6. HYPOTHETICAL ARGUMENTS REDUCED TO THE CATEGORICAL FORM.
The hypothetical syllogism so closely resembles the categorical that it may be changed to it by a slight alteration in the wording. After testing the hypothetical by its own rule, it may be expedient to reduce the argument to the categorical form, and subject it to a second test in which the categorical rules are applied. This reduction usually necessitates two steps; first, change the propositions which represent the antecedent and consequent to a subject term and a predicate term respectively and then unite them to form the major premise; second, supply a new minor term, if necessary.
Illustrations of Reduction; and Comparison of Hypothetical and Categorical Fallacies:
Hypothetical Form:
(1) If it has rained, the ground is damp;
It has rained,
∴ The ground is damp.
Categorical Form:
A M
The falling rain makes the G
ground damp,
A S
In this case rain has M
fallen,
A ∴ S
In this case the ground is G
damp ground.
It is seen that the argument in the hypothetical form is valid as the minor premise affirms the antecedent. Reducing to the categorical gives to the argument the mode
A
A
A in the first figure which we know to be valid.
Hypothetical:
(2) If one were wise, he would study;
But you will not study,
∴ You are not wise.
Categorical:
A A G
wise person would M
study,
E ∴ S
You will not M
study,
E ∴ S
You are not G
wise.
In the hypothetical form the argument is valid since the minor premise denies the consequent. Reducing tothe categorical gives mood
A
E
E in the second figure. This is valid.
Hypothetical:
(3) If the wind blows from the south, it will rain;
But the wind is not blowing from the south,
Hence it is not going to rain.
Categorical:
A M
South wind brings G
rain,
E S
This wind is not a M
south wind,
E ∴ S
This wind will not G
bring rain.
Hypothetically considered, the minor premise denies the antecedent and consequently the argument is invalid. Reducing to the categorical form, it is found that the major term is distributed in the conclusion, but is not distributed in the major premise; hence the fallacy of illicit major is committed.
Hypothetical:
(4) If a man is just, he will obey the golden rule;
This judge has obeyed the golden rule,
Hence he is just.
Categorical:
A A G
just man will obey the M
golden rule,
A This S
judge has obeyed the M
golden rule,
A ∴ This S
judge is a G
just man.
Hypothetically considered, the minor premise affirms the consequent and thus the argument is fallacious; when changed to the categorical we find the fallacy of undistributed middle. If other examples were taken, it could be proved that the hypothetical fallacy of denying the antecedent is usually equivalent to the categorical fallacy of illicit major; whereas the hypothetical fallacy of affirming the consequent amounts to undistributed middle.
In reducing some hypotheticals it is necessary to make use of such expressions as, “the case of” or “the circumstances that.” The attending argument will illustrate this:
If Jefferson was right, man was created free and equal;
(but) Man was not created free and equal,
∴ Jefferson was not right.
Reduced to the categorical:
The G
case of Jefferson being right is the case of manbeing created M
free and equal;
S
Man was not created M
free and equal,
∴ A
Jefferson (this man) was not G
right.
The argument is valid in both cases.