Gödel’s proof of God’s existence  is based on Aquinas’s ontological argument, which, in turn, goes back all the way to Avicenna, both of whom were influenced by Aristotelian school. That proof needs to be studied in depth, before my subsequent arguments can be understood.
According to Anderson’s emendations  of Gödel’s proof of God’s existence, for modal collapse to not occur (i.e. in order to be able to say anything intelligible about what God is and isn’t), God only has to possess positive properties, and no other properties but good ones. This makes resolving the issue of existence of non-positive properties (e.g. evil) somewhat problematic, yet, as I shall show, not irresolvable.
I am here proposing to understand this issue from the point of view of God’s modalities (my own interpretation of Spinoza’s modes). In some sense, I am here going to end up becoming an apologetic for Chassidic version of panentheism, as the position is explained by Tzvi Freeman in his short essay .
But first thing first, let’s understand what “positive” qualities in Gödel’s proof (with or without aforementioned emendations) really mean. Let’s, for the moment, first imagine ourselves as devil’s advocates. It is quite possible to say that “positive” is actually “negative,” and to say, in effect, that God is a Grand Sadist.
This being stated, the above exercise was not to prove that nihilistic perspective is valid, but to illustrate that it is logically sound to invert the “positive” with “negative” and, thus, substitute any other emotionally appealing or repugnant quality into the syntax of the proof, while retaining the proof’s strength.
But if both “positive” and “negative” perspectives are valid, is there a perspective that is still intuitively plausible, while remaining maximally neutral emotionally? Yes, there is. I call upon rationalism and empiricism as my guiding light, and will rely upon scientifically and philosophically sound reasoning to state the following: “positive” should mean, at its most basic, “perpetuating.”
As Derek Parfit has argued in his “Why anything? Why this?” essay , the reason our Universe is the way it is is because it possesses certain qualities that make said existence physically most likely. Naturally, it is perfectly reasonable to imagine all kinds of universes and parallel many-world universes with all kinds of set ups. The very fact that this very Universe of ours exists, is a testament to the fact that certain physical laws and arrangements that are inherent parts of it are what made it possible and, not insignificantly, sustainable/perpetuating. Perhaps, non-symmetric/non-reversible “time” itself “began” as something “selected” out of yet another meta-Selector, as carrying some property that is beyond most people’s (including my own) comprehension.
I’d argue, maybe other universes physically exist also, even at this very moment, some of which are disconnected from ours yet still real. However, along Parfit’s thought, their number is likely finite, as it’s perfectly reasonable to imagine a process of evolutionary-like selection, where universes with “faulty” set-ups/”physical DNA” either collapse or are utterly stagnant dead-ends or are even actively “consumed” by other, more vigorous universes, if the latter are connected to them. This would certainly constrain the amount of universes that are possibly existent.
Further, even without invoking physics, we can see that, on one hand, our universe is “fine-tuned” for emergence of life and, on the other hand, there are objective mathematical properties that are independent of everything, such as properties of prime numbers, that make our Universe, respectively, special and ordinary — and simultaneously at that.
Thus, the notion of “perpetuating property” from Parfit’s and evolutionary perspective, is a sound one for any existing Universe, and hence God, to possess.
This notion of perpetuation gives us the ability to reconcile evolution with theology and Gödel’s proof. Unfortunately, it does not further postulate anything emotionally warm or teleological about either God or His Universe in which we find ourselves. Sure, this allows us to be consistent with Parfit, Spinoza  and others. But Parfit’s Selector is not anthropomorphic entity and is not necessarily teleological. Hence, this still leaves with question: is teleology nullified?
In fact, teleology is not nullified. To understand it, we have to go back to Parfit and his evolution-like theory of pro-perpetuation Selector. As has been mentioned, it is perfectly clear, from our vantage point, that our Universe makes life possible. This universe possesses certain qualities/properties that, so far at least, perpetuated the universes that possessed them. But not only that, due to those same properties, there came to exist islands of space that contained life, e.g. our very own planet Earth.
More tellingly, animated life is not some completely unlikely occurrence in our fine-tuned universe. Rather, according to a paper by Jeremy England, given certain localized conditions, animated life is inevitable , i.e. necessary.
The arrival of biological life as necessary outcome, entails that our Universe operates on properties that are not only perpetuating, but also life-sustaining.
While it is clear that not all that is physically perpetuating is life-sustaining, the fact that life-sustaining properties eventually emerge from certain perpetuating properties is an important, fascinating observation. Furthermore, we must notice that, while physical laws/properties are descriptive, biological laws are both fuzzy-descriptive and prescriptive. We can see that with emergence of animated life, teleology is necessarily emergent. This does not contradict Parfit, and it does not begin to go against Spinoza — quite yet, at least.
The next step in biological evolution of life on Earth was emergence of hominids and, eventually, humans. The emergence of humans, however, cannot be separated from emergence of human societies. And it is here that life-sustaining properties are leading to emergence of classically Gödelian/Aquinasian good/positive properties.
