You’re correct that logical thinking falls short of proving human-caused global warming in and of itself, but you couple that with empirical evidence. Under all thinking roots logical thinking. Data and research only go so far: At some point, you have to try to take the evidence you have and apply it using logic. Indeed you need logic to even construct the studies in a way that they will yield useful results.
I understand the example is contrived, but the point is you have a framework for making conclusions. All of the data in the world won’t help you if you can’t arrange its into a way to make a conclusion from it. This is how logic underpins everything.
It’s sort of like physics. Everything is just physics at its basis.
