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 hypothesis.

Assuming that Universals do not, whilst Particulars do, imply the existence of their subjects, we cannot infer the subalternate (I. or O.) from the subalternans (A. or E.), for that is to ground the actual on the problematic; and for the same reason we cannot convert A. per accidens.