n which the antecedent
of the hypothetical major premise is affirmed; and the _Modus tollens_,
in which its consequent is denied.

(1) _Modus ponens_, or Constructive.

If A is B, C is D;
A is B:
.'. C is D.

If Aristotle's reasoning is conclusive, Plato's theory of Ideas is
erroneous;

Aristotle's reasoning is conclusive:
.'. Plato's theory of Ideas is erroneous.

Rule of the _Modus ponens_: The antecedent of the major premise being
affirmed in the minor premise, the consequent is also affirmed in the
conclusion.

(2) _Modus tollens_, or Destructive.

If A is B, C is D;
C is not D:
.'. A is not B.

If Pythagoras is to be trusted, Justice is a number;
Justice is not a number:
.'. Pythagoras is not to be trusted.

Rule of the _Modus tollens_: The consequent of the major premise being
denied in the minor premise, the antecedent is denied in the conclusion.

By using negative major premises two other forms are obtainable: then,
either by affirming the antecedent or by denying the consequent, we draw
a negative conclusion.

Thus (_Modus ponens_): (_Modus tollens_):

If A is B, C is not D; If A is B, C is not D;
A is B: C is D:
.'. C is not D. .'. A is not B.

Further, since the antecedent of the major premise, taken by itself, may
be negative, it seems possible to obtain four more forms, two in each
Mood, from the following major premises:

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

But since the quality of a Hypothetical Proposition is determined by the
quality of its consequent, not at all by the quality of its antecedent,
we cannot get from these two major premises any really new Moods, that
is to say, Moods exhibiting any formal difference from the four
previously expounded.

It is obvious that, given the hypothetical major premise--

If A is B, C is D--

we cannot, by denying the antecedent, infer a denial of the consequent.
That A is B, is a mark of C being D; but we are not told that it is the
sole and indispensable condition of it. If men read good books, they
acquire knowledge; but they may acquire knowledge by other means, as by
observation. For the same reason, we cannot by affirming the consequent
infer the affirmation of the antecedent: Caius may have acquired
knowledge; but we cannot thence