Sandstone lies above Coal; therefore Lias lies above Coal,' obviously admits of being stated in the form, 'Whatever lies above New Red Sandstone lies above Coal, Lias lies above New Red Sandstone; therefore Lias lies above Coal,' and consequently ought not to be rejected as having four terms. But the premisses 'Lias lies above New Red Sandstone, the Cretaceous System lies above the Oolitic,' contain no term common, nor any term capable (from a mere inspection of the language) of being represented as common, to the premisses, and hence they might fairly be rejected as containing four terms, and consequently leading to no conclusion. Even here, however, by any one who possessed sufficient special knowledge of Geology to be aware that the Oolitic System lies above Lias, the premisses might be represented as containing three terms only, and as necessitating the conclusion 'The Cretaceous System lies above New Red Sandstone.' But from such premisses as Lias lies above New Red Sandstone,' 'A painting should represent beauty of colour as well as beauty of form,' no conclusion whatever could be drawn by means of either logical or special knowledge. The premisses are, in fact, utterly alien to each other, or, in other words, they are not in pari materiâ. In examining an argument, the student may always avail himself of any special knowledge which he may possess, provided that, in his answer, he carefully distinguish between what is due to such special knowledge and what to a knowledge of the ordinary usages of language and of the rules of Logic.

In the first example given above, a mere knowledge of the rules of Logic, without any reference whatever to the usages of language, would not justify us in drawing any conclusion from the premisses; the slightest acquaintance with the usages of language would however enable us to represent the terms, which are apparently four, as three, and to infer the conclusion 'Lias lies above Coal.' But in the second example no acquaintance either with the rules of Logic or with the ordinary usages of language would enable us to draw the conclusion, 'The Cretaceous System lies above New Red Sandstone;' such a conclusion, though valid, is only justified by a special knowledge of Geology: no person, unacquainted with the facts of Geology, would be justified in admitting the conclusion as an inference from the premisses.

Where it is obvious that an argument is intended to be syllogistic, and only one premiss is stated, it is of course expected that the student will supply the other premiss.

In some of the examples, it may be an useful exercise to discuss the truth of the premisses as well as the legitimacy of the conclusion.