Was the Trinity looked upon by John of Damascus and Gregory of Nyssa as a combination of Jewish monotheism and pagan polytheism?

TL;DR: When the 3 quotes are considered in proper genre and context they fail to support OP's argument.

First, it is helpful to distinguish the following 3 angles when reading the Church Fathers talking about the Christian dogma of Trinity. (The section references mentioned below are from the Catholic encyclopedia entry "The Blessed Trinity")

1. Revelation: The "raw data", solely from how God revealed himself in the OT, in Jesus and in manifestations of the Holy Spirit, as recorded in the New Testament by different authors such as St. John, St. Paul, etc.

   • Without this revelation there is nothing to go by.
   • That is why we often speak of Trinity as "The Mystery of the Trinity".
   • This is 100% God initiated action, which is why for Christianity any proper understanding of the Trinity should not say more than what NT says.
   • See "Dogma of the Trinity" and "The Trinity as a mystery" sections.

2. Usage in the church: How Trinity is implied in baptism, doxologies, theologies, catechism, apologetical writing, refuting heresies, etc.

   • Through the writings we see how the Church Fathers appeal only to the New Testament as the source of their teaching of the dogma.
   • Language precision is not necessary, but appeal to NT is a must.
   • Greek philosophical concepts are sometimes used to assist in describing but not as a source for the dogma.
   • See "Proof of the doctrine from Scripture" and "Proof of the doctrine from Tradition" sections.

3. Language refinement: Development of how Trinity is defined in various Greek and Latin theologies by the Church Fathers, development of the formulas in the creed, etc.

   • This is where Greek philosophical concepts and language became critical, to the point of some philosophically inclined Church Fathers having to stretch existing terminologies or even invent new ones.
   • Borrowing Greek terminologies & concepts is like a physicist (Church Father) needing to describe his/her experiment using mathematical language. A mathematician (Greek philosopher) has no expertise in conducting the experiment, so proper credit belongs to the physicist.
   • 100% for description, not for the source (which is only NT).
   • Underlying mystery is still maintained. That is why for practical purposes, inability to define Trinity completely (in philosophical language) is unnecessary for belief, because God cannot be reduced to a formula.
   • The goal for definitions (used in the creeds) is for easy refutation of heresies.
   • See "The doctrine as interpreted in Greek theology" and "The doctrine as interpreted in Latin theology" sections.

Now responding to your 3 quotations. All of them need to be interpreted in context according to the proper genre of the work.

1. St. Gregory of Nyssa's The Great Catechism (c. AD 385) Chapter III, pdf here

   • The genre is Angle #2 above (usage in the church), for apologetic/catechical (teaching) purpose to explain the faith to the educated Greek speaking intelligentsia.
   • Full text of Chapter III for context:

     AND so one who severely studies the depths of the mystery, receives secretly in his spirit, indeed, a moderate amount of apprehension of the doctrine of God’s nature, yet he is unable to explain clearly in words the ineffable depth of this mystery. As, for instance, how the same thing is capable of being numbered and yet rejects numeration, how it is observed with distinctions yet is apprehended as a monad, how it is separate as to personality yet is not divided as to subject matter. For, in personality, the Spirit is one thing and the Word another, and yet again that from which the Word and Spirit is, another. But when you have gained the conception of what the distinction is in these, the oneness, again, of the nature admits not division, so that the supremacy of the one First Cause is not split and cut up into differing Godships, neither does the statement harmonize with the Jewish dogma, but the truth passes in the mean between these two conceptions, destroying each heresy, and yet accepting what is useful to it from each. The Jewish dogma is destroyed by the acceptance of the Word, and by the belief in the Spirit; while the polytheistic error of the Greek school is made to vanish by the unity of the Nature abrogating this imagination of plurality. While yet again, of the Jewish conception, let the unity of the Nature stand; and of the Hellenistic, only the distinction as to persons; the remedy against a profane view being thus applied, as required, on either side. For it is as if the number of the triad were a remedy in the case of those who are in error as to the One, and the assertion of the unity for those whose beliefs are dispersed among a number of divinities.

