Selected Mathematical Works: Symbolic Logic + The Game of Logic + Feeding the Mind: by Charles Lutwidge Dodgson, alias Lewis Carroll. Lewis Carroll

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СКАЧАТЬ 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.

      § 2.

       Reduction of a Proposition of Relation to Normal form.

      The Rules, for doing this, are as follows:—

      (1) Ascertain what is the Subject (i.e., ascertain what Class we are talking about);

      (2) If the verb, governed by the Subject, is not the verb “are” (or “is”), substitute for it a phrase beginning with “are” (or “is”);

      (3) Ascertain what is the Predicate (i.e., ascertain what Class it is, which is asserted to contain some, or none, or all, of the Members of the Subject);

      (4) If the Name of each Term is completely expressed (i.e. if it contains a Substantive), there is no need to determine the ‘Univ.’; but, if either Name is incompletely expressed, and contains Attributes only, it is then necessary to determine a ‘Univ.’, in order to insert its Name as the Substantive.

      (5) Ascertain the Sign of Quantity;

      (6) Arrange in the following order:—

      Sign of Quantity,

       Subject,

       Copula,

       Predicate.

      [Let us work a few Examples, to illustrate these Rules.

      (1)

      “Some apples are not ripe.”

      (1) The Subject is “apples.”

      (2) The Verb is “are.”

      (3) The Predicate is “not-ripe *.” (As no Substantive is expressed, and we have not yet settled what the Univ. is to be, we are forced to leave a blank.)

      (4) Let Univ. be “fruit.”

      (5) The Sign of Quantity is “some.”

      (6) The Proposition now becomes

      “Some | apples | are | not-ripe fruit.”

      (2)

      “None of my speculations have brought me as much as 5 per cent.”

      (1) The Subject is “my speculations.”

      (2) The Verb is “have brought,” for which we substitute the phrase “are * that have brought”.

      (3) The Predicate is “ * that have brought &c.”

      (4) Let Univ. be “transactions.”

      (5) The Sign of Quantity is “none of.”

      (6) The Proposition now becomes

      “None of | my speculations | are | transactions that have brought me as much as 5 per cent.”

      (3)

      “None but the brave deserve the fair.”

      To begin with, we note that the phrase “none but the brave” is equivalent to “no not-brave.”

      (1) The Subject has for its Attribute “not-brave.” But no Substantive is supplied. So we express the Subject as “not-brave *.”

      (2) The Verb is “deserve,” for which we substitute the phrase “are deserving of”.

      (3) The Predicate is “ * deserving of the fair.”

      (4) Let Univ. be “persons.”

      (5) The Sign of Quantity is “no.”

      (6) The Proposition now becomes

      “No | not-brave persons | are | persons deserving of the fair.”

      (4)

      “A lame puppy would not say “thank you” if you offered to lend it a skipping-rope.”

      (1) The Subject is evidently “lame puppies,” and all the rest of the sentence must somehow be packed into the Predicate.

      (2) The Verb is “would not say,” &c., for which we may substitute the phrase “are not grateful for.”

      (3) The Predicate may be expressed as “ * not grateful for the loan of a skipping-rope.”

      (4) Let Univ. be “puppies.”

      (5) The Sign of Quantity is “all.”

      (6) The Proposition now becomes

      “All | lame puppies | are | puppies not grateful for the loan of a skipping-rope.”

      (5)

      “No one takes in the Times, unless he is well-educated.”

      (1) The Subject is evidently persons who are not well-educated (“no one” evidently means “no person”).

      (2) The Verb is “takes in,” for which we may substitute the phrase СКАЧАТЬ