The current ongoings in LOST made me think about this subject again, because as it now is i.e. Sawyer would live on the island as a member of the initiative while his much younger self lives back in the states.

I for one don't believe that it would be possible to go back to a distinct point in time by whatever means. But let's assume for one moment that it IS possible.
I don't want to go into the usual "What if I kill my dad before he meets my mom" paradox.
Instead let's say I decide to go back just 10 minutes without spacial shift. This would mean that for 9.599999 minutes there are two "me"s existing at the very same spot.
First off: Let's assume that there are such things as souls. Wouldn't it contradict the concept of the unique soul that the very same soul exists TWICE at the same time at the same place?
Secondly: Let's say after 8 minutes the second me goes back another 5 minutes. That would mean for another 4.5999 minutes there are THREE "me"s existing at the same spot...!
The only consistent thing about this model is that only ONE "me" would live beyond the point of the first jump. Namely the third one...

In Sawyer's case that would mean that if he doesn't jump anywhen else or dies before the crash, his initiative self would live on AND he would theoretically be able to meet his younger self on the island after the crash.
Funny thought/plot models arise out of this...