I'm going to address Mr. Chumpville two ways. The first way is to look at the issue of increasing atmospheric CO2 concentrations from the perspective of Occam's Razor. As a reminder, Occam's Razor indicates that if there are two (or more) differing explanations as the cause of a particular observed phenomenon, then the simplest explanation is preferable. Note one thing about Occam's Razor, though - the explanations have to cover all of the data pertaining to the phenomenon. Not just part of it, ALL of it.
So, to begin. In the mid-1800s, civilization began to industrialize in earnest. 'Industrialization' means more manufacturing, and more manufacturing means more energy usage. Fossil fuels were vital for this, powering the factories and the trains and the steamboats first, and after a couple of decades, providing power for electricity.
I seriously doubt Mr. Chumpville would dispute that industrialization accelerated in the mid-1800s, and this was accompanied by significantly increasing consumption of fossil fuels for energy production.
So what would be a result of this? Well, it's again obvious that burning of fossil fuels produces CO2. Given that this byproduct was released to the atmosphere, a simple prediction would be that an increase in atmospheric CO2 concentrations would accompany industrialization. Since industrialization picked up steam (so to speak) in the mid-1800s, it would be expected that if it were possible to measure atmospheric CO2 concentrations from about that time, and to regularly sample the atmosphere and measure the CO2 concentration, an increase in atmospheric CO2 concentrations would be observable due to the increasing amounts of CO2 released to the atmosphere by the increasing amount of industrial activity.
Since atmospheric air is trapped in bubbles in ice sheets and glaciers, and because it is possible to accurately date the location of the ice layers in such formations, the bubbles trapped in ice provide regular samples of the atmosphere. So, when the concentrations of CO2 in the air trapped in the bubbles are measured, and then the concentrations are plotted over time, the results show an increasing trend in atmospheric CO2 concentrations
commencing essentially simultaneously with the rapidly increasing industrialization in the mid-1800s. Which is simple. And which is what was expected.
Famously, starting about 1958, atmospheric CO2 concentrations began to be measured directly at Mauna Loa (but also note that there are other locations where this has been done, just not for as long as at Mauna Loa). Mr. Chumpville objects to this because he says that the ice cores and the Mauna Loa station are at two different altitudes. But remarkably, the scientists don't have a problem with this. A good way to check to see if your method works is to compare it to something else done a different way.
So when the ice core bubble air CO2 concentrations from 1958 are compared to the Mauna Loa atmospheric CO2 measurement from 1958, the two values are very close. This kind of double checking makes scientists happy.
But still - how do they know for sure that the increasing atmospheric CO2 is from fossil fuels? Well, they looked at the isotopes of carbon in the fossil fuels (yes, they did) and they discovered a couple of things. One, there isn't any radioactive 14C, because the fossil fuels are much too old for there to be any 14C left. Two, the amount of the stable isotope 13C is less in the fossil fuels than in modern carbon reservoirs on Earth.
Sooo... the next prediction is that the Suess effect would be observed, essentially that there would be a reduction in the atmospheric 14C concentration, and a change in the ratio of 13C/12C (12C being the common C isotope) due to the burning of fossil fuels and the increasing amount of CO2 from them in the atmosphere, differing from the natural cycle.
And the Suess effect is observed. And not in just one material, but in many different ones: tree rings, corals, marine sponges, and carbonate cave formations. (Scientists like to make independent observations that can either add supporting evidence or provide countering evidence to a prevailing hypothesis.)
And guess what? Not only is the Suess effect observed, it observably commences
at just about the same time as the industrialization of the world, and at just about the same time that atmospheric CO2 concetrations trapped in ice bubbles are also observed as starting to increase.
In the most basic terms:
1. The world industrializes.
2. As the world industrializes, more fossil fuels are burned for energy.
3. Increasing fossil fuel consumption releases increasing amounts of fossil fuel CO2 to the atmosphere.
4. Samples of the atmosphere collected over time show atmospheric CO2 increasing, and the increase begins at the same time that industrialization rapidly accelerated.
5. The Suess effect, resulting from isotopic dilution of both 14C and 13C in Earth's atmosphere, is observed in different materials, and the Suess effect is also observed commencing at the same time as rapid industrialization and and at the same time that ice bubble air shows increasing CO2 concentrations.
Philosophically, the way that scientific evidence is used to support the validity of a particular explanation, and with the addition of Occam's Razor: to whit, that this cause-and-effect is fundamentally the simplest way to explain it -- it is a nearly irrefutable reality that increasing atmospheric CO2 concentrations are caused by the burning of fossil fuels.
Part II will be about what Mr. Chumpville said regarding the Suess effect.