Are souls eternal? Is this unambiguously attested in scripture? Is there extra-biblical evidence?
I'd say the discussion of souls, and especially the nature of the eschaton, is based on 'speculative theologies' founded on the few remarks in sacred Scripture.
Also, what most people who dispute this teaching are disputing is the purported horror of the eternal destination of unbelievers ...
We have to look at the evidence here. Christianity, for example, offers little.
Hell in the NT is the English translation of Gehenna. As discussed, the valley of Hinnom, south of Jerusalem, was impure ground, possibly the site of child sacrifice (although doubted) probably just pagan worship. It became a place where trash was dumped and the unwanted dead, people and animals, were left and burnt. It suited as a symbol of the fate of the wicked.
A more nuanced approach is that Gehanna is the place where the unwanted are left and, effectively, forgotten. They cease to exist. The view then is that Jesus is offering an analogy, that God would cease to bear in mind, as it were, those who offend God. By so doing, they simply cease to exist, they'd be a candle flame, snuffed out – Jews, Christians and Muslims see God as holding all things in being, and if God should cease to be mindful of things, then those things would simply cease to be.
The other references to fire again accord, really, with the idea of the disposal of the unwanted, the chaff after the harvest, so once again, the inference of hell and its fires in Scripture bear a greater resemblance to the town dump.
Come the Middle Ages, and the medieval mind really gets to work – demons, imps, tridents ... Dante's Inferno ... nearly every contemporary image of the suffering in hell owes more to medieval imagination than scriptural inspiration ... it's all rather hysterical.
Not, for a moment, to downplay Jesus warnings against being cast out – He was absolute in that regard – He feared for the people, Gehenna, as an analogy, evoked a very real and terrible outcome.
God was surely capable of, and free to, create a destination less appalling than unending torturous hellfire.
Or, to annihilate (the wages of sin = death)
Hence Sheol, in Hebrew thought, which evolves over time, and we have limbo and purgatory in the Christian tradition, and al-A'raf in Islam – an intermediate between heaven and hell, populated by those whose sins and virtues are evenly balanced.
In the Greek myths, there are the Fields of Asphodel, the abode of those who deserve neither the Elysian Fields (heaven) nor Tartarus (hell) and where they dwell for all eternity.
Bardo in Buddhism is something similar with regard to intermediate states.
I should imagine all traditions who have a sense of an afterlife or eschaton would consider intermediate states.
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A nugget of Christian eschatalogical speculation is derived from these text:
"But he that received the seed upon good ground, is he that heareth the word, and understandeth, and beareth fruit, and yieldeth the one an hundredfold, and another sixty, and another thirty." (Matthew 13:23)
"And some fell upon good ground; and brought forth fruit that grew up, and increased and yielded, one thirty, another sixty, and another a hundred. (Mark 4:8)
"And these are they who are sown upon the good ground, who hear the word, and receive it, and yield fruit, the one thirty, another sixty, and another a hundred. (Mark 4:20).
Exegetes speculate that one's celestial reward will be according to the fruit one brings forth – so in the Celestial City, some will live close to the centre, (the hundredfold), while those who were not so productive will be at some distance (sixtyfold) and those less so further off (thirtyfold) – but the scribe goes on to assert that each will gaze upon the 'Beatific Vision' accordingly, but none will see themselves as less or more, better or worse than their neighbour – so they who see a hundredfold experience a hundredfold according to their capacity, while they who see thirtyfold nevertheless experience a hundredfold according to their capacity ... and of course, no-one will think themselves better than their neighbour, because, again as the fathers said, "where you neighbour is, God is." Love will brook no politics.
I take comfort in that ...