The Plantingan Modal Ontological Argument is sound

I thank Philocat for accepting my challenge. The common philosophical definition of a sound argument is an argument in which the argument is logically valid and the premises are true [1]. So Philocat must show that not only is the Modal Ontological Argument (MOA) deductively valid but that the premises are true. First, I would like to clarify the definitions of two modal operators that are very important in the MOA. “Possibility: A proposition is possible if and only if it is true in some possible world. A being is possible if and only if it exists in some possible world” [2]. “Necessity: A proposition is necessarily true if and only if it is true in every possible world” [2]. These definitions are expressed via possible world semantics [3]. Another way to express them is the following. A proposition is necessarily true if it was logically impossible for the proposition not to be true. In other words, a proposition is necessarily true if, if the proposition was false, a logical contradiction would result. In contrast, a proposition is possibly true if it is not logically impossible that the proposition is true. Given these definitions, I think my opponent can agree with me that “God necessarily exists” is equivalent to “It is necessarily true that God exists.” The latter is a preferable expression since the former gives the impression that necessity is a characteristic, when it is in fact a modal operator. Argument Against MOA The argument against MOA that I will present is not my own invention; I found it on a blog post made by a user named Rayndeon [4]. Many of the following ideas are his own, not mine, but I will present the argument in my own words. Consider the following argument (I pick up the numbering from where Philocat left off) (6) It is necessarily true that God exists. (7) If it is necessarily true that God exists, then God exists. (S5 axiom) (5) God exists This argument is unimpressive, since it commits the fallacy of begging the question [5]. No atheist would agree that it is necessarily true that God exists, since that would mean that it is logically impossible that God exists, and the atheist clearly thinks it is logically possible that God does not exist. It is unclear how the theist would be able to demonstrate premise 1 to be true. However, I contend that this argument is logically equivalent to the MOA, and hence the MOA is question-begging. Given proposition 1 and the S5 axiom, we have the following deduction. (6) It is necessarily true that God exists. (8) If it is necessarily true that God exists, then it is possible that it is necessary that God exists. (S5 axiom) (9) It is possible that it is necessary that God exists. So (6) and (9) are logically equivalent. So a modal argument starting with (9) would be, despite appearances, begging the question. But the truth of (9) is exactly what my opponent’s argument requires to be true. Look at my opponent’s formulation of the argument. Since this formulation is slightly sloppy, I will rephrase the premises. P3, that “if God exists in at least one possible world, He exists in all possible words” means (3) if it is possible that God exists, then it is necessary that God exists. How does my opponent justify (3)? In his argument for (3), he is using premise (9) as justification for (3), and (3) is in fact an application of the S5 axiom. But since (9) and (6) are logically equivalent, what he is really trying to do is argue that it is logically impossible for God not to exist, which is question-begging. So when my opponent says that necessary existence is “greater” than contingent existence, he is saying that it is possible that it is necessary that a maximally great being exists. We can thus more clearly formulate my opponent’s argument as follows. (9) It is possible that it is necessary that God exists. (3) If it is possible that it is necessary that God exists, then it is necessary that God exists (S5 axiom) (6) It is necessary that God exists. (7) If it is necessarily true that God exists, then God exists. (S5 axiom) (5) God exists. As I showed, (9) and (6) are logically equivalent, so the argument is question-begging. To accept the first premise is to accept that it is logically impossible for God not to exist. But we have not actually been given a real argument that it is logically impossible for God not to exist- that would refute atheism by itself! My opponent claims, “As if He only existed contingently then he wouldn't be maximally great, yet he is defined as being so. Reductio ad absurdum, the negation of an absurd conclusion must be true. Ergo, God must exist necessarily.” But this does not follow. At best, this shows that “If God exists, then it is necessary that God exists.” But the argument is supposed to prove that God exists! It also seems, by the way, silly to say that “necessary existence is 'greater' existence than contingent existence, insofar as necessary existence entails a greater 'amount' of existence than contingent existence.” There is no such thing as an amount of existence. The confusion comes from assuming that necessity and possibility are properties, rather than modal operators. Possibility and necessity refer to propositions, not beings. “God is a necessary being” might be a useful shorthand for “It is necessary that the proposition that God exists is true,” but it does not follow that necessity is a property- my opponent has to prove it. Now, suppose my opponent claims, “We should assume that ‘(9) It is possible that it is necessary that God exists’ is true unless we prove otherwise. A reasonable rule is to assume the possibility of a thing or a proposition unless we have evidence that such a thing is possible.” A rule like that might work in regards to epistemic possibility, but we are talking about modal possibility. Rayndeon has an answer to this sort of objection- “However, one honestly wonders how such an approach would consistently apply to necessity. Recall that a proposition is necessary if and only if its negation is impossible, that is, its negation entails a contradiction or some metaphysical absurdity. If one were indeed to consistently apply the maxim ‘modal propositions are innocent until proven guilty,’ one ought to inquire, with respect to a purportedly necessary proposition if the negation of a proposition is really impossible. It seems that one is ruling the negation as ‘guilty’ and as impossible” [4]. Rayndeon makes the point that if you apply an “innocent until proven guilty” rule to propositions of necessity, you are making a big claim which requires justification, namely that it is logically impossible for the proposition to be false. So in order to prove that his argument is sound, Philocat must prove that it is logically impossible for God not to exist. Besides, as Rayndeon points out, if we applied an “innocent until proven guilty” rule to propositions of necessity, we can make absurd arguments proving that, for example, unicorns exist [4]. Here is an example of one such argument. (10) It is possible that it is necessary that Superman exists (after all, it is logically possible that denying the existence of Superman is a logical contradiction, right?). (11) If it is possible that it is necessary that Superman exists, then it is necessary that Superman exists. (S5 axiom) (12) It is necessary that Superman exists. (13) If it is necessary that Superman exists, then Superman exists. (14) Superman exists. Clearly, something has gone wrong here, but what? The answer is that propositions 10 and 12 are logically equivalent, and the argument is question-begging in favor of Superman’s existence. But just as we have no reason to believe that it is necessarily true that Superman exists, so has my opponent failed to show that it is necessarily true that God exists. Conclusion The resolution is “The Plantingan Modal Ontological Argument is sound,” and the burden of proof is on Pro to affirm the resolution. I have shown that Pro has not given any reason for believing that the premise that it is possible that it is necessary that God exists is in fact true. In order for Pro to uphold his burden, he must show that denying God’s existence entails a logical contradiction. If he fails to do this, then he fails to meet his burden of proof, and the debate goes to Con. [1] http://philosophy.hku.hk... [2] http://plato.stanford.edu... [3] http://plato.stanford.edu... [4] http://analyticabstraction.blogspot.com... [5] http://www.nizkor.org...