This is likely the most abstract feature of Gerson's list. I don't expect many people know what "nominalism" means, which would make "antinominalism" a bit obscure.
Simply stated, nominalism is the denial of universal properties or principles, the contention that only individual objects exist. For example, "redness" isn't a universal property or reality that exists independently from the collection of things that are red. "Redness" is just a name (hence the label "nominalism") for a shared feature (the color red) a collection of individual objects share.
Reading that description of nominalism you might be wondering what's at stake, philosophically and theologically, between nominalism and antinominalism. There are a few things.
First, a nominalist approach to reality would deny transcendentals such as the True, the Beautiful and the Good. This isn't to say that nominalists don't have a version of the true, the beautiful and the good. In the nominalist account of, say, the beautiful, the word/name "beautiful" is simply a word/name that describes a collection of objects we label "beautiful." More simply, in a nominalist account "beauty" is subjective, a word to describe our subjective judgements about what we consider beautiful. An antinominalist, Platonic account of Beauty, by contrast, argues that the Beautiful exists independently of objects and our subjective judgments. Beauty is not subjective. Beauty is real. The same goes for the True and the Good.
What's at stake, therefore, between nominalism and antinominalism is what theologians describe as a participatory metaphysics. The patristic imagination of the church fathers, which was heavily influenced by Greek philosophy, imagined salvation as participation, coming to share in the divine nature and life of God. Things become increasingly true, beautiful, and good the more they participate in the True, the Beautiful, and the Good, which is God's very own life. For human beings, this participation in the life of God is called theosis or divinization.
While we're here talking about nominalism and Christianity I should also mention the debates that swirl around the nominalism of Duns Scotus.
John Duns Scotus (1266-1308) was an influential medieval Scottish philosopher and theologian. According to thinkers associated with the movement called Radical Orthodoxy, theologians like John Milbank, Scotus represented a poisonous turn in Christian thought. According to Radical Orthodoxy Scotus turned away from the participatory metaphysics of the church fathers by introducing nominalism into Christian thought. This turn toward nominalism, as argued by Radical Orthodoxy, helped usher in the secular, modern age which has led to widespread skepticism, secularism, disenchantment, and religious disaffiliation.
The particularly toxic aspect of Scotus' nominalist thought, according to the Radical Orthodoxy crowd, concerned Scotus' assertion about the univocity of being. Recall, according to nominalism a word like "existence" is just a name for a class of individual objects. That is to say, we can gather a group of objects--a dog, a chair, an apple--and say that these things "exist." Just like my example of "red" above. Now, according to the church fathers up to the time of Thomas Aquinas adding God to this group of objects that "exist" was deemed illicit. God existed, true, but existed differently from physical objects. Being/existence is not "univocal," doesn't mean the same thing when applied to physical objects versus God. There only existed an "analogy of being" between God and physical objects. The existence of physical objects was analogous to God's existence, but fundamentally different.
According to Radical Orthodoxy, Scotus rejected the analogy of being and replaced it with the univocity of being when talking about God and physical objects. That is to say, God and physical objects existed "in the same way." The universal property of Being and Existence was rejected for a nominalist account of existence. Objects didn't exist because they participated in Being. "Existence" was, rather, just a name for a collection of objects, God among them.
Basically, nominalism flattens our imagination when it comes to existence. Our understanding of existence becomes literalistic. "Existence" comes to mean "physical object" rather than the mystical vision of God as the Being of being. And you can see how this turn would have ushered in the scientistic, materialistic vision of existence, the contention that only physical objects exist because existence is just a word we use to gather together a collection of physical objects. Existence isn't a property of the cosmos, existence is just a label, just a name, for a set of objects.
Turning back to our series.
We can see here how antinominalism is associated with an enchanted view of the world. Antinominalism claims that transcendentals such as the True, Beautiful and the Good are real. Because of this antinominalism sets before us a participatory metaphysics. We share God's life, become like God in the process of theosis. And finally, antinominalism preserves the ontological contrast between God's Being and the being of physical objects. God and physical objects don't exist "in the same way." The Mystery of Being persists.
