Scientific Survival

In CS Lewis' That Hideous Strength, a guillotined head immediately attached to scientific apparatus is kept alive and able to speak although it later transpires that the entity speaking through the "Head" is not the executed man but a demon. In addition, Lewis assumes souls.

In James Blish's Midsummer Century, a brain is kept alive and able to speak indefinitely in a case in a museum. In addition, a personality is a semistable electromagnetic field that fades away when it loses its computing apparatus and energy source.

In Poul Anderson's Harvest of Stars Tetralogy and Genesis, although brains die with their bodies, some personalities with their memories are incorporated into artificial, post-organic intelligences and thus survive indefinitely. There is no other means of survival.

This is a tripartite conceptual progression:

a brain kept alive in its skull;
a brain kept alive in a case;
a personality preserved in an AI.