We exchanged looks. All started to get up from our seats at the same time.  Jerome wants to talk about Set Theory? It was another Friday afternoon on Mission Street. Jerome hadn’t been by in a while. We all went for beers and ‘catch up.’ You have read about this scene before. No, we all sat back down resigned (and we like Jerome). As usual we let him tell us himself what he is getting at.

He began ‘Word tricks. Guys I think a lot of these paradox sorts of things are word tricks. That one where you get halfway to somewhere and you have to go halfway again, and again, and so it is not possible to reach your destination because you always just get half way there.  A word trick. You only have one beginning and so only one half-way. You don’t get a new beginning every time you reach halfway. Why not a new beginning every step, or half-step?  That is just one of these word tricks. It does not use the idea of ‘beginning’ the way ordinary people do.’

‘You all know about sets, and set theory. The set of all literary magazines, the set of all beer bars in Kern County, you know. Everything can be in a set.  And so there can be a set of all sets. You guys know about this.’

We all took a sip of our beers, answering ‘oh yea, sure, vaguely, briefly’ and so on.

‘This brings me to a so-called paradox I heard about with sets.  The set of all sets cannot include itself.  So that means there can’t be a set of all sets? That is what I say is another word trick.’

‘OK… ‘ We order another round.

‘It is really the set of all other sets. Then no problem.’

Jerome continued,

‘The set of all other sets is a different entity than the sets it includes. It has no peer. Sets mostly have peers.  The set of roses and the set of cactus flowers are peers. Sets that include sets can have peers. A set that stands alone in kind usually has peers. But it doesn’t have to. No set has to have a peer. The set of all sets has no peer.

‘Maybe I am not the first to think of this Guys.’

People think about this stuff. That is good.

END