Biden is a half president.

In most respects, President Joseph R. Biden is a thoroughly conventional president — a leader deeply respectful of precedent, a man whose style and values are shaped by living through more than half of the 20th century even as he ends his career navigating the disruptive politics of the 21st.

By contrast, the great foil of his presidency — predecessor Donald Trump — is in style and contempt for precedent the most radical person ever to hold the office.

Biden’s Oval Office address Wednesday night, however, underlined a paradox. There is one way that Trump represents continuity and Biden is the anomaly. This paradox is also the reason Biden won’t be his party’s nominee for a second term.

For most of American history — certainly since the start of the 20th century — the presidency has taken much of its power from the ability of its occupants to communicate. In other words, to use the singular power of the Oval Office to command the attention of the nation — more or less at will, on any topic or occasion — and shape the thoughts and mood of the country through the power of words and image. There is no better place to wage a national argument.

By this narrow but critical standard, it is Trump who used the presidential pulpit — and the mania and obsessive interest that followed him even after he lost it — in ways consistent with the grain of American history. He preoccupies the psyche of the nation, no less among those who loathe him as among the half or nearly half who are open to returning him to power.

It was Biden who is the tragic exception. He has been essentially a half president.