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It seems as if debates about divine natures, among the "laity," are usually preoccupied with what have been called first-order properties of those natures. So we see the perennial quibbling over naive definitions of "omniscience" or "omnipotence." But philosophically sensitive (or informed) theologians often appeal to higher-order divine properties more essentially:

Upon the question, which attribute is to be considered primary, opinions differ. Many eminent theologians favour the conception of pure actuality (Actus Purus), from which simplicity and infinity are directly deduced. Most modern authors fix on aseity (Aseitas; a = "from" se = "himself"), or self-existence; for the reason that, while all other existences are derived from, and depend on, God, He possesses in Himself, absolutely and independently, the entire reason of His uncaused infinite Being. In this, the most profound and comprehensive distinction between the Divinity and everything else, all other distinctions are implicitly expressed. Whether, and in what way, the distinctions between the attributes and the metaphysical essence, and among the attributes themselves have an ontological basis in the Divine nature itself was subject which divided Nominalists and Realists, Thomists and Scotists, in the age of Scholasticism (cf. Vacant, Dict. de théol. cathol., I, 2230-34).

(C.f. talk of a "central divine-attribute generator" in Williams[19].) Or elsewhere it is said:

... God’s simplicity is a second-order property, that is, a property of God’s first-order properties such as wisdom, power, goodness, and the like. The doctrine of simplicity may entail that God’s (real) first-order properties are identical. But does it entail that all of God’s (real) second-order properties are identical with his (real) first order properties (and thus that God’s simplicity is identical with whatever first-order properties suffice for identity with God)? It isn’t clear that it does. Since simplicity and other divine second-order properties supervene on his first-order properties, the latter entail the former; nothing could instantiate each of God’s (real) first-order properties without instantiating such properties as simplicity. But the converse may not be true. For couldn’t a thing be simple in the defined sense (namely, having all its first-order real properties identical with each other and with its being) without having the divine properties? (Numbers might be an example.) If it could, then simplicity is not identical with the real first-order properties that suffice to make God God.

Gericke[09] observes:

Does the Old Testament assume a hierarchy of properties arranged according to order? First-order properties and relations would be those that can only be instantiated by YHWH qua individual. For example, being spiritual can be instantiated by YHWH and other spiritual entities and phenomena. But the Old Testament does not assume that the property of spirit is itself a spirit, it only exists as a trope (in the metaphysical sense as the-spiritual nature-of-something/somebody). It is natural to suppose, however, that at least many first-order properties and relations can themselves have properties and relations. Here again we might think of YHWH’s property of divinity (e.g. generic godhood). Thus the property of YHWH’s divinity was thought to exemplify the property of being a type of entity. And of course, once we think of second-order properties for YHWH, it is natural to wonder whether there are third-order properties (properties of second- or, perhaps in cumulative fashion, of second- and first-order properties), and so on up through ever-higher orders.

Question: suppose that a divine being had first-order properties like (presumably) maxipotence (not omnipotence, for which the prefix "omni-" causes so much trouble) and It had those as "generated" by logical deduction from a second-order basis like (presumably) simplicity. However, does this being then have the third-order property sustains the distinction between first- and second-order properties? And so on and on: but if It does, would this conflict with the point of attributing simplicity to the divine nature? Have we reintroduced unlimited plurality into the divine essence by differentiating Its properties in such a way as by appealing to distinctions in order? One might say, "Yes, we have pluralized the divine nature infinitely, but this is still not a plurality that is incompatible with the simplicitarianism intended beforehand," but is simplicitarianism a useful thesis if it is compatible with infinite, abstract multiplicity accruing to an "absolute" monad?

