Science does not deal in absolute proofs. The scientific method depends upon falsification of alternative hypotheses until only one remains.
But “falsification” in science is not absolute. Instead, it is a matter of relative probabilities. Such “proof” by falsification of all alternatives is never final: All scientific laws, theories and hypotheses forever remain subject to falsification at any time–at least in principle, even if the odds of that ever happening are infinitesimally small.
All that is required to falsify an hypothesis, or to falsify the currently-accepted theory, is for an alternative hypothesis to be shown–by empirical evidence and quantitative analysis of the relative probabilities–to have a statistically-significant higher probability of being correct.
The CAGW hypothesis is that a) The Earth’s climate is warming, b) The warming is substantially a result of human emissions of CO2 and, c) The magnitude of the warming will be enough to have significant effects, and d) The net effects of the warming will be harmful, and e) The harm caused by the warming will be great enough to be worth the net costs of politically-coerced mitigation.
The alternative hypothesis–which is also the null hypothesis (<= click the link for more info)–is that a) The warming is substantially due to natural causes for which humans are not substantially responsible, and/or b) The magnitude of any human-caused warming will not be not be great enough to have significant effects by itself (regardless of the effects of any warming not caused by man,) and/or c) The net effects of warming will not be harmfull–or if they are, then not by enough to be worth the cost of politically-coerced mitigation.
The null hypothesis has never been falsified. There have been no peer-reviewed studies published that quantitatively analyze both p(CAGW | Historical-Temperature-Data) [the probability that CAGW hypothesis is true, given the historical temperature data] and p(NullHypothesis | Historical-Temperature-Data) [the probability that the Null Hypothesis is true, given the historical temperature data], showing that the former (CAGW) has a statistically significant higher probability of being true than the latter (the null hypothesis–that warming is substantially natural.) Not one.
But the reverse is not true:
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