Socrates presents two alternatives that might await one after death, and he says that either is a blessing. The main problem with his argument is that the two alternatives he presents do not exhaust all of the possibilities. Once other possibilities for what might occur after death are admitted, his argument is much less convincing.
Socrates might be right that either the dead are nothing, or death is a kind of 'relocation of the soul' (first premise), if we interpret 'relocation of the soul' broadly enough. But if we accept the first premise, it seems that we have little reason to accept the way he characterizes the (possible) relocation in premise 5. Other possibilities include transmigration of the soul, maybe into something unpleasant like a dung beetle or a dog, or an eternity of suffering in Hell. Neither of these would count as a blessing, and so (7) is not acceptable. (Of course, one could also question whether, even if Socrates was right about the shape of the afterlife, an eternity of questioning other people about the definitions of the virtues would be 'an extraordinary happiness.' (premise 6))
The other possibility is that the dead are nothing. However, the analogy that Socrates uses between death and a dreamless sleep can be questioned. The two are similar in the following way: both involve a lack of consciousness. However, I'm not so certain that a night of dreamless sleep is better than most of the days and nights of my life. And in any case, if a night of deep sleep is a good thing, it's good because one awakes from the sleep feeling refreshed and ready for the day. If death is nothingness, then one never awakes from it, so it can't be good for you in the same way that a night of dreamless sleep is.
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