The Modal Ontological Argument for God's existence is logically valid

A famous "proof" that 1 equals 2 goes like this: Let a=b. Then a^2 = ab, a^2 + a^2 = a^2 + ab, 2 a^2 = a^2 + ab, 2 a^2 - 2 ab = a^2 + ab - 2 ab, and 2 a^2 - 2 ab = a^2 - ab. This can be written as 2 (a^2 - a b) = 1 (a^2 - a b), and cancelling the (a^2 - ab) from both sides gives 1=2. [1] Is this a valid proof? A valid proof is one in which the conclusion must be true if the premises are true. [2] Certainly nobody can challenge the truth of the premise: "Let a=b. " So, either this proof is valid, or one equals two. But one doesn't equal two. We know, therefore, that the argument isn't valid. We know this even if we can't identify the error. The error is in there somewhere. In the above "proof," it happens that we can identify the error, but we would know the proof was invalid even if we didn't find the error. We would know this because: A valid proof is one in which the conclusion must be true if the premises are true. Therefore: If an argument starts with true premises and reaches a false conclusion, the argument is not valid. As it happens, we can identify the invalidity in the above mathematical proof. In the last step, we cancel (a^2 - ab) from both sides. That is, we divide both sides by (a^2 - ab). But, since a=b, (a^2 - ab) equals zero. So the "proof" divides by zero, which is not a legitimate operation; division by zero is undefined. When you divide by zero, you get nonsense. Nonsense and contradiction are no part of a valid argument. This can be rephrased: If an argument contains nonsense or contradiction, it is not valid. - Pro's argument contains nonsense, so it is not valid. According to that argument, god exists in all possible worlds. But "all possible worlds" includes many godless worlds. He is saying that god exists even in worlds without gods. That's nonsense. It's contradiction. It is no part of a valid argument. Pro's argument is not valid. The resolution is refuted. - How do we know that the possible worlds include godless worlds? By the definition of "possible worlds. " A possible world is one without logical contradiction. Godless worlds have no inherent contradiction, so some godless worlds are in the set of possible worlds. Therefore, when Pro asserts that god exists in all possible worlds, he asserts that god exists even in godless worlds. That's nonsense. It's contradiction. It is no part of a valid argument. The modal ontological argument depends entirely on this sleight of hand. We aren't supposed to notice that there are godless worlds among the possible worlds. - Second Refutation: It is false that god exists in godless worlds. Thus, one of the (intermediate) conclusions of Pro's argument is false. Since we've stipulated the truth of P1, and since Pro insists that his other premises are true, that leaves us only one possibility: The argument is not valid. As I've pointed out, we know the argument isn't valid even without identifying the specific error. But I'll mention some anyway: - Pro claims that god (maximally great being) wouldn't be god if he didn't exist in all possible worlds. That's pretty silly. Imagine saying to Jehovah, "You're not so much. There are possible worlds in which you don't exist! " No, Pro's claim that a god of one world is somehow diminished by not existing in another world is arbitrary and unsupportable. He bases this claim on his arbitrary and unsupportable interpretation of the term "maximally great. " - God's "greatness" is undefined confusion. Pro defines "great" as, "Of an extent, amount, or intensity considerably above the normal or average. " Can god be great in both tallness or shortness? Can he be greatest in both justice and mercy? No, these are obvious contradictions. Arguments based on god's "greatness" are subjective and whimsical. - "Maximal" is a hedge word. It doesn't mean maximum. It means "tending toward maximum, or, "as close to maximum as you can get without causing a logical contradiction. " This is so Plantinga won't get hung up by the obvious contradiction between, for instance, justice and mercy. This may preserve the argument from one contradiction: If we stipulated that greatness involved existing in a great many possible worlds, we wouldn't be insisting that god existed in every possible world. He wouldn't have to exist in godless worlds. But where does that leave the argument? If god doesn't exist in godless worlds, then there's no proof that he exists in this one. If we don’t take god's maximal greatness to be perfect greatness, then there is no valid way to reach Pro's conclusion that god exists. And if we do take "maximal" to mean "maximum" then we have the contradiction of god existing in godless worlds. - Pro doesn't like my complaint about transworld identity. There are possible worlds containing nothing but one grain of sand. Is this bit of grit Jehovah? Only if transworld identity works. For obvious reasons, the Stanford Encyclopedia of Philosophy says, "The subject of transworld identity has been highly contentious, even among philosophers who accept the legitimacy of talk of possible worlds. " [3] Pro is reduced to this: Of worlds consisting of only one smidgeon of grit, he must say that the grit is a maximally great god. That's nonsense. And nonsense is no part of a valid argument. - Pro says my Xal-X parody fails because Xal-X must be maximally great to exist in every possible world. This is another arbitrary redefining of "maximal. " At some times it consists of every possible greatness. But when that becomes awkward, it suddenly means only and exactly, "existing in every possible world. " That's equivocation. That's a logical fallacy. Pro's argument relies on a fallacy that is no part of any valid argument. - Conclusion: Pro's argument fails because it relies on equivocation (emergency redefinition of maximal greatness). It fails because it involves nonsense and contradiction (god existing even in godless worlds). It fails because one of the conclusions is false. (It is obviously not true that god exists in every possible world. Since Pro insists that his premises are true, it follows that the error has to do with validity. ) It fails because "maximal" does not mean what Pro thinks it means. (If it meant maximum or perfect, that would involve Plantinga (and Pro) in contradictions. ) It fails because relies on a term, "maximally great," which is undefined, subjective, a matter of caprice. - Pro has the burden of proof, but his argument is shot thru with patent flaws.