What influence did Greco-Roman philosophy have on the doctrine of "creatio ex nihilo"?

It appears that there are a great number of similarities between the teachings of the secular Hellenistic Jewish philosopher Philo Judaeus of Alexandrea, a follower of stoicism and the teachings outlined in John (particularly John 1).

Stoicism

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In response to Plato's explorations of whether abstract qualities (Such as justice and wisdom) have an independent existence (and his argument that these things do not truly "exist" by appealing to his Theory of Forms), Stoicism taught that these things did exist materially and in a corporeal form or "substance" (οὐσία).

According to the Stoics, the universe is a material, reasoning substance, known as God or Nature, which the Stoics divided into two classes, the active and the passive. The passive substance is matter, which "lies sluggish, a substance ready for any use, but sure to remain unemployed if no one sets it in motion." The active substance, which can be called Fate, or Universal Reason (Logos), is an intelligent aether or primordial fire, which acts on the passive matter:

The universe itself is God and the universal outpouring of its soul; it is this same world's guiding principle, operating in mind and reason, together with the common nature of things and the totality that embraces all existence; then the foreordained might and necessity of the future; then fire and the principle of aether; then those elements whose natural state is one of flux and transition, such as water, earth, and air; then the sun, the moon, the stars; and the universal existence in which all things are contained.

— Chrysippus, in Cicero, De Natura Deorum, i. 39

Stoicism also taught that

everything that exists depends on two first principles which can be neither created nor destroyed: matter, which is passive and inert, and the logos, or divine reason, which is active and organizing. The 3rd-century B.C. Stoic Chrysippus regarded pneuma as the vehicle of logos in structuring matter, both in animals and in the physical world. Pneuma in its purest form can thus be difficult to distinguish from logos or the "constructive fire" (pur technikon)

Philo's take

Perhaps by studying stoicism and noticing the Septuagint's use of pneuma (πνεῦμα),

ἡ δὲ γῆ ἦν ἀόρατος καὶ ἀκατασκεύαστος καὶ σκότος ἐπάνω τῆς ἀβύσσου καὶ πνεῦμα θεοῦ ἐπεφέρετο ἐπάνω τοῦ ὕδατος

this led Philo to conclude that the πνεῦμα θεοῦ (pneuma theou - Spirit of God) was the Logos (The Reason, thought or word for the formation of the universe.)

In his writings, Philo

...used the term Logos to mean an intermediary divine being, or demiurge. Philo followed the Platonic distinction between imperfect matter and perfect Form, and therefore intermediary beings were necessary to bridge the enormous gap between God and the material world. The Logos was the highest of these intermediary beings, and was called by Philo "the first-born of God". Philo also wrote that "the Logos of the living God is the bond of everything, holding all things together and binding all the parts, and prevents them from being dissolved and separated".

Plato's Theory of Forms was located within the Logos, but the Logos also acted on behalf of God in the physical world. In particular, the Angel of the Lord in the Hebrew Bible (Old Testament) was identified with the Logos by Philo, who also said that the Logos was God's instrument in the creation of the universe.

Relationship to Plato

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Obviously, Philo believed that the Logos created and was manifest vis-à-vis Plato's theory of forms, but the connections run much deeper. For example, Zeno, the founder of Stoicism studied under the platonists Xenocrates and Polemon at the Platonic Academy.

But most importantly, the genesis (pun intended) of the doctrine of Creato ex nihilo can be seen in how Philo interacts with Plato's work and the purpose and nature of Philo's works - two works in particluar - Philo's Quaestiones (or "Inquiries") and his Νόμων Ἱερῶν Ἀλληγορίαι - "Legum Allegoriæ," ( or "allegorical commentary") - both of which deal significantly or completely with interpretation of Genesis from Philo's Stoic perspective. In doing so, philo is attempting to sythesize Judaism and Stoicism

In another work, De Opificio Mundi (On Creation), Philo articulates the first known instance of creatio ex nihilo among the philosophers saying

Moses says also; "In the beginning God created the heaven and the earth:" taking the beginning to be, not as some men think, that which is according to time; for before the world time had no existence, but was created either simultaneously with it, or after it;

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In the first place therefore, from the model of the world, perceptible only by intellect, the Creator made an incorporeal heaven, and an invisible earth, and the form of air and of empty space: the former of which he called darkness, because the air is black by nature; and the other he called the abyss, for empty space is very deep and yawning with immense width. Then he created the incorporeal substance of water and of air, and above all he spread light, being the seventh thing made; and this again was incorporeal, and a model of the sun, perceptible only to intellect, and of all the lightgiving stars, which are destined to stand together in heaven.

And air and light he considered worthy of the pre-eminence. For the one he called the breath of God, because it is air, which is the most life-giving of things, and of life the causer is God

So in other word, God created the pneuma which was then used by the Logos to create.

Of these descriptions, Dr. Austryn Wolfson, the foremost scholar on Philo's works wrote that

all such expressions merely mean to convey the idea that God brought the world “out of non-existence into existence.”

Dr. David Runia, the penultimate authority on Philo agrees saying on pg 454 of "Philo of Alexandria and The 'Timaeus' of Plato"

this view is in the final analysis a metaphysicalaly refined variant of the creatio ex nihilo thesis. Although Matter would be only indirectly created by God, it is still the result of divine activity.

And the Internet Encyclopedia of Philosophy claims that

Before Philo there was no explicit theory of creation ex nihilo ever postulated in Jewish or Greek traditions.

Conclusion

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From the writings of Philo, we can see three things. First, From the statement that,

taking the beginning to be, not as some men think

Clearly, scholars believe "some men" is referring to Plato and to Jewish thought and Philo was responding to this and creating a different way to view Genesis.

Secondly, Philo is attempting to synthesize Jewish thought and Hellinistic Philosophy which indicates that Jewish Scholarship, like Plato, regarded matter as having always existed.

It seems then, that John 1, in claiming that

In the beginning was the Logos and the Logos was with God" John was affirming the teachings of Philo and attempting to Join the Stoics philosophical dialogue. John goes on to affirm this Cosmogony, saying

He was with God in the beginning. Through him all things were made; without him nothing was made that has been made. In him was life, and that life was the light of all mankind. The light shines in the darkness, and the darkness has not overcome it.

But then John takes it a step further and refines Philo's teachings saying not just that the Logos was with God at the beginning but that "The Logos WAS God" and that

He was in the world, and though the world was made through him, the world did not recognize him. He came to that which was his own, but his own did not receive him.

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The Logos became flesh and made his dwelling among us. We have seen his glory, the glory of the one and only Son, who came from the Father, full of grace and truth.

And of course, according to John that was Jesus and the embodiment of these abstract qualities did exist corporeally - in Jesus. So while it may seem that Jews did not understand Genesis 1 to speak of creatio ex nihilo, John did understand Genesis 1 this way. Ironically however, inasmuch as these doctrines echo the teachings of Philo's Legum Allegoriæ, this Makes John 1 the Allegorical reading of Genesis and the historic Jewish understanding (which differed according to Philo) and the associated cosmology the literal reading of Genesis.

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Authors note: In mousing over a few of the inline citations, you will find that several reference other stack exchange questions - for example a discussion about the firstborn of God or the Theory of Forms. These links provide good background and foundation for this question, and I think as you begin to explore these you will get a fuller picture of how Hellenistic Philosophy intersects with New Testament theology. It will be well worth your time.