forms, which men do not ordinarily
encounter except in the manipulation of syllogisms. Their
results might have been generalised as follows:--

(1) A "not" placed before the sign of Quantity contradicts
the whole proposition. Not "All S is P," not "No S is P,"
not "Some S is P," not "Some S is not P," are equivalent
respectively to contradictories of the propositions thus
negatived.

(2) A "not" placed after the sign of Quantity affects the
copula, and amounts to inverting its Quality, thus denying
the predicate term of the same quantity of the subject term of
which it was originally affirmed, and _vice versa_.

All S is "not" P = No S is P.
No S is "not" P = All S is P.
Some S is "not" P = Some S is not P.
Some S is "not" not P = Some S is P.

(3) If a "not" is placed before as well as after, the
resulting forms are obviously equivalent (under Rule 1) to the
assertion of the contradictories of the forms on the right (in
the illustration of Rule 2).

Not | All S is "not" P = No S is P | = Some S is P.
Not | No S is "not" P = All S is P | = Some S is not P.
Not | Some S is "not" P = Some S is not P | = All S is P.
Not | Some S is "not" not P = Some S is P | = No S is P.
]

[Footnote 4: _Formal_ to distinguish it from what he called
the _Material Obverse_, about which more presently.]

[Footnote 5: The mediaeval word for the opposite of a term, the
word Contradictory being confined to the propositional form.]

[Footnote 6: It is to be regretted that a practice has
recently crept in of calling this form, for shortness, the
Contrapositive simply. By long-established usage, dating from
Boethius, the word Contrapositive is a technical name for a
terminal form, not-A, and it is still wanted for this use.
There is no reason why the propositional form should not be
called the Converse by Contraposition, or the Contrapositive
Converse, in accordance with traditional usage.]

[Footnote 7: _Cf._ Stock, part iii. c. vii.; Bain,
_Deduction_, p. 109.]

CHAPTER IV.

THE COUNTER-IMPLICATION OF PROPOSITIONS.

In discussing the Axioms of Dialectic, I indicated that the
propositions of common speech have a certain negative implication,
though this does not depend upon any of the so-called Laws of Thought,
Ident