Aron Ralston was trapped for almost five days in the remote Bluejohn Canyon in Utah by a falling boulder, which had pinned him down by his right arm and wouldn't budge. The 27-year-old outdoor sports enthusiast knew he was very unlikely to be found and rescued. He hadn't told anyone else details of his route, or even that he had gone canyoneering, as it is called, in an area that he describes as "the red wasteland beyond the end of the roads". The probability was that he hadn't even been missed yet.

So, on 1 May 2003, 127 hours into this unimaginable ordeal, when his small supply of food and water had run out, Ralston faced the sort of terrible choice that all of us pray to be spared – whether peacefully to accept death as the inevitable consequence of a freak accident, or to make a last, desperate bid for life. Drastic measures would be needed. The only way he could free himself from the boulder's grip, he had realised, was by amputating his trapped arm. If the shock didn't kill him, the bleeding could.

With just a blunt penknife and a basic first-aid kit, Ralston managed to saw through his lower arm, where both his radius and ulna were already broken, and apply a tourniquet. Though delirious, he somehow then scaled a 65-foot rock wall and hiked eight miles until he was found. And, miraculously, he survived to tell the tale, first in a best-selling book, Between A Rock and A Hard Place, and now in a film.

127 Hours, a dramatised version of Ralston's extraordinary story by Oscar-winning writer-director Danny Boyle (Slumdog Millionaire, Trainspotting, Millions, Shallow Grave), is being shown next week as the finale of the London Film Festival and goes on general release in the US straight afterwards. James Franco plays Ralston in what Boyle has referred to as "an action movie with a guy who can't move".

But the debate already prompted by the film – which has been previewing at various film festivals in America – goes deeper than how to categorise it. 127 Hours has raised once again the question of just what constitutes a hero.

For some, Ralston is the ultimate all-action hero who hadn't let fear of death put him off following his instinct for adventure even before he got stuck in Bluejohn Canyon. Prior to his ordeal in Utah, he had to be dug out of an avalanche while ski-ing in Colorado. Only his head and one arm were visible above the snow.

To his admirers, Ralston's heroic courage lies in his ability not just to mutilate himself rather than accept death, but in his refusal ever to let the risks curtail his courting of adventure, the very antithesis of the modern-day affliction of the health and safety culture. He is a five-star example of getting to the very heart of what it means to be human by flamboyantly discarding the layers of protection the rest of us build – or allow to be built - around us. Here is a man who challenges nature to do its worst and lives to tell the tale in the mould of the pioneers who created America.

"The Aron Ralston story is truly amazing," gushes one of the many "what-a-guy" posts on the YouTube site where a trailer of the film is whetting many appetites. "Boyle's absolutely brilliant," reads another. "He took a hero and made an everyman out of him." But some will have no truck with such talk. "He's an idiot," claims another contributor to the debate, "for going out there without telling anyone where, when or that he was going." Some take that argument one step further. "This guy was not only reckless but an idiot. His mountaineering antics should have injured him or killed him a long time back before this incident. That is if anything in his book is true other than losing part of his arm." Which in turn prompted an angry riposte: "This guy was not an idiot. He was a fucking legend. He loved adventure and acting like a kid in a gigantic playground ... How can you judge someone like that who is a perfect example of what all humans dreams to be?"

This last comment takes us to the heart of the question of heroism. Does it consist of doing what the rest of us only aspire to? Are our heroes vicariously living out what we really want to be doing but are too scared/cowed/busy with our dreary 9 to 5 routines?

There are, of course, many sorts of heroism, not all of them to do with comic-strip characters who fight crime and save the world. In a world drenched in celebrities, the quiet heroes, for example, have a particular counter-cultural appeal. They might be everyday men or women who have changed the world – for example by inventing something that makes everyone else's life easier, like Stanley Rock, the scientist who invented the contraceptive pill.

Or they might be the volunteer lifeboatmen who go out 365 days a year, unheralded and largely unthanked, risking their own lives in the seas round Britain to save "idiots" like Ralston who get themselves into tight corners by their derring-do. Or they may simply shy away from any limelight, like Second World War spy, Eileen Neame, who never told her neighbours in Torquay of her heroism, and was only found out after her death last month and accorded a burial at sea.

Then there are those whose job can involve the call to heroism – the soldiers, sailors and airmen whose ultimate sacrifice on our behalf we recall on the 11th hour of the 11th day of the 11th month, or on the streets of Wootton Bassett. Or policemen killed in the line of duty trying to protect the rest of us. Or those like Captain Chesley Sullenberger who in January 2009 received worldwide acclaim for landing his US Airlines jet in the Hudson River so perfectly that he saved the lives of all 155 passengers on board.

Yet a study carried out by Newcastle University that same year, and published in the Journal of Risk Research, suggests that when individuals do something extraordinary while going about their professional business, the public tends to place such heroism in a different category from, say, the neighbour who rushes in to a burning house to save children. It is a tough demarcation to make. Where, for instance, does it leave off-duty policewoman, Elizabeth Kenworthy, who was hailed this week by the coroner at the 7/7 inquest as "a very exceptional person" for saving the lives of two victims of the suicide bombers at Aldgate Tube station? Would her heroism have been of a different order if she had been on duty? For her part, she insisted that it was just "rudimentary first aid".

