Description:
(In a logical Russellian sense): A formula that corresponds to "there
is precisely one thing F that is also G". In logical formalism:
(Ex)(y)(F(x) & (y)(Fy > x=y) & Gx).
An example, also due to Bertrand Russell is: The present King of France is bald. Since France has no King, this is not true.
Note that there are two ways in which (Ex)(y)(F(x) & (y)(Fy > x=y) & Gx) is not true. The first simply denies the whole statement, thus: ~(Ex)(y)(F(x) & (y)(Fy > x=y) & Gx), and the second does not deny the whole statement, but only the part Gy. thus: (Ex)(y)(F(x) & (y)(Fy > x=y) & ~Gx).

See also:
Literature:
Russell & Whitehead, any decent introduction to mathematical logic.
