One of the main claims of climate denial is that carbon dioxide is harmless, that there's no proof it can warm a planet. But this claim is against the law. Which law? The Law of Thermodynamics.
The temperature of this planet's surface is primarily set by the rate at which heat from the hot Sun moves to the warm Earth, and the rate at which heat from the warm Earth moves to the cold of space. (Some heat can also come from the core of the planet, but in Earth's case this is pretty trivial.) If either of these rates change, the planetary temperature is affected. If the rate at which heat moves from Earth into cold space slows down, the temperature of the planet's surface has to rise, there's simply no other option allowed by law. The energy arriving at Earth must either stay or depart, and if it can't depart at the same speed it arrives, the surface gets warmer.
Greenhouse gasses, by definition, scatter infrared radiation. Like car headlights shining into a bank of fog, the light does not pass through the gasses cleanly, but ends up bouncing around in all directions, including back towards the source. The greenhouse property of certain gasses is simple physical chemistry, trivially verified in the lab, and beyond dispute. Clearly, greenhouse gasses in our atmosphere will slow the transfer of heat (via infrared radiation) from the surface to the cold of space. There's no possible alternative, rising greenhouse gas concentrations must make the surface of a planet warmer (if all other factors remain constant).
And with just those two observation, the basic premise of global warming becomes an irrefutable fact. It's proven. Denial of that fact requires denying thermodynamics, which is a guarantee of failure.
Scientists aren't observing a warming planet and speculating that greenhouse gasses might be responsible, they already know that greenhouse gasses must warm the planet and are merely trying to quantify the magnitude of the effect.
More discussion below the orange squiggle.
I'm not trying to change any kossak's minds here, I'm pretty sure we all agree on this. I'm trying to refine an argument, to improve the rhetoric, to tweak the wording. I'm looking to have a bit of text ready the next time I hear the claim, one that is both very strongly worded and still scientifically accurate. I want to put the denialist on the defensive, make them justify themselves with something more rigorous than 'it's a hoax' or 'it's unproven'. I also need to keep this argument short and sweet, so there's little room to debate fine points of accuracy. This argument should not only be right, but it should be obviously right to those with less scientific training.
However, this argument attacks a specific denialist claim, but does not address a more scientifically valid one: that the warming induced by higher greenhouse gas concentrations will be mild, and insufficient to cause problems. A short refutation of that point does not exist, we pretty much have to rely on the mathematical competence of large numbers of climate scientists to assert that point. But if the denialist has to concede that warming is an inevitable consequence of the laws of physics, the argument can at least move forward to the next level.
So, suggestions? How would you reword this to make it stronger, clearer, more bulletproof?
Or is this blurb the wrong tactic, more likely to close minds than to open them?