This is the third in a series. First installment, second, Philipse's review.
Herman Philipse's strongest argument against Barry Miller's claim that existence is a a first-level property, a property of individuals, is the absurdity objection.
According to this objection, if existence is an accidental real first-order property of individual entities, so must non-existence be, but this would imply an absurdity. For in order to attribute truly a real property to a specific individual, we must be able to refer successfully to that individual by using a proper name, a pronoun, or by pointing to it, etc. However, we can refer successfully to an individual only if that individual exists or at least has existed, so that non-existence cannot be a real property. Hence existence cannot be an accidental real first-level property of individuals either.
The absurdity objection can be put like this:
a) Existence is a (real, non-Cambridge) property of individuals if and only if nonexistence is also a (real, non-Cambridge) property of individuals.
b) Non-existence cannot be a property of individuals: if an individual exists, then it cannot have the property of nonexistence.
Therefore
c) Existence is not a property of individuals.
Miller must accept (b) since he does not countenance nonexistent items in the manner of Meinong. He agrees with Frege, Russell, and Quine that everything exists. If so, then non-existence cannot be a real property of individuals. Otherwise, there could be an individual x such that x both exists and does not exist. That would be absurd, i.e., logically contradictory.
Miller must therefore reject (a). Now let's hear what Philipse has to say.
Miller replies to this argument [the absurdity objection] by claiming that whereas existence is a real property of individuals, non-existence is merely a Cambridge property. He proposes the following criterion for deciding whether the lack of a real property implies the presence of a real complementary property: "Lack of a real property F would bespeak the presence of a correlative real property non-F only if F and non-F were determinates of . . . one determinable property" (p. 23, quote from Miller). Since there is no determinable of which both existence and non-existence are determinates (like red and not-red may both be determinates of the determinable colour), non-existence is not a real property, but rather a Cambridge property. Hence, Miller rejects the [major] premise of the absurdity objection.
I do not think that this refutation is convincing. Why endorse Miller's criterion? A person could just as well propose a similar criterion for deciding whether we are talking about real properties: all real properties are either determinates of determinables, or determinables of determinates. Since this is not the case for existence, existence cannot be a real property. Furthermore, non-existence cannot be a Cambridge property, contrary to what Miller claims. He defined a Cambridge property as a property the presence or absence of which does not make a real difference to the individual that has it. Is it true, or is it even meaningful to say, that it makes no real difference to the goddess Athena whether she has the property of non-existence or not? Moreover, whereas all Cambridge properties are relational (p. 29), non-existence is not relational.
Philipse makes three counter-arguments in the second of the quoted paragraphs.
The second is question-begging and is easily dismissed. Miller rejects such Meinongian objects as the goddess Athena. So no question can arise with respect to it as to whether or not it has the property of non-existence.
The third counter-argument is this: All Cambridge properties are relational; non-existence is not relational; ergo, non-existence is not a Cambridge property. This begs the question at the major premise. If Miller is right, not all Cambridge properties are relational: non-existence is a Cambridge property that is not relational.
The first-counter-argument is also question-begging. The argument is: "all real [non-Cambridge] properties are either determinates of determinables, or determinables of determinates"; existence is not a determinate of a determinable, etc; ergo, existence is not a real property. Miller will simply run this argument in reverse: because existence is a real property, the major premise is false.
What we have here is (at least) a standoff. Philipse has failed to refute Miller. Can Miller refute Philipse? Perhaps not. If so, then we have a standoff. Miller's view is a contender. It is at least as good as the Fregean and Meinongian views. But all three views are open to objections.
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