In a letter written to a friend in 1917 Ludwig Wittgenstein reported: 'I work quite diligently and wish that I were better and smarter. And these both are one and the same.' The notion that being a smarter human being and a better person are in the end the same thing is one that Amartya Sen, a Nobel prize-winning economist who has made fundamental advances in welfare economics and the theory of social choice, finds appealing. Citing Wittgenstein's assertion at the start of the first chapter of The Idea of Justice and referring to it at several points in the book, Sen suggests that reason can do more than help people to achieve their goals. It can also enable them to criticise their goals, and in this way make them better people.

In Sen's view, a smarter world is sure to be a better world. Unlike some rationalists in the past, however, he does not think we need a conception of an ideal world in order to improve the one we live in. One of the recurring themes of The Idea of Justice is to contest the assumption that a theory of ideal justice is either necessary or desirable. Much of the book is a critique of the work of the late twentieth-century American liberal philosopher John Rawls. While Rawls's work has shaped academic discussion for over thirty years, it has had a negligible impact on political practice, and one of the reasons may be that his theory leaves so little room for politics. For Rawls, justice is a unique set of principles that reasonable people would choose from an imaginary initial position that ensures impartiality. Once these principles have been chosen all that remains is to set the right institutions in place. Conflicts about the scope of basic liberties and the distribution of resources will then be settled by applying the theory, which is a legal rather than political process.

It is a far-fetched view of how any society could operate, but Sen's objection is not to the lack of realism in Rawls's theory. It is the very idea of perfect justice that he questions. The reasons why society may be unjust are many and various; there is no reason to think that there is a set of just principles that everybody will accept. A just society will accord its members a range of basic liberties but also the capabilities needed to make use of them - in Isaiah Berlin's terminology, it will protect both negative and positive freedoms. Clearly, however, reasonable people will at times disagree as to which of these freedoms are most important. Again, though Sen argues strongly that justice should have a global reach, he knows that people will reasonably disagree about how wide the scope of particular requirements of justice should be. So, rather than opting for what he calls 'transcendental institutionalism' - the attempt to design an ideally just framework for society - Sen urges a comparative approach, which recognises the plural demands of justice while maintaining the struggle for a less unjust world.

In showing why those who pursue justice do not need an ideal of a perfectly just society, only a view about what would make the world a more just place, The Idea of Justice deserves to be acclaimed as a major advance in contemporary thinking. If the book succeeds in debunking rationalistic philosophies that claim to formulate principles of justice that everyone must accept, it still asks a great deal of reason - more, in fact, than reason can give. It is one thing to accept that the demands of justice are plural, another to recognise that they can be rivals - and not only in the sense that they must be ranked on a scale of comparative urgency because they cannot all be realised at the same time. In actual conflicts justice and injustice are not always as distinct and opposed as they seem in the seminar room. Quite often they are closely intertwined, sometimes in morally horrendous ways.

On any reasonable view, Allied saturation bombing of German cities in the Second World War inflicted severe injustice on civilian populations. A Nazi victory, on the other hand, would have spelt the complete death of justice in Europe. Leaving to one side the case that Allied bombing made that dreadful outcome less likely - despite clever-silly arguments to the contrary, I believe it may have helped - there is here an intractable moral dilemma. However one describes this dilemma - as a quasi-utilitarian trade-off between injustices of differing degrees of severity, or a tragic choice in which the injustices involved were of such different kinds as to be incomparable - one thing is clear: a readiness on the part of the Allies to sanction grave injustice was a precondition of any kind of justice surviving in Europe, and perhaps the world.

It will be objected that a case of this extreme kind does not prove much, but in differing degrees such conflicts of values are pervasive. Returning land that was wrongly seized generations ago may require unavoidable unfairness to those who have worked it in the meantime, while allocating housing or medical care according to need may entail acting unfairly towards those who are more deserving. Many other examples could be cited in which justice can be done only at the cost of inflicting injustice. These are endemic dilemmas, arising from the contradictions of human needs rather than from any kind of intellectual error, that cannot be fully resolved by any process of reasoning - however smart.

Reason is useful in clarifying the values that are at stake and the consequences of settling their conflict in different ways. But at a certain point reason leaves us in the lurch, and we must decide what to do. The notion that a smarter world is bound to be a better world is a modern version of Socrates' formula: knowledge and virtue are one and the same. This Socratic equation has always come up against the awkward fact of intelligent fanatics, people like Lenin and Hitler, who are ruthlessly reasonable in achieving their goals.

Of course it will be said that the goals of fanatics are themselves unreasonable. 'It is not particularly smart', Sen writes, 'for a group of people to act in a way that brings ruin to them all.' It is true that communism and Nazism both ended in disaster, even for many of their supporters. Still, unless being unreasonable is the same thing as being wicked, the argument is unconvincing. If Lenin and Hitler had received a thorough grounding in social-choice theory and were persuaded that the movements they led would come to nothing, would they have become well-intentioned liberal meliorists? Or would they have persisted in their fanaticism, preferring ruin to the survival of the societies they were bent on destroying?

In his luminous memoir, My Early Beliefs, in which he recants the rationalist creed of the Bloomsbury group, Maynard Keynes wrote of Bertrand Russell:

Bertie held two ludicrously incompatible beliefs: on the one hand he believed that all the problems of the world stemmed from conducting human affairs in a most irrational way; on the other hand that the solution was simple, since all we had to do was to behave rationally.

Keynes was not reminding his readers of the banal truth that it is difficult for human beings to be reasonable. His point was that human conflicts do not come about simply, or even mainly, because people make stupid errors. A smarter world might be more fun. There is little reason to think it would be less conflict-ridden, or more just.