Previously noted sympathies notwithstanding, I have grave and seemingly intractable problems with Platonism. Perhaps the most severe of these follows from Christian Theism, which suggests that there is one necessary being, God, without whom nothing which exists would exist (in the sense that all other things which exist are ontologically dependent upon God). This is the confession of the central creeds of the faith, starting with the Nicene-Constantinopolitan creed (325-381 A.D.), referred to affectionately by Catholics simply as the symbol of faith. There are, of course, (in my view, quisling) children of the Church who argue that the “all” in “all things visible and invisible” does not quantify over universals, but I think that interpretation exceptionally dubious. However, this is inside baseball at its worst, and bound to leave those uninterested in theological minutia bored or irritated, if not entirely lost.
There is, however, one problem I have with Platonism which is at once subtler, less indirect and more accessible than my principal objection. I have not yet developed this line of thought, and I am unacquainted with any literature which successfully fledges this out into a respectable argument (on that note, if anyone is aware of sources which further develop the thought I am about to present, I would welcome their reading recommendations), but I mean, here, merely to register a suspicion; to gesture, in a vague and lackadaisical way, in the general direction of a possibly indissoluble difficulty. As such, I abandon any pretense to having found a proof (in the form of a compelling falsifier) of anything and submit the comparably modest suggestion that I think I have found a problem. With that caveat, let me invite the reader into the weeds.
There is, I suspect, an under-appreciated difficulty with the Platonist’s claim that universals ‘exist.’ This, as I interpret it, is the central claim of Platonism; Platonism, if it signifies anything, signifies that for any x, if x is a universal then x exists. Symbolically:
(Where Ux means “x is a universal” and Ex means “x exists.”) This helps to differentiate Platonism from other competing views, such as neo-Meinongianism. The definition of full-blooded Platonism goes further than this, perhaps, but it certainly signifies no less than this.
Let us bracket, for the moment, concerns about using ‘exists’ as though it were a (first-order) predicate. I note in passing, however, that if one insists on existence being a second-order predicate indicating that the thing to which it applies has at least one first-order property, then platonic forms will have properties, and there an interesting puzzle arises, for all (first-order non-vacuous standalone) properties are universals, thus implying that universals may be properties of universals. Indeed, there may be cases where two (or more) universals are symmetrically related to each other as each other’s properties (each one being a property of the other(s)). This is all both interesting and moot, for even if all properties are universals, not all universals are properties, and the argument is, as far as I can see, compatible with any (metaphysical or semantic) analysis of ‘existence.’
It should also be appreciated that some views on universals may carry the implication that existence is a first-order predicate after all. I am not an expert on neo-Meinongianism, but it seems, on its face, to entail that existence is a property (for it maintains that there are actual non-existent objects, as well as actual existent objects). The Stanford Encyclopedia of Philosophy entry under Alexius Meinong does, however, note the following:
“Meinong’s distinction between judgments of so-being and judgments of being, combined with the indifference principle that being does not belong to the object’s nature (so-being), reminds one of Kant’s dictum that being is not a real predicate. Meinong did not accept the ontological argument either, and argued that “being existing” is a determination of so-being and can in a certain sense be properly accepted even of the object “existing golden mountain,” and, say, even of the object “existing round square,” whereas “existence”, which is a determination of being, will no more belong to the one than it does to the other (1907, §3; 1910, §20, 141 ).”
So perhaps it is unclear whether Meinong’s view, properly interpreted, does imply that existence is a first-order predicate. In any case, it may have this implication, and that suffices for maintaining that, for all we now, Platonism may have this implication as well. For the purposes of this post, therefore, I ask that the reader give me some leeway in allowing me to speak as though existence is a property.
A Platonist, as here understood, is committed to the existence of universals, and universals are those things which can be said of many. Existence, however, can be said of many. Existence is, therefore, a universal, and the Platonist is committed to its existence. But now we draw nearer to the problem. How is it that one platonic form can be a constitutive property of itself? Can existence be a property of existence? If existence must be said to exist, either it will be said to exist in some non-univocal sense, or else the statement will become transparently bankrupt of propositional content. In the first case, something may be said to exist either equivocally or analogously (the only alternatives to univocity). If equivocally, I defy (with nearly hubristic confidence) anyone to make heads or tails of the statement. On the other hand, analogous predication, being already difficult to make good sense of, leaves me, here, feeling as nauseous as I imagine it must feel to be lost at sea. At least with Theism I can make some headway with this philosophically abstruse doctrine, since there is a paradigmatic exemplar to be intimated (along with some reasons for suspecting that the created order would intimate its creator, in much like the way structural realists in the philosophy of science believe scientific theories intimate reality). How, though, can we make sense of analogously predicating predicates of predicates, much less predicating predicates of themselves? How can first-order properties have first-order properties which, themselves, have their subjects as first-order properties? Analogy does nothing to lubricate the discussion at this point.
Am I too infected with Theism to see what sense this could make? Even if we turn to a close (and theistic) cousin of Platonism, namely ‘absolute creationism,’ (according to which platonic forms do exist, but (necessarily?!) proceed necessarily from God as creatures), we find nothing which alleviates the perplexity. In fact, it adds to the perplexity by introducing the so-called bootstrapping problem, for there are properties which, in order for God to create them, God would already have to possess (if existence is a property, then it serves as a fine example; another example is the property of powerfulness, which God would need in order to create the property of powerfulness).
So where does all this leave us? Here, I’m afraid, my thinking proceeds with less precision than I am comfortable with, and with embarrassing, though seemingly unavoidable, obviousness. This is precisely why I proceed with such caution, as though clumsily feeling my way through a thick fog. I avoid committing myself with any rigidity to this point. Nevertheless, if I am right then Platonism turns out to be highly sophisticated gobbledygook. At least this will be true of wholesale Platonism (as opposed to constrained or qualified forms of Platonism, such as those prefixed with terms like ‘mathematical,’ ‘prepositional,’ ‘evolutionary,’ et cetera).
 Maria Reicher, “Nonexistent Objects,” in The Stanford Encyclopedia of Philosophy, edited by Edward N. Zalta (2015), accessed November 26, 2016. http://plato.stanford.edu/archives/win2015/entries/nonexistent-objects/
 Johann Marek, “Alexius Meinong,” in The Stanford Encyclopedia of Philosophy, edited by Edward N. Zalta (2013): http://plato.stanford.edu/archives/fall2013/entries/meinong/ adds: “… in the appendix to his 1915 (p. 739–40) Meinong himself interprets such incomplete objects as platonic universals without being (see also 1978, 368), and he also states there: “what words mean [bedeuten] is the auxiliary object, and what they designate [nennen] is the target object” (1915, 741).”
 Existence is a property of Being, and Being is a property of Existence, no? This is unclear due to my total lack of clarification (through conceptual analysis) of these terms, but it seems intuitive enough for the moment. I cannot see why there couldn’t be some relatively clear-cut case of this pernicious symmetry.
 I believe Vallicella argues that it does somewhere in: William F. Vallicella, A Paradigm Theory of Existence: Onto-theology Vindicated. Vol. 89. Springer Science & Business Media, 2002.
 Johann Marek, “Alexius Meinong,” in The Stanford Encyclopedia of Philosophy, edited by Edward N. Zalta (2013): http://plato.stanford.edu/archives/fall2013/entries/meinong/
 Thomas V. Morris and Christopher Menzel. “Absolute creation.” In American Philosophical Quarterly 23, no. 4 (1986): 353-362.