When an agreement and disagreement are thus stated in the first and second lines, the result stated in the third line must be a disagreement. But if the first and second lines both state disagreements no result can be drawn, for there is more than one mode of disagreement. This may be illustrated by the case of two witnesses to the same circumstance. If both tell the truth their stories will agree; if one tells the truth and the other does not, their stories disagree; but if neither tells the truth, their stories may or may not agree—that is, they may tell the same falsehood or different kinds of falsehood.
In the syllogism it is necessary to see that the comparisons made are real and not fictitious. False logic or fallacies arise where a comparison seems to be made which is not real. Part of one thing or class may be compared with the whole of another, and then an agreement affirmed or denied for the whole of the two things or classes, and this fatal fault in reasoning may be very carefully concealed. It can usually be detected by turning around the sentence in which the defective comparison is made. Thus:
Men are animals.
Horses are animals.
Therefore, men are horses.
This seems to be a perfectly fair specimen of correct syllogisms. But in the first line the class “men” is compared with only a part of the class “animals,” and in the second line the whole of the class “horses” is compared with another part of the class “animals,” and as the comparison is not restricted to the same objects no statement of agreement or disagreement can be made. We detect the insufficiency of the comparison by saying, it is true that all men are animals, but not true that all animals are men.
Another mode of making a seeming comparison without the reality is by using words in unlike senses. Thus:
All light bodies dispel darkness.
A bag of feathers is a light body.
Therefore, a bag of feathers will dispel darkness.