5. IRREGULAR ARGUMENTS.
It has been intimated that a syllogistic argument, in order to be logical, should be made to conform to the rules of the syllogism. It must not be inferred from this, however, that all deductive reasoning is included by the logical forms here treated. There seem to be arguments which yield valid conclusions, and yet which are not logical in the strict sense of the word. The following illustrate some of these forms:
(1) Quantitative Arguments.
John is taller than James,
Albert is taller than John,
∴ Albert is taller than James.
Here, apparently, is a fallacy of four terms: these four terms are (1) John, (2) taller than James, (3) Albert, (4) taller than John. Yet we know that the argument is valid. There is not a particle of doubt in the mind relative to the truth of the conclusion that “Albert is taller than James.” We are consequently forced to the inference that such quantitative arguments lie outside the field of syllogistic reasoning. The argument involves this new principle, “Whatever is greater than a second thing which is greater than a third thing is itself greater than a third thing.”
There are many other arguments similar to this which are not syllogistic in nature. To wit: A equals B, B equals C, C equals D; A equals D. A is a brother of B, B is a brother of C, C is a brother of D; A is a brother of D. A is west of B, B is west of C, C is west of D; A is west of D.
(2) Plurative Arguments.
These are arguments in which the propositions are introduced by more or most; e. g.: