Читать книгу Selected Mathematical Works: Symbolic Logic + The Game of Logic + Feeding the Mind: by Charles Lutwidge Dodgson, alias Lewis Carroll - Lewis Carroll - Страница 20

A Proposition of Relation, of the kind to be here discussed, has, for its Terms, two Specieses of the same Genus, such that each of the two Names conveys the idea of some Attribute not conveyed by the other.

[Thus, the Proposition “Some merchants are misers” is of the right kind, since “merchants” and “misers” are Specieses of the same Genus “men”; and since the Name “merchants” conveys the idea of the Attribute “mercantile”, and the name “misers” the idea of the Attribute “miserly”, each of which ideas is not conveyed by the other Name.

But the Proposition “Some dogs are setters” is not of the right kind, since, although it is true that “dogs” and “setters” are Specieses of the same Genus “animals”, it is not true that the Name “dogs” conveys the idea of any Attribute not conveyed by the Name “setters”. Such Propositions will be discussed in Part II.]

The Genus, of which the two Terms are Specieses, is called the ‘Universe of Discourse,’ or (more briefly) the ‘Univ.’

The Sign of Quantity is “Some” or “No” or “All”.

[Note that, though its Sign of Quantity tells us how many Members of its Subject are also Members of its Predicate, it does not tell us the exact number: in fact, it only deals with three numbers, which are, in ascending order, “0”, “1 or more”, “the total number of Members of the Subject”.]

It is called “a Proposition of Relation” because its effect is to assert that a certain relationship exists between its Terms.