Definition is the basis of language. Without a common understanding of terms, there can be no discussion. Anything that has not been falsified is theory unless it is proven to be true. Without a common understanding of terms, how can we know that a statement has been proven false? Mathematics is the most rigorous language in the sense that there is nearly universal understanding of terms among professional mathematicians, but it is still a language. The answer to your question is unambiguous; if a dog has a set of appendages that we will call "Legs" that consists of four of what we commonly call legs plus one tail, then the number of elements in the set of "Legs" is equal to 5. We could say that the set L = {a,a,a,a,b). Either way, it is simply a matter of definition - not really a 'goofy game'.