Can one include existence in a definition? Yes! Consider: "Let x be the most famous of those characters in War and Peace who actually existed." (Presumably, x is Napoleon.)
According to the definition, God exists.
Compare: Unicorns have one horn. This does not entail that there are unicorns, all of whom have one horn each.
Descartes thinks that divine simplicity matters here. Does it?
Begging the question. Logical competence.
Conceptual arguments: Anselm
I can conceive of a greater than the maximal being--in the verbal sense of conceive. But I can't coherently. But can I coherently conceive of the maximal being?
The argument shows that atheists are in trouble. But it does not show that agnostics are.
Modal arguments: Plantinga
Opposed argument.
Does this show probability 1/2 at least?
Tooley: consistency of non-modal sentences is the root of modality. But what do we include in "consistency"? Can something be red and green all over?
Idea: We get to analyze concepts. But however much we analyze a concept C, "there is nothing falling under C" will not be inconsistent. (Why not? And what if we analyze "there is" further?)
Modal arguments: Explicability
Objection 1: Definitional. But why? Why not take it as substantive?