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

THE VALIDITY OF THE SYLLOGISM. 2OI
position means that wherever there is a case of S being
P, it is also Q. Hence we may express the hypothetical
proposition in the form "All S which is P is Q," or
"All SP is Q."
For example, the propositions
"
If iron is impure, it is
brittle," and "All impure iron is brittle," express the two
aspects of intension and extension respectively. Other
examples are :
"
If a substance becomes gaseous, it absorbs
" "
heat = All substances in becoming gaseous absorb heat" ;
"If a substance is a metal it is a good conductor of heat
"
"
and = electricity All metals are good conductors," &c.
"
"
This change is sometimes called the reduction of hypo
thetical propositions to the categorical form. The term
"
"
reduction
is inaccurately applied here ; the two forms
of the judgment are not identical ; they emphasise the two
different aspects of the meaning, intension and extension.
Hypothetical syllogisms may consequently
pressed in categorical forms :
(a) Modus ponens
"
If life is full of distraction, it is exhausting ;
Modern life is full of distraction ;
Therefore modern life is exhausting."
This becomes a regular syllogism in Barbara.
(b) Modus tollens
"
also be ex
If Aristotle is right, slavery is a justifiable social
institution ;
But slavery is not this ;
Therefore Aristotle is not right."
This becomes a regular syllogism in Camestres^ fig. ii., the
chief importance of which mood consists in its representing
the extremely common mode of argument which is exem
plified
in the "destructive 1
hypothetical syllogism.
If the
consequent of the major premise in the hypothetical syllog
ism is negative, it is denied by an affirmative (A), and the
mood is Cesare:
"
If S is P, Q is not R ; Q is R ; .-. S is not P."
" No case of S being P is a case of Q being R ;
This is a case of Q being R ;
Therefore this is not a case of S being P."