Or how much of you is left after shooting a Polar Bear?
Seriously, I think .308 might be a bit light for big bears. By today's hunting standards, anyway.
Most serious bear hunters go with the 30-06, or even the .338 (talk about penetration!). As always, shot placement is the critical factor. For chance encounters, I carry a Remington 870 with slugs and buckshot.
I had a conversation in the sports store at Fort Wainwright a few years ago with a hunter from the "lower 48" who was going moose-hunting- he asked what pistol to carry for grizzly bear encounters. Of course, the standard answer is that it doesn't matter- just be sure to file off the front sight, so it doesn't hurt so much when the bear shoves it up your @$$. (Of course, now hat S&W has a .50 caliber revolver, we may have to rethink that...)