papers presented at the conference “Logica 2002″ (June 18-21, 2002, Castle Zahradky, Czech Republic) and published in: T. Childers and O. Majer (eds.), Logica’2002, Prague 2003
As Plato notices (Phaed. 96e-97b) there are two possible ways to get a pair. One (I shall call it pairing) is to bring two units together and the other (halving) is to cut a unit into two halves2. If the units are small objects like pebbles or coins then to use pairing is much easier, though. It would need a good deal of work to break a pebble or to cut a coin, while to bring such two things together you need nearly nothing: given two pebbles you get a pair of pebbles immediately.