St Bobby's hit on something here about viewing the possibilities in terms of our personal perception of the percentages involved, as non-expert outsiders.
The way I see it, we don't have to "prove" that climate change is taking place, or that mankind's activity is all or part of the cause. All that needs to happen is a fraction of a percentage of possibility that it might be the case for action to become necessary.
This situation is genuinely unique, in that we simply cannot afford to lose the stake we are gambling with. The climate deniers could be right, in spite of the evidence mounting up, but if they are wrong we wont be here for them to say "sorry".