But goodness/positivity are no longer descriptive properties. Goodness, while it can be described, is rather a prescriptive property. Goodness are human-society maximizing properties, and it consists, essentially, of societal laws and the demands on humans imposed by their group’s customs, be they primitive or complex.
But if human laws are goodness, isn’t there an evolution (more precisely co-evolution) of these laws and societies that live under those laws, that lead to some societies being more vital than others, where vitality also includes both conquest and cultural transmission? Immense literature has been written on the subject, but Martin Nowak, Peter Turchin, Ara Norenzayan, Joseph Heinrich, and J.D. Unwin are definitely a few researchers who soundly resonate with my thoughts.
I will not burden you with exposition of their thoughts and impressive research, but will expedite my answer here: it is a resounding yes. Evolution operates not just at the level of individuals, but also at the level of groups and cultures.
Therefore, the next stage of human evolution has led to the emergence of properties that are not only perpetuating, life-sustaining, and good, but also of properties that are Godly. And it is now that teleology truly emerges and Spinoza’s anti-teleologic approach is subsumed.
The direction in which humans (or, to be more precise: Jews) are evolving (possibly, not quite there but ought to get to) is not as via being separate atomized individuals or even just members of a community: they are builders of, to use an anthropomorphic expression figuratively, “body of Ha-Shem.”
But an important issue is still unresolved: if physical Universe is part of God, and humans are “building” God, are those two different Gods? The answer is an unequivocal no. And the way to understand it is via modality and unfolding.
To extend Parfit, God begins by containing a non-teleologic Selector while also being the Selected(s), and Rejected(s) (due to that Being’s Infinitude). The universes being selected for contain perpetuating properties. The next steps are those properties that are life-giving. The next step are properties that are good. The next step are properties that are Godly.
God has different modalities, and they are enclosed within each other. The most primitive, most original modality, at least one that’s comprehensible to me, is one that operates non-teleologically: via physical and chemical laws, be they quantum-statistical or classical — one can look at it as blind “Will,” to use Schopenhauerian term, but it’s important to emphasize its blind, non-teleological character. The more evolved, much more rare modality, operates via life-sustaining laws of biology, where proto-teleology begins to emerge, but it’s all still a mostly-blind “Will.” The further upgrade in God’s modality is emergence of good/positive properties, which marks beginning of strongly prescriptive human laws and a considerable strengthening in teleology.
The beginning of true teleology might (symbolically) be linked with the act of Creation described in Genesis (kind of the “embryonic stage” of God’s teleological modality). After the Creation, the next fundamental event (again, symbolically) might be marked with the Covenant between the Jews and God, the first formalization of Halakhah. It can also be metaphorically equated with the emergence of Godly teleology from its “childhood “and constraining, soliciting the sons and daughters of Israel into their Godly Obligations. It was the very first bar/bat mitzvah, i.e. that fateful day in Sinai, when they became the very first “sons and daughters of mitzvot”. This important event marks the beginning of God’s modality that operates on properties that are not only perpetuating, life-sustaining, and good — but also Godly.
Modalities, thus, help solve the issue that only-the-positive properties are admissible in Gödel’s proof, after Anderson’s emendations are introduced into it. The issue of existence of evil is now explained by it being of a more primitive modality than the higher modality of goodness and, of course, Godliness. Evil has often happened via physically perpetuating properties exhibited by God’s more basic modality – a.k.a. “acts of God/nature”. However, sometimes “life-sustaining” modality can be a source of evil, via, say, an attack by another human/human group or an animal.
One can even try to argue about borderline cases, as certainly, evil can be expressed in different ways. For example, Aztecs were sacrificing humans. It is evil in our eyes, but their laws and customs considered it to be good, and they had an actual society. In this case, we are in position of being touched by Godliness, and our logic goes beyond goodness: it is about Godliness. Indeed, once God unfolds a new modality, the standards for evil become wider. They are, hopefully, not going to go down, but it’s not something that should be taken for granted: after all, Judaism is all about Halakhah and conforming human and societal action — it’s about doing (via following mitzvot), and not just believing. This explanation is in line with Maimonides’s  “The Guide for the Perplexed.” The difference is in emphasis: I emphasize culture (focusing on Torah-based cultures as blueprint for correctness/evolutionary success), aggregates (including of intellectual beings vis-a-vis their societies) and unfolding Godly modalities, while Maimonides emphasizes the individual, his life, and his intellect, together with his culturally (Torah) mediated virtues that assist in survival.
And as you can also see now, I’ve recreated something akin to Chassidic panentheism together with tzimtzum without resorting to Lurianic Kabbalah (which, by the way, some rational Rabbis of Medieval epoch counted as utter fabrication) — on rational-empirical basis, in tradition of Aristotle, Avicenna, Maimonides etc.