Those are the key ingredients of Alain Badiou's philosophical cocktail, which is shaking the foundations of Western liberal democracy. Jennifer Wallace meets the abstract outsider thrust to the front of the ideological battleground

The theatre hall at London's Institute of Contemporary Arts is packed. Outside, tousled-haired student-types and earnest activists from left-wing think-tanks mill around, waiting hopefully for returned tickets.

Inside, the lucky ones watch as the latest big name in French philosophy, Alain Badiou, on a rare visit to London, walks up to the platform to begin his lecture on the War on Terror.

"The ideological field is a battlefield and not some soft or delicious place for discussion among friends," he declares. "In the context of the War on Terror, we have to create a new dialectics. Outside the contemporary war between happiness and sacrifice, it is possible to pursue the way of peace, a peace that is not only the end of war but that is beyond the war."

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The audience is rapt, half-inspired and half-confused. Is this politics? Philosophy? Terrorism? Yoga?

Grey-haired and sober-looking, Badiou is an intriguing contradiction. His underlying message is radical, nothing less than the questioning of all traditional values of Western liberal democracy, such as the principle of human rights, respect for others' opinions, tolerance for other cultures, the importance of free elections and the right to happiness. But his words are measured and difficult to understand, his books full of mathematical symbols and his sentences hard to pin down.

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Badiou has been catching international attention only in the past five years - since the September 11, 2001, terrorist attacks on the US - although he is 69 and his magnum opus, Being and Event , first came out in French in 1988. "At the time of its publication, this book did not lend itself to immediate comprehension," Badiou explains with typical bravado in the foreword to the English translation, which has just finally been published. "We were at the end of the Eighties, in full intellectual regression."

Now, in the era of Osama bin Laden and George W. Bush, it seems his hour has come. His apocalyptic assertions appeal to those who believe we have reached a political stalemate, and his discussion of what multiculturalism should mean obviously touches a raw nerve. Democracy, he maintains, is in hock to big business. "Today, there is no possible distinction between the capitalist world, the power of the rich and so on, and the democratic form of the state," he says before the ICA lecture. The great Western values of tolerance of alternative cultures and respect for the Other hold good only if those other cultures do not rock the system, if they can be sucked into the power structures of the democratic state. And if not, there will be war. "The great and terrible wars, such as the war in Iraq or Afghanistan, are wars for democracy. So there is a clear relationship between democracy and war," he says. Democracy is not intrinsically good, but only the least worst option - and for Badiou, that is not good enough.

Instead, Badiou posits a politics supported by some very abstruse philosophical logic, where there is no range of relativistic opinions and it is not possible to respect all cultures, but there is a notion of absolute truth to which one must be faithful. An event happens - for example the Nazi invasion of France or the French Government's recent response to riots in immigrant-dominated areas - and one must simply resist because the issues are clear-cut and objectively true. The days of party politics are over. "We have to find a new dialectics between individual discipline and collective discipline," he says. "We need to have organisations that are appropriate to concrete situations, not general or abstract organisations such as the Communist party." Instead, it is a matter of the individual continually responding to local events with a strong conviction of the validity of his or her struggle. It supposedly means decisive action, not words.

But if that sounds to you like a philosophical manifesto for al-Qaeda, Badiou would ask you to think again. "There is a great difference between the dogmatic conception of truth and my conception of truth," he interjects with a smile. "In the dogmatic conception, truth is not the outcome of any event but something structured, like the existence of God, and you have to obey it. In my conception, truth is something that happens, and afterwards you have to create the consequences. A new space is opened by the event." Badiou is an atheist, but, when pressed on his beliefs, he talks of equality between people as an absolute good, equality "between men and women, between different countries".

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Surprisingly, he does not consider 9/11 an "event" because, in his terms, nothing really changed as a result. Al-Qaeda is not offering anything new. "To kill so many people without saying why - all that means (is) that it cannot be universal; it is not a proposition of emancipation, engaging with the new collective process of freedom and equality." And the US just responded with business as usual. "The war between the US and the terrorists is just a war between two closed conceptions of life," he says.

Badiou's philosophy has been characterised as a mixture of Plato's belief in absolute truth and Sartre's emphasis on personal decision and action. There is a surprising twist of Derrida, too, in his arguments about process rather than goals. "We share the same enemies," Badiou quips.

He was born in Morocco and came to France aged five. Although all his education was in France, and he became professor of philosophy at the Ecole Normale Superieure in Paris, his early years in Morocco had a symbolic effect on his attitude to his country and to power. "For Derrida (born in Algeria) and for me, there is something decentred. We are not exactly classically French. We are a mixture of French and something else, and that is important."

It is probably because of this outsider's perspective that Badiou has been engaged in the issue of the sans-papiers in France - the illegal immigrants and migrant workers whose problems came to international attention during the riots in the suburbs outside Paris last year. He was one of the founding members of the Unified Socialist Party, which was active in the struggle for the decolonisation of Algeria. In 1985, he formed a pressure group, L'Organisation Politique, which has campaigned for the regulation and rights of the sans-papiers . Last autumn, he wrote a piece in Le Monde , which is republished in his new book, Polemics , about the plight of his adopted son who is black and who he says is continually harassed and arrested by the police for no reason. "We have the riots we deserve. A state in which what is called public order is only a coupling of the protection of private wealth and dogs unleashed on the children of working people and people of foreign origin is despicable," he states.

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But despite this career of political activism Badiou's vision is remarkably abstract. What does he mean by a "new space" or "new politics"? How does he know that his "truth" is better than that of the fundamentalists? During the lecture at the ICA, the audience was getting a little frustrated. They wanted Badiou to name the enemies, to give concrete examples of successful political struggles, so that they can understand his arguments. Even Badiou's regular translator, Peter Hallward, who chairs the ICA discussion, challenges Badiou on his refusal to tackle the question of economics because it means acknowledging and engaging with the capitalist system.

Surely, Hallward points out, you have to think about the reality of the situation, the fact that people's wealth or poverty has an impact on their lives and their points of view. But Badiou shrugs his shoulders. "Do not be afraid of abstraction," he tells us. "When the concrete world is really horrible, abstraction is good."

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Jennifer Wallace is a fellow of Peterhouse College, Cambridge. Alain Badiou's Polemics is published by Verso, ?17.99.