Last year, Prospect magazine conducted a poll of 'global public intellectuals'. Readers were invited to vote for five such figures from a longlist of a hundred, selected according to criteria which stipulated that a public intellectual is someone who has shown "distinction in their own field along with the ability to communicate ideas and influence debate outside of it".

This definition takes it for granted that the public intellectual is an expert or a specialist, probably an academic, able to communicate with an audience larger than that made up of the other practitioners in his field. The public-ness of public intellectuals, therefore, consists in their ability to reach beyond the limits of their spheres of expertise – though it's precisely the "distinction" achieved within those specialisms that confers the authority required to get a hearing outside them. But a hearing for what exactly? Here, the Prospect criteria are more ambiguous. It's not clear, for instance, that 'communicating' one's ideas to a wider public is quite the same as 'influencing debate' outside one's field. Two distinct models of the public intellectual appear to be in play, therefore: in one, call it the 'popularising' model, the intellectual makes his work accessible to an audience of non-specialists – scientists such as EO Wilson and Steven Pinker, both on the original list, are public intellectuals in this sense; in the other, call it the 'political' model, the intellectual takes advantage of his academic prestige in order to pronounce on matters of broad public interest.

In his magnificent new book Absent Minds, the Cambridge academic Stefan Collini argues that such 'terminological strain' is characteristic of much of the literature devoted to the question of the intellectual (a corpus that dates back a little over a hundred years to the Dreyfus Affair in France). Collini makes it clear that as long as there have been intellectuals (and the word made its first appearance in English some time around 1880), there have been debates about their relationship with the universities and their qualifications for expounding on public affairs. And there's nothing new either about the anxiety that intellectuals might be a thing of the past.

Judging by the story Collini tells, it is very unusual for a public intellectual to be both a populariser and a political actor; and the eventual winner of the Prospect poll, Noam Chomsky, certainly isn't. Chomsky garnered nearly 5,000 of the 20,000 votes cast, not for his work in theoretical linguistics, but for his political activity (all those open letters to the New York Review of Books, the speaking tours, and the apparently unending deluge of pamphlets bearing his name) – something confirmed by David Herman in his summary of the results.

Chomsky, Herman said, belongs to a tradition dating back to Zola, Russell and Sartre, in which a "major thinker or writer... speaks out on the great public issues of his time, opposing his government on questions of conscience rather than the fine print of policy." Herman went on to lament the fact that Chomsky, who is in his dotage, has no obvious successors and that the "grand tradition of oppositional intellectuals" therefore appears to be at an end, even if Chomsky's victory suggests we still "yearn" for such figures.

Claims that intellectuals are, or ought to be, 'oppositional' and that the ones who manage to be so are usually French, Collini says, are staples of discussions about intellectuals, especially in Britain (Absent Minds is subtitled 'Intellectuals in Britain'). Collini also points out that the habit of adding the word 'public' to the word 'intellectual' is a relatively recent phenomenon and is almost invariably expressive of anxieties about the academicisation of intellectual life and the perceived inability of specialist intellectuals to make contact with a non-specialist public.

It is often said that contemporary intellectuals who betray their vocation by failing to act or to 'speak out' are guilty of a latter-day trahison des clercs. Collini notes that this phrase has acquired an almost 'liturgical' status in English-language discussions of the obligations of intellectuals, but also, significantly, that when it is used in this way it acquires a sense precisely the reverse of that given to it by its originator Julien Benda in his 1927 book of the same name. (Collini devotes a chapter to La Trahison des Clercs and its English reception by, among others, TS Eliot, and another to one of Benda's self-proclaimed successors, Edward Said, whose 1993 Reith Lectures are examined in pitiless detail.)

According to Benda, the 'clerc', a more or less untranslatable term to which 'intellectual' is merely a rough approximation, is not a citizen of the earthly kingdom of politics. Rather, he is a denizen of what Benda calls the kingdom of the intellectual or the universal, whose task it is to bring esoteric truths to the citizens of the mundane republic. Intellectual betrayal, therefore, consists not in refusing to speak out, but in sullying the purity of the universal by elevating worldly or 'lay' passions to the status of eternal truths.

This seems to run counter to the contemporary understanding of the trahison des clercs. However, Collini suggests that there is more than a whiff of Benda's essentially Platonic outlook in the idea that the authentic intellectual is the 'alienated' intellectual and that it's his job to, as the saying goes, 'speak truth to power'. The distinction between the clerc and the man of action (Machiavelli's prince, say) leaves open a space in the lay world in which to challenge "established power in the name of reason and morality". And, importantly, it also allows one to distinguish between, to adopt David Herman's terms, answering the call of conscience and morality, on the one hand, and grubbing about in the "fine print of policy" on the other.

Benda was not entirely consistent, therefore, in his belief that for a true clerc the "greatest treason is to become an intellectual"; after all, his intellectual heroes – Goethe, Voltaire and Rousseau – were hardly models of detachment. And there's a further significant tension in Benda's book, the implications of which are far-reaching: his decisive stand in favour of the French response to German aggression in 1914 suggests that his critical-intellectual stance was not one of absolute opposition. Indeed, he rejected the "mystical pacifism" of those intellectuals for whom their country was always in the wrong – even when it was right. In other words, he made no dogmatic presumption in favour of the 'justice' of defeat and allowed that sometimes right is on the side of the victors. (George Orwell, an intellectual who, in what Collini calls a "paradox of denial", refused to acknowledge that he was one, made very similar arguments to these before and during World War II.)

Collini draws an important lesson from this: the real betrayal of the intellectuals, he suggests, is to confuse being critical with being merely oppositional and to assume, as Chomsky once put it, that the responsibilities of intellectuals are deeper than the "responsibility of people" and that consequently the intellectual-as-truth-teller can presume to speak on behalf of the voiceless. If he's right about that, then perhaps we should be more sanguine about the disappearance of the 'grand tradition' of which Chomsky is the last living representative.

Jonathan Derbyshire is reviews editor of The Philosophers' Magazine. He regularly writes for the Financial Times and the Times Literary Supplement