οὐ γὰρ δήπου τοῦτό γε σαφῶς δοκεῖτε εἰδέναι ὡς οὐδὲν ἔτι ἐγὼ ἔσομαι, ἐπειδὰν τοῦ ἀνθρωπίνου βίου τελευτήσω:
He seems to affirm here that he will be nothing after his death, but in the rest of his speech he intends to prove the opposite. logically it would be more correct to say here that: it seems to me that you do not understand it clearly that i will not be nothing when I finish my human life. Maybe the first negative should still influence the sub clause.
I see this as a rhetorical question. ‘You surely don’t suppose to know this clearly, (namely) that I’ll be nothing in the future, whenever I depart my mortal life’. He then goes on to give his evidence for immortality.