Daniel Novotny writes,
I have discovered (something like) the circularity objection in Sousedik's translation of Frege's "Dialog with Punjer on Existence" into Czech. It's about two pages; here are some snippets (very rough translation):
First we might find difficulties with the assertion that existence is a property of the second order, i.e. the property of "falling under a concept". This is not incorrect but we need to take notice of something that -- as far as I know -- has gone unnoticed, namely that this "property" is under closer scrutiny a relation. "To fall under" is evidently a two-place predicate expressing not the relation of the concept to the thing (as it seems from Frege's exposition) but rather of the thing to the concept. ..."
. . . If we accept that "falling under" (or more precisely: "to have under") is a name of the relation, a sentence [e.g., "Men exist"] speaks not only of the concept of "men" but also of something that falls under this concept. . . . .
In order to say truthfully that the concept F has under itself the individual x, the condition of x's existence needs to be satisfied. This seems obvious but the question arises what does this word "exist" express in this case? ... it cannot be the second-order property, since it is, as we have seen a relation; we ask here about existence which is presupposed by this second-order relational propery as its necessary condition.
Now I have never read anything by Professor Sousedik, and I would be very surprised if he has ever read anything by me. So it is particularly gratifying to find that he is making points that are almost exactly the same as points I have made in published papers, my existence book, earlier posts and in a forthcoming manuscript, copies of which I sent to London Ed, Peter L., and a few others. I will couch the points in my own preferred jargon.
1. The second-level property of being instantiated is a relational property, one logically parasitic upon the two-place relation *___ instantiates ---* or *___ falls under ---*. Being instantiated is like being married. Necessarily, if a first-level concept is instantiated, then it is instantiated by an individual, just as, necessarily, if a person is married, then he is married to someone (distinct from himself), the Fargo, North Dakota woman who 'married' herself notwithstanding. (We won't speculate on the question how such a self-marriage is consummated.)
2. It follows from #1 that the grammatical form of a sentence like 'Men exist' is not the same as its logical form. Grammatically, it has a subject-predicate form. Logically, however, it is relational: the concept man is instantiated by one or more individuals. So not only is the sentence not about men, but about a concept; it is also refers -- with "studied ambiguity" to cop a phrase from Quine -- to one or more individuals.
3. Now if concept F is instantiated, then it is instantiated by an individual that exists. This is obvious, as Sousedik remarks. What is less obvious, but still quite clear, is that the instantiating individuals cannot exist in the sense of being instantiated. Obviously, no individual is instantiable; only concepts are instantiable. If you insist that existence is the second-level relational property of being instantiated, then you obviously cannot say that the existence of Socrates is the second-level relational property of being instantiated.
4. What this shows is that the 'Fressellian' attempt to reduce existence to instantiation fails miserably. It ends up presupposing as irreducible what it tries to reduce, namely, genuine (pound the lectern, stamp the foot!) existence. Another way of saying that the account presupposes what it tries to reduce is by saying that it is circular. We want to know what existence is. We are told that existence is a property of concepts, the property of being instantiated. Reflection on this property, however, reveals it to be relational and thus parasitic upon the dyadic relation of instantiation. For this relation to hold, however, its terms must exist, and not in the sense of being instantiated. So we are brought back to what we were trying to reduce to instantiation, namely, the existence that belongs to individuals.
Despite the clarity of the above, Peter L. balks, and London Ed baulks. It is high time for both of them to cry 'uncle' and admit that I am right about this. Or must I sic the Czech contingent on them? [grin]