Bugmaster comments on 6 Tips for Productive Arguments - Less Wrong
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If there was a mechanism that simultaneously increased CO2 absorption, the levels wouldn't have been rising. For the measurements, you mean, like vast conspiracy that over reports the coal that is being burnt? Yes, that is possible, of course.
One shouldn't do motivated search, though. There is a zillion other mechanisms going on, of course, that increase, and decrease the effects. All the immediately obvious ones amplify the effect (e.g. warming releases CO2 and methane from all kinds of sources where it is dissolved; the snow is white and melts earlier in spring, etc). Of course, if one is to start doing motivated search either way, one could remain ignorant of those and collect the ones that work in opposite, and successfully 'counter' the warming. But that's cherry picking. If one is to just look around and report on what one sees there is a giant number of amplifying mechanisms, and few if any opposite mechanisms; which depend on the temperature and are thus incapable of entirely negating the warming because they need warming to work.
I was thinking of a scenario where you measured CO2 emissions, but forgot to measure absorption (I acknowledge that such a scenario is contrived, but I think you get the idea).
That's a possibility as well, but I was thinking about more innocuous things like sample contamination, malfunctioning GPS cables, etc.
In all of these cases, your math is correct, and your basic physics is correct, and yet the conclusion is still wrong.