In one of his books, Stanley Fish tells a story about taking his nephew to a restaurant in North Carolina.

When he came to pay, he handed his Visa card to the waitress, "whom I had been admiring in a way natural to a boy who had grown up in the Fifties and who therefore had never grown up". As she gave it back to him, she surprised and delighted him by asking, "Are you Stanley Fish the Miltonist?"

This was indeed the field where Fish first became an academic celebrity. It has long been said of Paradise Lost that John Milton's God is a self-righteous bore, while Satan has all the reckless glamour of the rebel (and uses arguments against "the tyranny of Heaven" similar to those used by the poet himself in pamphlets arguing for the execution of Charles I). This has led writers from William Blake to Philip Pullman to suggest that Milton was "of the Devil's party without knowing it".

Fish has his own take on this. Most readers are indeed fascinated by Satan, he argued in Surprised by Sin (1971), but this is entirely deliberate. Milton wants us to feel a degree of sympathy for the Devil as a way of making us reflect on our own sinfulness. The merits of this interpretation have now been intensively debated for close to four decades.

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His rare fame as a Miltonist and his straight-talking style made Fish the natural choice as opening speaker at the Milton symposium, organised by the University of London's Institute of English Studies this July to mark the 400th anniversary of the poet's birth. He duly delivered a highly entertaining broadside against the "guerrilla Miltonists" and a younger generation of critics.

Milton studies can get pretty acrimonious, but none of this makes Fish sound like a particularly radical figure. His major work has focused on 17th-century literature, and particularly on writers he finds congenial, he says, because they are "obsessed by problems of right action and how right action is first to be defined and then implemented".

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He describes his critical approach as "interpretive in the fairly traditional sense - trying to figure out what the poet is up to, beginning with a focus on the intricacies of the verse. That, of course, requires some historical knowledge of the meanings of words, the genres in which the poet is working. You have to have read and thought about the predecessors - which in Milton's case means almost everyone who had written anything in the history of the world up to that time."

Although he has never practised as a lawyer (and doesn't even have a law degree), since the late 1970s Fish has combined literary scholarship with teaching law. His current title is Davidson-Kahn distinguished university professor of humanities and law at Florida International University. This mainly requires him to explain topics such as contract and First Amendment law to budding attorneys, although he occasionally brings a poem into class to liven things up.

Even this does not exhaust Fish's range of interests. He is a well-known newspaper columnist and a leading academic administrator, serving from 1999 to 2004 as dean of the College of Liberal Arts and Sciences at the University of Illinois at Chicago. He claims to have found the constant challenges and risk of burnout "exhilarating" and deplores the academics who "always see the administrator as the enemy".

"Faculty in the United States tend to view administrators with suspicion and believe that if there weren't any administrators the job of teaching would be very much easier. My view is that if there weren't administrators the job of teaching would be impossible."

The iconoclastic Fish is anything but a pillar of the Establishment. "Conservative political circles have considered me a monster for the past 40 years," he says cheerfully, "because I was involved in the introduction and promotion of the teaching of theory, I was associated with opening up the canon (to) work coming from areas that had been neglected or unrecognised: the study of gay and lesbian writers, Black American studies, postcolonial studies. All of that should be welcomed. It provides new materials for academic interrogation, analysis and clarification."

He was a determined upholder of academic standards, adopting the motto "good enough isn't good enough" and making his mission clear at the earliest possible moment.

"One of the first things I did was to tell a department they couldn't hire someone," he recalls. "I was brought to the University of Illinois with the specific charge of raising the visibility of the liberal arts college. And the way you do that is by raising the quality and intensity of the scholarship being done by faculty members. So it was important early on to send a signal to the faculty that the standards under which they may have been operating were going to be replaced by others."

When he left this job, Fish tells us in the introduction to his new book, Save the World on Your Own Time, he continued to do a bit of teaching and to stalk the campus, picking up waste paper, berating his students, claiming that he "hadn't the slightest interest in whatever opinions they might have" and generally trying to put the world to rights. Such obsessive behaviour might be tolerated in a dean, but they were hardly appropriate for an ex-dean, so he decided to put his ideas into print.

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Many of the chapters sound like bluff common sense - "Do your job", "Don't try to do someone else's job", "Don't let anyone else do your job" - but together they amount to an eloquent polemic about the nature of the university that skewers most of the pieties of Right and Left.

At its heart is a claim that teachers shouldn't try to "fashion moral character, or inculcate respect for others, or produce citizens of a certain temper", because that is not their job. When they do try to achieve such goals, it usually amounts to "practising without a licence and in all likelihood doing a bad job at a job they shouldn't be doing at all".

In terms of what goes on in the classroom, Fish argues, "The line of virtue is very clear: are you asking academic questions or are you trying to nudge your students in some ideological partisan direction? That's the line - which some people find difficult to draw and I find perhaps suspiciously easy to draw."

