Santa's singleton

Here's a question which I'm sure bugs all my logical readers. Modern mathematics standardly recognises partial functions which can take something as input but deliver nothing as output (like the reciprocal function which isn't defined for zero). Do we also need to allow for co-partial functions which can take nothing as input but deliver something as output? Exciting eh?

Well, perhaps not so very thrilling. But for what it is worth, here's a version of a paper in dialogue form given to the Serious Metaphysics Group here in Cambridge this evening. Not exactly the talk as delivered (with help from Rob Trueman!): the discussion has led me to cut out a long passage which was getting too involved by half and to tinker elsewhere a small amount.

One comment: if/when I get round to further rewriting this a bit, I'd drop the 'Santa' example, as I don't want any noise coming in from issues about fiction. It would be better to use e.g. 'Vulcan' instead.