pothesis.

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_.

Assuming, again, a certain _suppositio_ or universe, to which in a given
discussion every argument shall refer, then, any propositions whose
terms lie outside that _suppositio_ are irrelevant, and for the purposes
of that discussion are sometimes called "false"; though it seems better
to call them irrelevant or meaningless, seeing that to call them false
implies that they might in the same case be true. Thus propositions
which, according to the doctrine of Opposition, appear to be
Contradictories, may then cease to be so; for of Contradictories one is
true and the other false; but, in the case supposed, both are
meaningless. If the subject of discussion be Zoology, all propositions
about centaurs or unicorns are absurd; and such specious
Contradictories as _No centaurs play the lyre--Some centaurs do play the
lyre_; or _All unicorns fight with lions--Some unicorns do not fight
with lions_, are both meaningless, because in Zoology there are no
centaurs nor unicorns; and, therefore, in this reference, the
propositions are not really contradictory. But if the subject of
discussion or _suppositio_ be Mythology or Heraldry, such propositions
as the above are to the purpose, and form legitimate pairs of
Contradictories.

In Formal Logic, in short, we may make at discretion any assumption
whatever as to the existence, or as to any condition of the existence of
any particular term or terms; and then certain implications and
conclusions follow in consistency with that hypothesis or datum. Still,
our conclusions will themselves be only hypothetical, depending on the
truth of the datum; and, of course, until this is empirically
ascertained, we are as far as ever from empirical reality. (Venn:
_Symbolic Logic_, c. 6; Keynes: _Formal Logic_, Part II. c. 7: _cf._
Wolf: _Studies in Logic_.)

CHAPTER IX

FORMAL CONDITIONS OF MEDIATE INFERENCE

Sec. 1. A Mediate Inference is a proposition that depends for proof upon
two or more other propositions, so connected together by one or more
terms (which the evidentiary propositions, or each pair of them, have in
common) as to justify a certain conclusion, namely, the proposition i