What the science says...
The global dimming trend reversed around 1990 - 15 years after the global warming trend began around 1975. So it can't explain what began the global warming trend. Aerosols have a cooling effect on Earth's climate. When aerosols thin, the result is a lack of cooling, not a warming effect. That's not just semantics - take aerosols out of the equation and in the absence of any other forcings, global temperatures would remain steady.
So what is driving the warming? In the past, solar variations have been the main driver in climate change. A comparison of solar activity and temperature over the past 1150 years shows a close correlation between solar activity and temperature. However, the correlation ends around 1980 when temperatures started rising but solar levels remained steady.
Another suspect in climate change is cosmic radiation which is thought to increase cloud cover (hence cooling the earth). However, again there has been no correlation between temperature and cosmic ray flux since 1970. In fact, all the usual suspects in natural climate change - volcanic activity, orbit wobbles, solar variations are conspicuous in their absence over the past 30 years of long term global warming.
The only forcing that causes warming and also correlates with current temperature rises is atmospheric CO2. It's risen 100 parts per million over the past 120 years - in the past, that kind of change has taken 5,000 to 20,000 years. As CO2 rose over the 20th century, the only mystery has been why global temperatures actually cooled from 1950 to 1980. I even read one study in 1980 where the researcher posed the question "why aren't we seeing any global warming with all this CO2 in the air?"
The answer is now apparent with recent studies in aerosol levels and global dimming. Atmospheric aerosols caused a global dimming (eg - less radiation reaching the earth) from 1950 to 1985. In the mid-80's, the trend reversed and radiation levels at the Earth's surface began to brighten. From 1950 to the mid-80's, the cooling effect from aerosols was masking the warming effect from CO2. When aerosol cooling ended, the current global warming trend began.
Intermediate rebuttal written by John Cook
Update August 2015:
Here is a related lecture-video from Denial101x - Making Sense of Climate Science Denial
Last updated on 4 August 2015 by MichaelK. View Archives