Is the Holy Spirit, the Spirit of the Father? It's a pretty simple question, so I don't really know if there is much I can add to the body.
I will answer from the Trinitarian perspective.
The two terms are synonymous...
But when they hand you over, do not worry about how or what you are to say; for it will be given you in that hour what you are to say. For it is not you who speak, but it is the Spirit of your Father who speaks in you. -Matthew 10:19-20
When they arrest you and hand you over, do not worry beforehand about what you are to say, but say whatever is given you in that hour; for it is not you who speak, but it is the Holy Spirit. -Mark 13:11
...and yet, while the Father "is spirit"...
God is spirit, and those who worship Him must worship in spirit and truth. -John 4:24
...the Father is not "the Holy Spirit."
But when He, the Spirit of truth, comes, He will guide you into all the truth; for He will not speak on His own initiative, but whatever He hears, He will speak; and He will disclose to you what is to come. -John 16:13
If the Holy Spirit was just the Father in His spirit form, then He would in fact be speaking on His own initiative. Since Jesus makes it clear that the Spirit will not speak on His own initiative, but will do what He is told (basically), that indicates there is One with more authority who is "over" Him.
Conclusion: From these passages we can conclude that "the Holy Spirit" is not the Father (though the Father "is spirit") and yet, the "Spirit of your Father" is synonymous with "the Holy Spirit." Perhaps the best explanation is that the Spirit is "of" the Father in the sense that He comes forth from the Father, without confusing the two as if they were one Person.
(Although I'm willing to answer my own question, no one should let that deter them from also submitting an answer. Also, for the record, I'm a Trinitarian.)
Yes, the Holy Spirit is the Spirit of the Father. This is proven by many scriptures.
If we examine the following synoptic parallelism, Luke and Mark identify the one speaking in the apostles as the "Holy Spirit," but Matthew identifies it as "the Spirit of your Father" (i.e., "your Father's Spirit"). Therefore, the Holy Spirit is the Spirit of the Father.
But when they deliver you up, do not take thought hor or what you shall speak, for it shall be given to you in that same hour what you shall speak. For, it is not you who speak, but the Spirit of your Father who speaks in you.
But when they shall lead and deliver you up, do not take thought beforehand what you shall speak, nor premeditate. But, whatever shall be given you in that hour, speak that, for it is not you who speak, but the Holy Spirit.
And when they bring you to the synagogues, and magistrates, and powers, do not take thought how or what thing you shall answer, or what you shall say. For, the Holy Spirit shall teach you in the same hour what you should say.
In De Trinitate ("On the Trinity"), Book XV, Ch. XXVI, St. Augustine wrote,
Deinde in illa summa Trinitate quae Deus est, intervalla temporum nulla sunt, per quae possit ostendi aut saltem requiri, utrum prius de Patre natus sit Filius, et postea de ambobus processerit Spiritus Sanctus. Quoniam Scriptura sancta Spiritum eum dicit amborum.
Ipse est enim de quo dicit Apostolus: Quoniam autem estis filii, misit Deus Spiritum Filii sui in corda vestra: et ipse est de quo dicit idem Filius: Non enim vos estis qui loquimini; sed Spiritus Patris vestri, qui loquitur in vobis.
Et multis aliis divinorum eloquiorum testimoniis comprobatur Patris et Filii esse Spiritum, qui proprie dicitur in Trinitate Spiritus Sanctus
which is translated as,
Furthermore, in that highest Trinity which is God, there are no intervals of time, by which it could be shown, or at least inquired, whether the Son was born of the Father first and then afterwards the Holy Spirit proceeded from both, since holy scripture calls him (i.e., the Holy Spirit) the Spirit of both.
For, it is he (i.e.., the Holy Spirit) of whom the apostle says (Gal. 4:6), "But because you are sons, God has sent forth the Spirit of His Son into your hearts," and it is he (i.e., the Holy Spirit) of whom the same Son says (Matt. 10:20), "For it is not you who speak, but the Spirit of your Father who speaks in you."
And it is proved by many other testimonies of the divine word, that the Spirit, who is specially called in the Trinity, the Holy Spirit, is the Father's and the Son's.
As Augustine notes, the Holy Spirit is the Spirit of both the Son and the Father. Other scriptures in the New Testament also prove this.
The Holy Spirit is the Spirit of the Father:
But if the Spirit of Him who raised Jesus from the dead dwell in you, He who raised Christ from the dead shall also vivify your mortal bodies by His Spirit who dwells in you.
