  Sumterms are introduced as syntactic entities, and sumtuples are introduced
as semantic entities. Equipped with these concepts a new description is
obtained of the notion of a sum as (the name for) a role which can be played by
a number. Sumterm splitting operators are introduced and it is argued that
without further precautions the presence of these operators gives rise to
instance of the so-called sum splitting paradox. A survey of solutions to the
sum splitting paradox is given.
