Peter van Inwagen and Anselm's Ontological Argument/Descartes (In Progress)

In the fourth edition of his highly acclaimed Metaphysics, Peter van Inwagen reviews the ontological argument set forth by Anselm of Canterbury: he explains that Anselm evidently thought atheism or the utterance of atheistic statements makes the atheologian produce formal contradictions. Now contradictions may be implicit or explicit: an explicit contradiction would be "It is snowing and it is not snowing," assuming the speaker had the same referent in mind for "snow" and other qualifications were met. Another example is "That object is a square and that object is a circle." Both utterances are blatant contradictions given the fundamental assumptions for traditional western logic, and for that reason, they're both necessarily false. Logicians also label contradictions as logically impossible statements--they are incoherent as well as Richard Swinburne notes. Should one view the profession of atheism in a similar light? Are statements about the nonexistence of God inherently contradictory? That is the way van Inwagen seems to interpret Anselm's ontological argument: atheism ostensibly entails an explicit contradiction. But the reader should not assume that van Inwagen necessarily agrees with this ostensible entailment.

Van Inwagen builds on the points outlined above; he contends that Anselm's ontological argument possibly addresses the question, why should there be anything at all? He then poses a conditional proposition, namely, if Anselm logically demonstrates that God necessarily exists, then he establishes that there must be something that exists (i.e., there cannot be nothing). While the ontological argument does not prove that this cosmos must exist, it indicates that something must obtain (pp. 129-130). However, two monks (Gaunilo and philosopher-theologian Thomas Aquinas) have resisted this argument. So has philosopher Arthur Schopenhauer and astrophysicist Paul Davies. Therefore, to simplify the discussion, van Inwagen leaves Anselm in order to discuss the ontological argument devised by Rene Descartes, the French philosopher and mathematician (1596-1650 CE). I must admit that the move is a curious one to me but I will not demur: van Inwagen reckons that the Cartesian version is easier to state and follow. Why not start with it at first?

Like its argumentational predecessors, some philosophers accuse the Cartesian ontological argument of being faulty, invalid, or possibly absurd. Immanuel Kant decided to challenge the argument by noting that it assumes existence is a real predicate which can be added to other properties that characterize a thing (i.e., it can be attributed to a subject). However, Kant maintains that existence is a conceptual predicate: by using the reckoning of Kant, van Inwagen demonstrates why opponents of the ontological argument might think the argument is incoherent, absurd or invalid. He wields the example of someone pitting existent Homer (the Ionian poet) against non-existent Homer (the non-existent version of the Ionian): another work sets forth the example of existent versus non-existent steak. Or what about imputing existence to things we know do not exist, like unicorns? Such arguments have ruled the day until now, but van Inwagen accuses such philosophical objections of concentrating on the periphery of the ontological argument instead of its center (p. 132).

To show the potential difficulty with Kantian thinking, Metaphysics introduces the concept of necessary existence. For the sake of parsimony, let's define a necessary being as an entity that obtains in all possible worlds; regardless of the possible world under consideration, a necessary being would exist in it. Another denotation of "necessary being" is that such an entity must exist or obtain (it cannot not exist). A necessary being is not contingent upon anything or anyone: it existence is a se, not ab alio. Furthermore, the non-existence of a necessary being is just as impossible as a round square, square circles, a four-sided Euclidean triangle or a married bachelor.

Armed with the concept of necessary existence which stands in opposition to contingent existence or even bare existence, van Inwagen then demonstrates that one problem with Kant's rejoinder to the ontological argument is that it can be shown that necessary existence is a property and it's possible to construct an argument that resembles the Cartesian argument, but yet does not treat "existence" as a real property. Nevertheless, it is important to make a distinction between existence and necessary existence.

Van Inwagen gives some examples of things that do not have necessary existence (they are not necessary beings) such as all human beings, the Taj Mahal, Mount Everest, the sun, and "for all we know," this universe is contingent (not necessary) because it's possible that although it exist, if the initial conditions were different, then this universe would likely not have existed. The point of these examples is that necessary existence is a property whereas mere existence is not: an object can exist without being a necessary object (p. 132-133).

While it's possible for someone to doubt that necessary existence could be an actual property of an object or thing, the point is that necessary existence is a possible property and it's a property (i.e., predicate) in the way that existence apparently is not. More importantly, necessary existence is not susceptible to the Kantian rejoinder since necessary existence, if it is a real property, could be added to a subject in a subject-predicate construction. So when van Inwagen establishes that necessary existence is a potential property, he then sallies forth this argument:

• A perfect being has all perfections.
• Necessary existence is a perfection.
Hence, A perfect being has necessary existence.
• Whatever has necessary existence exists.
Hence, A perfect being exists.

How should we evaluate the foregoing argument? To be sure, it's an improvement upon the Anselmian and Cartesian ontological arguments, but does this argument have its own flaws? While it is certainly better to posit necessary existence as a perfection instead of mere existence, van Inwagen points out why this version of the ontological argument is flawed. 

One problem is that the argument is invalid for the same reason the Cartesian version misses the mark: the premises of the retooled argument do not strictly entail its conclusion. To illustrate what's wrong with the "improved" version of Descartes' argument for the existence of God, van Inwagen introduces the notion of a negmount, which is a necessarily existent golden mountain. This object has three all negmontanic properties (i.e., necessary existence, being made of gold, and being a mountain). With this apparatus at hand, van Inwagen produces a counterexample to the improved Cartesian argument in order to test its validity. The argument goes this way (p. 134):

• A negmount has all negmontanic properties.
• Necessary existence is a negmontanic property.
Hence, A negmount has necessary existence.
• Whatever has necessary existence exists.
Hence, A negmount exists.

How does this argument fare. The answer to this question is fairly easy since negmounts do not exist; that tells us the conclusion is false and it's possible that the argument could never be true. A similar argument could be produced to show that round squares necessarily exist, but we've already established that such a conclusion would be false. But where does the argument for a necessarily existence negmount go wrong? Why is the conclusion not necessarily entailed by the premises?