Why does the Holy Spirit proceed from the Father only in Greek Patristic tradition, whereas the Spirit proceeds from both the Father and Son in our tradition? How does the Spirit proceed? What's the big deal, either way?
There's something of a can of worms contained inside that question, because arguments about single and double procession have sometimes been driven by something other than theological interests, and thus have not always been consistent. In other words, there's more than one way to argue for each one, and there are different implications tied up in the different approaches.
No one who takes the Bible seriously can deny that the Spirit proceeds from the Father, because Jesus said as much: John 15:26. If all that happened in the East were that they refused to go beyond this, that might be one thing, though I think anyone who doesn't joyfully confess that the Spirit proceeds from the Father and from the Son is missing out. But the denial of double procession and the arguments used to support that denial can be troubling. This is not to say that the West acted reasonably in adding a clause to a creed from an ecumenical council, that they always defended it well, or that double procession hasn't sometimes been argued in a way that contained its own troubling implications.
Double procession has several striking advantages:
1. It explains the relationship of the Son to the Spirit, while single procession does not.
2. It explains why the Spirit is not Son, which is another weakness of single procession. Or to put it another way:
3. It explains what is distinctive about the Son.
4. Properly explained, it maintains the point that the Father is the fons deitatis without reducing the Son to a second-order deity.
I particularly like the way this important doctrine comes to expression in Richard of St. Victor's work On the Trinity.
What first came to mind was our Lord's prayer in John 17:
“I do not ask on behalf of these alone, but for those also who believe in Me through their word; that they may all be one; even as You, Father, are in Me and I in You, that they also may be in Us, so that the world may believe that You sent Me.
The glory which You have given Me I have given to them, that they may be one, just as We are one; I in them and You in Me, that they may be perfected in unity, so that the world may know that You sent Me, and loved them, even as You have loved Me. Father, I desire that they also, whom You have given Me, be with Me where I am, so that they may see My glory which You have given Me, for You loved Me before the foundation of the world..."
Jesus' prayer is for the unified Kingdom, "an hour... when the true worshipers will worship the Father in spirit and truth; for such people the Father seeks to be His." Then, must not the Spirit proceed from both the Father and the Son, as the Father is in the Son? As the Church's divine likeness, doesn't the Spirit proceed from Christ, to the communion of believers?
I'm forming questions to ask an EO priest, for when I get the opportunity to ask him. There's an EO church near my parents' house. My conviction is with our tradition, however I genuinely want to learn both dimensions. I previously had a ministry to our county jail, before I ran from it like a coward. All sorts of questions come from all sorts of people in jails.
As Ruben has noted, the Western Church changed the Creed, a document that had the approval of an Oecumenical Synod without trying to reach consensus on the matter with the rest of the Church. This proud act was a cause of division in the Church Catholic.
Source: Wikipedia, Nicene Creed
The Vatican stated in 1995 that, while the words καὶ τοῦ Υἱοῦ ("and the Son") would indeed be heretical if used with the Greek verb ἐκπορεύομαι — which is one of the terms used by St. Gregory of Nazianzus and the one adopted by the Council of Constantinople — the word Filioque is not heretical when associated with the Latin verb procedo and the related word processio.
Whereas the verb ἐκπόρευομαι (from ἐκ, "out of" and πορεύομαι "to come or go") in Gregory and other Fathers necessarily means "to originate from a cause or principle," the Latin term procedo (from pro, "forward;" and cedo, "to go") has no such connotation and simply denotes the communication of the Divine Essence or Substance. In this sense, processio is similar in meaning to the Greek term προϊέναι, used by the Fathers from Alexandria (especially Cyril of Alexandria) as well as others.
Partly due to the influence of the Latin translations of the New Testament (especially of John 15:26), the term ἐκπορευόμενον (the present participle of ἐκπορεύομαι) in the creed was translated into Latin as procedentem. In time, the Latin version of the Creed came to be interpreted in the West in the light of the Western concept of processio, which required the affirmation of the Filioque to avoid the heresy of Arianism.
(Joh 14:26) But the Helper, the Holy Spirit, whom the Father will send G3992 πέμπω (pempō) in my name, he will teach you all things and bring to your remembrance all that I have said to you.
(Joh 15:26) But when the Helper comes, whom I will send G3992 πέμπω (pempō) to you from G3844 παρά (para) the Father, the Spirit of truth, who proceeds from the Father, G1607 ἐκπορεύομαι (ekporeuomai) Latin: procedit he will bear witness about me.
(Joh 16:7) Nevertheless, I tell you the truth: it is to your advantage that I go away, for if I do not go away, the Helper will not come to you. But if I go, I will send G3992 πέμπω (pempō) him to you.
It seems that the original context of the creed was the eternal relationships between the persons of the Trinity and the Greek word used implied origin so that "from the Father" was appropriate – the generation of the Son and the proceeding of the Spirit.
The words "and from the son" were added in light of a concern relating to the deity of the Son, thus, to show that as the Spirit proceeds in time and in relationship from the Father so too he proceeds from the Son – but the concept of deriving origin is not implied in the Latin word used.
The Reformers kept the Filioque on the basis of exegesis.