Problem with time travel in PoA

[slurm3001]

No: HPFGUIDX 31375

Hi, I've just read all the messages concerning the time travel in 
PoA, but I still can't find a logical explanation for the rescue from 
the dementors. 
After all, Harry1 could only have been saved by (time-travelling) 
Harry2's Patronus if Harry1 had survived the dementors in a different 
way in order to travel back in time and become Harry2. But in the 
book it is completely illogical:
Harry1 survives because of Harry2 AND Harry2 only exists because 
Harry1 survived
In other words: Harry is only able to travel back in time because he 
survived the dementors in the first place (otherwise he would be 
dead). Yet the given reason for his survival is the rescue by his 
future self. That's a total contradiction.

The problem could have been evaded by Harry managing to do the 
Patronus the first time, thereby securing his survival to travel back 
in time and rescue Buckbeak.

What's your opinion?

slurm