"At Florence in 1439 therefore, the earlier strictures on any theory of 'two principles' were repeated, but the decree went on to declare "what the holy doctors and fathers say, namely, that the Holy Spirit proceeds from the Father through the Son," led to the position that there was only one principle of origin, but that the Son as well as the Father was this one principle. This made the Son 'joint cause' and, as he was "God from God, light from light' in the creed, so also 'principle of origin from principle of origin.' Supporters of the West contended that if the Eastern tradition contained -and therefore authorized- the phrase, 'through the son,' it was obvious that "there is no difference between saying 'from the Son' and saying 'from the Father through the Son' "for the two phrases were 'identical in force'" That was the very objection that Eastern theologians voiced to the compromise, arguing that 'through the Son' was a Latin device for foisting the heretical Filioque on the Greeks. Like the reunion at Lyons this compromise at Florence proved too little too late politically; and even though 'the debate over the Filioque, an endless labyrinth of arguments and counterarguments, continued for more than eight fruitless months,' it also failed to solve the issue theologically, with both sides eventually returning to their historic positions on the doctrine of the Holy Spirit" (Jaraslov Pelikan, The Christian Tradition: A History of the Development of Doctrine, Vol. 2, The Spirit of Eastern Christendom (600-1700), p. 277).
Column notes from Pelikan op cit:
CFlor (1439) Def. (Mansi 31A:1029-30); Eug IV Ep. 176 (Hofmann I-II:71)
Joh.Argyr.Proc.8 (PG 158:1004)
Joh.Bek.Un.1.20 (PG 141:60-61)
Thdr.Agall.Argyr. (PG 158:1040)