Written 1 August 2012; edited and reviewed 19 March 2021.
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Consider a particular hole H in a piece of Swiss cheese. H is not nothing. It has properties. It has, for example, a shape: it is circular. The circular hole has a definite radius, diameter, and circumference. It has a definite area equal to pi times the radius squared: A=πr2 If the piece of cheese is 1/16th of an inch thick, then the hole is a disk having a definite volume. H has a definite location relative to the edges of the piece of cheese and relative to the other holes. H has causal properties: it affects the texture and flexibility of the cheese and its resistance to the tooth. H is perceivable by the senses: you can see it and touch it. You touch a hole by putting a finger or other appendage into it and experiencing no resistance.
Now if anything has properties, then it exists. H has properties; so H exists.
The foregoing was set-up for the question. H exists and the piece of cheese exists. Do they exist in the same way? Not by my lights. The hole depends for its existence on the piece of cheese; the latter does not depend for its existence on the former. H is a particular, well-defined, indeed wholly determinate absence of cheese. It is a particular, existing absence. As an absence of cheese it depends for its existence on the cheese in which it is one of the holes.
So I say the hole exists in a different way than the piece of cheese. It has a dependent mode of existence whereas the piece of cheese has a relatively independent mode of existence.
On the basis of this and other examples I maintain that there are modes of being or existence. (I am using 'being' and 'existence' interchangeably.) To be precise, I maintain that it is intelligible that there be modes of being. This puts me at odds with those, like Peter van Inwagen, who consider the idea unintelligible and rooted in an elementary mistake:
. . . the thick conception of being is founded on the mistake of transferring what properly belongs to the nature of a chair -- or of a human being or of a universal or of God -- to the being of the chair. (Ontology, Identity, and Modality, Cambridge 2001, p. 4)
Did I make a mistake above, the mistake van Inwagen imputes to thick theorists? Did I mistakenly transfer what properly belongs to the nature of the hole -- its dependence on the piece of cheese -- to the being (existence) of the hole?
I plead innocent. Perhaps it is true that it is the nature of holes in general that they depend for their existence on the things in which they are holes. But H is a particular, spatiotemporally localizable, hole in a particular piece of cheese. Since H is a particular existing hole, it cannot be part of H's multiply exemplifiable nature that it depend for its existence on the particular piece of cheese it is a hole in. The dependence of H on its host is due to H's mode of existence, not to its nature.
Suppose there are ten quidditatively indiscernible holes in the piece of cheese: H1, H2, . . . H10. Each exists. Each has its own existence. But each has the very same nature. How then can this common nature be the factor responsible for making H1 or H2 or H3, etc., dependent on the particular piece of cheese? The dependence of each hole on its host is assignable not to the nature common to all ten holes but to each hole's existence as a mode of its existence.
Now of course this will not convince any thin theorist. But then that is not my goal. My goal is to show that the thick theory is rationally defensible and not sired by any obvious 'mistake.' If any 'mistakes' are assignable then I 'd say they are assignable with greater justice to the partisans of the thin theory.
Metaphilosophical Coda
Talk of 'mistakes,' though, is out of place in serious philosophy. For apart from clear-cut logical blunders such as affirming the consequent, quantifier shift fallacies, etc. any alleged 'mistakes' will rest on debatable substantive commitments.