Wolfgang Schwarz

Temporary Membership

OK, back. The bike trip was cool.

Meanwhile, in the comments, David Sanford raised the question whether sets gain and lose members. One might say yes, for arguably

*) If y is the set of all Fs, then x is a member of y iff x is F.

Since the wall in front of me is white and there is a set of white things, by (*), the wall is a member of that set. But last year, that wall was green, and surely it was never the case that something green was a member of the set of white things; so the wall was not a member of that set last year. It follows that the set of white things gained a member when I painted the wall.

Or so one might say. In fact, the set of white things is like the the set of bigger things: it is underspecified. Ordinary things have colours at times (and at worlds and at places). So we should speak of the set of things that are currently (and here and now) white. The wall is a member of that set, and it is so always (and everywhere and necessarily). If ordinary things have colours at times (worlds, places) by having simply white (counter)parts at these times (worlds, places), we can also say that there is a set of simply white things, and that the set of white things at a given time (place, world) is a set of things with a simply white (counter)part at that time (place, world).

More philosophy soon.