What is odd about the filioque is the nature of the disute--that the holy spirit came from both the father and the son was traditional christian belief, a part of trinitaian orthodoxy upheld against every eastern variation of the monophysites. What made it controversial was its insertion by the Roman church into the nicene creed in order to make this point clear to the newly converted tribes of the west, some of whom who had been arians and did not understand the trinity.
But to Photius the insertion of the filioque as a stick with which to beat the Roman church, claiming it to be heretical. And as I stated in my other post eventually arranged a council to deny the addition of the filioque to the creed, and to approve expansion in constantinople's ecclesiatical power.
The final evidence against photius is that after he had been excommunicated for the second time he was also banished by the byzantine emperor on grounds of treason.
Regardless, I do not see any refutation of Soloviev in your posts. But I do appreciate you giving them some consideration and look forward to engaging you again.
The "second procession" confounds the temporal mission of the Spirit with the Eteranal Procession from the Father. It is an error analogous to confusing the Incarnation with the Eternal Begottenness of the Son. As such it is the root and ground of almost all Western errors most of which flow from a confusion between the Uncreated and the created (created grace being the one which is most obnoxious).
It is absurd to claim that denying the filioque supports Arianism, since the Holy Fathers of the First and Second Ecumenical Councils which opposed the Arians and their offshoot the pneumatomachians did not confess it, and found the Creed as originally written without the filioque sufficient statement of the Orthodox faith against them. To claim it is also to calumnate the Holy Fathers of the Council of Ephesus who forbade changes to the Creed of which the filioque is the only one attempted since. I realize that the Council of Toledo, which promulgated the error, thought it was a good way to deal with the persistence of Arianism in the West where it was very popular among the Vandals and Visgoths. However, the Popes of Rome did not concur until the time of the schism (which from the point of view of Constaninople dates to 1009 or 1014). St. Gregory the Dialogist (whom you call St. Gregory the Great) caused the Creed in its original wording without the heretical filoque to be carved in silver tablets in St. Peter's in Rome. I am told the tablets are still there for all to see.
It is likewise absurd to claim that the filioque is in any way important to opposition to monophysitism. The destruction of the monarchy of the Father--the traditional ground of the unity of the Godhead as opposed to the Western notion of God's unity being grounded in an abstractly conceived "common essence"--does nothing to oppose the error of confounding Christ's human and divine natures.
I often have the clear sense in discussing the classical heresies with Westerners that you by and large have forgotten what the issues were.
It was in fact the papal assent to the filioque (either in the no longer extant election encyclical of Pope Sergius VI or in the extant cornation rite for the German Emperor Henry II--hence the ambiguity of dates) which caused the Popes of Rome to be removed from the Diptychs of the Great Church of Constantinople. The unfortunate embassy of Cardinal Humbert in 1054 was an attempt to restore communion which had already been broken by Rome's acceptance of the modified Creed.
I would not dryly that when Emperors agree with you, their ecclesiatical acts are taken as "evidence" for your side, but when they are heretics in both our judgements, their acts are used polemically against the "Easterners".