Newtonian mechanics is a deterministic system. This means that knowing the present position and momentum of the earth, the moon and the sun can allow us to predict with absolute certainty when and where an eclipse of the sun will be visible on the earth.
The weather is a chaotic (nonlinear) system governed by the butterfly effect: the flapping of the wings of a butterfly in the Amazon can cause a hurricane in the Atlantic. This means the weather is unpredictable more than a few weeks into the future.
The best example of this is Hurricane Rita. A few weeks after Hurricane Katrina destoyed New Orleans, Rita (a more powerful storm) entered the Gulf of Mexico. Just 5 days before Rita made landfall, all the sophisticated mathematical models of the National Weather Service predicted Rita would destroy Houston. Do you remember Houston being destroyed that summer?
The temperature of the earth is determined by the law of conservation of energy. This law of physics is deterministic, like Newtonian mechanics. So, the temperature of the earth is a function of energy in (solar radiation + geothermal heat; most people ignore this) - energy out (infrared radiation lost to outer space. Volcanic eruptions blast a lot of dust, desbris and gases into the atmosphere. This blocks solar radiation, meaning the earth will cool (assuming no change in the loss of infrared radiation). The year after Mt. Tambora erupted was called the year without a summer.
Greenhouse gases are opaque to infrared radiation and reduce heat lost from the surface of the earth. So, if solar radiation striking the earth does not change, increasing the greenhouse gas content of the atmosphere will cause the earth to warm.
But if this is the case, why haven’t humans caused the earth to warm before the Industrial Revolution because they produced carbon dioxide in breathing and in burning wood?
There is a natural carbon cycle (photosynthesis removes carbon dioxide from the atmosphere and respiration or burning wood adds it to the atmosphere). Since this natural cycle is a steady state, there was no net increase or decrease in carbon dioxide in the atmosphere before humans started digging up fossil fuels and burning them as a source of energy. The carbon in fossil fuels is sequestered in the earth and is not cycling. When humans burn fossil fuels this adds carbon dioxide to the atmosphere that should not be there. Ergo, we should see an increase in carbon dioxide in the atmosphere after the Industrial Revolution. Since that is exactly what we see, we can state unequivocally that the law of conservation of energy predicts the earth will warm when humans burn fossil fuels, but not bio-fuels (e.g., ethanol, bio-diesel, or wood). A forest fire simply adds carbon dioxide to the atmosphere that the living trees removed from the atmosphere. This is a zero-sum game, while burning fossil fuels is not a zero-sum game.