use of them in the formal disputations of
graduands in the Universities. It was the custom for the Disputant to
expound his argument in this form:--

If so and so is the case, such and such follows.
So and so is the case.
[.'.] Such and such follows.

To which the Respondent would reply: _Accipio antecedentem, nego
consequentiam_, and argue accordingly. Petrus Hispanus does not give
the Hypothetical Syllogism as a Syllogism: he merely explains the
true law of Reason and Consequent in connexion with the Fallacia
Consequentis in the section on Fallacies. (_Summulae. Tractatus
Sextus._)

II.--DISJUNCTIVE SYLLOGISMS.

A Disjunctive Syllogism is a syllogism in which the Major Premiss is
a DISJUNCTIVE PROPOSITION, _i.e._, one in which two propositions are
declared to be mutually incompatible. It is of the form Either A is B,
or C is D.[3]

If the disjunction between the alternatives is really complete, the
form implies four hypothetical propositions:--

(1) If A is B, C is not D.
(2) If A is not B, C is D.
(3) If C is D, A is not B.
(4) If C is not D, A is B.

Suppose then that an antagonist has granted you a Disjunctive
Proposition, you can, using this as a Major Premiss, extract from
him four different Conclusions, if you can get him also to admit the
requisite Minors. The Mode of two of these is technically called MODUS
PONENDO TOLLENS, the mode that denies the one alternative by granting
the other--A is B, _therefore_ C is not D; C is D, _therefore_ A is
not B. The other Mode is also twice open, the MODUS TOLLENDO PONENS--A
is not B, _therefore_ C is D; C is not D, _therefore_ A is B.

Fallacy is sometimes committed through the Disjunctive form owing to
the fact that in common speech there is a tendency to use it in place
of a mere hypothetical, when there are not really two incompatible
alternatives. Thus it may be said "Either the witness is perjured,
or the prisoner is guilty," when the meaning merely is that if the
witness is not perjured the prisoner is guilty. But really there is
not a valid disjunction and a correct use of the disjunctive form,
unless four hypotheticals are implied, that is, unless the concession
of either involves the denial of the other, and the denial of either
the concession of the other. Now the prisoner may be guilty and
yet the witness be perjured; so that two of the four hypotheticals,
namely--

If the witness is perjured, the prisoner is not gui