I. Paradox: Welcoming death but condemning suicide (61b-63e).
A. Consider the following propositions:
[i] Some people are better off dead.
[ii] Suicide is generally wrong (Socrates own case being an important exception!).
Socrates says that it would be surprising if [i] is false, but they all agree
[ii]is true. This will be a contradiction only if one also assumes
[iii] If one ought to do something, then that thing is good for one.
If you believe [i] and [ii], you must deny [iii]; thus the basis for the prohibition on suicide must be something other than self-interest (e.g., the interests of others; however even the interests of others seems insufficient to establish a general ban on suicide).
B. Religion as a basis for the ban on suicide.
b. If the gods have no reason for the prohibition, then the prohibition is arbitrary and the gods irrational.
c. If the gods have any reason whatsoever, then it is in virtue of those reasons alone that suicide is wrong (appealing to divine entities is superfluous).
d. If the gods have a reason but we can't know what it is, then no reason whatsoever can be given for the wrongness of suicide.
II. Critique of the Cyclical Argument
A. Recall the argument:
 Being alive has an opposite, namely being dead.
2. Second premise is taken for granted by Socrates and interlocutors, but seems to contradict Plato's own thoughts about the soul and God -- they are eternal (this is an ad hominem objection).
3. Third premise is false, if opposites must be taken as contradictories. The contradictory of being alive is being not-alive. Many things are neither alive nor dead.
4. Even if the argument were sound (it isn't), it would not establish that you going on living; it only establishes that life is caused by death.
B. If there is no perpetual cycle of death and life, and if there are a finite number of souls, then ultimately every living thing will be dead.
1. There is no impossibility in all living things ending up dead.