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The evidence to convince me would include events that have actually happened which can't be questioned by others equally qualified (see www.iceagenow.com for example), proof carbon dioxide can increase heat in an open system (ie not one with physical window glass), proof a few extra percentage of it actually can make differences thousands of times greater than its input, and finally and best of all stop pretending they can predict one of the most complex systems in the universe (as outside the earth we are not aware of anywhere else with life on it besides weather systems including liquid water).
The main reason for asking is the latest claim is they want to stop the mean temperature rising by 2', but is that from 1900, 1950, 2000, now, or when? You can't have a rise of 2' from now as that changes every day, so has to be from a certain point. And would also ask them exactly what is the correct temperature level for the planet?