The position or proposition put by the OP, that the Holy Spirit is simply the divine influence or the "mind" of God and NOT a separate person is the principle contention of Arians. This does not make it wrong, just important; that is, I record this to make clear that it on this precise matter that Arians (with Binitarians) and Trinitarians part company.
Therefore we must clarify two matters:
1. The Greek word πνεῦμα (pneuma = wind breath spirit) is used in an almost bewildering array of meanings in the NT as BDAG's long list shows. ONE of those shades of meaning is:
- BDAG: "spiritual state of mind, disposition", eg, 1 Cor 4:21, Gal 6:1, Eph 4:23, 1 Peter 3:4, etc.
- Thayer: "the efficient source of any power, affection, emotion, desire,"
This real issue here is - Can such a meaning be extrapolated to all instances in both man and God? Arians say "yes" and Trinitarians say "no".
Another way to pose the same question is - What is the evidence of the personhood of the Holy Spirit?
2. Personhood of the Holy Spirit
The usual evidence for the independent personhood of the Holy Spirit consists of the following:
- The passages in John 15:26 – 16:14 repeatedly talk about the Holy Spirit as a separate person from either the Father or Jesus. Further, this same passage also repeated used the masculine first person demonstrative pronoun, ἐκεῖνος.
- 1 Cor 2:10, 11 (see also Isa 40:13, 14) also identifies the Holy Spirit as a separate person because of His teaching and instructing function. See also Rom 15:19 and Ps 104:30.
- In Matt 12:31, 32, Mark 3:28, 29, and Luke 12:8-10 the unforgivable sin is defined as blasphemy against the Holy Spirit. This is an expansion of Isa 63:10-14 where people grieved the Holy Spirit. Such a sin would not be even possible if the Holy Spirit were not both a person and divine. Note further, that these passages make a clear distinction between sinning against the Son or Father as opposed to the Holy Spirit, again, shown that the Holy Spirit is distinct.
- The Holy Spirit is called ἄλλον Παράκλητον, that is “another comforter” (or advocate or helper), John 14:16, 26, 15:26, 16:7 (compare 1 John 2:1). Note that Jesus uses the adjective ἄλλος (allos) meaning another one similar to Jesus; as distinct from ἕτερος (heteros) meaning another of a different kind. Thus, the Holy Spirit is called a “comforter” and was to be a divine being like Jesus (1 John 2:1).
- In 1 Cor 12:11 it is the Holy Spirit who decides about spiritual gifts and their distribution. This passage attributes volition and sentience to the person of the Holy Spirit.
- Possibly the best verses to demonstrate the individuality, personhood of the Holy Spirit is found in Rom 8:26, 27, which says –
In the same way, the Spirit helps us in our weakness. For we do not
know how we ought to pray, but the Spirit Himself intercedes for us
with groans too deep for words. And He who searches our hearts knows
the mind of the Spirit, because the Spirit intercedes for the saints
according to the will of God.
Now, there are two features about the important passage in 1 Cor 2 about the Holy Spirit:
- The Holy Spirit is called, "the Spirit of God" consistent with lots of other such passages, eg, Matt 3:16, 12:28, Rom 8:9, 14, 15:19, 1 Cor 3:16, 6:11, 7:40, 12:3, 2 Cor 3:3, Eph 4:30, Phil 3;3, 1 Peter 4:14, etc. The Holy Spirit is called the "the Spirit of Christ" in Rom 8:9, Phil 1:19, 1 Peter 1:11. This latter designation is consistent with the Holy Spirit's primary function to teach us about, and make us like Jesus Christ:
However, when the Spirit of truth comes, He will guide you into all
truth. For He will not speak on His own, but He will speak what He
hears, and He will declare to you what is to come. He will glorify Me
by taking from what is Mine and disclosing it to you.
- The passage in 1 Cor 2 is parallel to Rom 8:26, 27 (quoted above) about the independent work of the Holy Spirit in revealing the thoughts and intention of God to humans in the various ways that He does this such as:
- To produce the fruit of the Spirit (Gal 5:22 & 23, see especially v24-26) and so to sanctify (make distinct) the church members.
- The above changed life is to be a distinguishing sign or seal of God’s ownership of our lives and a guarantee of better things to come (Eph 1:13, 4:30).
- To provide specific guidance for the church (John 16:7-12, 14:17, 15:26 – see also Ecclesiology) namely (a) Convict of sin, (b) Instruct in Righteous (= right doing), (c) Convict of judgement to come
- To build up the church with spiritual (supernatural) gifts and abilities, 1 Cor 12:7, 14:12, and to influence/teach others John 7:37-39. See Rom 12:6-8, 1 Cor 12:8-10, 28-30, Eph 4:11, 1 Peter 4:10, 11, 1 Tim 4:14, Ex 35:30-33, etc.
- To strengthen the members in their daily walk to live the Christian ideals, Eph 3:16, 17, Heb 2:4, and maintain unity in the Christian community (Eph 4:3-6). The Christian must be born of the Spirit (John 3:5) by receiving the gift of the Spirit (Acts 2:38) and walk by the Spirit (Gal 5:25, John 6:63, Phil 3:3, John 4:24). In fact the whole life of Christian is to put aside the “psychical” mind and live by the Spirit (1 Cor 2:14, 1 Cor 15:44-46, Gal 5:17, Jude 19, John 6:63, 1 Peter 3:18). In short, the Holy Spirit is the only way we can know God, 1 Cor 2:10, 11, 14, John 16:13.
- To teach the church more of the character and work Jesus and thus, imitate Jesus, John 7:38, 39, 15:26, 16:12-15, Rom 8:4, 11, Eph 3:17, 18, 4:3-6, 1 Thess 1:6, 4:8, 1 Cor 2:14.
- The Holy Spirit inspired the prophets to write Scripture, and explains such spiritual truths to us. John 14:16, 17, 15:26, 1 Cor 2:6-16, Eph 1:17-19, 2 Peter 1:21, 2 Tim 3:15, 16, 1 Thess 1:5, Heb 9:8, 1 Peter 1:12, Ps 119:18.
In conclusion, all this shows the extremely close and mysterious relationship between the Holy Spirit, Jesus and the Father.