Immortality

In plain terms

For immortality to be worth wanting, whatever survives has to be you. That is a stronger requirement than survival of something.

And it is where the doctrines divide. If a soul detaches and continues, it needs enough of your memory, character and perspective to count - and Aquinas himself held that a separated soul is not the person, which is why bodily resurrection is required to complete it. If a body is reassembled, the question is whether a reassembled thing is the same one or a replica.

There is also the question of whether it is desirable. Williams argued that an endless life would eventually exhaust every project and every desire, leaving a being with nothing left to want - which turns immortality from a hope into a description of tedium without end.

As a philosopher would put it

The Phaedo offers several arguments - from opposites, from recollection, from the soul's affinity with the unchanging, and the final argument from the soul's essential connection to life. Their weaknesses were noted in antiquity.

The Christian doctrine is resurrection, and the difference from Platonic immortality is substantial: the person is a body, death is real, and continuation depends on an act of God rather than on the soul's nature.

The personal identity literature applies directly. If psychological continuity constitutes identity, then a duplicate with your memories is you, which produces the fission problem; if bodily continuity does, then reassembly after dispersal is a hard case.

Williams's tedium argument is the standard objection to desirability: categorical desires give a life its shape and would eventually be exhausted, so an immortal being becomes either bored beyond endurance or so changed as not to be the same person. Nagel and others reply that new desires might keep arriving indefinitely.

What is actually disputed

Whether immortality is possible and whether it is desirable.

The possibility question turns on personal identity. Psychological continuity accounts make survival conceivable through any medium that preserves the right relations, and produce the duplication problem: if two beings have your memories, both cannot be you, and neither has any better claim. Bodily accounts avoid that and make reassembly after millennia of dispersal hard to state.

The desirability question is genuinely open. Williams's argument is that categorical desires are finite and their exhaustion leaves nothing; his critics reply that this underestimates how much there is, or that identity can survive substantial change.

What is worth separating is that the traditions rarely offered indefinite continuation as such. Most offered a transformed condition, and several - the Indian ones in particular - regard endless continuation as precisely the problem to be escaped.