- Existence-tropes would be absurd (see below).
- 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.
- 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.
- 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:
- 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.
- Now X will itself either exist or not. To make things worse, suppose that there is another trope, X-minus = "G's nonexistence."∄
- 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.)
- Accordingly, suppose that when X exists, this is because there is some trope Y = "X's existence" that X occurrently has.
- 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).
- 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.
- 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 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 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?).