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

THE VALIDITY OF THE SYLLOGISM. 203
(b} Similarly, from the minor premise alone, A is B,
we cannot draw the conclusion C is D, unless the
relation of Reason and Consequence
is admitted to
hold between them i.e., unless the major premise is
conceded as well as the minor.
We must notice, before leaving the subject of the
hypothetical proposition, that all such propositions can
be brought into the form
"
if S is M it is P." Usually
there is no difficulty
in doing so. But occasionally the
hypothetical with four terms,
"
if S is M, P is con
R,"
ceals the unity of the judgment which it expresses, by
giving no obvious point of union between S and P.
The empty symbolic statement, with the four letters,
always does this; but it may happen when the judg
ment is expressed in significant words.
The following examples will illustrate what we have said.
In each case we give (a) the form with four terms, (b) the
fundamental form with three terms.
() If the report is true, what you say is untrue.
(b) If the report is true, it proves the untruth of what
(a)
you say.
If two parts of hydrogen combine with one part of
(b)
oxygen, water is formed.
If the combination of two parts of hydrogen with one
part of oxygen takes place, it (i.e., the combina
tion) forms water.
(a) If some agreement is not speedily arrived at between
employers and workmen, the trade of the will be ruined.
country
(b) If trade continue to be injured by this strike, it will
soon be ruined.
Sometimes, in the four-term form, "if S is M, P is R," the
point of union between S and P consists in P being a species
of the genus S : "if savages are cruel, the Patagonians are
cruel"; or S and P may be co-ordinate species
common genus :
under a
"
if virtue is voluntary, vice is voluntary."
Similar considerations show that the two forms of the