Alan Reyes has posed another deep question: "So to expand my question from earlier, how would Epicurus have proved the nonexistence of the afterlife either by way of direct empirical experience or by using a syllogistic argument form as he did with the swerve and the infinity of the universe?"
You'll note that the way this is phrased the presumption is that Epicurus considered his arguments on the swerve and infinity to be based in syllogisms, and that may only be true in part. But for purposes of this discussion let's generalize the question and ask "What arguments did Epicurus use to 'prove' that there is no life after death?"
I think it is fair to say that Epicurus used a number of arguments in addition to the contention in PD2 that death is nothing to us because all good and evil comes to us through sensation, and death is the absence of sensation. Probably the best source for a list of those arguments is going to be in Lucretius, particularly in Book Three. The argument occurs roughly in the following sequence, but this following list is not a statement of the argument. It's really necessary to go through Book 3 and pull the argument out of these topics:
- Our mind and spirit is material, just like everything else, and although it is composed of very special particles, it too is physical and it is inseparable from the body and dies with it.
- The Mind and body are born together and age together, and the mind can be sick just like the body can.
- The mind may be composed of particles that are immortal, but it is not immortal itself. Even if the particles of our mind came together in the same arrangement in future ages, our minds would have no memory of being us as we are now, just as our minds now have no memory of ever being together in the same combination and arrangement in past ages.
- Our minds and spirits are born and die with our bodies.
- Our minds and spirits are able to experience things only through sensation, and death brings the end of all sensation, so the state of being dead is nothing to us, and time after our death has no more relevance to us than did the time before we were born.
So with that as background, "What arguments did Epicurus use to 'prove' that there is no life after death?"