Composer Richard Wagner’s feelings about Jews were summarized in his statement that “I hold the Jewish race to be the born enemy of pure humanity and everything noble in it.”

His virulent anti-Semitism poses a painful problem for music-lovers and particularly for Jews. He was not only a despicable human being but a great artist, and we want to believe that all geniuses are decent human beings — kind, generous, fair, selfless, and modest.

The notion that genuises are always noble is something we carry with us from childhood. Children need and want admirable role models; it’s only later in life that they may learn that George Washington kept slaves, that Shoeless Joe Jackson couldn’t say it wasn’t so (that he helped throw the 1919 World Series), that Sir Francis Bacon was a crook, and that Wagner was, as Leon Botstein, the president of Bard College, has called him, “a racist ass.” (Bard is holding a Wagner music festival beginning Aug. 14.)

Wagner’s life-long racism leads to a number of vexing questions. How responsible was he for what came after — Hitler and the Holocaust? Can anything be said in his defense? How should Israel — and Jews in general — respond to his music?

So frequently do people whom we admire wind up becoming fallen idols that maybe we need a phrase to describe this phenomenon. The Dr. Jekyll-Mr. Hyde syndrome?

If there were a Hall of Fame for composers, would Wagner qualify? Or would he be excluded, the way Pete Rose is kept out of the Baseball Hall of Fame because he bet on baseball games and lied about it?

Perhaps we could even mathematically measure our disenchantment with geniuses — by multiplying the estimated size of their accomplishment with the size of the gross offense. In which case, Wagner would surely rank at or near the very top. As the poet W.H. Auden once said, Wagner may well have been the greatest artist who ever lived, but he was also “an absolute s__t.” (Auden didn’t mince words.)

One possible explanation for the prevalence of fallen heroes: As Botstein has nicely put it, “You can’t be Ozzie and Harriet and Picasso at the same time.” Extreme people tend to remain extreme.

Why aren’t gifted people always admirable? Botstein, interviewed at his home on the Bard campus, replied: “Forget about it. This is the absolutely paradoxical reality. It’s true in art, in science, in literature. Great ambition, after all, requires a disproportionate ego. Those of us who weren’t wunderkinder [child prodigies] probably learned restraint in school.”

“The sane people are in the audience, not on stage,” Botstein continued. “Only crazy people go on stage. It’s a terrifying event. You really have to be off your rocker to get up in a costume or fancy clothes and go out here and sing — to really play your heart out and reveal your intimate self in front of crowd. These are not normal people. You can’t choose deviancy, abnormality, in a supermarket and link it with goodness.

“Look at Beethoven,” he went on. “If he had been born today, he would have become a gas-station attendant. No one would have tolerated the eccentricity of his behavior. He would have been medicated beyond recognition.

Leon Botstein, president of Bard College and a conductor, started the Bard Music Festival 20 years ago — and has scheduled programs focusing on Wagner beginning Aug. 14. STEVE J. SHERMAN

“We want to eat our cake and have it, too. We want to romanticize genius and throw out the things we don’t like. But being nice and ethical and honest isn’t built into the hardware of greatness. We impose a kind of restrictive morality on people — and also want them to be exceptional.

“Albert Einstein, by modern ethical standards, was a womanizer. Should we sacrifice the genius of his mental imagination, re-conceptualize our ideas of time and space, just because he wouldn’t sleep only with his wife? He would have been brought up on charges of sexual harassment.

“The world of art, science, great scholarship, great thinking, is a world of deviance. Our average neighbor doesn’t think great thoughts, write great poetry, or re-conceptualize our understanding of the natural world.”

As Botstein suggests, gifted people — powerful people in general — may, with their exaggerated sense of themselves, conclude that garden-variety rules of ethical conduct don’t apply to them. Recent examples in this country include congressmen, governors, and even presidents.

Botstein’s contention that there is a link between genius and abnormality has been made before. The literary critic Edmund Wilson, in a famous essay “The Wound and the Bow,” suggested that “genius and disease … may be inextricably bound up together,” and invoked the myth of the ancient Greek Philoctetes, who possessed a magic bow whose arrows always hit their mark. Poor fellow, he also had a disgusting, suppurating wound on his foot, where he had bitten by a serpent — the horrible odor from which protected him from thieves eager to possess his bow.

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Wagner was no “casual” anti-Semite, given to occasional disparaging remarks about Jews. (Even Beethoven was guilty of that.) He was obsessed with the notion that Jews were responsible for just about anything untoward that happened to him — and everything evil in the universe. As he once wrote to his sometime friend, the composer Franz Liszt, his hatred of Jews was “as necessary to my nature as gall is to the blood.”

In 1850, he anonymously published an essay, “Judaism in Music,” arguing that popular Jewish composers — meaning Felix Mendelssohn and Giacomo Meyerbeer — were polluting the mainstream of German music. They lacked creativity; they were just imitators. In 1869, he republished the essay, and expanded on it — this time with his name on it.

