Could the Sun be causing climate change?

In climate change debates, one hears a lot about the Sun. A favorite argument of those opposed to action is that the warming we're presently experiencing is due to increases in solar output, also known as solar brightening, and not from greenhouse gases.
Before critiquing this argument, first remember what the IPCC says about human contribution to climate change:
There is new and stronger evidence that most of the warming observed over the last 50 years is attributable to human activities.
Note that the IPCC says most of the recent warming is due to human activities. This leaves as much as 50% of the recent warming not attributed to humans.
It is certainly possible -- and fully consistent with the IPCC -- for solar to have contributed some part of the warming we are experiencing.
The real question is whether solar brightening could be the dominant cause of the recent warming, with humans playing a minor role. That is unlikely, for the following reasons:

We have good measurements of the output of the sun over the past few decades and they show that total solar irradiance has varied by only 0.07% in that time. For more on this, see the review by Foukal et al. in Nature. Combined with our estimates of climate sensitivity, this observed increase in solar output cannot produce anywhere near the observed increase in temperature over the past few decades.
If the climate turns out to be much more sensitive than previously thought, and solar brightening turns out to be responsible for the temperature increase, one has to explain why increases in CO2 and other greenhouse gases are not also driving large temperature increases. Based on our present understanding, it would be difficult for solar brightening to be driving a large warming without greenhouse gases also significantly contributing.
But what about more exotic explanations, like galactic cosmic rays (GCRs)? The idea here is that GCRs stimulate cloud formation. Since clouds are powerful regulators of our climate, variations in GCRs can cause climate variations.
This is an interesting idea for which there is little evidence, for or against. As a result, the scientific community leaves it an open issue. More data will eventually establish whether this is a reasonable explanation.
In the meantime, however, one has to consider greenhouse gases a much more likely culprit. And if it turns out that GCRs are the dominant cause of the recent temperature rise, one still has to explain why greenhouse gases are not affecting our climate.
Program Note: As you probably know, at present there is no way to get an RSS feed for a particular Gristmill author. As a result, I'm going to start posting links to my new Gristmill stories on my old blog. If you get an RSS feed to that site, you'll be alerted whenever a new grist story by me is released.