The ontological arguments justify a belief in God

This round I will be introducing the model ontological argument, a modified version of it, formal mathematical proof, and answers to two common objections.Modal Ontological argument [1] Our understanding of God is a being than which no greater can be conceived. The idea of God exists in the mind. A being which exists both in the mind and in reality is greater than a being that exists only in the mind. If God only exists in the mind, then we can conceive of a greater being—that which exists in reality. We cannot be imagining something that is greater than God. Therefore, God exists. At this point of time, I will offer no further elaboration on this argument, what I want to focus on is more complex ontological arguments, the next being a formal mathematical proof of God's existence using formal logic.Godels Ontological proof: Godel's ontological argument is a valid formal proof that concludes with God's existence. This ontological argument is quite different to most in the sense that it only uses mathematic functions to create the next premise. The principles that many of the Axioms pre-suppose to be true don't need to be debated, I assume that both parties agree on things like positiveness is relative to our moral asthetic sense. Other logical laws will also be supposed to be true throughout this debate to allow smooth arguments and rebuttal, like simple logical functions (negation as failure, bivalence etc) [2]A worded version of this argument is shown here as well:Definition 1: x is God-like if and only if x has as essential properties those and only those properties which are positiveDefinition 2: A is an essence of x if and only if for every property B, x has B necessarily if and only if A entails BDefinition 3: x necessarily exists if and only if every essence of x is necessarily exemplifiedAxiom 1: Any property entailed by—i.e., strictly implied by—a positive property is positiveAxiom 2: If a property is positive, then its negation is not positive.Axiom 3: The property of being God-like is positiveAxiom 4: If a property is positive, then it is necessarily positiveAxiom 5: Necessary existence is positiveAxiom 6: For any property P, if P is positive, then being necessarily P is positive.Theorem 1: If a property is positive, then it is consistent, i.e., possibly exemplified.Corollary 1: The property of being God-like is consistent.Theorem 2: If something is God-like, then the property of being God-like is an essence of that thing.Theorem 3: Necessarily, the property of being God-like is exemplified.Conclusion: Infering x as God is justified as God-like properties are exhibited.This formal proof is also a justification for premise 3 in the model ontological argument and a rebuttal to Kant's objection in his critique of pure reason, which I will attempt to investigate in more detail further on.Modified modal ontological argument: [3]1) God is that which nothing greater is possible, i.e. the greatest possible being.2) It is at least possible for God to exist in reality. That is, whether or not God actually exists in the real world, He at least exists in some possible set of circumstances. So, God might have existed in the real world.3) If something exists only in the mind but is possible, then that something might have been greater than it is. For example, a majestic mountain that exists only in the mind might have been greater: the mountain existing in reality.4) Suppose God exists only in the mind and not in reality.5) Then there is a possible being that is greater, namely God existing in reality.6) So it is possible for something to have been greater than God.7) Since God is that which nothing greater is possible, then it is possible for something to be greater than that which nothing greater is possible.C: Premise 7 is not possible and therefore its negation is true, God exists.This argument in logical symbolism: [4]And now, I have a rough idea of what my opponent is going to say in rebuttal, so lets dismantle it before hand all in the name of premptive headaches:Gaunillo's islandA monk called Gaunillo made a disagreement with Anselm's modal ontological argument not long after its formulation, he created the famous Gaunilo's island as a response to the argument. He claimed that the term God was interchangeable with any 'greatest possible thing,' and thus the argument couldn't possibly work. There are a few things wrong with his objection, the biggest being that it is wrong, but also that it doesn't actually invalidate the argument. Technically, the modal ontological argument is still sound, and thus the conclusion necessarily follows. So what is wrong with Gaunilo's island?It is Demonstratebly false and employs faulty logicGaunilo's island doesn't actually work, in fact, the modal ontological argument doesn't work on anything other than the greatest possible being. To refute the argument:P1) There exists an island greater than the perfect island.P2) Such an island has no physical boundaries or formsP3) Such an island is capable of thought and beingP4) Such a being is tri-omniP5) This tri-omni being is God.The island parody simple proves God. The reason why Gaunilo didn't see this is because he never imagined these premises could be added to his argument. In short, there is no such thing as the greatest possible island, there will always be something greater until the 'island' exhibits God-like qualities. It is similar to claiming there exists the greatest possible integer, no such thing.One popular objection: "A perfect island, presumably, is one with an abundance of lush palm trees and pristine beaches. The more of these an island has, the better it is. There is, however, no intrinsic maximum number of trees or beaches that an island could have; for any island that can be imagined, there is another, greater island, with one more palm tree and one more beach. There is, then, no island than which no greater island can be conceived. The concept of the perfect island is incoherent; there can be no such thing." [5] Kant's Objection:Immanuel Kant, in his book, Critique of pure reason, claims that existence is not a predicate, and thus the modal ontological argument fails. This objection is undermined by Godel's formal proof, however we will look a little further regardless.The first problem with Kant's objection is that it is self-defeating. In essence, it states that there exists a God which does not exist. This self-defeating claim is akin to saying that 'I know what God is like, and I know that he doesn't exist.' The second problem is that it is like gaunilo's criticism, false. A God that exists in every possible world has nessecary existence, one that doesn't merely has contingent or possible existence. We define the greatest possible being as having nessecary existence as opposed to contingent/possible existence and so a being with nessecary existence is greater than a being with possible existence.Kant's objection is demonstrably wrong since it can be shown that a being that exists in reality is greater than one that doesn't.Concluding, all the arguments I have presented are logically valid. Good luck to Con in his responding address.Sources:[1] http://www.iep.utm.edu...[2] http://www.debate.org...[3] http://www.angelfire.com...[4] http://www.debate.org...[5] http://www.existence-of-god.com...