On Feb 11, 2009, at 5:04 PM, Matthew West wrote:
I don't think so, mia culpa for trying to be too cute. I'll try again. Types are sets, OK. Why not just call them 'sets', then? I suspect the reason is that while all types are sets, not all sets are types. Some sets are, other sets are just damn silly sets. FOr example, the set of all triangular pieces of 3-space might be a type, but the set of all African lions over three years old, my aunt, the number 14 and the sodium atoms contained at this moment in my left pinkie's fingernail, might not be a type. The point being that a set really can be a set of anything, assembled for no rational reason at all; but (I suspect) you don't want to be this liberal with what counts as a type (?). If I'm right, what criterion distinguishes the sets which are types from the other, sillier, sets? If I'm wrong, why not just say "set" instead of "type" everywhere?
[MW] I’m pretty certain any set is allowed, otherwise the powertype stuff doesn’t make a lot of sense.
Then I REALLY don't understand why you don't just use the word "set", which is about as common and as thoroughly described as any concept has ever been in the history of mankind. Why deliberately multiply confusion by coining a new word (worse, re-using an old word) for such an incredibly standard notion?