   • Chapter III is showing how Trinity is the best way to understand the nature of the Christian God (who is still a mystery, by the way, indicated by the 1st sentence). So here's Gregory of Nyssa affirming the source is Angle #1 (revelation). The rest of the chapter beginning with "But when you have gained the conception of what the distinction is in these..." is an Angle #3 activity (speculative understanding of the mystery), and Gregory's advice is for the believer NOT to commit an error by straying to the Jewish heresy (not accepting Jesus as the Word), or to the Pagan heresy (by construing the Christian God polytheistically). There is NOTHING here indicating Gregory of Nyssa saying that the dogma of Trinity is derived from pagan sources.
   • The year was around 385 AD, after major debates on the formulation of the doctrine (an Angle #3 activity) had been done.

2. St. John of Damascus (675-749 AD)'s De Fide Orthodoxa (An Exact Exposition of the Orthodox Faith) Book I Chapter VII (Concerning the Holy Spirit, a reasoned proof) pdf here

   • The genre is traditional Christian theology (Angle #3) deriving mostly from theologians of the 4th and 5th centuries, providing a comprehensive overview of Christian dogma. Damascene supports his writing through logic and quoting Scripture. (summary taken from here)

   • Full Text of Chapter 7 for context:

     Moreover the Word must also possess Spirit. For in fact even our word is not destitute of spirit; but in our case the spirit is something different from our essence. For there is an attraction and movement of the air which is drawn in and poured forth that the body may be sustained. And it is this which in the moment of utterance becomes the articulate word, revealing in itself the force of the word. But in the case of the divine nature, which is simple and uncompound, we must confess in all piety that there exists a Spirit of God, for the Word is not more imperfect than our own word. Now we cannot, in piety, consider the Spirit to be something foreign that gains admission into God from without, as is the case with compound natures like us. Nay, just as, when we heard of the Word of God, we considered it to be not without subsistence, nor the product of learning, nor the mere utterance of voice, nor as passing into the air and perishing, but as being essentially subsisting, endowed with free volition, and energy, and omnipotence: so also, when we have learned about the Spirit of God, we contemplate it as the companion of the Word and the revealer of His energy, and not as mere breath without subsistence. For to conceive of the Spirit that dwells in God as after the likeness of our own spirit, would be to drag down the greatness of the divine nature to the lowest depths of degradation. But we must contemplate it as an essential power, existing in its own proper and peculiar subsistence, proceeding from the Father and resting in the Word , and showing forth the Word, neither capable of disjunction from God in Whom it exists, and the Word Whose companion it is, nor poured forth to vanish into nothingness , but being in subsistence in the likeness of the Word, endowed with life, free volition, independent movement, energy, ever willing that which is good, and having power to keep pace with the will in all its decrees , having no beginning and no end. For never was the Father at any time lacking in the Word, nor the Word in the Spirit.

     Thus because of the unity in nature, the error of the Greeks in holding that God is many, is utterly destroyed: and again by our acceptance of the Word and the Spirit, the dogma of the Jews is overthrown: and there remains of each party only what is profitable. On the one hand of the Jewish idea we have the unity of God's nature, and on the other, of the Greek, we have the distinction in subsistences and that only.

     But should the Jew refuse to accept the Word and the Spirit, let the divine Scripture confute him and curb his tongue. For concerning the Word, the divine David says, For ever, O Lord, Your Word is settled in heaven. And again, He sent His Word and healed them. But the word that is uttered is not sent, nor is it for ever settled. And concerning the Spirit, the same David says, You send forth Your Spirit, they are created. And again, By the word of the Lord were the heavens made: and all the host of them by the breath of His mouth. Job, too, says, The Spirit of God has made me, and the breath of the Almighty has given me life. Job 33:4 Now the Spirit which is sent and makes and establishes and conserves, is not mere breath that dissolves, any more than the mouth of God is a bodily member. For the conception of both must be such as harmonizes with the Divine nature.

   • In other words, John Damascus, writing long after the doctrine of Trinity was settled, said that the only element borrowed from paganism is the "distinction in subsistences", which to me is an Angle #3 activity (language refinement) to help describe the Trinitarian God. The language borrowing doesn't add/remove God's attribute or add/remove the 3 persons (to make it 4 or 2, for instance). Therefore, I don't think that counts as a pagan source of the dogma. If we look at Chapter 1 title of the book it is quite obvious that the source is only OT and NT:

     "That the Deity is incomprehensible, and that we ought not to pry into and meddle with the things which have not been delivered to us by the holy Prophets, and Apostles, and Evangelists."

More resources:

1. PDF of Wolfson's book. Your quote appears on page 362 (PDF page 401)
2. Reviews of Wolfson's book: here and here
3. Excellent Stanford Encyclopedia of Philosophy's History of Trinitarian Doctrines