affairs are without logical criteria; that Logic must be confined to
symbols, and considered entirely as mental gymnastics. In this book
prominence will be given to the character of Logic as a formal science,
and it will also be shown that Induction itself may be treated formally;
but it will be assumed that logical forms are valuable as representing
the actual relations of natural and social phenomena.

§ 7. Symbols are often used in Logic instead of concrete terms, not only
in Symbolic Logic where the science is treated algebraically (as by Dr.
Venn in his _Symbolic Logic_), but in ordinary manuals; so that it may
be well to explain the use of them before going further.

It is a common and convenient practice to illustrate logical doctrines
by examples: to show what is meant by a Proposition we may give _salt is
soluble_, or _water rusts iron:_ the copulative exponible is exemplified
by _salt is savoury and wholesome_; and so on. But this procedure has
some disadvantages: it is often cumbrous; and it may distract the
reader's attention from the point to be explained by exciting his
interest in the special fact of the illustration. Clearly, too, so far
as Logic is formal, no particular matter of fact can adequately
illustrate any of its doctrines. Accordingly, writers on Logic employ
letters of the alphabet instead of concrete terms, (say) _X_ instead of
_salt_ or instead of _iron_, and (say) _Y_ instead of _soluble_ or
instead of _rusted by water_; and then a proposition may be represented
by _X is Y_. It is still more usual to represent a proposition by _S is
(or is not) P, S_ being the initial of Subject and _P_ of Predicate;
though this has the drawback that if we argue--_S is P_, therefore _P is
S_, the symbols in the latter proposition no longer have the same
significance, since the former subject is now the predicate.