But there may be room for another great baseball player to reside in that lofty neighborhood. That case is convincingly made in "Hank Greenberg: Hero of Heroes," a new biography by John Rosengren.
There isn't any doubt about Greenberg's greatness as a hitter, or his contributions as a player. He was twice a Most Valuable Player -- once as a first baseman, once as an outfielder. He was the premier right-handed power hitter of his time, hitting 58 home runs in a season in an era when that number had much greater significance than it would later.
Greenberg played on four Detroit Tigers pennant-winning teams and two World Series champions. And he spent 47 months in the American military during what would have been the prime of his career. He returned from World War II, after a four-year absence from baseball, to hit the grand slam that clinched the 1945 American League pennant for the Tigers.
Greenberg's Hall of Fame credentials make him exceptional. But what also set this career apart from others was not only performance, but the fact that Greenberg was Jewish. In his time and place, being a Jewish ballplayer was a ticket to a steady diet of bigotry and abuse.
These themes of the Greenberg story have been addressed before, in the brilliant documentary, "The Life and Times of Hank Greenberg," written and directed by Aviva Kempner. But the historical value of these topics makes the book-length treatment completely justified.
Greenberg grew up in the Bronx, which turned out to be further from Detroit than a map could indicate. When he came to the Tigers in the early 1930s, the city was already a baseball hotbed. But it was also, Rosengren reports, the nexus of American anti-Semitism.
This was the home of Henry Ford, the pioneer in car manufacturing, whose publication, The Dearborn Independent, was a vehicle for virulent anti-Semitic attacks. From its articles, Ford later made four pamphlets entitled "The International Jew." Ford alleged that there existed a Jewish conspiracy to bring down Christianity.
Some of this material found a ready audience, both at home and abroad. Adolf Hitler told The Detroit News in an interview: "I regard Henry Ford as my inspiration."
And this was also the home base of Father Charles Coughlin, "the radio priest," who was a Roman Catholic priest at the National Shrine of the Little Flower in suburban Detroit. He had a nationwide listenership for his pro-Nazi, anti-Semitic broadcasts.
Perhaps the best description of Father Coughlin was contained in contemporary song lyrics by the great Woody Guthrie:
Yonder comes Father Coughlin, wearin' the silver chain,
Gas on his stomach and Hitler on the brain.
As a backdrop for this, there was Hitler coming to power in Germany, instigating the widespread persecution of Jews that was to lead to the Holocaust.
Given all this, Greenberg became a symbol of hope, Rosengren writes, not only for Detroit Jews, but for Jews throughout America. He was a big, strapping, powerful fellow whose legendary clouts defeated one negative stereotype after another.
And Greenberg conducted himself in a manner that won more admirers. Bud Shaver, sports editor of the Detroit Times, wrote that: "Greenberg's popularity is built upon sounder foundation than mere ability to hit a baseball. Greenberg has an attractive personality, crowd appeal."
When Greenberg chose not to play on Yom Kippur, the Day of Atonement, in 1934, the poet Edgar A. Guest produced a poem that suggested this act reached across ethnic and religious lines. The poem, which is in part a conversation between two Irishmen, concludes with these lines:
We shall miss him on the infield and shall miss him at the bat,
But he's true to his religion -- and I honor him for that!
Greenberg was, in Rosengren's analysis, a force for assimilation.
"He had begun to change the way Jews thought about baseball and the way baseball fans -- Americans -- thought about Jews," Rosengren writes. "Hank became the face -- and muscles -- of Judaism in America. He single-handedly changed the way Gentiles viewed Jews."
One of the strengths of the book is the author's ability to weave the social and the baseball narrative together. Greenberg was subjected to heaps of anti-Semitic slurs from opposing dugouts.
Every time Greenberg and/or the Tigers succeeded, it was a blow against bigotry. Greenberg certainly understood his role. "Being Jewish did carry with it a special responsibility," he said. "I came to feel that if I, as a Jew, hit a home run, I was hitting one against Hitler."
In the end, Greenberg triumphed as a competitor, but also as a human being.
Red Smith, the premier American sportswriter of his generation -- perhaps of any generation -- called Greenberg: "One of the greatest players of our time, one of the most unselfish team men, one of the finest gentlemen."
This book does what it sets out to do: Making clear that Hank Greenberg, in overcoming prejudice, became not only an important figure in baseball, but in American society.
Mike Bauman is a national columnist for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.