While the idea of "proof" here is just a distraction, we have vastly more than merely "statistical correlations". We know that we've significantly increased the CO2 concentration in our atmosphere, and we have a pretty good idea of what that does to a climate:
"Of all the planets in our solar system, Venus is the hottest one, even hotter than Mercury, the planet closest to the sun. Venus, whose daytime temperature can reach 900 degrees Fahrenheit (464 degrees Celsius), is surrounded by a thick gaseous layer that consists mostly of carbon dioxide. When the sun's rays reach Venus, the carbon dioxide traps the heat within, causing a kind of planetary greenhouse effect."
"Of all the planets in our solar system, Venus is the hottest one, even hotter than Mercury, the planet closest to the sun. Venus, whose daytime temperature can reach 900 degrees Fahrenheit (464 degrees Celsius), is surrounded by a thick gaseous layer that consists mostly of carbon dioxide. When the sun's rays reach Venus, the carbon dioxide traps the heat within, causing a kind of planetary greenhouse effect."
From http://curiosity.discovery.com/question/venus-hottest-planet
EDIT: Also, you seem to be confused about what the law of the excluded middle says.