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The SEP article on tropes discusses this notion of "piles" of tropes. The PI stands for primitivist individuation of tropes, meaning their individuation admits of no informative analysis or explanation. On that view, nothing prevents one from assigning multiple exactly similar tropes to the same object, which is metaphysically redundant and makes no empirical difference:

In defense of PI, its proponents now point to a special case of piling, called ‘pyramiding’ (an example being a 5 kg object consisting of five 1 kg tropes). Pyramiding does seem genuinely possible. Yet, if piling is ruled out, so is pyramiding (Ehring 2011: 87ff.; cf. also Armstrong 1997: 64f.; Daly 1997: 155). According to Schaffer, this is fine. For, although admittedly not quite as objectionable as other types of piling (which he calls ‘stacking’), pyramiding faces a serious problem with predication: if admitted, it will be true of the 5 kg object that “[i]t has the property of weighing 1 kg” (Schaffer 2001: 254). Against this, Ehring has pointed out that to say of the 5 kg object that “[i]t has the property of weighing 1 kg” is at most pragmatically odd, and that, even if this oddness is regarded as unacceptable, to avoid it would not require the considerable complication of one’s theory of predication imagined by Schaffer (Ehring 2011: 88–91).

Suppose that A exists by having at least one existence-trope. However, if there are demioperations, then A has at least two demiexistence-tropes (two 1-demiexistence tropes, compared to one 0-demiexistence trope being a full existence-trope proper), then four 2-demiexistence tropes, and so on and on, until it would have uncountably many, one for every real-numbered subquantum of unity in the interval (0, 1].

The number of r-demiexistence tropes, then, would be at least 2 = ℝ, but then could we imagine objects having degrees of existence based on variations in either (A) the size of ℝ under various forcings or axioms or (B) the intended range of possible division for the general notion of demiexistence? So to say, imagine that one's personal copy of ℝ was set to ℵ24, whereas someone else's was set to ℵ1192. Would the one person have a larger amount of existence than the other? Or if someone's existence could be separated directly into X > ℝ parts, so that the number of demiexistence tropes they sustain (and are sustained by) is greater than ℝ: would that be equivalent to having a greater degree of existence?

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    You can do that, but the question is whether this is anything like what we intend by "degrees of existence". When people talk about "thin" and "thick" existence what they have in mind is that different types of entities (say, abstract vs concrete) exist to a different degree, more or less "fully". Not that the same type of enitity can be made "fuller" by piling it up numerically. In other words, the degrees attach to types of existents, not to tokens. What would be the pre-formal notion that your "cardinality of existence" is supposed to pick out?
    – Conifold
    Aug 29, 2023 at 7:15
  • @Conifold the only background I came into this with was a random article about the degrees-of-existence concept, how it had, according to the author, fallen out of favor, but could be rehabilitated by a helpful application to the question of presentism. Otherwise, my only reasoning is to suppose that iterated modality by chains of existence-tropes has an inverse structure in piled-up demiexistence tropes. Aug 29, 2023 at 7:30
  • Well, his examples are of the same thick/thin sort attaching to types. Plato's sensible shadows existing less "fully" than intelligible prototypes, Meinong's subsistent pseudo-objects less than real objects, etc. Passage of time "diminishing" existence seems like the most promising for a purely numerical conception, but that would work on the model of a linear continuum rather than cumulative hierarchy of cardinals.
    – Conifold
    Aug 29, 2023 at 7:50
  • @Conifold the target I have in mind is a reformulation/replacement of divine simplicity: assume that God's set of existence-tropes is infinite, then suspend the separation axiom at or before that set, so that God has so many such tropes that He has more than can be separated into proper subsets (in fact, just say that none of them can be separated at all). That this would be an image of divine simplicity would depend on something like Hamkins' exploration of set-theoretic mereology modulo Cantor's "God is the ens simplicissimum" remark. Aug 29, 2023 at 8:49
  • "It is the unique, completely individual unity, in which everything is, which comprises everything, the ‘Absolute’, for human intelligence unfathomable, also not subject to mathematics, unmeasurable, the “ens simplicissimum”, the “Actus purissimus”, which is by many called “God”." "The true infinite or Absolute, which is in God, permits no determination whatsoever... The absolute can only be acknowledged but never known — and not even approximately known." Emphasis mine. Absolute's tropes do not sound like a set. And how do the degrees of existence fit in?
    – Conifold
    Aug 29, 2023 at 11:04

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