Damascius on the Different Schools of Thought Regarding Soul

Some philosophers extend immortality from rational soul to the animate condition of the body, e.g. Numenius [frg. 46a]; others as far as nature, e.g. Plotinus in certain passages [IV vii 14]; others, again, as far as irrational life, e.g. of the ancients Xenocrates [frg. 75] and Speusippus [frg. 55] and, of more recent authorities, Iamblichus and Plutarch; others confine it to rational soul, such as Proclus and Porphyry; others limit it further to intelligence alone, making the opinionative function perishable, as many Peripatetics do; others to the universal soul, by which they think individual souls are absorbed.

(Damascius' commentary on Plato's Phædo, as translated by L. G. Westerink. Taylor has the same comment, but put more abstrusely, and apparently misattributed to Olympiodorus.)

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Well, there you have it from a primary source: what is your immortal part? Turns out there's six schools of thought among the Platonists alone.