Quietly in public, loudly in private, climate scientists everywhere are saying the same thing: it's over. The years in which more than 2C of global warming could have been prevented have passed, the opportunities squandered by denial and delay. On current trajectories we'll be lucky to get away with 4C. Mitigation (limiting greenhouse gas pollution) has failed; now we must adapt to what nature sends our way. If we can.

This, at any rate, was the repeated whisper at the climate change conference in Copenhagen last week. It's more or less what Bob Watson, the environment department's chief scientific adviser, has been telling the British government. It is the obvious if unspoken conclusion of scores of scientific papers. Recent work by scientists at the Tyndall Centre for Climate Change Research, for instance, suggests that even global cuts of 3% a year, starting in 2020, could leave us with 4C of warming by the end of the century. At the moment, emissions are heading in the opposite direction at roughly the same rate. If this continues, what does it mean? Six? Eight? Ten degrees? Who knows?

Faced with such figures, I can't blame anyone for throwing up their hands. But before you succumb to this fatalism, let me talk you through the options.

Yes, it is true that mitigation has so far failed. Sabotaged by Clinton, abandoned by Bush, attended halfheartedly by the other rich nations, the global climate talks have so far been a total failure. The targets they have set bear no relation to the science and are negated anyway by loopholes and false accounting. Nations like the UK, which is meeting its obligations under the Kyoto protocol, have succeeded only by outsourcing their pollution to other countries. And nations like Canada, which is flouting its obligations, face no meaningful sanctions.

Lord Stern made it too easy: he appears to have underestimated the costs of mitigation. As the professor of energy policy Dieter Helm has shown, Stern's assumption that our consumption can continue to grow while our emissions fall is implausible. To have any hope of making substantial cuts we have both to reduce our consumption and transfer resources to countries like China to pay for the switch to low carbon technologies. As Helm notes, "there is not much in the study of human nature - and indeed human biology - to give support to the optimist".

But we cannot abandon mitigation unless we have a better option. We don't. If you think our attempts to prevent emissions are futile, take a look at our efforts to adapt.

Where Stern appears to be correct is in proposing that the costs of stopping climate breakdown, great as they would be, are far lower than the costs of living with it. Germany is spending €600m just on a new sea wall for Hamburg - and this money was committed before the news came through that sea-level rises this century could be two or three times as great as the Intergovernmental Panel on Climate Change has predicted. The Netherlands will spend €2.2bn on dykes between now and 2015; again they are likely to be inadequate. The UN suggests that rich countries should be transferring $50 to $75bn a year to poor ones now to help them cope with climate change, with a massive increase later on. But nothing like this is happening.

A Guardian investigation reveals that the rich nations have promised $18bn to help the poor nations adapt to climate change over the last seven years, but they have disbursed only 5% of that money. Much of it has been transferred from foreign aid budgets anyway: a net gain for the poor of nothing. Oxfam has made a compelling case for how adaptation should be funded: nations should pay according to the amount of carbon they produce per capita, coupled with their position on the human development index. On this basis, the US should supply more than 40% of the money and the European Union over 30%, with Japan, Canada, Australia and Korea making up the balance. But what are the chances of getting them to cough up?

There's a limit to what this money could buy anyway. The Intergovernmental Panel on Climate Change says that "global mean temperature changes greater than 4C above 1990-2000 levels" would "exceed ... the adaptive capacity of many systems". At this point there's nothing you can do, for instance, to prevent the loss of ecosystems, the melting of glaciers and the disintegration of major ice sheets. Elsewhere it spells out the consequences more starkly: global food production, it says, is "very likely to decrease above about 3C". Buy your way out of that.

And it doesn't stop there. The IPCC also finds that, above 3C of warming, the world's vegetation will become "a net source of carbon". This is just one of the climate feedbacks triggered by a high level of warming. Four degrees might take us inexorably to 5C or 6C: the end - for humans - of just about everything.

Until recently, scientists spoke of carbon concentrations - and temperatures - peaking and then falling back. But a recent paper in the Proceedings of the National Academy of Sciences shows that "climate change ... is largely irreversible for 1,000 years after emissions stop". Even if we were to cut carbon emissions to zero today, by the year 3000 our contribution to atmospheric concentrations would decline by just 40%. High temperatures would remain more or less constant until then. If we produce it, we're stuck with it.

In the rich nations we will muddle through, for a few generations, and spend nearly everything we have on coping. But where the money is needed most there will be nothing. The ecological debt the rich world owes to the poor will never be discharged, just as it has never accepted that it should offer reparations for the slave trade and for the pillage of gold, silver, rubber, sugar and all the other commodities taken without due payment from its colonies. Finding the political will for crash cuts in carbon production is improbable. But finding the political will - when the disasters have already begun - to spend adaptation money on poor nations rather than on ourselves will be impossible.

The world won't adapt and can't adapt: the only adaptive response to a global shortage of food is starvation. Of the two strategies it is mitigation, not adaptation, which turns out to be the most feasible option, even if this stretches the concept of feasibility to the limits. As Dieter Helm points out, the action required today is unlikely but "not impossible. It is a matter ultimately of human wellbeing and ethics".

Yes, it might already be too late - even if we reduced emissions to zero tomorrow - to prevent more than 2C of warming; but we cannot behave as if it is, for in doing so we make the prediction come true. Tough as this fight may be, improbable as success might seem, we cannot afford to surrender.

monbiot.com