The whole purpose of Craig writing this book is that he believes that the existence of abstract objects poses a threat to the traditional understanding of the doctrine of Divine Aseity. So before he begins writing further on Platonism, he first unpacks and provides the biblical basis to this doctrine.
Craig draws primarily from two biblical sources in order develop this doctrine, the prologue of John’s gospel, and several passages from the epistles of Paul. With the biblical data established, Craig then moves onto the teaching of the early church fathers to see if the biblical data was interpreted differently than we might understand it today. This post will focus on the material on John’s gospel.
In the beginning was the Word,
and the Word was with God,
and the Word was God.
He was in the beginning with God.
All things came into being through him,
and without him not one thing came into being.
What has come into being in Him was life,
and the life was the light of all people.
The light shines in the darkness,
and the darkness did not overcome it. (1.1-5)
Craig draws attention to the fact that although God and His Word (logos in the Greek) already existed in the beginning, everything else is said to have come into being through him. With this, John draws a distinction between God and everything else that exists. And “John thus implies that there are no eternal entities apart from God, for everything other than God has come into being.” 
It would then seem that in order for the Platonism to be faithful to the biblical text, they would have to somehow construe the term “all things” in a manner that is not really referring to everything. Modern day examples of uses of language like this would be saying things like “everybody was at the party,” or “there is nothing in the fridge.” It is clear from these uses that they are not meant to be understood in a rigid literal fashion. Rather, the use of the terms “everybody” and “nothing” are speaking of a certain class of things.
According to Craig, statements which say something about all members of a class (not just some members) is what is referred to as a universally quantified statement. Universally quantified statements can be either affirmative, in which case terms like “all,” “every,” and so forth are used, or they can be negative, in which terms like “no,” “none,” or “nothing” are used with respect to them class of things being talked about. The relevant class of things is referred to as the domain of quantification.
With this discussion of quantification handled, Craig points out that verse three of John’s prologue is a universally quantified statement. “All things came into being through him, and without him not one thing came into being.” “The first part of v. 3 is an affirmative, universally quantified statement, while the second part of the verse is a negative, universally quantified statement. The question is: does John intend the class of things he is talking about to be unrestricted or is he talking merely about a restricted class of things?” 
In order to help answer this question, Craig points out that the reader can mistakenly ask the wrong question, namely “did John have abstract objects explicitly in mind when he said ‘all things came into being through him’?”  Craig points out that it may be entirely possible that John was not thinking of abstract objects (perhaps because he was not aware of such systems of thinking) when he wrote this passage. But in the same regard, John was also very likely not thinking of things like black holes, quarks, and other subatomic particles. But it seems almost certain that were someone to explain such entities to John, he would doubtlessly say that these too would fall within the domain of objects created by God. But for the heavy weight Platonist, abstract objects exist Just as equally as any other object we encounter in our perception of the world around us. “Abstract entities may be even more remote from direct sense perception than micro-entities, but they are, according to Platonism, just as real, so that if subatomic entities lie in the domain of John’s quantifiers, so do numbers. So if abstract objects exist, as the Platonist thinks, it would seem arbitrary to exempt them from the domain of John’s quantifiers.” 
Craig devotes more time to arguing that he believes John does not exclude anything from his domain of quantification (except of course, God Himself). But he finishes his treatment of John’s prologue by asking whether or not John really was ignorant of the idea of abstract objects.
Craig points out that historians have noted a remarkable similarity between the writings of John and Philo of Alexandria. Citing the German scholar Jutta Leonhardt-Balzer:
“Both use the Logos in a way similar to that of the Wisdom literature; both describe the logos as temporally prior to creation (Op. 17; 24; Jn. 1.1-2) Insofar as they go beyond the Wisdom tradition, they call him ‘God’ (Som. 1.228-230; Jn. 1.1). Both connect the operation of the Logos with the beginning of the world (Conf. 146; Jn. 1.1-2) and see the world as created ‘through’ (δια) the Logos (Cher. 127; Jn. 1.1-2). Both connect the Logos with light (Som. 1.75; Op. 33; Conf. 60-63; Jn. 1.4-5, 9) and see in the Logos the way for people to become God’s children (Cong. 145-146; Jn. 1.12) Both make a clear distinction between the Logos with God and the Logos in creation, whereby not only the prologue to John but both bring the statements of Genesis to bear on the Logos with God. 
Craig draws attention to one part of this quote, namely, the idea that “both Philo and John connect the Logos with the beginning of the cosmos.”  In his work On the Creation of the World, Philo argued that “the world of ideas [that is, the plans and blueprints by which God created the universe] cannot exist anywhere but in the divine Logos… In Philo’s view, then, there is no realm of independently existing abstract objects.”  Craig concludes his treatment of John’s prologue by stating that he finds it highly probable that John was at least somewhat aware of Platonistic ideas, and still held to the belief that there are no uncreated, independently existing objects apart from God Himself.
 Craig, William Lane, “God Over All: Divine Aseity and the Challenge of Platonism.” 14.
 ibid. 15.
 ibid. 16.
 Jutta Leonhardt-Balzer, qtd. in Craig, “God Over All,” 19.
 Craig. 19.
 Craig. 23.