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It's occured to me that Kant's famous argument that "existence" is not a predicate whatsoever, which eventually became the prevailing position on the subject due to Frege and Russell, seems a bit strange when one grants the existence of abstract objects. Suppose, for example, that there is some shadowy world of Platonic Forms out there, and among such forms is "Existence." Obviously, it would seem that Existence, in that case, exists, which seems at odds with the notion that existence cannot be a property of objects at all (And I assume that abstract objects are no exception)

Is there any way to make sense of this?

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  • Kant's precise claim was that existence is not a "real" predicate, not that it cannot be used as a predicate. When it is so used, it is predicated not of an object but of a (typically implicit) description of a concept, and so it is a second-order property, as Frege-Russell suggest. "Existence exists", where "Existence" is the proper name of a Platonic individual, is analogous to "Socrates exists", and the names here stand for whatever descriptions we use to pick out those individuals. The predicate "exists" then attaches to those descriptions, it is not a property of individuals themselves.
    – Conifold
    Feb 6 at 4:22
  • I understand that much. My question, though, is if granting that properties have real existence at all (In this case, as abstracta in some platonic world) would require adopting the view that existence is a property of individuals (And thus a first-order property). It seems to me that this is indeed the case, since the Platonic Form "Existence" would obviously exist and thus be an individual whose property is existence, even if this "having-existence" occurs through self-exemplification. Feb 6 at 4:29
  • People usually distinguish universals ("properties") and abstract objects, see SEP, so Existence need not predicate of itself. But even if it does for some hardcore Platonist, I do not see why this exalted Exists should have much to do with the run of the mill "exists in reality" that Kant or Anselm, whom he criticizes, are talking about. Existence may well exist (on platonic postulation), but it does not make "exist" first order property. Making Exist = exist is just a circular reformulation of that very claim.
    – Conifold
    Feb 6 at 4:49
  • Well, a hardcore Platonist of that breed would essentially be positing that predicates/properties themselves are actually existing objects living in some other realm out there. Intuitively, at least, that would make it so "Exists" (The hypothetical Form) and "exists" (The run-of-the-mill notion of existing) are really just referring to the same thing. This just leads back to my question, in turn: If Universals are, in truth, objects, would that not make it so second-order properties do predicate of individuals after all? Thus collapsing the first-order/second-order distinction entirely. Feb 6 at 5:10
  • Kant is not an existentialist... Feb 6 at 5:59

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Insofar as we equate a specific set of quantifications-over with a given catalog of ontology, then in the Quine-Putnam indispensability argument, for example, we quantify over, and hence commit ourselves to the existence of, certain abstract objects. Now, can we go on to ask, "Do pure quantifiers exist?" or then whether we quantify over the quantifiers themselves? This would allow us to still have a self-participating existence Form, albeit not so clearly a Form-as-a-simple-property so much as a Form-as-a-supreme-exemplar (or as-second-order, at least?).

Some versions of Meinongianism might countenance the idea that the theory of existence-as-a-property has a truthmaker among nonexistent objects, more specifically nonexistent properties (which we might then be quantifying over while attributing a nonexistence property to at the same time!). In that sense, "there would be a nonexistent property of existence," or at least the nonexistence of the property is itself something that exists (since it is quantified over, after all).

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  • "albeit not so clearly a Form-as-a-simple-property so much as a Form-as-a-supreme-exemplar (or as-second-order, at least?)." Can you elaborate on this part? Feb 6 at 16:53
  • @JohnathanGreen if the Form of the Existential Quantifier existentially quantifies over itself, so to speak, the Form need not be conceived of as a monadic property so much as an abstract polyadic function, perhaps. A relation, then, one might say. This seems like second-order quantification to me, if not higher-order quantification as well (quantifying over quantifications over quantifiers, etc.). The true Form here would presumably be the maximum of this subsystem, one would suppose, some nth-order being say. Feb 6 at 17:50
  • Interesting. I didn't know you could have polyadic properties just by having an object relate to itself. In that sense, the Form of the Existential Quantifier would indeed seem to be a quantifier of "maximum order," so to speak. Perhaps such a thing is just what Plato conceived as the Form of the Good? Feb 6 at 18:10
  • @JohnathanGreen I think he says somewhere something about the Form of the Good surpassing the Forms of Being, Truth, and/or Knowledge, so a Form of a "component" of knowledge might not be great enough to be auto to agathon, here. Feb 6 at 20:13

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