Socrates's first logical fallacy is a form of post hoc ergo propter hoc—that is, after this, because of this—and is centered on Socrates's argument that his personal god or spirit, the daimonion, who normally opposes him when he does something likely to harm himself, has remained silent from...
the time Socrates left for the trial to its conclusion:
Probably what has occurred to me has turned out to be good. ... For there is no way that the accustomed sign [from his personal spirit] would not have opposed me unless I were about to do something good.
Socrates assumes that there exists a direct cause and effect relationship between the spirit's silence and the rightness of his actions during the trial. In other words, because the spirit fails to speak to Socrates, Socrates takes no other actions or makes further arguments to save himself, his conclusion being that death cannot be bad if he was not warned to avoid it.
A second logical fallacy occurs when Socrates argues that being dead results in one of two things:
For either it is like being nothing and the dead man has no perception of anything, or else, in accordance with the things that are said, it happens to be a sort of change and migration of the soul from the place here to another place.
This fallacy is called begging the question (petitio principii), which does not mean "prompting the question" as used commonly by people who don't know its proper meaning. Begging the question means that one assumes a conclusion that is not proven. Socrates makes the argument that death is not bad because it is either nothingness, a never-ending sleep with no dreams, or one's soul migrates to Hades, the Greeks' underworld, where, after having been released by honest judges in the underworld, a good man would be free to
... associate with Orpheus, Musaeus and Hesiod and Homer, how much would any of you give? For I am willing to die many times if these things are true. ...
Here, Socrates assumes that an afterlife based on "things that are said" will be his destiny—certainly, he believes in this afterlife, but believing is not the same as knowing—and so his conclusion, based on assumption, may or may not reflect reality. Socrates's logic here is similar to someone arguing that the Bible must be true because it is the word of God—basing an argument on another argument that is a belief rather than a fact.