The Senate's impeachment trial of Donald Trump is unprecedented: It's the first time a president has been tried twice, and the first time an ex-president has been tried at all. The fact that it is taking place is a testament to how outrageous Trump's conduct was in his last months in office. Even opponents of the impeachment trial, such as the editors of the Wall Street Journal, concede that it was impeachable behavior.

His supporters have nonetheless devised several arguments in his defense. They are not strong.

It's unconstitutional to convict a former president. Neither the text of the Constitution nor the founding-era debates over it speak specifically to a scenario in which a president commits serious misconduct just before leaving office. It doesn't seem to have been on anyone's mind in the 1780s. But several features of the text suggest that it allows for the conviction of a president after leaving office. It provides, for example, that the Senate has the power "to try all Impeachments."

Both the text and the debate indicate that impeachment had several purposes, some of which would be furthered by allowing it to apply to former federal officials. Alexander Hamilton called impeachment "a method of national inquest into the conduct of public men," for example. The Senate has repeatedly taken up impeachment cases of former officials, and even when it has declined to do so has sometimes noted that it had the power to do it.

Considerations like these have led most scholars to conclude that the Senate can convict former officials — a consensus reached long before Trump became president. Brian Kalt, a scholar whom Trump's own legal defense has cited multiple times, has defended this view for decades.

It would set a bad precedent. If the Senate convicts Trump, runs the argument, it would be possible to impeach and convict former Presidents Barack Obama and Jimmy Carter, too. That's true, theoretically. But public opinion and the two-thirds threshold for conviction are sufficient checks against the frivolous use of impeachment. Congress unquestionably had the power to impeach Obama and Carter while they were in office, and didn't; the House has impeached presidents only four times in history.

Failing even to try Trump would set a worse precedent. It would mean that a president who has been given the boot by voters could scheme to stay in office anyway. If he fails, there won't be any time for Congress to do anything about it before he departs. If the view that ex-presidents cannot be subject to impeachment trials prevails, presidents will have a stronger incentive to try to retain power by illicit means.

Trump isn't guilty of inciting violence, and the First Amendment protects him. The fallacy here is the assumption that the Senate can convict Trump only for committing a statutory crime. Both Hamilton and James Madison spoke more broadly of impeachable offenses as violations of the public trust. Congress could rightly oust a president for inciting violence even if no court of law would ever send him to jail for it — which is only fitting, since being deprived of office is a smaller imposition than being imprisoned. It's a mistake, in any case, to view Trump's Jan. 6 speech in isolation: It was part of a course of conduct designed to pressure state and federal officials to break the law to let him keep office.

It's pointless. Republicans who say a Senate trial is a waste of time because Trump will inevitably be acquitted are talking in circles: They're trying to justify their refusal to convict by pointing to ... their refusal to convict. Whether it was prudent for Congress to take up impeachment is a reasonable question, but it's independent of the question before each senator, which is whether Trump's behavior deserves conviction or acquittal. Is it better for the country and the Constitution for there to be one more vote against the post-election campaign that led to the Capitol riot, or one fewer?

The trial is a cynical ploy to hurt Republicans politically. Republican senators will have to choose between the public at large, which favors conviction, and their own party's voters, who oppose it. So what? Politicians often have to upset some voters. Sometimes the right thing to do is to take the unpopular stance, and sometimes it's to buck one's own party. Resentment at being asked to decide is not a reason to vote for or against conviction.

By requiring a two-thirds vote of the Senate to convict, the Constitution created a presumption for acquittal. So the arguments for acquittal don't have to be persuasive. They just have to sound plausible. Lucky for Senate Republicans.

Ramesh Ponnuru is a Bloomberg Opinion columnist. He is a senior editor at National Review, visiting fellow at the American Enterprise Institute and contributor to CBS News.