In his speech to the jury, Socrates provides three arguments against fearing death:
(1) Fearing death is cowardly and shameful.
(2) One should always do what is right, whatever the consequences, even if it means facing death. (Plato's Republic is devoted primarily to defending this position.)
(3) We do not know what death really means, but if we fear death that implies we think we know what death is, and to think one knows what one does not know is "the worst kind of ignorance."
These three separate arguments are all intertwined in Socrates' speech: We do not know what death is, in particular we do not know whether it is good or bad, but we do know that acting unjustly and/or cowardly is wrong. Therefore we should always act in accordance with justice, and we should never do what we know to be wrong, even at the risk of death.
While explaining his own lack of fear of death in this way, he encourages the jury to fear for themselves, lest they do harm to themselves by acting unjustly:
I think that what I am going to say will do you good: for I have something more to say, at which you may be inclined to cry out; but I beg that you will not do this. I would have you know that, if you kill such a one as I am, you will injure yourselves more than you will injure me. Meletus and Anytus will not injure me: they cannot; for it is not in the nature of things that a bad man should injure a better than himself. I do not deny that he may, perhaps, kill him, or drive him into exile, or deprive him of civil rights; and he may imagine, and others may imagine, that he is doing him a great injury: but in that I do not agree with him; for the evil of doing as Anytus is doing - of unjustly taking away another man's life - is greater far. And now, Athenians, I am not going to argue for my own sake, as you may think, but for yours, that you may not sin against the God, or lightly reject his boon by condemning me. For if you kill me you will not easily find another like me. For if you kill me you will not easily find another like me, who, if I may use such a ludicrous figure of speech, am a sort of gadfly, given to the state by the God; and the state is like a great and noble steed who is tardy in his motions owing to his very size, and requires to be stirred into life. I am that gadfly which God has given the state and all day long and in all places am always fastening upon you, arousing and persuading and reproaching you. And as you will not easily find another like me, I would advise you to spare me. I dare say that you may feel irritated at being suddenly awakened when you are caught napping; and you may think that if you were to strike me dead, as Anytus advises, which you easily might, then you would sleep on for the remainder of your lives, unless God in his care of you gives you another gadfly. And that I am given to you by God is proved by this: - that if I had been like other men, I should not have neglected all my own concerns, or patiently seen the neglect of them during all these years, and have been doing yours, coming to you individually, like a father or elder brother, exhorting you to regard virtue; this I say, would not be like human nature. And had I gained anything, or if my exhortations had been paid, there would have been some sense in that: but now, as you will perceive, not even the impudence of my accusers dares to say that I have ever exacted or sought pay of anyone; they have no witness of that. And I have a witness of the truth of what I say; my poverty is a sufficient witness. [30c-31c]Nothing could be less "skeptical", in the way that word is so often misused, than Socrates' haughty advice delivered so scornfully to those who in theory stand in judgement over him. Such talk is obviously not intended to "make friends and influence people"!
For over 2400 years now (Socrates was executed in 399 BC) some people have wondered why it was that Socrates chose to antagonize the jury, rather than putting on a more conventional defense. In fact, the jury vote was close enough to strongly suggest that if Socrates had been less confrontational and less condescending, he most likely would have been acquitted.
But Socrates could not be other than Socrates. He conducted himself at his trial just as he had always done, at least since the day he received "the command of the oracle", as he understood it, to examine himself and his fellow Athenians. This cannot be over-emphasized: Socrates could not act differently simply because his life was now at stake. And he explains exactly why that is so in the speech itself.
In fact, Socrates won't even lower himself to explicitly refute the charges against him! Instead of directly countering the charge of impiety, he raises the question (using R.E. Allen's paraphrase): "Does one or does one not acknowledge the Gods of the City ... if one doubts ... certain of the terrible stories told about them?"!! And instead of directly answering the charge that he corrupted the youth of Athens, Socrates poses the question: "Does one corrupt the youth by expressing ... doubts?"!! Socrates' "defense" amounts to his open declaration that he does not genuinely know whether the charges against him are true or not, because we do not know with certainty what piety and virtue are - but Socrates insists that this is just as true for his accusers and judges as it is for him. In fact, Socrates makes a central point of his argument that he is superior to his accusers and judges precisely because he knows that he does know these things - whereas they believe that they do!
As R.E. Allen explains it, Socrates does not present a "defense against the charges" so much as he makes his own "counter-claim". Socrates has, in effect, put his accusers and the members of the jury on trial, and he has convicted them, to their faces, of "villainy and injustice" (as Allen puts it). And just in case there is any doubt about what he really thinks, he tells them all that he has nothing to fear "for it is not in the nature of things that a bad man should injure a better than himself".
The Apology is one of the greatest works in the history of rhetoric. But this is philosophical rhetoric, which is only interested in arriving at the truth, not in winning an argument. And one cannot arrive at the truth unless one begins with the acknowledgment that one does not yet know the truth. In contrast there is what R.E. Allen calls "base rhetoric" which begins with the assumption that one knows the truth already, and such "base" rhetoric is employed only to cajole others to one's own position. Very often base rhetoric is also called simply sophistry, and one of the hallmarks of sophistry, in this negative sense, is that a skilled sophist is able to convince people that a case that is truly weak is really strong, and vice versa:
"Socrates does not state but shows the difference between base rhetoric and philosophical rhetoric and shows also that the difference is not merely a matter of form. The verdict of the Athenians indicates that, just as Meletus and those around him do not know what piety and impiety are, so the Athenians do not know what sophistry is, or what it really means for the stronger argument to be strong. Standing at a distance, they cannot tell the dog from the wolf. What is shown is not said, and cannot be said except to those who have learned to see and need not hear it." [Allen 1984, p. 73]Whew! I'm really just starting to scratch the surface. In the next installment I will back up a little and give a more general overview of the Trial of Socrates. It occurs to me that I might be assuming more knowledge than most people are likely to have.....
The Varieties of Sceptical Thought:
 Sceptical Scepticism
 Socrates on Death
 Socrates' Advice to the Jury
 Richard Popkin
 Overview of the Trial of Socrates
 "Socrates of all mortals is the wisest"