According to the syllogistic rules the middle term “element” is here undistributed, and no conclusion can be obtained; we cannot tell then whether hydrogen is or is not a metal. Represent the terms as follows
A = hydrogen,
B = element,
C = metal.
The premises then become
| A = AB, | (1) |
| C = CB. | (2) |
The reader will here, as in a former page (p. [62]), find it impossible to make any substitution. The only term which occurs in both premises is B, but it is differently combined in the two premises. For B we must not substitute A, which is equivalent to AB, not to B. Nor must we confuse together CB and AB, which, though they contain one common letter, are different aggregate terms. The rule of substitution gives us no right to decompose combinations; and if we adhere rigidly to the rule, that if two terms are stated to be equivalent we may substitute one for the other, we cannot commit the fallacy. It is apparent that the form of premises stated above is the same as that which we obtained by translating two negative premises into the affirmative form.
The old fallacy, technically called the Illicit Process of the Major Term, is more easy to commit and more difficult to detect than any other breach of the syllogistic rules. In our system it could hardly occur. From the premises
| All planets are subject to gravity, | (1) |
| Fixed stars are not planets, | (2) |
we might inadvertently but fallaciously infer that, “Fixed stars are not subject to gravity.” To reduce the premises to symbolic form, let
A = planet
B = fixed star
C = subject to gravity;
then we have the propositions