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_: M G A The falling rain makes the ground damp, ―――――――――――――――― ――――――――――― S M A In this case rain has fallen, ――――――――――――――――― S G A ∴ In this case the ground is 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 { A to the argument the mode { A in the first figure which we know to be { A valid. _Hypothetical_: (2) If one were wise, he would study; But you will not study, ∴ You are not wise. _Categorical_: G M A A wise person would study, ――――――――――― S M E ∴ You will not study, ――― ――――― S G E ∴ You are not wise. ――― ―――― In the hypothetical form the argument is valid since the minor premise { A denies the consequent. Reducing to the categorical gives mood { E in { E 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_: M G A South wind brings rain, ―――――――――― S M E This wind is not a south wind, ――――――――― ―――――――――― S G E ∴ This wind will not 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_: G M A A just man will obey the golden rule, ―――――――― S M A This judge has obeyed the golden rule, ――――― S G A ∴ This judge is a just man. ―――――