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What does the U.S. Constitution really have to say about whether the Senate must put a president's Supreme Court nominee to a vote? President Barack Obama says the Constitution "is pretty clear on what happens next": He nominates, and the Senate says yes or no in a timely fashion. Republicans think the Constitution gives the Senate the right, not just the power, to give the president's nominee a hearing or to refuse to do so.

They're both wrong. Here's what the Constitution says about filling Supreme Court vacancies: nothing. In fact, the Constitution says nothing about the size of the Supreme Court at all. Congress could pass a law leaving the number of justices permanently at eight. Or it could expand the number to 23. All the Constitution requires is that there be a Supreme Court. Beyond that, we're in the realm of politics.

Article III, Section 2 of the Constitution says that "judicial power of the United States, shall be vested in one Supreme Court, and in such inferior courts as the Congress may from time to time ordain and establish." That's right, Congress doesn't have to create any lower federal courts at all. It could rely on state courts to handle all federal law issues with a right of appeal to the Supreme Court.

From the fact that the lower courts are optional, you can deduce that the Supreme Court isn't. But the size of that court is left undefined. In theory, I think, it could consist of a single judge. The interpretation of the Constitution would rest his hands. You could even call him Anthony Kennedy.

When it comes to nominations, Article II, Section 2 says that the president "shall nominate, and by and with the advice and consent of the Senate, shall appoint," among other officials, "judges of the Supreme Court."

The word "shall" sounds like a directive. But remember that Article II, Section 3 says that the president "shall take care that the laws be faithfully executed." According to the Obama administration, as it's expressed his views in the Supreme Court case involving executive action on immigration, this provision doesn't obligate the president to enforce every law all the time. The word "shall" confers some discretion on the executive. Presumably, if Obama didn't want to nominate a replacement for Justice Antonin Scalia at all, it would be within his constitutional discretion not to do so.

As for the Senate's "advice and consent," it's hard to argue that this requires the body to put a nominee to a vote. The Senate has essentially complete control over its own rules and practices. Most prominently, it has long used the filibuster, which is a rule of procedure that deviates from the principle of majority rule. You might think the filibuster is undemocratic and unconstitutional, but you can't do anything about it, because it's up to the Senate to decide how to operate.

Given this self-control, the Senate certainly possesses the de facto authority to refuse to confirm or even consider a nominee. This would amount to reducing the number of justices on the court — but that, too, is within Congress's control.

Changing the number of justices isn't unprecedented. Most famously, President Franklin Delano Roosevelt supported legislation in 1937 to pack the court by adding new justices for every justice older than 70. At the time, six of the nine justices were past that mark — a reminder that the current court isn't that old in comparison. In essence, Roosevelt was proposing a court of 15.

At other times in U.S. history, the number of justices has been as low as six and as high as 10 — all as determined by statute. There's obviously no requirement that the number be odd. If Congress wants a gridlocked court that affirms case by a divided vote, it can have it, according to the Constitution.

The Obama administration could argue that, so long as the statutory number of justices is nine, it's obligated to nominate a replacement and the Senate is obligated to give or withhold its consent. On this view, only a statute passed by Congress and signed by the president can change the total number of justices.

But this would be highly formalistic argument, inconsistent with the functionalism that the administration has rightly espoused in the immigration case. The word "consent" implies a choice by the Senate to say yes or no. Add the word "advice," which isn't usually given a technical constitutional meaning in this context, implies a right to express a view.

The upshot is that the Constitution really doesn't answer the question of what the president or the Senate must do after the death of Justice Scalia. It sets the ground rules for a political battle — and the politicians can fight it out. That's OK. Our Constitution has its good points — and one of them is that it doesn't solve every political question. Nor should it.

Noah Feldman, a Bloomberg View columnist, is a professor of constitutional and international law at Harvard.