Wagner had a muddled and messy mind. Actually, Mendelssohn had converted to Lutheranism as a child. Besides, his music and Meyerbeer’s were quite different — Mendelssohn wrote no operas, and he didn’t even like Meyerbeer’s music. And in keeping with Wagner’s narcissistic personality, both composers had helped Wagner with his career — Meyerbeer had even given him money.

Wagner’s everyday conversation was strewn with vulgar anti-Semitic remarks — about Jews with hooked noses, about “bloated” Jewish bankers.

One of the most repellent of his comments:

In 1871, Cosima, his wife, told him about a fire at a theater in a Jewish section of Vienna, during which 416 Jews died. Wagner’s “drastic joke,” as she called it: All Jews should be burned during a performance of “Nathan the Wise.” (Cosima, Liszt’s daughter, like her husband was an obsessional Jew-baiter. “Nathan the Wise,” written in 1779 by Gottfried Ephaim Lessing, was a plea for religious tolerance.)

Wagner was positively paranoid about Meyerbeer, believing that he knew that Wagner had written “Judaism in Music” and therefore had it in for him: He imagined a cunning and ruthless conspiracy against him “by a great expert in such things, Mr. Meyerbeer….” When a performance of “Tannhäuser” ran into trouble, Wagner believed that it did not “come about by chance; it is the work of Meyerbeer.” Wagner’s envy of Meyerbeer’s success, in fact, is considered to have played a pivotal role in Wagner’s suddenly becoming a Jew-hater.

Later, Wagner denied that Jesus was a Jew. He referred to a synagogue service he had heard as a “nonsensical gurgling, yodeling, and cackling.” After reading a book about the struggle for survival among animals, he commented that what “remains are the rats and mice — the Jews.” Although he sometimes said he favored having Jews integrate into Christian society, at least once he said he favored expelling Jews from Germany entirely.

When Hermann Levi, a Jew, was about to conduct performances of “Parsifal,” Wagner told Cosima that if he were a member of the orchestra he wouldn’t like to be conducted by a Jew.

When he and Cosima read about German successes in the Franco-Prussian war of 1870-71, they were thrilled. Until they saw, with disgust, who had written the article: “Unfortunately the description is by a Jew [J. Rodenberg].”

Even Wagner’s operas seem to carry anti-Semitic overtones. Such Wagnerian characters as Mime, Alberich, Hagen, Klingsor, Kundry, and Beckmesser can be interpreted as Jewish caricatures, argues Marc A. Weiner in his book “Richard Wagner and the Anti-Semitic Imagination” (1997) — from their speech, from their singing, from their roles, from their body language. “All of the stereotypical cardboard, cookie-cutter features of a Jew… show up all over the place in his musical dramas,” Weiner said in a newspaper interview.

Beckmesser, the pedantic, ludicrous singer in “Die Meistersinger,” is certainly meant to be Jewish — he was modeled after Eduard Hanslick, a critic who disparaged Wagner. (Hanslick denied being Jewish; Wagner insisted that he was because his mother had been Jewish — although she had converted to Catholicism, and Hanslick was brought up Catholic.)

Weiner, professor of Germanic studies at Indiana University, is persuasive: It’s hard to believe that Wagner, possessed as he was with Jew-hatred, could write 10 major operas without his anti-Semitism sneaking in.

Botstein and others maintain that even if the operas are somewhat anti-Semitic, these days most audiences don’t notice the anti-Semitism.

If it weren’t enough that Wagner was a vicious anti-Semite, he was also guilty of a lot else. He was clearly a megalomaniac — a corollary of his narcissism. Milton E. Brener, a lawyer, writes in “Richard Wagner and the Jews” (2006) that Wagner judged people by their willingness or talent “to help in a great cause, namely, his own.” The New Yorker music critic, Alex Ross, has cleverly said that “There was a Charlie Rose in his head whose topic every night was Wagner.”

Also, Wagner lied and lied. As William Berger writes in “Wagner Without Fear” (1998), to him “the truth was always incidental.”

Wagner also was in the unfortunate habit of seducing married women — like Cosima (who was first married to conductor Hans von Bülow), to whom he once confessed, matter-of-factly, that he preferred married women to maidens.

Wagner is even frequently blamed for the rise of Hitler and the Holocaust.

In fact, Brener notes, some anti-Wagner scholars leave the impression that “without Wagner, the Holocaust would never have occurred….” He himself disagrees, pointing out — among other things — that Hitler’s “Mein Kampf” has only one reference to Wagner.

Still, Wagner was a favorite of Hitler’s, who once said that that whoever “wishes to understand National Socialism must first understand Wagner.” (The line is spoken by the Hitler character in the recent movie “Valkyrie.”)

Hitler certainly had a special fondness for Bayreuth, the opera house that Wagner built for his own operas. Thomas Mann, the novelist, called it “Hitler’s Court Theater.”

