SeP = No S is P ;
SoP = Some S is not P.
These forms are useful when it is desired that the symbol which is used to denote the proposition as a whole should also indicate what symbols have been chosen for the subject and the predicate respectively. Thus,
MaP = All M is P ;
PoQ = Some P is not Q.
It will further be found convenient sometimes to denote not-S by Sʹ, not-P by Pʹ, and so on. Thus we shall have
SʹaPʹ = All not-S is not-P ;
PiQʹ = Some P is not-Q.
It is better not to write the universal negative in the form All S is not P ;[92] for this form is ambiguous and would usually be interpreted as being merely particular, the not being taken to qualify the all, so that we have All S is not P = Not-all S is P. Thus, “All that glitters is not gold” is intended for an O proposition, and is equivalent to “Some things that glitter are not gold.”
[92] Similar remarks apply to the form Every S is not P.