Fish has "no objection whatsoever to the fact that the make-up of a college's departments may have been influenced by political considerations", as when courses on history or culture reflect the demographics of the student population. But, he insists, those working in such departments mustn't then "become political in the sense of seeing themselves as activists in various causes rather than as academics analysing texts and other phenomena".

As long as political issues remain live, Fish suggests, it is not the job of faculty to take sides. This, he accepts, can mean adopting a neutral stance towards practices that later generations find strange, even abhorrent.

"At the time of segregation in the South," he explains, "there was a legislative system and a political milieu in which these questions were considered and dealt with - much too slowly, in the eyes of many, including me."

But arguing for reform in the classroom would have been to deny the academy its distinctive role.

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Today, it is not the job of "professors who cannot tell the difference between a soapbox and a teacher's podium" to preach for or against environmental activism, gay marriage, abortion or American imperialism. But, as Fish is careful to point out, it also means avoiding the kind of bland liberal pieties that most of us think of as totally uncontentious.

What could be more natural than "to encourage and on occasions even to force students to engage as respectful equals with people of other races, cultures, religions, and ideologies"?

Yet even this, he writes, amounts to "an unjustifiable form of indoctrination" since "it would not be the preferred (ethical) model of some libertarians, free-market economists, Orthodox Jews, fundamentalist Christians, Amish and members of the Aryan Nation, all of whom, the last time I looked, are American citizens and many of whom are college students."

Fish makes short work of two contentious issues. Conservatives often complain about the dominance of leftwingers within the American academy. While he doesn't dispute the claim, he believes the situation arose naturally out of complex historical factors such as the GI Bill, which "gave people like me - children of working-class immigrants - the opportunity to attend college and enter the professorate, bringing with them the largely union politics they grew up with".

But though he is opposed to heavy-handed interventions such as quotas, Fish very much supports a policy that would probably prove just as effective - greatly increasing the pay and perks of the average academic.

He is equally clear about presidents of universities whose outspokenness attracts controversy. President Larry Summers of Harvard University was absolutely not doing what he was paid to do when his comments on women in science led to hostile headlines across the world and eventually his resignation. "There are constraints," admits Fish, "which some would consider invidious and leading to grave sins such as inauthenticity or violations of freedom of expression, but I would say, 'No, it's just part of the job'."

One of the essential glories of the academic world, in Fish's view, is that it "will tolerate 30 years of promise without delivery. It is more than tolerated, it is what is expected. What is required is that people work seriously on a set of problems. I have been writing about Paradise Lost for 45 years. When I change my mind or have a new insight, I write a new piece, and that is responded to by other people, but nobody has a time clock telling me 'Come on, get on with it, what's the answer? You can't just keep dithering about for 45 years.' I have been allowed to dither about for 45 years."

So what had such intensive study of a single author done for him as a person?

"I've been asking people at the (London) conference what it is that sustains their lifelong or career-long interest in Milton.

"One answer I was given is that it's like having a good workout, because of the way that Milton challenges his readers on ethical, political, moral and ideological questions. Submitting yourself to that work is like going to the gym, so you will say after having done it, 'That was strenuous, but it was really good for me.'?"

Beyond this rather limited benefit, however, Fish says he doesn't believe that "reading Milton or Shakespeare or Tolstoy or other canonical authors will necessarily make you - or me - a better person, or turn young men and women into moral responsible persons or anything like that".

More generally, universities can't legitimately claim to be able to deliver many of the things other people might want them to. If funders, employers, legislators or parents hope they are going to produce citizens who are tolerant or politically engaged, decent or diligent, pliant or patriotic (or anything else), they can't honestly promise to do so.

So how should universities approach their paymasters and the wider public? Come out fighting for the academy and its values, is Fish's answer.

"Most senior administrators believe they have to make the case for universities in terms that donors and legislators and parents and officials of the particular administration will hearken to. But my argument is that once you do that you've surrendered your enterprise - you've said in effect we're only good if we can in some way validate ourselves in the terms you recognise and value. I don't think that's a winning hand."

Many key academic values - such as a commitment to "intellectual analysis of questions that may never have a definitive or even a useful answer" - are never likely to enjoy broad popular support.

But Fish still argues that it is more honest and probably more effective for administrators "to stand up for those values ... and when those values are dismissed or scorned, challenge the scorner to exhibit even the slightest knowledge of what really goes on in the classroom or the laboratory; and when he or she is unable to do so, ask, 'Is that the way you run your business, by pronouncing on matters of which you are wholly ignorant?' Now this advice may not be good advice - although the defensive strategies currently employed by administrators are spectacularly ineffectual - but it is certainly not advice to be passive or lie low."

But how far does Fish really believe such an approach might succeed in winning over these scorners?

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"I think they might be willing to accept it if I could talk to every single one of them. The book is an attempt, no doubt likely to fail, to do that."