Someone has even said that the fifth installment of Wagner’s magnum opus “Der Ring des Nibelungen” — after “Das Rheingold,” “Die Walküre,” “Siegfried,” and “Götterdammerung” — was the Holocaust.

No wonder that today, writes Berger, Wagner “has become symbolic of everything evil in the world” — which was his own view of the Jews.

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Wagner has his defenders.

Brener writes, “Never did he refuse the help or the friendship of anyone because he or she was a Jew, or on any other racial or religious background.”

Wagner, in fact, had several key Jewish friends, and Jews were among his most loyal admirers and supporters.

A Jewish impresario, Angelo Neumann, arranged for Wagner’s operas to be played all over Europe.

One of Wagner’s Jewish friends, who lived in Wagner’s home, was a disturbed pianist named Josef Rubinstein, who hated his Jewishness. He had written to Wagner asking for “de-Judaization”: “I am a Jew— for you, that says everything. All those characteristics noticeable in the present-day Jews I too possessed. … How can I keep from going under, since I myself am a Jew?” He sought an antidote for his Jewishness from Wagner — who welcomed him into his household.

Eighteen months after Wagner died, in 1883, Rubinstein shot himself.

Another Jewish admirer and friend of Wagner’s was Hermann Levi, the son of a rabbi who himself was non-observant. Wagner admired Levi, and tried again and again to persuade him to allow himself to be baptized. Levi would have none of it.

Oddly enough, Theodor Herzl, the “father” of Zionism, said he conceived the idea of a Jewish state while listening to Wagner’s “Tannhäuser.” (Perhaps because the opera argues for listening to the heart as well as the head.)

When Wagner died, two of the 12 pallbearers at his funeral were Jewish: Levi and the choirmaster Heinrich Porges.

Also in Wagner’s favor: In 1880, Wagner was twice asked to sign a petition protesting the granting of full citizenship to the Jews. He refused both times, explaining that he preferred to just write music, not to get involved in such mundane matters. (His anti-Semitic admirers, like Cosima’s ex-husband, were furious.) One Wagner biographer, the great Ernest Newman, speculates that Wagner refused to sign for fear of offending all the Jews surrounding him.

What’s the verdict? Jacob Katz, who was a professor of Jewish educational and social history at the Hebrew University of Jerusalem, wrote in “The Darker Side of Genius: Richard Wagner’s Anti-Semitism” (1986): the facts “prove to be incriminating enough, without burdening him in addition with the horrible deeds of Hitler.”

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How should Jews respond to Wagner’s music today? It’s still a troublesome subject.

In pre-state Israel, Wagner’s music was banned after Kristallnacht, in 1938. And although his music has occasionally been played in Israel, there’s still an informal ban. David Stern, director of the Israel Opera (and the famous violinist Isaac Stern’s son), has said he will honor the Wagner ban as long as Holocaust survivors remain alive. Botstein doesn’t play any Wagner when he conducts the Jerusalem Symphony Orchestra, of which he’s music director.

Daniel Barenboim has conducted Wagner’s music in Israel and elsewhere, although he is Jewish. The Metropolitan Opera’s James Levine is in the same camp, and both men have conducted Wagner operas in, of all places, Bayreuth. Still, Barenboim has called Wagner’s writings “monstrous,” and declared that if he could spend 24 hours with any composer, “Wagner doesn’t come to mind.” (Mozart did.)

Botstein also favors letting Wagner’s music be heard in Israel. He has eloquently written — in “Richard Wagner and His World,” being published in conjunction with the Bard Festival — that “[o]nly an active and critical encounter with Wagner as a composer and dramatist can clarify his place in modern European Jewish history, in the history of anti-Semitism, and in the Nazi era. Israel must restore Wagner to the stage for the sake of the survivors, so that the causes of the Holocaust can be better understood….”

Still, it’s no accident that the first composer to be featured at the Bard Music Festival was a philo-Semite, Johannes Brahms. The second composer: Mendelssohn. Wagner is No. 20.

As opposed to Botstein and others, there’s the provocative comment of The New Yorker’s music critic, Ross: “In an odd way, Bayreuth may be the best argument for keeping the Israeli ban on Wagner in place…. If there is a place where Wagner alone is allowed to be heard, there should also be a place where Wagner is asked to be silent.”

As for any individual’s response to Wagner’s music, it’s clearly a personal decision. There’s nothing wrong with despising Wagner and avoiding his music. This writer confesses that he can no longer enjoy listening to Maria Jeritza sing, having learned that in the 1940s she led a pro-Nazi lobby in Hollywood. (Besides, a lot of sopranos are much better.) Someone else enjoys listening to Wagner, thinking how aggrieved the composer might be knowing that he was entertaining a Jew.

The overall lesson about Richard Wagner is that we must simply acknowledge that even unquestionable geniuses, like Wagner, may be thoroughly loathsome.

It’s just an unfortunate fact of life that the devil, if he doesn’t have all the good tunes, sometimes has a good many of them.