ism, probably because they have no connexion
with the mode of reasoning together to which he appropriated the
title. The fallacies connected with them are of such a simple kind
that to discuss as a question of method the precise place they should
occupy in a logical treatise is a waste of ingenuity.[1]

I.--HYPOTHETICAL SYLLOGISMS.

If A is B, C is D |
A is B } MODUS
[.'.]C is D | PONENS.

If A is B, C is D |
C is not D } MODUS
[.'.]A is not B | TOLLENS.

A so-called Hypothetical Syllogism is thus seen to be a Syllogism in
which the major premiss is a HYPOTHETICAL PROPOSITION, that is to
say, a complex proposition in which two propositions are given as so
related that the truth of one follows necessarily from the truth of
the other.

Two propositions so related are technically called the ANTECEDENT or
Reason, and the CONSEQUENT.

The meaning and implication of the form, If A is B, C is D, is
expressed in what is known as the LAW OF REASON AND CONSEQUENT:--

"_When two propositions are related as Reason and Consequent, the
truth of the Consequent follows from the truth of the Antecedent,
and the falsehood of the Antecedent, from the falsehood of the
Consequent_".

If A is B, C is D, implies that If C is not D, A is not B. If this
subject is educative, it quickens the wits; if it does not quicken the
wits, it is not educative.

Admitted, then, that the law of Reason and Consequent holds
between two propositions--that If A is B, C is D: admitted also the
Antecedent, the truth of the Consequent follows. This is the MODUS
PONENS or Positive Mode, where you reach a conclusion by obtaining the
admission of the Antecedent. Admit the Antecedent and the truth of the
Consequent follows.

With the same Major Premiss, you may also, under the Law of Reason
and Consequent reach a conclusion by obtaining the denial of the
Consequent. This is the MODUS TOLLENS or Negative Mode. Deny the
Consequent and one is bound to deny the Antecedent.

But to guard against the fallacy technically known as FALLACIA
CONSEQUENTIS, we must observe what the relation of Reason and
Consequent does not imply. The truth of the Consequent does not
involve the truth of the Antecedent, and the falsehood of the
Antecedent does not involve the falsehood of the Consequent.

"If the harbour is frozen, the ships cannot come in." If the harbour
is not frozen, it does not follow that