Rep. Jackie Speier (D-Calif.) has called on McConnell to recuse himself. But the issue is far more serious. The real question is for the chief justice, who presides over the president’s trial: Can he accept an oath that he knows is false? Can he seat a juror who he knows has pledged not to be impartial?

During the impeachment of President Andrew Johnson, this question became a serious issue. Sen. Thomas Hendricks objected to swearing in the Senate’s president pro tempore, Benjamin Wade, because under the rules of succession, if Johnson were convicted, Wade would have become president — casting doubt on Wade’s pledge of impartiality. That objection threw the Senate into a fierce debate until, for reasons unknown, Hendricks withdrew his objection.

That precedent should matter today. Any senator is privileged to object to any other senator taking an oath. The chief justice would then have to decide whether the oath can be sworn honestly. As there seems no way that McConnell’s oath could be honest, Chief Justice John G. Roberts Jr. should forbid McConnell from taking it. Whether he so rules or not, the decision could be appealed to the Senate as a whole. Should the Senate openly accept a false oath — perjury — in a proceeding to determine the president’s guilt?