The fire dispute
Purgatory was one of the subjects they argued about at length. Here the history gets interesting, because the Greeks didn't deny what the Latins taught about praying for the dead. They had always done it. What troubled them was how the Latins talked about it: the very word "Purgatory," the idea of a purifying fire in a particular place, and the legal language of satisfaction.
Some of the Greek theologians argued that the souls of the dead are purified by sorrow and by the prayers of the living, without any need to speak of a literal fire. The Latins held the older Western images dear, but they also saw that the substance was the same. Both sides agreed that souls who die in grace without having finished their repentance are helped by the prayers, Masses and alms of the living.
What the decree says
The decree of union, Laetentur Caeli, of July 1439, repeated and sharpened the teaching of the Second Council of Lyons from 1274. It says that souls who die truly penitent in the love of God, before making full satisfaction by the fruits of penance, are cleansed after death by "purgatorial punishments," and that the suffrages of the living faithful, meaning Masses, prayers, almsgiving and other works of piety, help them. The souls of those who have no sin to be cleansed, it says, are received at once into Heaven.
Look at what's not there. The decree doesn't say that the fire is literal, or that Purgatory is a place. It speaks of "purgatorial punishments" and leaves what they are to the mystery. The two sides found agreement on the essentials by refusing to force a single picture on the other.
Before and after
The council built on Lyons II, which had included the same teaching in the profession of faith the Byzantine Emperor sent in 1274. That union didn't last. Florence's didn't either: most of the Greek bishops signed, but Mark of Ephesus refused, and once the delegates returned home, the union was rejected by the people and clergy of Constantinople. The city fell to the Turks fourteen years later.
But the doctrinal formulation survived, and it became the basis for Trent a century later. A Catholic reading Florence today can take two things from it. The Church doesn't make a dogma of her images, and she is willing to say less in order to say what is true.
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