The Catholic doctrine does not posit two independent sources of the Holy Spirit. The decree of Florence in 1439 speaks of the Father and the Son as one principle of the Spirit’s procession. The Father remains source without source; the Son receives all that he has from the Father except being Father. The formula must be read within that account of the divine relations rather than as a claim that the Spirit has two separate causes.
Greek and Latin terminology developed differently. This made the interpretation of patristic texts an essential part of the dispute. The expression “through the Son” required explanation, not automatic identification with either agreement or contradiction. Florence attempted to state how the relevant formulations could express a common doctrine.
The history of adding words to the conciliar Creed raises a further question about authority and liturgical reception. A defence of the theological proposition should address that question directly. It should not assume that every objection to the insertion is identical with rejection of the Son’s relation to the Spirit.
The unions of Lyons in 1274 and Florence in 1439 also demonstrate the difference between a conciliar agreement and its lasting reception within communities. Political necessity shaped the negotiations, but it cannot by itself determine whether the theological arguments were true. In Catholic interpretation Florence remains a doctrinal authority even though the union did not produce enduring general communion between Rome and the Byzantine churches.