'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_.
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.