Twenty years later, when the British foreign secretary, Arthur Balfour (sponsor of the 1905 Aliens Act to restrict Jewish immigration to the UK), wanted the government to commit itself to a Jewish homeland in Palestine, his declaration was delayed - not by anti-semites but by leading figures in the British Jewish community. They included a Jewish member of the cabinet who called Balfour's pro-Zionism "anti-semitic in result".

The creation of the state of Israel in 1948 has not put an end to the debate, though the issue has changed. Today, the question is about Israel's future. Should it become a "post-Zionist" state, one that defines itself in terms of the sum of its citizens, rather than seeing itself as belonging to the entire Jewish people? This is a perfectly legitimate question and not anti-semitic in the least. When people suggest otherwise - as Emanuele Ottolenghi did on these pages last Saturday - they simply add to the growing confusion.

Ottolenghi contends that "Zionism comprises a belief that Jews are a nation, and as such are entitled to self-determination as all other nations are". This is doubly confused. First, the ideology of Jewish nationalism was irrelevant to many of the Jews, as well as non-Jewish sympathisers, who were drawn to the Zionist goal of creating a Jewish state in Palestine. They saw Israel in purely humanitarian or practical terms: as a safe haven where Jews could live as Jews after centuries of being marginalised and persecuted.

This motive was strengthened by the Nazi murder of one-third of the world's Jewish population, the wholesale destruction of Jewish communities in Europe, and the plight of masses of Jewish refugees with nowhere to go.

Second, you do not have to be an anti-semite to reject the belief that Jews constitute a separate nation in the modern sense of the word or that Israel is the Jewish nation state. There is an irony here: it is a staple of anti-semitic discourse that Jews are a people apart, who form "a state within a state". Partly for this reason, some European anti-semites thought that the solution to "the Jewish question" might be for Jews to have a state of their own. Herzl certainly thought he could count on the support of anti-semites.

What is anti-semitism? Although the word only goes back to the 1870s, anti-semitism is an old European fantasy about Jews. The composer Richard Wagner exemplified it when he said: "I hold the Jewish race to be the born enemy of pure humanity and everything noble in it." An anti-semite sees Jews this way: they are an alien presence, a parasite that preys on humanity and seeks to dominate the world. Across the globe, their hidden hand controls the banks, the markets and the media. Even governments are under their sway. And when revolutions occur or nations go to war, it is the Jews - clever, ruthless and cohesive - who invariably pull the strings and reap the rewards.

When this fantasy is projected on to Israel because it is a Jewish state, then anti-Zionism is anti-semitic. And when zealous critics of Israel, without themselves being anti-semitic, carelessly use language, such as "Jewish influence", that conjures up this fantasy, they are fuelling an anti-semitic current in the wider culture.

But Israel's occupation of the West Bank and Gaza Strip is no fantasy. Nor is the spread of Jewish settlements in these territories. Nor the unequal treatment of Jewish colonisers and Palestinian inhabitants. Nor the institutionalised discrimination against Israeli Arab citizens in various spheres of life. These are realities. It is one thing to oppose Israel or Zionism on the basis of an anti-semitic fantasy; quite another to do so on the basis of reality. The latter is not anti-semitism.

But isn't excessive criticism of Israel or Zionism evidence of an anti-semitic bias? In his book, The Case for Israel, Alan Dershowitz argues that when criticism of Israel "crosses the line from fair to foul" it goes "from acceptable to anti-semitic".

People who take this view say the line is crossed when critics single Israel out unfairly; when they apply a double standard and judge Israel by harsher criteria than they use for other states; when they misrepresent the facts so as to put Israel in a bad light; when they vilify the Jewish state; and so on. All of which undoubtedly is foul. But is it necessarily anti-semitic?

No, it is not. The Israeli-Palestinian conflict is a bitter political struggle. The issues are complex, passions are inflamed, and the suffering is great. In such circumstances, people on both sides are liable to be partisan and to "cross the line from fair to foul". When people who side with Israel cross that line, they are not necessarily anti-Muslim. And when others cross the line on behalf of the Palestinian cause, this does not make them anti-Jewish. It cuts both ways.

There is something else that cuts both ways: racism. Both anti-Jewish and anti-Muslim feeling appear to be growing. Each has its own peculiarities, but both are exacerbated by the Israeli-Palestinian conflict, the invasion of Iraq, the "war against terror", and other conflicts.

We should unite in rejecting racism in all its forms: the Islamophobia that demonises Muslims, as well as the anti-semitic discourse that can infect anti-Zionism and poison the political debate. However, people of goodwill can disagree politically - even to the extent of arguing over Israel's future as a Jewish state. Equating anti-Zionism with anti-semitism can also, in its own way, poison the political debate.

· Brian Klug is senior research fellow in philosophy at St Benet's Hall, Oxford, and a founder member of the Jewish Forum for Justice and Human Rights

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