WASHINGTON — In the first argument of its new term, the Supreme Court on Monday considered whether states may abolish the insanity defense, a question that seemed to puzzle several of the justices, who drew conflicting lessons from history, moral philosophy, constitutional law and the brutal crimes at the heart of the case.

James Kahler of Kansas was sentenced to death in 2011 for killing four family members, but his lawyers said he had severe depression that made it impossible for him to understand reality or to distinguish right from wrong.

Kansas eliminated the insanity defense about two decades ago, so he was barred from raising the defense that he had been mentally ill. Sarah Schrup, a lawyer for Mr. Kahler, said that was a radical departure from American legal traditions.

“For centuries,” she said, “criminal culpability has hinged on the capacity for moral judgment, to discern and to choose between right and wrong. The insane lack that capacity.”