government does not provide. That doesn’t mean such schools are state actors in the eyes of the Constitution any more than a church-run homeless shelter becomes a state actor simply because it contracts with the government to provide human services.

Last week Oklahoma’s charter school board asked the Supreme Court to hear the case and to clarify again that the First Amendment does not permit a state to discriminate against a private charter school solely because it is religious. To parents who want their children to attend charter schools that emphasize computer science or Cherokee culture or the performing arts, Oklahoma says yes. To parents who want their children to study in a charter school that inculcates Catholic values, Oklahoma says no. Such anti-religious hostility was once common in America. But the Constitution forbids it, even if not everyone has gotten the message.