Exceptive propositions are universal when the exceptions are mentioned. Universal propositions necessitate asubject more or less definite, as the predicate of such must refer to the whole of a definite subject. It follows that in exceptive statements definiteness is secured when the exceptions are mentioned, therefore it becomes clear how all such propositions must be universal. Of the illustrations, the first and third propositions are universal. Any exceptive proposition is particular when the exceptions are referred to in general terms or when the subject is followed by et cetera. The second illustrative proposition is particular.
(7) Exclusive Propositions.
Of all propositions which vary from the logical form the exclusive is the most misleading. Exclusives are accompanied by such words as “only,” “alone,” “none but,” and “except.” Their peculiarity rests in the fact that reference is made to the whole of the predicate, but only to a part of the subject. For example, in the exclusive proposition, “Only elements are metals,” metals is referred to as a whole while elements is considered only in part. The true meaning is “Some elements are all metals,” or to put it in logical form, “All metals are elements.” The easiest way to deal with an exclusive is to interchange subject and predicate (convert simply) and call the proposition an A.
PROCESS ILLUSTRATED:
| Exclusive Proposition | Reduced to Logical Form |
| 1. None but high school graduates may enter Training School. | All who enter Training School must be high school graduates. |
| 2. Only first-class passengers are allowed in parlor cars. | All parlor cars are for first-class passengers. |
| 3. Residents alone are licensed to teach. | All who are licensed to teach are residents. |
| 4. No admittance except on business. | All who have business may be admitted. |
| 5. Only bad men are not-wise. | All who are not-wise are bad men. |
| 6. Only some men are wise. | All who are wise are men. |
It is claimed by good authority that the real nature of the exclusive is best expressed by negating the subject and calling the proposition an E; e. g., exclusive: “Only elements are metals”; logical form: “No not-elements are metals” (E). In a succeeding chapter it is explained how an E admits of first simple conversion and then obversion. The following illustrate these two processes:
Original E: “No not-elements are metals.”
Simple conversion: “No metals are not-elements.”
Obversion: “All metals are elements.”
From this it may be seen that the statement, “The easiest way to deal with an exclusive is to interchange subject and predicate and call the proposition an A,” is substantially correct.