Originally posted by Messiah
That is the difference between 'non-existence' - which is abstract and Ø - which is not.
If you look in ANY Webster's dictionary, both the abstract of 'non-existence' and the mathematical term 'Zero' are listed as definitions. There are two official connotations. If you wish to recognize only one, that is your privilege, but in communicating with other individuals, it is often necessary to recognize both.
I do, of course, recognize that people commonly wish to refer to 0 or empty sets...even empty space, as though it were nothing. However, in philosophy, it is always best to have your semantics completely clear from the start, and the semantics of "nothing" (the word) are rather clear: If there is anything there, anything at all, it isn't nothing (which seems so obvious to me, but I have done the extra research to make sure, and semantics and etymology seem to agree with me).
Thus, if there is something there (be it an empty set (which is something), the word "nothing" (which is also something), or the number 0 (which is clearly something)), it becomes both incorrect and misleading to use the word "nothing" to refer to it...of course, if I were to ask you what was inside the empty set or the empty space, then "nothing" would be the correct answer, but if I can refer to the set or word as something then it is incorrect to also refer to them as "nothing".