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    It is amusing how Old Testament is supposed to contemplate conceptions that only emerged in 20th century, and is called to answer questions about them. A quest of the same ahistorical nature as musing whether Elements consider first or second order arithmetic. As Kant spelled out, God's "intuitive" intellect does not function the way human "discursive" intellect does, and it is the nature of the latter that forces it into ever evolving dissections and hierarchies where God's timeless "single act of comprehension" (Boethius) suffices. What we introduce to capture simplicity is on us only.
    – Conifold
    Aug 20, 2023 at 0:30
  • @Conifold I often wonder where the really technical notion of simplicity is supposed to be found in the older texts. I think I've seen the Shema appealed to, but I don't get the abstract-simplicity "vibe" from the Shema (tawhid seems more abstract, though I don't know why it seems like that to me). Other older phrases like El Elyon or El Shaddai support "greatest-of-all" and "power-over-all" but even "I am that I am" doesn't clearly have anything to do with not-having-distinctive-properties/aspects, does it? Aug 20, 2023 at 2:10
  • Replace God with Fairy and this whole talk of trying to figure out whether His first or second order properties are simple or complex becomes a fool’s errand.
    – user62907
    Aug 20, 2023 at 3:47
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    @thinkingman perhaps I should've included the definition of divine simplicity in the OP; it is not a generic attribution of "simplicity" but the specific thesis that the divine nature doesn't have parts, not even in the sense of having multiple other attributes or real internal distinctions. I have almost never sympathized with the concept of divine simplicity, but I have tried to understand it on the terms of those who do reason from it in their analysis, here. That it would be a property-of-other-properties is a structural factoid regardless of its concrete meaning. Aug 20, 2023 at 4:34
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    Indeed divine simplicity if it exists ought to be viewed from a higher order perspective not unlike an infinity groupoid as some kind of univocity/univalence, if one starts from the usual first order. For example the idea of of the mind is united to the mind in the same way as the mind is united to the body, thus such equivalence is a kind of simplicity, and perhaps is simplicity itself... Aug 20, 2023 at 21:57

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Almost. In any attempt to determine whether a maxipotent entity is characterised by an unending descent of order sets, the issue of inflexive superpotency claims the primary denotation of convertive ablifumination. With due phenomenation to the au clair plformitesse of Derrida and Foucault, one might assert an oblique pertination of serriform phenomenologies, underpinning which, moreover, co-severated dualities of an inalienated tropus compound the intercorrelation of modalities of conception. Interpolating qualities of graduated divinity may, however, infrequently be encountered in philosophical contentions of the Prague school, although many commentators question the validity and significant of such claims, resting, as they do, upon insubstantiated conjectures open to the test of prudus produs when insufficiently counter-supported by derivative compound infersuations. To my simple mind it seems that there is an unresolved incompatibility, therefore, between the simultaneous possession of the attributes of maxipotence and simplicity, no amount of sophistry might unravel.

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  • I recognize the joking nature of the answer (c.f. the Sokal affair), though then it does evoke the question of what value is really to be had by complicated theological definitions: how are useful/nontrivial lines of reasoning to be distinguished from fruitless poetry? What justifies description-of-God X instead of some other description Y? If God can be a circle whose circumference is nowhere and whose center is everywhere, how are we not in the land of beyond-arbitrary vagueness? Aug 20, 2023 at 1:36
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    That's very sporting of you, Kristian. I have no excuse for my tomfoolery, apart, perhaps, from the fact that I spent the entire day yesterday cleaning out the old chicken shed for some new rescue chickens, so I needed to let off steam but lacked the brain power to write a proper answer! (Your questions are always out of my reach.) If you think my spoof detracts from your question, let me know and I will delete it at once. All the best. Aug 20, 2023 at 6:23
  • I shouldn't object to your answer: it raises an important subquestion about the intelligibility of theological language, especially when God becomes the minotaur in the labyrinth of abstractions. I also think it's often a sign of insight when philosophical commentary is humorous (have you ever heard Kant's quip about drinking Leibnizian monads with his coffee in the morning?) and was introduced to analytic philosophy very much through a semi-famous joke about runaway brain-controlled trolleys. Aug 20, 2023 at 6:59
  • Ha! I hadn't seen the trolley spoof before- very clever! Aug 20, 2023 at 7:11

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