An introductory text-book of logic - Mellone, Sydney - Rare Books at ...

2OO CONDITIONAL ARGUMENTS AND
for there may be many good reasons why he refuses,
although his character is not avaricious.
(c)
"
If oxygen and nitrogen exist on Mars, life is possible
there; these elements do exist in that planet, hence life
is possible there."
Though the minor premise is not an established fact,
this argument is formally valid. To affirm the antecedent
is to declare that the condition exists, and this justifies the
affirmation of the consequent.
(<t)
"
If life is possible on Mars, the planet has warmth
sufficient for protoplasmic metabolism ; but the planet has not
warmth sufficient, and therefore life is not possible on it."
The minor premise again goes beyond our present know
ledge ; but the argument is formally valid. To deny the
consequent is to declare its non-existence ; and this justifies
us in denying that the condition (stated in the antecedent)
exists.
Hence the rule for hypothetical syllogisms is this :
Either affirm the antecedent, or deny the consequent.
In the former case, as in (c), we have a constructive
hypothetical syllogism; in the latter, as in (d), a de
structive hypothetical syllogism. These are sometimes
spoken of as the modus ponens and modus fallens
respectively.
4. We have seen that a hypothetical proposition
expresses a relation between two concepts or two
judgments. When expressed in the hypothetical form
the proposition invites us to attend more to the relation
between the concepts employed than to any special
instances. But if we attend chiefly to the particular
instances, actual and possible, to which the proposition
may be conceived to apply, then we may express the
proposition in a categorical form, the universal affirma
tive A. Thus, take the proposition,
"
If S is P it is
Q."
Looked at on the side of extension, in other words,
looking at the instances of its application, this pro-