in favour of the symbolic method.
But, as an introduction to philosophy, the common Logic must hold its
ground. (Venn: _Symbolic Logic_, c. 7.)

Sec. 4. Does Formal Logic involve any general assumption as to the real
existence of the terms of propositions?

In the first place, Logic treats primarily of the _relations_ implied in
propositions. This follows from its being the science of proof for all
sorts of (qualitative) propositions; since all sorts of propositions
have nothing in common except the relations they express.

But, secondly, relations without terms of some sort are not to be
thought of; and, hence, even the most formal illustrations of logical
doctrines comprise such terms as S and P, X and Y, or x and y, in a
symbolic or representative character. Terms, therefore, of some sort are
assumed to exist (together with their negatives or contradictories) _for
the purposes of logical manipulation_.

Thirdly, however, that Formal Logic cannot as such directly involve the
existence of any particular concrete terms, such as 'man' or 'mountain,'
used by way of illustration, is implied in the word 'formal,' that is,
'confined to what is common or abstract'; since the only thing common to
all terms is to be related in some way to other terms. The actual
existence of any concrete thing can only be known by experience, as with
'man' or 'mountain'; or by methodically justifiable inference from
experience, as with 'atom' or 'ether.' If 'man' or 'mountain,' or
'Cuzco' be used to illustrate logical forms, they bring with them an
existential import derived from experience; but this is the import of
language, not of the logical forms. 'Centaur' and 'El Dorado' signify to
us the non-existent; but they serve as well as 'man' and 'London' to
illustrate Formal Logic.

Nevertheless, fourthly, the existence or non-existence of particular
terms may come to be implied: namely, wherever the very fact of
existence, or of some condition of existence, is an hypothesis or datum.
Thus, given the proposition _All S is P_, to be P is made a condition of
the existence of S: whence it follows that an S that is not P does not
exist (_x[y]_ = 0). On the further hypothesis that S exists, it follows
that P exists. On the hypothesis that S does not exist, the existence of
P is problematic; but, then, if P does exist we cannot convert the
proposition; since _Some P is S_ (P existing) would involve the
existence of S; which is contrary to the hy