As the economic and scientific arguments accumulated, the Germans managed to persuade other countries to adopt the 2C target, turning it into official European policy. The proposal was always controversial, with African countries and island states, in particular, arguing that it was too much warming and would condemn them to ruin. The island states cited the potential for a large rise of the sea, and African countries feared severe effects on food production, among other problems.

But as a practical matter, the 2C target seemed the most ambitious possible, since it would require virtually ending fossil fuel emissions within 30 to 40 years. At Cancun in 2010, climate delegates made 2C one of the organizing principles of negotiations.

The talks culminating in Paris next year are seen as perhaps the best chance ever to turn that pledge into meaningful emissions limits, in part because President Obama has gone far beyond his predecessors in committing the United States, the largest historical producer of greenhouse gases, to action. That, in turn, has lured China, the largest current producer, into making its first serious commitments.

Yet even as the 2C target has become a touchstone for the climate talks, scientific theory and real-world observations have begun to raise serious questions about whether the target is stringent enough.

For starters, the world has already warmed by almost one degree Celsius since the Industrial Revolution. That may sound modest, but as a global average, it is actually substantial. For any amount of global warming, the ocean, which covers 70 percent of the earth’s surface and absorbs considerable heat, will pull down the average. But the warming over land tends to be much greater, and the warming in some polar regions greater still.

The warming that has already occurred is causing enormous damage all over the planet, from dying forests to collapsing sea ice to savage heat waves to torrential rains. And scientists realize they may have underestimated the vulnerability of the ice sheets in Greenland and Antarctica.