If that’s what the script says, the “you’re alive” line may have been improvised by Fox and, in that respect, makes sense
Fox is channeling a frazzled teenager who’s just seen his friend get killed
Seeing Doc’s name in the phone book reminds him he’s in the past, when Doc’s still alive.
Question: Why hasn’t everything else he’s seen already tell him he’s in the past?
Answer: It does, but Marty’s new to time travel and, again, emotionally traumatized.
So no, a phone book doesn’t confirm scientifically that Doc is, at that moment in 1955, alive. But Marty’s not a scientist. To Marty, the phone book simply confirms Doc EXISTS in 1955. He concludes Doc must be alive because, if Doc exists, he MUST be alive (because Marty knows where and when Doc will die in 1985)
Note: It might have made more sense for Marty to say, “good, you’re here” instead, but again, “you’re alive” tells us more about Marty’s state of mind at that moment
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