ality or Inequality. But both lay
stress upon Coexistence and Succession, and we shall find that the
distinctions between Simple Sequence and Causal Sequence, and between
Repeated and Occasional Coexistence, are all-important in the Logic of
Investigation. But for syllogistic purposes the distinctions have no
relevance.

CHAPTER II.

THE "OPPOSITION" OF PROPOSITIONS.--THE INTERPRETATION OF "NO".

Propositions are technically said to be "opposed" when, having the
same terms in Subject and Predicate, they differ in Quantity, or in
Quality, or in both.[1]

The practical question from which the technical doctrine has been
developed was how to determine the significance of contradiction.
What is meant by giving the answer "No" to a proposition put
interrogatively? What is the interpretation of "No"? What is the
respondent committed to thereby?

"Have all ratepayers a vote?" If you answer "No," you are bound to
admit that some ratepayers have not. O is the CONTRADICTORY of A. If A
is false, O must be true. So if you deny O, you are bound to admit A:
one or other must be true: either Some ratepayers have not a vote or
All have.

Is it the case that no man can live without sleep? Deny this, and you
commit yourself to maintaining that Some man, one at least, can live
without sleep. I is the Contradictory of E; and _vice versa_.

Contradictory opposition is distinguished from CONTRARY, the
opposition of one Universal to another, of A to E and E to A. There is
a natural tendency to meet a strong assertion with the very reverse.
Let it be maintained that women are essentially faithless or that "the
poor in a lump is bad," and disputants are apt to meet this extreme
with another, that constancy is to be found only in women or true
virtue only among the poor. Both extremes, both A and E, may be false:
the truth may lie between: Some are, Some not.

Logically, the denial of A or E implies only the admission of O or I.
You are not committed to the full contrary. But the implication of the
Contradictory is absolute; there is no half-way house where the
truth may reside. Hence the name of EXCLUDED MIDDLE is applied to the
principle that "Of two Contradictories one or other must be true: they
cannot both be false".

While both CONTRARIES may be false, they cannot both be true.

It is sometimes said that in the case of Singular propositions, the
Contradictory and the Contrary coincide. A more correct doctrine is
that in