I think one of the more important lessons here is that sharpening terms vary from user to user and it's important to make sure you know what the heck the other person is talking about before you embark on a new tack for your sharpening voyage.
Jon is of course right, as far as the general run of knife enthusiasts who have contact with traditional Japanese knife shapes. They (the knives, not the enthusisasts) are the new "single bevels." Jon uses their language because that's the sea in which he swims.
It's not as easy for me though, mostly because I'm old and was around when a "double bevel" meant part of a two-stage, multi-bevel on each side of the blade, and that's what I got used to. I don't fight for the old definition, and for the same reasons don't go to the shore to order the tide in and out. As is so frequent with linguistic issues, there's no right or wrong just prevalence; and -- worth reiterating -- the most important thing is to get on the same page as the person to whom you speak.
Since MAC entered the conversation: It's not MAC dogma, but MAC Pros are one of the knives which really do benefit from a "double bevel" (in my old sense), with the double allowing a really nice balance between absolute sharpness, durability and simplicity of maintenance. If you have something which allows really fine angle control, like an Edge Pro, the angles should be something like 10/15*, with only mild assymetry. If you're freehanding, sharpen a little more acute than 15*, going all the way through your stone progression, except for the finest stone. Then tilt the knife up just a little bit for a micro bevel on your second finest and finest stone. If you deburr after the first angle, you might or might not get away without deburring on the second.
Just when you thought it was safe... There's no agreement on the names of the two stages of the bevels. Some people call the edge angle the "primary" bevel, and others call the angle behind it and up the face of the blade the "secondary." Some people use the terms the other way around. Again, check before you start arguing.
Keep your hands inside the ride at all times, and for God's sake don't throw food to the grips.