[FOM] Finite Set Theory

[Dean Buckner]

Friedman
>  What is a grammatical mirage? Can you explain this as well as I have
explained the emptyset and singletons?


Mirages are difficult to explain, especially to those convinced of the
reality of what they appear to represent.

I'll try.  Some words like 'shoe' apply to just one thing at a time.
But collective nouns like 'pair' apply to more than one thing at a time.
The word 'one' in 'one pair' tells you that 'pair' applies once, but to
two things.  Thus if there is just one pair of things, there are only
two things, no third thing.  

One who imagined that it applied in fact to one thing, a pair-thing, is
thus in the grip of the mirage, and a powerful one.  But 'pair', like
'set' is just a way of denoting many things at once.  There is not one
thing denoted, but many.

Thus: no singleton set, no empty set.  A single of shoes is one shoe.  A
nothing of shoes is nothing.