This just over the transom from Samuli Isotalo:
I recently started reading your book A Paradigm Theory of Existence and the following kind of argument against the view that existence is a first-level property came to my mind. Probably you and many others have considered something like this, but I send it anyway.
Suppose existence is a first-level property and to exist is to instantiate this property. Now, given that some substance a instantiates some property P, we most likely want to say that this property P itself also exists. Thus, given that some substance exists, we want to say that the property, existence, it instantiates, also exists. But if to exist is to instantiate a property, existence, then it seems that in order for this property to exist, it needs to instantiate a further property, existence2. But then we also want to say that this property, existence2, exists, therefore it needs its own property, existence3, and so on ad infinitum.
You make three points.
The first is that, if existence is a first-level property, a property of concrete individuals or substances, and if the existing of substance a is its instantiating of this property, then the first-level property of existence must itself exist. I agree. For if existence did not itself exist, then neither a nor any concrete individual would exist. This holds no matter to which category we assign existence. No matter what existence itself is, were it not to exist, nothing would exist. But if you read me carefully, you will see that I resolutely deny that existence is a property (where properties are defined in terms of instantiation) of anything, whether individuals, properties, concepts, linguistic expressions, worlds, . . . whatever.
Your second point is that if existence is a property of individuals, and existence itself exists, then there has to be a second property, existence2, in virtue of whose instantiation existence1 exists. But this doesn't follow. For it may be that existence is a self-instantiating property, roughly in the way a Platonic Form is self-exemplifying. (But we needn't digress into a discussion of Plato, his Forms (eide), participation (methexis) in Forms, the Third Man Regress, etc.)
Consider the property of being concrete. Is it itself concrete? No, it is abstract. Now consider the property of being abstract. Is it itself abstract? Yes. Therefore, the property of being abstract is self-instantiating. (Notice: I did not say self-exemplifying. A property is not an exemplar.). The same holds for other putative properties: self-identity is self-identical, causal inertness is causally inert, omnitemporality is omnitemporal.
So why can't existence be self-instantiating? I am not saying that it is, but if it is, then, to your third point, the infinite regress cannot get started. Note also that if properties are necessary beings, as many philosophers maintain, and if existence is a property of individuals, then too the infinite regress could not arise.
Thus, treating existence as a first level property leads to an infinite regress. Existence seems to always pass on to some further property, like a slippery piece of soap that one cannot catch. What if we say that the property existence itself just exists, without it instantiating any further property? Then it seems that we have arrived at a picture very much like the one you are endorsing, namely, existence itself as Paradigm. For then we have this one property existence, which alone exists without it pointing to anything further, and every other thing exists in relation to it, by participating in it or instantiating it. But then it seems that to call such a thing ‘property’ is misleading, for properties are ontologically posterior to substances. Now, this reminds a lot of Aquinas, when he says, e.g. in De Ente et Essentia that existence itself is to be understood as something absolute and every other thing as participating in it.
What you are missing is that I deny that existence is a property. So your criticisms do not touch my view. What I conclude, after a complicated argument that I cannot here summarize, is that existence is more like a paradigmatic individual. It is not a predicable entity. It is more like the opposite of a predicable entity. It is not a property of individuals, properties, or anything else. As I said above, self-existent Existence, as that in virtue of which everything else exists, resembles a Platonic paradigm. You are right to catch the similarity to Aquinas, although my argumentation is wholly non-Thomistic. It is unlike any of his Five Ways. This because it it not based on an Aristotelian substance ontology, but on a fact ontology deriving from Gustav Bergmann and D. M. Armstrong.
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