I shall always advise to call in the aid of the farmer and the physician, rather than the professor," wrote the 18th-century philosopher and politician Edmund Burke when contemplating man's right to food and medicine. He believed politics should be concerned with practical, not theoretical, matters and this reading suggests philosophy has little to offer the world of politics.

But philosophy graduates - particularly philosophy, politics and economics students - dominate UK politics. Prime Minister David Cameron, foreign secretary William Hague, Labour leader Ed Miliband and his brother David all studied PPE at university. So did David Willetts, the universities and science minister; Danny Alexander, the chief secretary to the Treasury; shadow home secretary Yvette Cooper; and Ed Balls, shadow chancellor of the Exchequer.

Plato would approve. In his ideal society, the ruling guardians were rigorously schooled in philosophy, logic and mathematics. For him, this was the perfect preparation for power. But what do modern philosopher-politicians make of the matter?

James Purnell, the former secretary of state for work and pensions, holds a PPE degree from the University of Oxford and has long clamoured for a more theoretical approach to politics.

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"Philosophy teaches you to question the assumptions behind what you think. It teaches you to organise things into systems of thought and to be a sceptic. Those who haven't studied philosophy can find that quite irritating."

Not that Purnell is afraid of annoying people. He points to Socrates, whose constant questioning got on people's nerves.

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For many, this is the reason why theory should be left at the door: philosophers are too fond of the abstract. Oliver Letwin, minister of state at the Cabinet Office (philosophy and history, University of Cambridge), might not put it in quite those terms, but he upholds the distinction between practical and theoretical politics.

"It is useful to have some people engaged in abstract thinking and theorising, but I wouldn't say that everyone should be. In fact, I think it's necessary that not everyone is."

So does philosophical training effectively preclude practical thinking? Labour MP Barry Gardiner calls the question "romantic nonsense".

"Being adept at philosophy doesn't mean you can't be practical. If that were the case, we'd be very poor human beings."

He is perfectly placed to comment. Studying philosophy at Harvard University sparked his interest in social justice; he then left the academy, he recalls, to act on it. Philosophy drew him to politics because it gave him his values.

It is a harmonious relationship, then, when those in power cite their core convictions - perhaps gifted by or refined through philosophy - as justification for their politics. But what happens when politicians are not philosophically equipped?

"Modern-day politics suffers from a considerable deficit in the arena of philosophy," argues Gary Hart, a former US senator and presidential contender, who has called Soren Kierkegaard his intellectual hero. Hart sees political beliefs as inseparable from their religious and philosophical counterparts.

"Now," he laments, "too many political figures operate on instinct, either their own or those of the noisy herd. They have read and thought far too little about the roots of their convictions. If convictions are not well founded, then careerism, special-interest influence and shallow party loyalty all replace conviction and courage. Too many political figures don't really know what they stand for."

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But Gardiner points to a wider philosophical influence. Key philosophical works have "permeated the intellectual climate in which politics is conducted", he says. "People who have never heard of John Rawls and Michael Sandel are now operating on assumptions that were not commonly held 30 or 40 years ago."

Sir Derek Morris, chairman of the Competition Commission before becoming provost of Oriel College, Oxford, agrees. "Philosophy influences society via its impact on related subjects. It has had a powerful effect on how economists think. With a delay and through various osmotic processes, that does influence policy and people's welfare in general."

John Stuart Mill was swimming against the tide when he argued for equal suffrage for women in On Liberty (1859) and The Subjection of Women (1869). But his arguments did pave the way for later change. More recently, Demos, the think tank, has used Indian economist-philosopher Amartya Sen's human welfare insights to evaluate government policy. Philosophy can shape not just the actors but the theatre itself.

For some, though, it is still consigned to the wings. Philosopher and scholar Roger Scruton says: "I wish the world of politics were influenced by philosophy but it isn't, except at the margins. There is a tendency on the Left to give scope to people with ideas, but they tend to be sociologists or amateur windbags. On the Right, people who think tend to be regarded with suspicion, as (people) who might go off the rails on account of some idea they have."

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Scruton, for one, would rather hear David Cameron's philosophy expressed more succinctly.

"Philosophy is valuable in teaching politicians to shut up, but harmful in teaching amateur philosophers to hold forth. It doesn't act on its own. It sharpens what is there, in character and will."

Perhaps it is unrealistic to expect anyone to faithfully perform the roles of both philosopher and politician at the same time. And maybe that is because the one is, at least in part, defined by not being the other. That is certainly how Malcolm Tucker, the snarling attack dog in the BBC political satire The Thick of It, would appear to have it in his unique brand of careers counselling.

Malcolm Tucker: What do you want to be? Come on. Do you want to be a prick that works here for a year, then goes away and joins a think tank to write, "Oh, on the one hand this and on the other hand that", or do you want to be a soldier?

Jamie: Have you got your eyes on the prize?

Oliver Reeder: I've got my eyes on the prize.

Malcolm Tucker: Good.

Oliver Reeder: What is the prize?

Malcolm Tucker: I don't know - you need to ask the brainy guys.