KthulhuHimself's Argument is valid

I hope we have a spirited discussion about this critically important issue. I am also involved in the mathematics field. Essentially this debate is about whether my opponent’s argument proves what it sets out to prove. Hence the objections I will make are aimed toward the conclusion or the premises in question rather than about what one might conclude if this argument was convincing. I am not quite sure if the argument that my opponent presents is the full version of what he intends to present or not. Thus I will assume it is but reserve the right to edit my objections to fit his defenses(since I am not sure what he has in mind). I would also like to point out well-defined and well-ordered are not strictly speaking the same thing(one refers to a mathematical property, while the other is ambiguous and is not defined by the Affirmative). Hence the argument does not follow currently, this must be addressed otherwise my opponent loses this debate automatically. With those clarifications made, let us look at the argument itself. De Problemis Praeliminaribus: The most difficult problem for my opponent to overcome will be his lack of justification for the second premise. The principal problem is the distinction between defined at all, and well-defined. The proof is essentially made from the field of philosophy of language, however it requires some big assumptions that I will exploit now. I would ask my opponent why they need to be well-defined and not simply coherent definitions. That is, coherent definitions are necessarily non-paradoxical and non-contradictory hence we need a reason to suppose that well-defined definitions are necessary. In order to avoid premise 2, one can simply deny existence needs definitionary qualities whatsoever. If no humans existed to provide definitions for things, then no definitions would exist. This is the way if no humans were to exist, there would be no languages. The absolute point is my opponent has a huge burden to meet if he wants to justify this premise 2, because he must that existence is contingent upon definition. To quote a famous philosopher, existence is not a predicate. The epistemic question whether we can define something using our admittedly limited language that is beyond our sense experience has nothing to do with whether the thing has ontological status. This is fundamental to any type of ontology which takes reality seriously. In order to easily refute this premise, one can easily appeal to the fact that false definitions are possible. If we simply defined things into existence, then there ought to be unicorns somewhere objective. The concept of unicorns are not incoherent or paradoxical but yet they do not exist. Hence definitions are independent of existence. What that means is exists has nothing to do with what something is, but whether something is hence it is independent of any language used to describe it. De Proposito Tertio As of right now, my opponent has not provided the paradox to be evaluated by independent examination, hence this premise has not been justified even without the rest of my criticisms. “All the sciences have a relation, greater or less, to human nature; and. .. however wide any of them may seem to run from it, they still return back by one passage or another. Even Mathematics, Natural Philosophy, and Natural Religion, are in some measure dependent on the science of MAN; since they lie under the cognizance of men, and are judged of by their powers and faculties. ” -David Hume, A Treatise on Human Nature In order for my opponent to prove this must show mathematics are objective features of reality rather than constructs in our head for understanding the world. Otherwise, there is no reason to think mathematics ought to be the language one uses to express the definition in. One can simply express it any language which one sees fit. That is, my opponent must show that mathematical truths are a priori analytic judgments and not synthetic or else I see no reason why I ought to think mathematics is any better than any other language at defining concepts or entities. We may have pragmatic reasons for accepting this truth for certain phenomena but I needn’t accept it for all phenomena especially supposed non-physical phenomena. As Hume talks about in his Enquiry on Human Understanding, mathematics seem to be either relations of ideas(and therefore necessary but not substantive) or matters of fact(contingent but substantive). Either way mathematical truths are not the ultimate arbiter of existence. De Proposito Quarto There is a huge problem with this as well, and this is not arguing that God is not limitless so I would appreciate it not being construed as such. The fundamental problem is the distinction between properties and definition. That is, while God does have the properties of unlimited power, unlimited love, unlimited knowledge, etc. It does not follow that the definition of God ought to include this. God is by definition(if we are construing a monotheistic perspective), the creator of the universe. However, God has the properties of omniscience, omnipotence, and omnipresence. The problem is God would still be God if he lacked these properties, because all that is necessary for being God is the creation of the universe by said agent. Hence in order for opponent to prove this premise, he must prove the definition of God necessarily must include these properties rather than these being simply properties of God(hence not definitional). If he cannot prove this, then the conclusion does not follow. Conclusio There are many other problems I could rise with the argument but as I am not sure whether my opponent has provided his full defense and I do not want to build up strawmen, thus I have provided arguments strictly based on the argument itself. However, I think voters would agree that these are sufficient reasons to reject the argument anyway. There are plenty of ambiguities and inconsistencies and thus I urge a vote in the Negative.