The phrase "of Him who raised Jesus from the dead" refers to the Father. "The Spirit of Him" dwells in the Christian. "He who raised Christ from the dead" is the Father. "His Spirit" is the Father's Spirit, the Holy Spirit, who dwells in the Christian.
The Holy Spirit is frequently referred to as "His Spirit," where the possessive pronoun "His" evidently refers to the antecedent "God the Father" (cp. Num. 11:29; Isa. 48:16; 1 Cor. 2:10; Eph. 3:16; 1 John 4:3). Therefore, the Holy Spirit is the Father's Spirit.
The Holy Spirit is the Spirit of the Son:
But you are not in the flesh, but in the Spirit, if so be that the Spirit of God dwell in you. Now if any man does not have the Spirit of Christ, he is none of his.
For I know that this shall turn to my salvation through your prayer, and the supply of the Spirit of Jesus Christ,
Searching what, or what manner of time the Spirit of Christ who was in them did signify, when it testified beforehand the sufferings of Christ, and the glory that should follow.
And because you are sons, God has sent forth the Spirit of His Son into your hearts, crying, "Abba!" "Father!"
I personally have always pictured the trinity in a particular way, that helps me understand it. I don't believe there's anything biblical to say 'this is how it is' but I don't think it contradicts anything that the Bible says either - if it does I'd appreciate someone pointint that out.
I generally see:
- God - he is outside our time and space, he is the God who knows all and we would generally deem call 'Father'.
- Jesus - obviously he's also God, but he was fully human. I don't believe he had the power of God the Father or was all knowing which is why he prayed. He was God in human form that lived within our world and was subject to all it's physical laws.
- Holy Spirit - Again, this is God. I tend to picture the spirit as being God the Father manifesting his power in our world. The spirit is how God is able to interact with this world and hence is what fills us with joy, heals us and gives us the gifts of the spirit. The Holy Spirit isn't constrained by our physical laws (hence we can all be filled with the spirit at once - omnipresent).
They are all God, like you consist of multiple parts (body, mind, soul), it is difficult to reconcile these things together but combined they all describe who you are. The same is true for God, all these combined represent who God is.
I'm going to go out on a limb and say "No", the Holy Spirit is not the Spirit of the Father. That would imply the Father is something comprised of Spirit and something(s) else, or that the Holy Spirit is lesser than the Father or the Son. The general idea is that all three persons of the trinity are co-equal and co-eternal. The Bible is pretty clear that God is Spirit. That means all the persons of God are Spirit.
It doesn't help that the basic creeds describe the Son as begotten by the Father, or the Holy Spirit as proceeding from the Father and from/through the Son, as those terms imply causation and temporal ordering.
The way I think about it currently is there is one uncreated nature which is God (I find using terms other than "being" or "person" is helpful to disambiguate what we're talking about). The Father personifies the Will or Way of God, the Son personifies the Reason or Truth of God, and the Holy Spirit personifies the Life of God.
Jesus said to him, “I am the way, and the truth, and the life"
If Adonay is referring to the Father, yes.
[Act 28:25-26 KJV] 25 And when they agreed not among themselves, they departed, after that Paul had spoken one word, Well spake the Holy Ghost by Esaias the prophet unto our fathers, 26 Saying, Go unto this people, and say, Hearing ye shall hear, and shall not understand; and seeing ye shall see, and not perceive:
[Isa 6:8-9 KJV] 8 Also I heard the voice of the Lord, saying, Whom shall I send, and who will go for us? Then said I, Here [am] I; send me. 9 And he said, Go, and tell this people, Hear ye indeed, but understand not; and see ye indeed, but perceive not.
Is the Holy Spirit, the Spirit of the Father?
Yes, That is the part of God that carries out the word of God, or the will of God. God speaks his word and the Holy Spirit makes sure it get don't according to God's will. Genesis 1;2 The Spirit of God was moving over the surface of the water, waiting for God to speak.
Even today the Holy Spirit is waiting for you to speak God's word, It is hard to be effective witness with out it, in you to carry out God's will. Acts 1; 4,5 this tells you that you need the baptism of the Holy Spirit or you witness will be weak. John baptized with water you will be baptized with the Holy Spirit and fire. The world is still happening and it still needs witness, to be a effective witness you need it. We didn't walk with Jesus we didn't see Jesus were not call to be apostle, No but you are called to be a witness. Not a run down and kick in the head witness, But one who has the power of God following out of them to destroy the works of the enemy on the Earth. Read Mark chapter 4 again Don't Kick people or hit them over the head with it either hit yourself over the head with it. Then learn to love people with it. It works.