Another take on that professional-private tension is provided by contrasting Aron Ralston's 127 hours with the 69 days that 33 Chilean miners spent trapped underground maintaining their hope and not going to pieces. There is an essential difference between the two cases, beyond the extent of their endurance.

The miners worked in a dangerous profession not for the adrenalin rush of going underground (as opposed, say, to potholers), but for economic necessity. They have families to support and the $400 (£250) a week they could earn by going down the elderly San José mine, whatever safety concerns had been expressed about it, was their real incentive. They were not, in the words of one of Ralston's You Tube champions, "kids in a gigantic playground" but individuals who, like their fathers and grandfathers before them, felt they had no other viable choice.

Danny Boyle's film does not avoid these troubling questions around Ralston's heroism. It shows him, for example, carving his name into the sandstone of the canyon wall, as he lies trapped, and including dates for both his birth and his death. He even videotapes his goodbyes to loved ones. Here is a man who was also human enough seriously to contemplate giving in.

Boyle gives us Ralston warts and all. So when pre-accident, he bumps into two women hikers, he preens like a peacock, wins them round, then abruptly dumps them and goes his own way. "I don't think we figured in his day at all," one reflects to the other at the sight of Ralston swaggering away into the wilderness without a backward glance.

This highlights another problem with those whose heroism we admire. They can, simultaneously, have feet of clay. A couple of years ago I was sent to interview Joe Simpson, the climber whose astonishing feat of survival in the Peruvian Andes after his partner cut the rope that connected them, was documented in the award-winning 2003 film, Touching the Void. Reading and watching Simpson's story had left me in awe of this colossus, but in the flesh he was tiny and tetchy, as when he dismissed his climbing partner, as too busy being married and having children. That doesn't sound so awful, I suggested. "The fact that I've never married and never have any intention of marrying, and have made sure I can't have children," he told me proudly, "is simply because I don't like the little bastards, and I don't want to get married...I'm a selfish bastard."

Perhaps being a selfish bastard helps shapes the circumstances that makes heroes. If you are the sort to feel a duty to go on living for your children, you don't contemplate climbing K2. Alison Hargreaves died there in 1995, days after being acclaimed a hero as the first woman to reach the summit alone, unsupported and without artificial oxygen. She left two small children without a mother. At the time, those who criticised her were accused of sexism, but this summer Olympic medallist James Cracknell faced similar questions when he almost died trying to row, run and cycle his way across America. What use was such a stunt to his wife and two small children at home, it was asked?

Changing nappies and doing the school run doesn't tend to provide many opportunities for acts of transparent heroism – but sometimes it requires heroic stamina and endurance to do it well. But then that just goes to show that heroes can also give us lesser mortals chips on our shoulder.

Our collective habit as a society of focusing narrowly on one well-publicised heroic aspect or set of circumstances in an individual's life, and then applying it to everything else about that individual is well established. Like Simpson, Aron Ralston is now top of the pile on the motivational speakers' circuit, commanding fees of $5,000-$10,000 a go.

Such presentations usually involve telling the story one more time, and then pretending there is a link between the decision he made to cut his arm off when trapped in an isolated canyon and the decisions that his corporate audiences will be making about where to open the next branch of McDonald's, or how best to arrange the cashiers' rota in their bank. Speaker and audience collude in the make-believe that heroism is infectious, and can therefore be caught by contact with a heroic individual, and that it spreads seamlessly between different aspects of that individual's life.

Dawn French and Jennifer Saunders, acute observers of the foibles of human nature, tried on more than one occasion in their sketch shows to remind us that Dame Ellen MacArthur, the diminutive yachtswoman who thrilled the domestic audience with her heroism in single-handedly circumnavigating the globe in 2005, could also weep and whinge with the best of them, as evidenced in her video diaries on board ship. But we didn't really want to hear. We like to keep our heroism straight and uncluttered, not nuanced and with a dark side.

In the same way, when Terry Waite survived the appalling ordeal of being held hostage in Lebanon for four years until 1991, he was universally and rightly applauded on his release for his heroic endurance in the most inhuman of conditions. But to mention that Waite had gone to Lebanon in the first place against all advice (having been fatally compromised, experts believed, by his public association with the Reagan administration official, Colonel Oliver North) was considered bad form.

Perhaps it all dates back to one of our templates for fashioning heroes – Christian-ity's long-established penchant for saint-making. For nigh on 2,000 years it has tended to be an all-or-nothing business, shining the spotlight only on what the Church still calls "heroic virtue". But it is a flawed template because it omits all the other details that drag would-be saints down to the level of everyone else.

So when Pope Benedict on his recent trip to Britain beatified – one step short of awarding a halo – the Victorian convert cardinal, John Henry Newman, there was no mention of his occasionally acid pen, his sulks, his "particular friendships" with fellow clerics which potentially cut across church teaching on homosexuality, or even his clearly stated scepticism, during his lifetime, about the whole saint-making business. Instead Newman – like so many heroes today, including Aron Ralston – was presented as essentially two-dimensional, his heroic aspects lauded to high heaven and the rest politely overlooked.