`  ::Thanks again for your patience. I'll continue to discuss this on user talk pages as you've both requested, and I apologise for taking up so much space here. I did, in fact, realise (but didn't mention) that membership in a set is also, as you put it, an ``undefined symbol``: this is what I meant by asking what it is that makes us consider things as members of sets or groups at all. ::I suppose that my questions about definability in general relate more to a discussion of first-order logic than to set theory. Again, sorry for the inconvenience and thanks very much for your time. I will look into ZF set theory and model theory more closely; I greatly appreciate these suggestions. -Tastyummy (forgot to log in)`