I run my loader rear tires at about 12 PSI. I had not checked them for a while and a month ago they seemed kind of soft...and I think they were at something like 6 PSI...
One thing to keep in mind is that with fill in the tire the air bubble is smaller, and when the tire deforms pressure increases faster inside than it would if the tire only had air in it. So it may make sense to carry a little less pressure in the tire than you would if you only had air in it, if the tire is loaded with liquid.
Now my front tires are foam filled...wonder what pressure that equates too... /forums/images/graemlins/confused.gif
Lower pressure in my mind equates to better traction to some degree, since the tire contact patch would be greater if the tire flattens a bit on the bottom. I think the reason I started running lower pressure was because I got the impression from other posters here that lower pressure and tire deformation was gentler on the grass. But since then I have stopped using the tractor for mowing...but then again, I still have to get on the better part of the yard now and then, so I have not changed my practice any with respect to tire pressure...