I advert to the word "trope" as used in philosophy and not as used in narrative analysis (although I can see a reflection of either sense of the word, in the other use). The argument goes:

  1. Existence-tropes would be absurd (see below).
  2. Suppose that a theory of properties should be able to handle the epistemic possibility that there is an existence-property (an existence operation in predicate, not quantifier, position). Then the theory of tropes is not an adequate theory of properties.
  3. Suppose that a theory of existence-as-a-property should be able to handle the epistemic possibility that properties are tropes. Then existence-as-a-property is not an adequate theory of existence.
  4. So either trope theory or existence-as-a-property, or both, is/are misguided.

Reasoning: please bear with me; this came up as part of my most outlandish attempt yet at an ontological argument for God. Ignoring God in general, though, let us use G to generically refer to some-being-or-other:

  1. If, "G exists," is made true by G's having a property of existence X, and X is a trope, in particular the trope "G's existence," then G exists when it has its particular existence-trope adequately predicated of it.
  2. Now X will itself either exist or not. To make things worse, suppose that there is another trope, X-minus = "G's nonexistence."
  3. Suppose in general that whenever some A exists, it is by having its appropriate existence-trope at hand. Assume that necessary existence is when A's existence-trope exists but A's nonexistence trope doesn't exist. (This was (so to speak) where the Ouija board in my head started communications with the ghost of Anselm.)
  4. Accordingly, suppose that when X exists, this is because there is some trope Y = "X's existence" that X occurrently has.
  5. Then suppose that Y exists, and so because of another trope Z = "Y's existence," and so on and on, ad infinitum et absurdum (c.f. Bradley's regress).
  6. Now, in order for every X, Y, Z, ... to exist, those tropes will have to be detached from their counterparts X-minus, Y-minus, Z-minus, etc. Even more delicately, X-minus itself either exists or not, so there is some XX = "the existence-trope for X-minus" and XX-minus (the pertinent nonexistence-trope), etc.
  7. Although I can't tell, yet, if there's anything contradictory/radically unstable about (1) through (6), it just does seem infinitely absurd to me. So existence-tropes are absurd; so either trope theory is derivatively absurd or existence-as-a-property is. QED

Maurin[??] mentions the question of existence-tropes, but does not (at a glance, anyway) bring up such an objection from absurd infinity. de Ray[22] uses the phrase "existence-tropes" in an endnote, more or less in passing (though note the similarity between his self-existent Existence and my V-equals-V's-existence below). Costa[19] talks of "higher order existence tropes," seemingly indicating that any existence-tropes are also higher-order compared to others (not (just) that there are orders of existence tropes themselves), but so far I don't see any reference to a mirror-of-Bradley's-regress, there. But one might ask about a trope that was its own existence-trope, some V = V's existence. Would there have to be terminal (initial), self-looping existence-tropes to salvage trope theory or existence-as-a-property, here? But how would these uphold the existence of other things A unless they were something like V = V's-and-A's-existence? Seeming absurdity yet again, then.

To be sure, I jumped from "actuality is symmetrical with the diamond and box operations" to "actuality is symmetrical with the truth operation," wherefore I had thought at first that "does not exist" ≠ "does exist not" (since ¬◊ ≠ ◊¬), which I took to demonstrate the presence, in the rest of the toy system, of a substantive nonexistence property. But then I thought, "It is not actually..." does equal, "It is actually not..." so either there is no substantive nonexistence property, here, or somehow a local absence of an existence property is identical to the presence of a nonexistence property (how?).

  • 2
    From what I understand, on the most defensible versions of the theory, tropes are not properties, nor are they objects or mixtures of the two. They are sui generis and there are restrictions on predicating them that might block your regress. Also, even existence as a predicate does not have to be committed to a single item predicable of anything that (naively) 'exists'. Indeed, the verb is promiscuous and we have independent reasons to posit different kinds of 'existence' predicates (for concreta and abstracta, say).
    – Conifold
    Aug 23 at 10:08
  • @Conifold I'll be wanting to look into those options/qualifications, because despite my OP question, I also started thinking over an application to iterated modality that seems like it might allow for iterations that don't collapse (and which might mesh with the essentialism-based picture of modal language). It would be frustrating if I couldn't overcome my impression of "absurdity" when such an application is available (maybe I could convince myself that the counter-absurdity of the application outweighs the appearance of Bradley's mirror, though). Aug 23 at 15:13


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