“We met the moment,” President Obama said about the Paris climate talks on Saturday. “We came together around the strong agreement the world needed.”

Those are optimistic words, and indeed the Paris agreement, a 195-country affair representing the culmination of decades of climate negotiations, offers some cause for hope. The document aims to hold the global average temperature to “well below” 2 degrees Celsius above pre-industrial temperature levels.

As ambitious as this sounds, the agreement contains no binding rules on how to meet this (or any) temperature goal. All greenhouse gas emission targets are voluntary and left to individual countries to determine. This choose-your-own-emissions strategy skirts the political problems that disarmed the Kyoto Protocol, but it may have also rendered the Paris agreement too weak to prevent widespread climate catastrophe. The pledges submitted thus far leave a scary gap between what’s needed and what countries aspire to do.

The following chart from the World Resources Institute, an environmental advocacy group, shows just how wide that gap remains. The bars in the chart show several research groups’ predictions for how much global temperatures will rise if all countries adhere to their pledges. These commitments, called Intended Nationally Determined Contributions, were submitted in advance of the Paris talks and are based on each country’s willingness to act, rather than what’s needed to meet a temperature target. The particulars of each bar are less important than what they all show: In no simulation does this Paris climate treaty keep the world below 2 degrees of warming.

The numbers show that until nations implement more stringent emission controls, the 1.5 and 2 degree targets are nothing more than wishful thinking. “It’s just bullshit for them to say: ‘We’ll have a 2C warming target and then try to do a little better every five years,’ ” climate scientist James Hansen told the Guardian. “It’s just worthless words. There is no action, just promises. As long as fossil fuels appear to be the cheapest fuels out there, they will be continued to be burned.”

And that’s a huge problem, because the science shows that to address climate change, we need to leave a lot of fossil fuel untapped. A study published in the journal Nature earlier this year calculated that meeting the 2 degree target will require leaving 80 percent of global coal, 50 percent of natural gas and 33 percent of oil untouched until at least 2050.

So far, no country has promised to leave their fossil fuels untapped. While clean energy advocates insist that new low-carbon energy technologies will provide a net economic benefit, taking economically important fuels off the table may be politically impossible, especially in countries whose economies depend on energy production. And vested interests are ready to fight efforts to reduce fossil fuels. Exxon, for example, spent decades protecting their interests in exploiting those fuels. As a result, scenarios for keeping global temperature rise under 2 degrees almost universally depend on so-called “negative emissions,” theoretical technologies for removing carbon dioxide from the atmosphere that are thus far non-existent in any scalable form. “It is hard to underplay the fundamental reliance on the massive uptake of untried negative emission technologies to maintain the legitimacy of the Agreement,” wrote Kevin Anderson, deputy director of the Tyndall Centre for Climate Change Research.

Like previous agreements, the Paris one puts its faith in future actions. The so-called “ratchet mechanism” asks countries to revisit their INDCs every five years, report what they’ve done and, voluntarily, aim to make each subsequent pledge “a progression beyond” the previous one. The problem is that we’re running out of time, and it’s not even clear that countries will meet even the modest targets they’ve already submitted.

The U.S. pledge to reduce emissions by 26 percent to 28 percent below 2005 levels by 2025, for instance, could quickly unravel if the next president decides to overturn Obama’s climate policies. Even if a Democrat follows Obama in the White House, Republicans in Congress could still block the Clean Power Plan and other policies essential to making those important, but insufficient, targets.

Taming climate change would be easy if it were just a math or science problem. Stop emitting. Problem solved. But our political and economic systems appear unwilling to reduce consumption. Meeting the 2 degree target can’t be done by changing lightbulbs or buying electric cars. Instead, it will require a “revolution in how we consume and produce energy,” Anderson wrote.

“However much people profess to care about climate change, they do not seem willing to vote for this — nor do politicians seem willing to really try and persuade them,” Michael Grubb, an energy and climate expert at University College London told The Daily Telegraph. “All the evidence from the past 15 years leads me to conclude that actually delivering 1.5C is simply incompatible with democracy.”

Some activists see the tide changing. Now that the world’s governments have announced their intentions, “the rest of us can hold them to those promises, or at least try,” journalist-turned-activist Bill McKibben wrote at Grist. “What, you want to build a pipeline? I thought you were going to go for 1.5 degrees.”

Such optimism is heartening, but it also sounds familiar. Before the Paris talks, I spoke with about a dozen people who’ve been involved with climate issues since the Kyoto Protocol was negotiated in 1997. Many of them, including McKibben, recounted the optimism they’d felt at the end of the Kyoto conference. “It felt like the whole world was actually trying to solve a problem,” McKibben told me. “When the final protocol was drafted, I remember thinking that this was very important. I thought that we had won something.” Eighteen years later, he’s fighting essentially the same battle.

Despite the treaty’s binding targets and a committed timeline, the Kyoto Protocol failed to live up to its initial promise. President Bill Clinton had committed to Kyoto, but his successor, George W. Bush, reneged on his campaign promise to regulate power plants’ emissions of carbon dioxide and abandoned the Kyoto treaty. Canada eventually pulled out too.

The Kyoto Protocol isn’t the abject failure that it’s sometimes portrayed as in the U.S. (It pioneered important concepts and procedures and created some important infrastructure for addressing climate change, for instance.) But temperatures continued to climb under its watch.

The global temperatures have now risen to 1 degree above pre-industrial levels. As well intentioned as it might be, the Paris agreement will ultimately be judged by whether it succeeds in capping rising temperatures. The current document relies on magical thinking to accomplish this goal. Barring some incredible breakthrough in clean energy development, our only hope may be an unpopular one — restraint.