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

CONDITIONAL ARGUMENTS. 197
of the principle of Sufficient Reason. It has two
usual forms :
(1) If S is P it is Q. This asserts that a relation
between two concepts P and Q holds universally, with
out qualification, so that whenever P is predicated,
it follows that Q must be. The simplest examples
are for Mathematics :
is
"
If a triangle is equilateral it
equiangular." It is the natural form for scientific
laws or principles :
"
If the planet Venus does not
rotate upon her axis, but always turns one face to the
sun and the other to the outer cold, Venus is incapable
of life."
supporting
(2) If S is P, Q is R. This asserts a connection
between two judgments, such that if one is true the
other follows.
"
If a triangle is rectangular, the square
on the hypotenuse is equal to the sum of the squares
on the other two sides."
"
If the force of gravity on
the planet Mars is too small to prevent water-vapour
from escaping into space, there is no life on Mars."
"
If organic life is possible on a planet, oxygen must
be present in the atmosphere or in water."
The student will see later what these examples
make evident that the two forms of the hypothetical
proposition
are at bottom the same.
Distinctions of quantity and quality in hypothetical pro
positions may be made by the introduction of the words
"always," "never," "sometimes," "sometimes not." Thus
"
If S is P it is always Q,"
is always equiangular," corresponds
"
if a triangle is equilateral it
to the form A of the
categorical proposition; "if S is P it is never O,"
"if a
triangle is right-angled it is never equiangular," corres
ponds to E; "if S is P it is sometimes "if a Q," figure is
a parallelogram it is sometimes a square," corresponds to I ;
"if S is P it is sometimes not "if a O," triangle is rect
angular it is sometimes not isosceles," corresponds to O.