Thanks for the link. It would seem to me that it's all a matter of how you define the word property. Since words are part of a natural language, there is no one given true definition, so one has to be chosen before starting an argument, like an axiom if you are mathematically inclined. But still, it doesn't feel relevant for the question at hand, which is, how to prove an existing Santa exists? This clearly is an instance of assuming the thesis before proving it. The same can be done for any property, like proving that a blue santa is blue. I suppose that the premise of proving that an "existing santa exists" is not really a stronger statement after all than the original question of whether just "santa exists".